On the Question of Piston Friction: with 4 tables

An experimental study of piston friction, carried out

On the Question of Piston Friction: with 4 tables

An experimental study of piston friction, carried out

Submitted 1913 | SovietRxiv: ru-191301.07272 | Translated from Russian

Pre-reform orthography. The original is printed in the Russian spelling used before the 1918 reform (ѣ, і, ъ).

Full Text

Vl. G. Karpenko,
mechanical engineer, laboratory assistant of the Tomsk Technological Institute.

On the Question

of Piston Friction.

An experimental study of piston friction, carried out
in the Laboratory of Heat Engines of the Tomsk Technological
Institute of Emperor Nicholas II.

With 13 drawings in the text and 4 diagrams in the appendix.

Tomsk.
Typo-lithography of the Siberian Association of Printing.
1913.

Preface

“... at the present time there can be no possibility of determining with accuracy the magnitude of the frictional force, which develops in one case or another, unless at least some preliminary experiments are performed.”
N. Petrov. Friction in Machines, 1886, p. 430.

The experiments of numerous authors who have worked on the investigation of the friction of lubricated bodies have not yet led, up to the present time, to entirely definite and exact laws of friction. The reason for this, undoubtedly, is the nature of the phenomenon itself. Anyone who has ever dealt with the investigation of the friction of lubricated bodies knows how variable the frictional force is under comparatively insignificant changes in conditions. Undoubtedly, this is also the reason why, to this day, many authors cannot agree in their views on the influence upon friction of one factor or another; and to this day this question is decided experimentally even in such cases as friction in journals, which has been investigated many times by various persons.

While carrying out, in the Laboratory of Heat Engines of the Tomsk Technological Institute, experiments investigating the operation of the machine of the “Otto-Deutz” works, the author, among other things, had to encounter the question of the magnitude of the piston friction of this machine. Solving the question on the basis of the data available concerning friction in journals proved impossible; therefore it was necessary to undertake a special investigation of piston friction in the said machine. The experiments with this machine yielded such interesting results that they prompted the author to proceed to a further investigation of piston friction in other machines of the laboratory. The subject became broader. A comprehensive illumination of the question was required, and therefore it was necessary to touch upon the friction of lubricated bodies in general. It was necessary to coordinate the question with respect to the experiments on the investigation of friction by various authors. All this greatly increased the amount of material; the work became of interest as an independent subject; this prompted the author to publish all the experimental material and the results of the experiments in the form of a study of the question of piston friction.

In presenting the present work to the attention of the reading public, the author considers it necessary to point out some of its special features.

The magnitude of the piston-friction force cannot be measured directly by any instruments; therefore, in investigation one has to determine not the friction force, but its function—the work of friction. But the work of friction likewise cannot be measured; it can only be calculated on the basis of a series of observations; and the errors of individual observations, measurements, and calculations accumulate in the final result and lower the accuracy of the results. Herein lies the great difference between our experiments and experiments that have been conducted to investigate friction in trunnions, and in which the friction force was measured directly.

The author is of the opinion that, even with comparatively large errors in individual observations and calculations, the results of the investigation may be considered to have achieved their aim, provided only that all errors can be indicated and their probable magnitude calculated. On the basis of these considerations, the author paid particular attention to a critical treatment of all the experimental material, to the calculation of mean errors, and devotes a separate chapter to all this. But it is extremely difficult to make sense of so complicated a question as piston friction, occurring under the most varied conditions, chiefly of temperature; therefore the author anticipates, on his part, possible errors in the assessment of one phenomenon or another, and consequently considers that further criticism, supported in certain cases by experimental data from interested persons, is highly desirable in the interests of the question raised. For the present, however, the author will consider himself satisfied if, by his work, he has succeeded in providing methods for the theoretical and practical investigation of piston friction in each individual case.

In concluding the preface, the author cannot refrain from expressing his deep gratitude to Professors V. L. Matveev and B. P. Weinberg for the advice and guidance which they gave the author during the conduct of the experiments and during the processing of the material. The author also offers his thanks to all those persons who in one way or another contributed to the performance of the work, and also to the laboratory mechanic A. Ya. Tkachenko, who worked considerably on the rearrangement and dismantling of the machines.

Tomsk. March 1913.

Vl. G. Karpenko.

On the Internal Friction of Lubricant

	Page
1. Force of internal friction. Coefficient of internal friction. Angular velocity of shear	5
2. Critical velocity of fluid motion	5
3. Change of the coefficient of internal friction with temperature	6
4. Specific viscosity according to Engler	8
5. Data from our investigations of the viscosity of lubricants	8

On the Friction of Lubricated Bodies

	Page
6. Resistance force of rubbing surfaces	12
7. Coefficient of friction	13
8. Difference between the coefficients of friction of lubricated and unlubricated bodies	13
9. Unsuitability of the coefficient of friction for characterizing piston friction	14
10. Specific frictional resistance	15
11. Dependence of the specific frictional resistance on the angular velocity $\varphi$	16

Arrangement and Execution of the Experiments.

Description of the machine of the “Otto-Deutz” works . . . . . . . . . . . . . . . . . 21
Specific pressure due to the weight of the piston and to the pressing force of the rings. Normal pressures . . . . . . . . . . . . . . . . . 22
Description of the compressor of the “Rud. Meyer” works . . . . . . . . . . . . . . . 23
Specific pressure due to the weight of the piston and to the pressing force of the rings 24
Description of the “Gornsby Akroyd” machine . . . . . . . . . . . . . . . . . 24
Specific pressure due to the weight of the piston and to the pressing force of the rings. 25
Varying factors in the investigation of piston friction . . . . . . . . . . . . . 25
Duration of the experiments . . . . . . . . . . . . . . . . . . . . . . . 25
Conduct of the observations . . . . . . . . . . . . . . . . . . . . . . 26
Sample record of observations . . . . . . . . . . . . . . . . . . . . . 27
Mechanical method. Conduct of observations and duration of the experiments. . . . . . . . . . . . . . . . . . 27
Variable factors . . . . . . . . . . . . . . . . . . . . . . . . . 28
Work of rotation of the flywheel, shaft, and distributing mechanism 29

Chapter III.

Processing and Critique of the Experimental Material.

Determination of the work of piston friction by the calorimetric method. Mean error of determination . . . . . . . . . . . . . . . . . . . 31
Actual deviation of the results from the mean value of the work of friction. Causes producing the deviations . . . . . . . . . . . . . . . 32
Influence of the variable temperature of the lubricating layer on the deviations . . . . . . . . . . . . . . . . . . 33
Influence of internal heat exchange on the results of the calorimetric experiments . . . . . . . . . . . . . . . . . 34
Influence of external heat exchange on the results of the calorimetric experiments . . . . . . . . . . . . . . . . . 37
Influence of the heat of compression on the results of the calorimetric experiments 41
Influence of high temperatures on piston friction . . . . . . . . . . . . . 45
Additional experiment to the calorimetric experiments for determining the influence of high temperatures on piston friction . . . . . . . . . . 47
Mechanical method of investigating piston friction . . . . . . . . . . . . . . 49
Mean error in determining effective power . . . . . . . . . . . . . 50
Mean error in determining indicated power . . . . . . . . . . . . . 51

Mean error in determining the indicated work of the machine as a pump (suction and delivery strokes) . . . 51
Mean error in determining the work of rotation of the flywheel, shaft, and valve gear . . . 51
Mean error in determining piston friction . . . 54
Note to Table X . . . 55
Note to Table XI . . . 56
Friction in the connecting-rod mechanism . . . 57
Review of the calorimetric experiments . . . 58

Chapter IV

Results of the Experiments

Effect of pressure on piston friction . . . 61
Effect of piston rings on friction . . . 62
Effect of the magnitude of the friction surface on the magnitude of the friction force . . . 64
Effect of speed on piston friction . . . 64
Effect of lubricant viscosity on piston friction . . . 68
Effect of temperature on piston friction . . . 70
Work of piston friction in the “Otto-Deutz” machine . . . 71
Practical conclusions from the results of the experiments . . . 72
Formula for the approximate calculation of the work of piston friction . . . 76
Conclusion . . . 77

INTRODUCTION.

Methods for Investigating Piston Friction.

At the present time there are no special works on the investigation of piston friction; therefore this question remains, up to now, entirely unstudied, while its solution is urgent not only in laboratory practice but also in engineering in general. The reason for this state of the question is the difficulties involved in setting up experiments to investigate piston friction. The chief difficulty consists in the fact that the magnitude of piston friction cannot be measured during experiments by any instruments either in the form of the frictional force or in the form of the work of friction. One has to approach the determination of friction from afar, which is associated with a whole series of difficulties and possible errors. It is also beyond doubt that one reason why piston friction has not yet been studied is the difficulty of constructing such a testing machine as would make it possible to investigate friction under conditions as close as possible to the actual working conditions of the piston. Meanwhile the conditions under which the piston has to operate are very varied. In heat engines combustion takes place inside the cylinder, and the surface of the cylinder is cooled by water of various temperatures; in steam engines condensation of steam occurs in the cylinder and water mixes with the lubricant, while the cylinders of some engines are heated by steam; in water pumps the cylinder is filled with water, and in compressors air circulation takes place.

All this indicates that the question of piston friction cannot be solved in a general form. The solution of particular cases requires the indication of methods of investigation that are the simplest and most accurate, and such that they could be used either directly in testing a machine or in the form of supplementary experiments.

In our investigation of piston friction on the machines of the laboratory, we used two methods: the calorimetric method and the method applied by Prof. V. L. Malyshev in investigating the work of a two-stroke engine¹. In the subsequent presentation of the work we shall, for simplicity, call this method the mechanical method.

Introduction

§ 2.

The calorimetric method was applied by the author for the first time. Its idea is based on those thermal investigations to which internal-combustion engines are subjected. As is known, in the investigation of these engines a heat balance is drawn up, in which the heat supplied to the engine is balanced against all the items of its expenditure. This balance may be represented in the form of the equation

\[ U = U_i + U_b + U_{\mathrm{pr}} - U_p + U_n, \tag{1} \]

where $U$ is the heat supplied to the engine; $U_i$ is the heat corresponding to the indicated work; $U_b$ is the heat carried away by the cooling water; $U_{\mathrm{pr}}$ is the heat carried away by the products of combustion; $U_p$ is the heat corresponding to the work of piston friction; $U_n$ is the heat corresponding to the discrepancy and to a whole series of quantities of heat loss which it is difficult to determine with sufficient accuracy, for example, losses from incomplete combustion, from radiation, etc.

From equation (1) we see that all quantities on the right-hand side of the equation have a plus sign, except the quantity of heat of piston friction, which enters the equality with a minus sign. This quantity is introduced with a minus sign on the basis of the following considerations. The indicated work consists of the effective work and all the losses that arise from the friction of the piston, the connecting-rod mechanism, and the shaft. Otherwise we cannot determine the indicated work; meanwhile, the heat that is produced by piston friction is carried away by the cooling water and enters into the quantity $U_b$. Consequently, by inserting the quantities $U_i$ and $U_b$ into equation (1), we thereby introduce twice into equation (1) the quantity of piston-friction work with a plus sign; therefore, in order to draw up a correct heat balance, we must introduce the quantity $U_p$ with a minus sign.

The work of piston friction, as we shall see later, in unfavorable cases may amount to as much as 25% of the indicated power of the engine, and therefore it is impossible to neglect it in drawing up the heat balance.

The calorimetric method is based on the removal of the heat of friction by the cooling water. The arrangement of the experiment consists in putting the machine being tested into operation from an external source of energy, while water is passed through the jacket. As soon as the temperature of the cooling water becomes constant, observations are begun: the temperatures of the water entering and leaving are recorded at definite intervals of time, as well as the water consumption. The quantity of heat removed may be calculated from the equation

\[ U_p = (t_1 - t_2)w, \tag{2} \]

where $t_1$ and $t_2$ are the temperatures of the water entering and leaving the cylinder jacket, and $w$ is the quantity of water per unit time.

§ 2. Calorimetric Method

From the quantity of heat $U_p$, the work of piston friction can be determined on the basis of the equation

\[ R_p=\frac{U_p}{632.3}, \tag{3} \]

where the value 632.3 is the thermal equivalent of one horsepower-hour.

The calorimetric method is associated with errors due to heat exchange with the air of the room; therefore this method gives good results under low-temperature experimental conditions. But as soon as the temperature of the outgoing water becomes higher than the room temperature, heat losses due to radiation begin to increase and become noticeable at a temperature of $50^\circ$—$55^\circ$ C.

The question of friction at high temperatures has to be solved in another way. From a series of calorimetric experiments at low temperature, it is possible, with sufficient accuracy, to determine the work of piston friction and, in parallel with it, the expenditure of energy at the distribution board. The difference between these quantities represents the losses of energy in the wires, in the rheostat, in the electric motor, in the belt transmission, and so on up to the piston itself. If, after this, experiments are carried out with a high cylinder temperature and the energy required to set the machine in motion is noted, then the piston friction can be determined by a simple calculation from the equation

\[ R_p=E-r \tag{4} \]

where $E$ is the energy at the distribution board, in horsepower, and $r$ is the loss in transmitting the energy to the piston.

In our experiments we proceeded as follows. First the machine was allowed to run on illuminating gas, and, when the cylinder had warmed up to the highest temperature that one can encounter in practice, it was switched over to external energy. This transition could be made very easily, because while operating on illuminating gas the machine drove the electric motor idle; consequently, it was only necessary to stop the supply of gas and connect the electric motor into the circuit, and the transfer of energy began to take place in the reverse order. After this the machine began to cool under the influence of the cooling water, and the piston friction, owing to the increase in the viscosity of the oil, began to increase.

The record of energy at the distribution board gave us the law of variation of friction, and calculation by equation (4) gave the magnitudes of friction at various cylinder temperatures.

As the experiment showed, with this method one can come very close to the true values of the work of piston friction at high temperatures.

Introduction

§ 3.

The mechanical method for determining piston friction is based on the following conclusions. As is known, the work of friction of moving parts in engines may be calculated from the equation

\[ R = N_i - N_e, \tag{5} \]

where $N_i$ is the indicated work and $N_e$ is the effective work; for internal-combustion engines this equation is written as

\[ R = N_i - N_i' - N_e, \tag{5a} \]

where the quantity of the indicated work of the pump, $N_i'$, is also included.

The work of the resistances $R$ includes the work of rotation of the flywheels, the crankshaft, and the valve gear, the work of piston friction, and the work of friction in the crosshead bolts and the connecting-rod head. From this work of resistance it is possible to separate the work of rotation of the flywheels, the crankshaft, and the valve gear, $R_k$, if this work is determined by supplementary experiments. The difference $R - R_k$ will represent the work of piston friction and the work of friction of the connecting-rod mechanism, $R_{\mathrm{tr}}$.

Thus, the procedure for investigating piston friction by the mechanical method will be as follows.

First, the work of rotation of the flywheels, the crankshaft, and the valve gear is determined at various numbers of revolutions. For this purpose the shaft elbow is disconnected from the connecting rod and the flywheels are rotated by means of a belt drive from an electric motor. The electrical energy is determined from the distribution board; from the latter the losses in the electric motor and belt drive are subtracted, and in this way the work of rotation of the flywheels is determined. In order to make it more convenient to use the results of the investigation of the work of rotation of the flywheels, these results are presented on a diagram in the form of a curve, with the numbers of revolutions plotted on the axis of abscissas and the work on the axis of ordinates. With the aid of this diagram we can calculate the work of piston friction for any experiment with the engine.

We shall not dwell here on a consideration of the accuracy of either method; all this will be seen from the further review of our experiments in Chapter III. Here we shall only say that each of these methods has its advantages and shortcomings; therefore we think that, in any experimental investigation of piston friction, the parallel carrying out of experiments by the two methods can serve only for a better clarification of the question.

Chapter I

On the Internal Friction of Lubricants

With respect to each lubricant, engineering practice gives three indications: the flash temperature, the viscosity, and the specific gravity. In studying the friction of lubricated bodies, viscosity must have the most essential significance, since from viscosity we can judge the magnitude of the coefficient of internal friction, on which depend both the force and the work of friction.

The force of internal friction is taken to be the resistance that a liquid offers when its various layers are displaced relative to one another with constant velocity. This force will be proportional to the surface of the layer $Q$, to the difference of the velocities of the two layers $v_1 - v_2$, and inversely proportional to the distance $l$ of these layers from one another. This dependence is represented by the equation

\[ F = \mu Q \frac{v_1 - v_2}{l}; \tag{6} \]

where $\mu$ is the coefficient of proportionality, expressing the force of friction when $Q$, $v_1 - v_2$, and $l$ are equal to unity, and bearing the name of the coefficient of internal friction. As soon as the displacement of the layers begins, so too begins an increase of the angle of shear with a definite angular velocity.

With the passage beyond the limit of elasticity, the connection between the particles is broken: they begin to move relative to one another, while at the same time the bodies relax, or undergo relaxation. Consequently, as a result of relaxation, the force of internal resistance of the body will decrease. With a constant external force, however, the angular velocity must increase, but this will occur only up to a certain limit, since according to equation (6) the force of internal resistance increases with an increase in angular velocity; consequently, the decrease of the force of resistance as a result of relaxation and its increase with the increment of angular velocity must at a certain moment balance each other, and then to a definite angular velocity there will correspond a definite force of resistance, or force of internal friction, and, conversely, to every force of resistance there will correspond a definite angular velocity, just as, in elastic deformation, to a definite force there corresponds a definite angle of shear. Thus, we may represent equation (6) in the form of equation (7)

\[ F = \mu Q \varphi, \tag{7} \]

where $\varphi$ is the angular velocity.

At the present time the motion of liquids in tubes has been studied. In this connection it has been found that the phenomenon of shear can be observed only up to

Chapter I. On the Internal Friction of Lubricant. § 3.

a certain limiting velocity. Beginning with a certain velocity, vortical motions of particles appear in the layer, which create entirely different dependences of the magnitude of the force of internal friction on the velocity. The velocity at which vortical motions of particles begin is called the critical velocity; it is the greater, the greater the viscosity of the substance and the smaller the radius of the tube¹.

Up to the critical velocity, liquids obey Poiseuille’s law (Poseuille) (1842), expressed by the equation

\[ Q=\frac{\pi P R^{4}}{8\mu L}\,t, \tag{8} \]

where $Q$ is the quantity of liquid that has flowed out, $P$ the pressure, $L$ the length of the tube, $R$ the radius of the tube, $t$ the time, and $\mu$ the coefficient of internal friction. At velocities greater than the critical one, the law of outflow of a liquid is different; from the experiments of Osborne Reynolds and from the latest experiments of E. Bose and D. Bauert² it follows that for different bodies the law of outflow differs, and that with the transition through the critical velocity the viscosity does not increase for all bodies.

In the opinion of B. P. Weinberg, expressed to me personally, the phenomenon of a critical velocity must also exist in every layer of liquid, with the critical velocity being the greater, the greater the viscosity of the substance and the greater the thickness of the layer. The dependence between the force of friction and the velocity up to the critical velocity, in B. P. Weinberg’s opinion, may be expressed by the equation

\[ F=k_{1}v, \tag{9} \]

where $k_{1}$ is the coefficient of proportionality. During the transitional state, when vortical motions begin, by the equation

\[ F=k_{1}v+k_{2}v^{2}, \tag{10} \]

and at velocities above the critical velocity

\[ F=k_{2}v^{2}. \tag{11} \]

This opinion reconciles the formerly existing disagreement among physicists, of whom some adhered to Newton’s opinion, expressed by equation (9), and others to Coulomb’s opinion, expressed by equation (10). For us, however, equation (9) is of significance, because the viscosity of lubricating oils and the very small thickness of the layer give grounds for assuming that, in our experiments investigating the work of piston friction, we are dealing with velocities far below the critical velocity.

To determine the coefficient of internal friction of bodies, various methods of deforming a body are used, in which its form changes at a constant rate. For more viscous bodies, use is made—

§ 3. Variation of the coefficient of internal friction with temperature.

require displacement, forcing through a tube, etc.¹); for liquids, passing them through tubes of various diameters. There are comparatively many methods, but the results obtained up to now cannot be recognized as perfectly exact, and therefore usually only the order of magnitude of the values of the coefficients of internal friction $\mu$ is indicated. From this point of view, the experiments of Prof. N. Petrov on vegetable and mineral oils, published as early as 1885 in the Bulletin of the St. Petersburg Technological Institute, are of interest to us.

To determine the coefficient of internal friction, N. Petrov used glass tubes of very small diameter, since all experiments were at velocities below the critical one. For the accuracy of the experiments, great precision was required in determining the dimensions of the tubes, and a perfectly uniform internal diameter of the tubes along their entire length.

All this, of course, could not be attained with absolute accuracy, and therefore, with small tube diameters (approximately from 2.5 to 0.5 mm), the influence of these errors, in our opinion, must be such that the magnitudes of the friction coefficients according to Prof. Petrov’s determinations have value only as indicators of the order of these magnitudes. From the following table, compiled from the data of Prof. Petrov’s experiments,²) we can see what enormous significance a change in temperature has for the magnitude of the coefficient of internal friction of a lubricant. Using the method of graphical interpolation, on the basis of Prof. Petrov’s graphical tables, we calculated the percentage change of the coefficient of internal friction when the temperature is raised from 20° and 40° C by one degree.

Table I.

Name of oils	Coefficient of internal friction at 20° C	Coefficient of internal friction at 40° C	Change in % per 1° C at 20° C	Change in % per 1° C at 40° C	Specific gravity
Vegetable oils:
Spermaceti	0.0036	0.0018	4.4	2.8	—
Olive	0.0086	0.0036	4.3	3.3	—
Rapeseed	0.0094	0.0041	4.3	3.4	—
Mineral oils:
Transparent:
Oleonaphtha No. 3	0.0113	0.0040	4.5	3.0	0.900
Rops factory locomotive oil	0.0184	0.0054	6.5	3.7	0.903
Baku machine oil	0.0205	0.0064	7.3	6.7	0.902
Black:
Rops factory oil	0.0305	0.0090	6.7	5.6	0.910
Baku Petroleum Company oil	0.0840	0.0200	10.0	5.0	0.917

¹) Experiments of Prof. B. P. Weinberg, “Toward the study of bodies with large values of the coefficient of internal friction.”

²) N. Petrov, Description and Results of Experiments on the Friction of Liquids and Machines. St. Petersburg, 1886.

The coefficient of internal friction is expressed in this table in milligrams per $1\ \mathrm{mm}^2$ in 1 sec.

From the table it is evident that the changes in the coefficient of internal friction are different for different oils and different temperatures. The greater the viscosity by which an oil is distinguished, the more strongly the coefficient of internal friction changes with temperature. How much a change of temperature can affect the coefficient of internal friction of bodies may be seen from the experiments of Prof. B. P. Weinberg¹. He found that for tar at $20^\circ$ C. this change is expressed, for an increase of $1^\circ$, as 38%, and at $40^\circ$ C. as 23%; for asphalt, at $20^\circ$ C. as 44%, and at $40^\circ$ C. as 30%.

The interesting data from Prof. N. Petrov’s experiments on determining the coefficient of internal friction of oils cannot be used for our purposes, because they refer to those sorts of lubricant which we did not have at our disposal. On the other hand, it must generally be noted that it is impossible to compile, for practical use, general tables of the coefficients of internal friction of various lubricants, especially mineral ones, since all these oils do not possess great constancy in their properties. This prompted us to undertake an independent investigation of the properties of the lubricating materials used by us in working with machines.

If we now turn to Poiseuille’s equation (8), then from it we can see that the time required for a liquid to flow through one and the same tube, at some given temperature, is directly proportional to the coefficient of internal friction, and, consequently, we may write

\[ \frac{t_1}{t_2}=\frac{\mu_1}{\mu_2}. \tag{12} \]

This proportionality gives us the possibility of judging the coefficient of internal friction of a given oil by the viscosity which is usually indicated in engineering according to Engler. The method of determining viscosity is reduced to determining the time of flow of the lubricant through the tube in the Engler viscometer. The time found, referred to the time of flow of water in the same apparatus, gives the specific viscosity.

We have compiled Table II, representing the change in the viscosity of a lubricant with temperature. The table has data for three lubricants: for a mixture of cylinder oil No. 1 with machine oil No. 6 in the volume ratio $1:1$, for one machine oil No. 6, and for vaseline oil. The first mixture was used by us for lubricat—

§ 5. Data of our investigations of the viscosity of lubricants

of cylinders of internal-combustion engines, the second for lubricating compressor cylinders.

Table II.

Mixture: temperature, °C	Mixture: duration of outflow, min.	Mixture: duration of outflow, sec.	Mixture: specific viscosity	Machine oil: temperature, °C	Machine oil: duration of outflow, min.	Machine oil: duration of outflow, sec.	Machine oil: specific viscosity	Vaseline oil: temperature, °C	Vaseline oil: duration of outflow, min.	Vaseline oil: duration of outflow, sec.	Vaseline oil: specific viscosity
20°	50	—	130,4	20°	14	28,6	37,75	20°	—	52,7	2,29
29°	20	18	53,0	27°	11	—	28,70	30°	—	43,2	1,88
35°	12	15	32,0	33°	7	19	18,65	35°	—	39,0	1,70
42°	8	13	21,4	47°	3	12,5	7,94	43°	—	35,2	1,53
52°	4	49,4	12,6	53°	2	17	5,96	54°	—	32,4	1,41
60°	2	52,4	7,5	66°	1	23,4	3,62	63°	—	30,0	1,30
67°	2	05,8	5,5	81°	—	56	2,43	68°	—	29,2	1,27
77°	1	35,6	4,16	89°	—	48	2,09	82°	—	27,4	1,19
83°	1	13,6	3,20	108°	—	36,6	1,59	105°	—	26,0	1,13
93°	1	2,6	2,71	120°	—	33	1,44	124°	—	25,4	1,10
106°	—	52,4	2,28	149°	—	28	1,22	—	—	—	—
103°	—	39,6	1,72	—	—	—	—	—	—	—	—
140°	—	33,3	1,45	—	—	—	—	—	—	—	—

The determination of viscosity was carried out with Engler’s viscosimeter, the time being determined for 100 cubic centimeters of lubricant. To make use of graphical interpolation, diagram 1 (drawing 1) was compiled from this table. In this diagram, temperature is plotted along the axis of abscissas, and specific viscosity along the axis of ordinates, from 0 to 150 and from 0 to 30. The numbers outside the grid denote the specific gravity.

From this diagram it is evident that the form of the curve of specific viscosity is identical with the curves of variation of the coefficient of internal friction obtained by Professor N. Petrov. These curves are of hyperbolic form; in general they are some sort of polytropic curves, which it is difficult to express by an equation, but from them it is very easy to determine the specific viscosity at any temperature. Knowing the viscosity, one can also calculate the coefficient of internal friction, since it is known that for water it is equal to 0,0104 g/cm/sec. at 20° C.

Using diagram 1, we can obtain the percentage change in viscosity with a change of temperature by 1° C. For the mixture 1/1 it is equal to 9,2% at 20° C. and 6,5% at 40° C.; for machine oil No. 6 it is equal to 5,3% at 20° C. and 5,8% at 40° C.

Besides the oils indicated, in investigating the work of piston friction we tested various mixtures. They consisted of a mixture of 1/1 with kerosene. The following Table III characterizes these mixtures with respect to viscosity and specific gravity at 20° C.

On the basis of this table diagram No. 2 was compiled, where viscosity is plotted along the axis of abscissas and specific gravity along the axis of ordinates. This diagram is of interest in that it is completely identi—

Chapter I. On the Internal Friction of Lubricant. § 5.

…with the diagram of the dependence between specific gravity and viscosity for a $1/1$ mixture at various temperatures. The last curve

Diagram 1.

Fig. 1.

can be constructed by using diagram No. 1, where the change in specific gravity with temperature is represented by an inclined line. Both indicated curves coincide with one another at all points. This gives…

§ 5. Data from Our Investigations of the Viscosity of Lubricants

gives us grounds to conclude that an admixture of kerosene to a mixture of $1/1$ cylinder and machine oils has the same effect on the given properties of the lubricant as an increase in temperature has on the mixture. This

Table III.

Mixture No.	Time, sec.	Specific viscosity	Specific gravity
1	41,0	1,78	0,853
2	79,0	3,40	0,870
3	98,0	4,20	0,873
4	111,1	4,83	0,874
5	153,0	6,65	0,876
6	161,0	7,00	0,879
7	181,1	7,87	0,882
8	232,3	10,11	0,885
9	274,0	11,90	0,887
10	418,3	18,20	0,890
11	1072,8	46,70	0,899
12	3000,0	130,40	0,905

was also noted by Prof. N. Petrov. He says that an admixture of solar oil to black wagon oil reduces internal friction in the same way as heating does, whereby the addition of $n^\circ/\%$ of solar oil is approximately equivalent to $n^\circ$ of heating. The action of kerosene is the same as that of solar oil, but it is taken in twice as small a quantity as the latter.¹

Specific gravity.

Diagram 2.

Drawing 2.

The indicated mixtures were of value to us only in investigating the influence of the viscosity of the lubricant on the magnitude of the work of friction. As a lubricating material for the cylinders of an internal-combustion engine these mixtures have no significance, since kerosene readily evaporates and burns out; therefore, in preparing mixtures with kerosene, we were not interested in the percentage ratio of the constituent parts, as having no practical significance.

On the Friction of Lubricated Bodies.

6. The most important question in the investigation of the friction of machine parts is the question of the magnitude of the resistance offered by the rubbing parts. So long as between them there is a layer of lubricant sufficient to isolate the metallic surfaces from one another, we are dealing with the force of internal friction in the layer of oil. The magnitude of this force is expressed by formula (6) of the preceding chapter in the form of the equation

\[ F=\mu Q\frac{v}{l}, \tag{13} \]

where $v$ is the relative velocity of the rubbing parts, $l$ is the thickness of the lubricant.

From this formula, however, one sees neither the influence of pressure nor the influence of temperature. Meanwhile both factors are of enormous importance for the magnitude of the force of friction. Introducing into formula (13) the value of the pressure per unit surface $p$, we may obtain an expression for the dependence of $F$ on the pressure

\[ F=\frac{\mu v Qp}{lp}=\frac{\mu v P}{lp}, \tag{14} \]

where $P$ is the total pressure on the rubbing surfaces.

However, the dependence between the force of friction and pressure is not as simple as it is represented by equation (14). This equation includes the magnitude of the thickness of the lubricant layer $l$, which depends on the pressure. What this dependence is cannot at present be stated with certainty. According to the data of Prof. N. Petrov, it is inversely proportional to the square roots of the pressures. The dependence between temperature and the force of friction is determined, on the one hand, by the change in the coefficient of internal friction $\mu$, and, on the other, by the change in the thickness of the lubricant layer. We already know from § 3 about the change of $\mu$ with temperature; as for the change in the thickness of the lubricant layer, we can only state conjecturally that the denser the lubricant, the more difficult it must be for it to be squeezed out of the gap between solid bodies. The higher the temperature, the more fluid the lubricant, and the thinner the lubricating layer. The experiments and calculations of Prof. N. Petrov run counter to this conception¹. Prof. N.’s explanation of this

§ 7. Coefficient of Friction.

Petrov finds it in the change of curvature of the rubbing surfaces. Be that as it may, the influence of a change in temperature on the thickness of the lubricant layer is unquestionable; and therefore the influence of a change in temperature on the force of friction is extremely complex, and for the time being it can be established only experimentally in each individual case.

Considering equation (14), we come to the conclusion that the quantities $\mu$ and $l$ entering into it are certain functions of $P$ and $T$. On the basis of the hydrodynamic theory of friction of lubricated solids, the thickness of the oil layer depends simultaneously on the forces of internal friction and on the capillary properties of the oil. If to this we add the indication that the thickness of the layer depends on the curvature and on the properties of the surface of the solid bodies, and on the method of lubrication, then the indeterminacy of the quantity $l$ will become clear. Moreover, the quantity $l$ in practice cannot be measured, since, according to the calculations of Prof. N. Petrov, at a pressure of 1 atm. and a velocity of 1 m per sec., it is expressed for journals by a value of 0.03–0.04 mm.

Thus, formula (14) for calculating the force of resistance $F$, owing to the indeterminacy of the quantities entering into the right-hand side of the equality, is unsuitable. Therefore the quantity $F$ is determined in experiments by direct measurement, while to characterize friction the ratio of the force of frictional resistance to the total pressure is used:

\[ \eta = \frac{F}{P}. \tag{15} \]

The quantity $\eta$ is called the coefficient of friction of machine parts. From all that has been said above it can be seen that the quantity $\eta$ depends on the coefficient of internal friction $\mu$, on the magnitude of the surface area $Q$, on the velocity $v$, on the layer thickness $l$, on the pressure $P$, and on the temperature $T$. All this, except for the last dependence, can be represented by an equation if we substitute into equation (15) the value of $F$ from equation (14):

\[ \eta = \frac{\mu v}{lp}; \tag{16} \]

or

\[ \eta = \frac{\mu v Q}{lP}. \tag{17} \]

The dependence of the magnitude of the coefficient of friction on all the indicated factors remains exactly the same as that indicated also for the force of friction. Therefore, if all the conditions under which the value of the coefficient of friction was obtained are not specified, it has no practical significance.

The concept of the coefficient of friction arose at a time when friction at rest and sliding friction of dry bodies were studied. There the magnitude of the coefficient of friction for every material is quite definite, because it depends neither on pressure, nor on surface area, nor on velocity, nor on temperature (Cou—)

lomb). There the coefficient of friction is a characteristic of the given material with respect to friction. But the sliding friction of completely dry bodies is encountered comparatively rarely in practice, for example in braking, in lathe and grinding work; therefore the well-known tables of coefficients of friction, compiled by Rennie and by Morin, give the values of the coefficients of friction of bodies that have been lubricated, but then wiped in such a way that there is no layer of lubricant between the rubbing surfaces (!?). But this already at once changes the matter sharply: the coefficient of friction proves to depend on the pressure; therefore in the tables mentioned there are coefficients for different pressures, while in handbooks (Hütte) it is added, although very obscurely, that the magnitude of the resistance of friction also depends on the speed of motion and on the temperature. It is clear that as soon as a lubricant appears between the rubbing surfaces, the coefficient of friction loses its definiteness; it ceases to be a characteristic of the friction of the given materials. Any value of the coefficient of friction of lubricated bodies, taken separately, without indicating the whole series of conditions under which it was obtained, has no significance. But in a series of other values of the coefficients of friction, it acquires the significance of an intermediate term and can serve only as an indication of the direction taken by the force of friction under the influence of a change in one factor or another.

Despite such uncertainty, the magnitude of the coefficient of friction will undoubtedly always be of interest to engineers, since in practice knowledge of the ratio of the forces acting on bodies to the forces of frictional resistance is of paramount importance. Besides knowing the losses associated with friction, it is sometimes necessary to know the permissible load on the surface of the rubbing bodies, since the destructions that are caused as a result of an excessive increase in the coefficient of friction can be considerable. It is therefore important to know that pressure per unit surface at which the lubricant begins to be squeezed out, and contact of the solid bodies occurs. Of course, this can be indicated only by a whole series of values of the coefficients of friction; but here it is important to note that under a certain pressure contact of solid bodies occurs, and that the beginning of this contact must always be known. On the other hand, the influence of pressure on the coefficient of friction at large loads is great in comparison with the influence of the other quantities entering into formula (16), i.e. $F$ is always much smaller than $P$.

9. As soon as we pass to small pressures with a high viscosity of the lubricating layer, the roles of the quantities entering into formula (16) change, and the very magnitude of the coefficient of friction loses practical meaning; this is clearly seen when calculating the coefficients of friction from equations (16) and (17) for piston machines. Press—

§ 10. Specific frictional resistance.

the pressure on the surface of the cylinder in them is composed of the pressure of the piston rings and the weight of the piston. The contact pressure of the rings encountered in practice rarely exceeds 0.5 kg/cm²; as for the pressure due to the weight of the piston, it ranges from 0.7 kg/cm² for water-cooled pistons to 0.05 kg/cm² for pistons not cooled by water. In many cases, with a trunk piston the weight of the piston, at least theoretically, disappears entirely, since the pressure due to the weight is transmitted to the stuffing boxes. In cases, however, where the rings are removed with a trunk piston, the pressure on the cylinder walls will be equal to zero; and since in this case the frictional resistance due to the viscosity of the lubricant is not equal to zero, the coefficient of friction according to formulas (16) and (17) assumes an infinitely large value¹. Since the fluctuations of the pressure from the weight of the piston on the cylinder walls occur within the limits from 1 kg to 0, it is clear that the corresponding coefficients of friction must fluctuate from some very small value (less than unity) to an infinitely large one. The slightest errors in determining the pressure on the surface entail large changes in the coefficient of friction.

All that has been said induces us, in our experiments, to abandon the calculation of the coefficient of friction and to use, for the characterization of each experiment, the force of frictional resistance

\[ F=\frac{A_{\mathrm{k}}}{v} \tag{18} \]

and the specific frictional resistance

\[ f=\frac{F}{Q}, \tag{19} \]

where $A_{\mathrm{k}}$ is the work of friction, $v$ the mean velocity of the piston, and $Q$ the surface of the piston.

Undoubtedly, all the properties inherent in the coefficient of friction also pertain to the specific frictional resistance. From the change of this quantity one can always judge the influence of all those factors which also influence the coefficient of friction. Substituting in equation (19) the value of $F$ from equation (13), we obtain

\[ f=\frac{\mu v}{l}. \tag{20} \]

This equation shows us that the specific resistance depends on pressure only insofar as the thickness of the layer changes with it, since the coefficient of internal friction, according to Newton’s hypothesis, does not depend on pressure. As for the influence of temperature on the specific resistance, it is the same as on the coefficient of friction, since $f$ and $\eta$ depend equally on $\mu$ and $l$. (Compare formula 16 with the 20th.)

The advantages of using specific resistance to characterize the friction of machine pistons should be considered to be the independence of this quantity from the surface area and its slight dependence on pressure. The specific resistance of friction makes it possible to judge the friction of machines independently of their size and, conversely, from their size to judge the losses associated with piston friction.

If we assume that the friction force of pistons is determined by the internal friction of the lubricant, then the specific resistance of friction can be represented, on the basis of equation (7), as follows:

\[ f=\mu \varphi, \tag{21} \]

i.e. the specific resistance of friction is directly proportional to the coefficient of internal friction $\mu$ and to the angular velocity of shear $\varphi$.

On the basis of the hypothesis set forth by us in § 1, namely that a definite dependence is always maintained between the shear force and the angular velocity, we arrive at the conclusion that, in the friction of lubricated bodies, the magnitude of the specific resistance should not depend on the relative velocity of the moving parts, because with an increase in this velocity the thickness of the lubricating layer also increases and, consequently, the angular velocity remains constant.

But this proposition still requires experimental confirmation, because the statements of various authors are so contradictory on the question of the influence of velocity on the magnitude of internal friction that it is difficult to draw any general conclusion. Nevertheless, the generality, indicated by Prof. B. P. Weinberg, of the shear formulas for elastic deformation and during the shearing of a lubricant layer, as well as the proposition adopted by us concerning constancy between force and angular velocity, make it possible to elucidate to some extent the phenomena of friction in lubricated bodies.

Hirn already knew of the dependence of the layer thickness on the velocity of the moving parts; but in this respect the data of Prof. N. Petrov are of interest, who, as is known, determined in his experiments the quantity

\[ \varepsilon+\frac{\mu}{\lambda}+\frac{\mu}{\lambda_1}, \]

where $\varepsilon$ is the thickness of the layer, and $\lambda$ and $\lambda_1$ are the coefficients of friction of the lubricating liquid with the metallic surfaces. According to Prof. Petrov’s calculations, the second and third terms of this expression are so small in comparison with $\varepsilon$ that in some cases they may be neglected. Speaking of the influence of velocity on the indicated quantity $\varepsilon+\frac{\mu}{\lambda}+\frac{\mu}{\lambda_1}$ in experiments with the Caillet, Shandlin, and Becker machine, Prof. Petrov cites, for comparison, experiments with colza oil and with light mineral oil¹, giving the coefficient of internal friction as 0.00270 for colza oil and 0.00263 for mineral oil. These quanti-

§ 11. Dependence of the Specific Resistance on $\varphi$.

The values $\mu$ could not, of course, have an influence on the magnitude

\[ \varepsilon+\frac{\mu}{\lambda}+\frac{\mu}{\lambda_1}, \]

whereas the latter, in the experiments compared, proved to be different. The only cause of this difference is the velocity. We calculated the ratios of the magnitudes

\[ \varepsilon+\frac{\mu}{\lambda}+\frac{\mu}{\lambda_1} \]

and of the velocities and found that the former are as $1:0.846$, the latter as $1:0.892$. A comparison of the experiments with castor oil and with a mixture of castor oil with mineral oil gives a velocity ratio of $1:0.845$, and a ratio of

\[ \varepsilon+\frac{\mu}{\lambda}+\frac{\mu}{\lambda_1} \]

of $1:0.849$.

At high pressures the proportionality of the change is not preserved; it is not preserved at low velocities either, but here we apparently have to do with contact of the metals with each other.

On the basis of experiments with a wagon axle, Prof. N. Petrov compiled Table LXXIX¹, which we reproduce here in the form of Table IV, but with the addition of a column for the force of friction, which is also of interest to us.

Table IV.

Force of friction $F$.	Velocity $v$.	Temperature of rubbing parts.	$\varepsilon+\dfrac{\mu}{\lambda}+\dfrac{\mu}{\lambda_1}$	Temperature of rubbing parts.	$\varepsilon+\dfrac{\mu}{\lambda}+\dfrac{\mu}{\lambda_1}$	Remarks.
6.73	236	12.5	0.00226	12.2	0.00275	Castor oil.
6.67	415	13.6	483	13.4	538	Castor oil.
6.87	239	13.5	179	13.0	198	Mixture No. 69.
6.87	418	13.0	381	12.4	417	Mixture No. 69.
9.58	235	12.7	380	12.4	450	Light mineral oil No. 71.
10.30	415	13.3	816	14.1	777	Light mineral oil No. 71.
10.20	227	13.6	329	12.7	408	Dark mineral oil No. 70.
10.20	410	13.7	636	12.7	831	Dark mineral oil No. 70.

The data of the table clearly show that, with an increase in velocity, the thickness of the layer increases; moreover, a certain proportionality is observed in the changes of these quantities.

On the basis of the indicated experiments, Prof. Petrov gives, for approximate calculations, the formula²

\[ \varepsilon=\varepsilon_0+0.000001\,(v-v_0), \]

which may be represented in the form

\[ \frac{\varepsilon-\varepsilon_0}{v-v_0}=0.000001; \]

that is, the reciprocal of our angular velocity is obtained, which Prof. Petrov took to be the same for all the lubricants tested by him.

In order that, in the friction of lubricated bodies, a definite angular velocity be maintained, it is necessary that the thickness of the lubricant be capable of increasing under the action of the hydrodynamic pressure of the liquid. This condition is also present in the experiments of Prof. Petrov, because in Klein’s, Schanzlin’s, and Becker’s machines the bearing brasses could move apart under the pressure of the lubricant without any additional increase in pressure; and in the experiments with a railway axle the thickness of the lubricant could increase owing to the peculiarities of railway axleboxes in general. In those cases, however, where the thickness of the lubricant cannot increase—for example, in the case of rotation of a journal in a non-separable cylinder—there we must find a change in the force of internal friction proportional to the relative velocity, as follows from equation (13). In those cases where the lubricant can increase, but with an additional increase of pressure, we shall have an intermediate phenomenon. To such experiments we must assign the experiments of Stribeck, Lasche, Dettmar, and Heimann, in which the brasses of the bearings tested are either pressed together by the bearing bolts, or constitute a non-separable bushing. On the basis of their experiments, Stribeck and Lasche hold the opinion that, with increasing speed, the coefficient of friction at first decreases (Stribeck) and, after a certain minimum, increases, but much more slowly than the speed increases; at speeds above 10 m/sec, however, the coefficient of friction does not increase with speed (Lasche).

Prof. Stribeck explains the initial decrease in the value of the coefficient of friction by the fact that, owing to the increase in the lubricant layer, the contact of the metallic parts gradually diminishes; but afterward, after a certain minimum, it begins to grow rapidly (at low pressures proportionally to the speed) because a constant thickness of lubricant remains. But this proportionality is observed only over a small interval of change in speed; the further change in the coefficient of friction proceeds much more weakly than the speed changes at the same time. Prof. Stribeck explains this by a certain further increase in the thickness of the layer. While agreeing with Prof. Stribeck’s explanations concerning the fall of the coefficient of friction to a certain minimum, the subsequent phenomenon of the cessation of change in the thickness of the layer, and then its renewed increase with increasing speed, seems to us incomprehensible. It seems to us that the increase in the thickness of the layer must continue all the time while the speed is increasing; but as soon as the clearance between the journal and the bearing brasses is filled, then, as the layer increases, the clearance too will increase, but only insofar as the construction of the bearing permits this. It is clear that at this time, to the adopted load on the bearing, there is added the pressure of the resistance of the bearing bolts. Therefore the coefficient of friction, calculated by formula (15),

§ 11. Dependence of the specific resistance on $\varphi$.

in reality does not correspond to the pressure that exists on the surface of the rubbing bodies. This also serves as the cause of the apparent increase of the coefficient of friction after a certain minimum in the experiments of Prof. Stribeck and others. What the law is for the change of pressure with increasing speed we do not know, but there is no doubt that the thickness of the layer nevertheless continues to increase, insofar as this is permitted by the increase of the clearance between the journal and the bearing brasses under the pressure of the liquid.

The above also explains the phenomenon that the increase of the coefficient of friction after the minimum is more considerable for small loads than for large ones. In fact, the growth of the layer thickness under small loads proceeds more rapidly; it more rapidly reaches the magnitude of the clearance, and then the additional pressure begins to increase more rapidly; moreover, the relative influence of this additional pressure at smaller loads is more considerable on the coefficient of friction than at larger ones.

It also becomes clear to us that a definite load corresponds to a definite speed at which the coefficient of friction assumes its minimum value. The greater the pressure on the rubbing surface, the smaller the lubricating layer at one and the same speed, and the greater, consequently, the angular speed

\[ \varphi = \frac{v_1 - v_2}{l}. \]

Consequently, the greater the load, the greater the relative speed at which the layer thickness reaches the magnitude of the clearance. Thus the magnitude of the clearance determines, on the one hand, the minimum of the coefficient of friction, and on the other, that speed at which this minimum is obtained.

That each bearing has its own minimum of the coefficient of friction is confirmed by Prof. Stribeck’s experiments with Sellers and Magnolia bearings.

We can judge the influence of the magnitude of the clearance on the magnitude of friction from the experiments of O. Lasche. From his spatial diagram¹) we can see that the force of friction falls with increasing clearance. The same thing we can see from Heimann’s diagram²), where the ordinates of the curves of the change of friction for clearances of 0.05 mm and 0.12 mm differ from one another by almost a factor of two. G. Dettmar, on the basis of his investigations³), comes to the conclusion that the coefficient of friction varies proportionally to the square root of the speed $v$. Meanwhile, as Heimann says, $x$ in the expression

\[ \frac{f_1}{f_2} = \frac{v_1^x}{v_2^x} \]

¹) O. Lasche. Z. d. V. d. I. 1902. S. 1955.
²) H. Heimann. Z. d. V. d. I. 1905. S. 1165.
³) G. Dettmar. E. T. Z. 1899. S. 381.

Chapter I. On the Friction of Lubricated Bodies. § 11.

fluctuates in Dettmar’s experiments with a solid bronze bearing from 0.385 to 0.620, and only the mean value from all the experiments $(x = 0.51)$ confirms Dettmar’s own conclusion. As for the various authors, the value of $x$ fluctuates still more strongly: for Lasche $x = 0.30$, while for Morra and Mantel $x = 0.66$. Lasche even arrives at the conclusion that the coefficient of friction does not depend on velocity beginning with 10 m/sec, i.e., at high velocities his $x$ becomes zero. In the latter case one must assume either constancy of angular velocity, or a rise in the temperature of the lubricating layer at high velocities, which was most likely the case, since Lasche conducted the experiment with a solid bearing. It seems to us that, in general, for all the authors mentioned, the temperature of the lubricant increased somewhat with increasing velocity, which served as the cause of the decrease in the magnitude of friction.

With this we shall also limit our references to authors who, in one way or another, confirm our idea concerning the angular velocity $\varphi$, because the given question is not the main subject of our work and is necessary to us only insofar as it will further explain the results of our experiments.

Chapter II.

Arrangement and execution of the experiments.

The friction of the piston was investigated by us on three machines: on a gas engine of the “Otto Deutz” works, on a compressor of the “Rud. Meyer” works, and on a kerosene engine of the “Hornsby-Akroyd” works.

The gas engine was built in Germany by special order of the head of the heat-engine laboratory of the Tomsk Technological Institute, Prof. V. L. Malyshev. The principal feature of this machine is that it can operate on any fuel, both gaseous and liquid; moreover, in this machine it is possible to vary the compression ratio, the number of revolutions, and to measure the temperature of the cylinder walls. The change in the number of revolutions is achieved by means of the governor, for which it is necessary only to change the governor springs. During operation, when the number of revolutions changes, the governor shifts the fulcrum of the distribution lever, whereby the height of valve lift changes and, consequently, the quantity of the charge changes. In order to make it possible to measure the temperature of the cylinder walls, sockets for thermometers were drilled through the jacket. The depth of each socket is such that the lower surface of the thermometers is 4.5 mm from the inner, working surface of the cylinder. Oil was poured into the bottom of the sockets, and the bulb of the thermometer was immersed in it. The sockets are arranged on the upper surface of the cylinder in such an order that one of them is near the combustion chamber, another in the middle of the cylinder, and the third at the end of the working stroke of the piston. This was done so that one could judge the temperature of the walls along the cylinder during operation of the machine. To judge the temperature of the cylinder walls, of course, these three points are insufficient, because the temperature of the walls also changes greatly from the lower part of the cylinder, where the cooling water enters, to the upper part, where the water leaves the jacket; but the installation of thermometer sockets in the lower part of the cylinder is impossible owing to the design features of the machine.

In other respects this machine represents the usual type of gas engine of the “Otto-Deutz” works. It is four-stroke, single-acting, rated at 10 h.p. at 200 revolutions per minute. The cooling of the cylinder and of the compression chamber is carried out separately. The cylinder is open on one side, and the piston enters it in the form of a long plunger.

The principal dimensions of the machine are as follows: cylinder diameter $D_c = 219.96$ mm, with the mean error of the arithmetic mean $\pm 0.0047$ mm; piston diameter $D_p = 219.67$ mm, with mean error $\pm 0.030$ mm; the clearance between the surfaces of the cylinder and the piston

\[ \delta=\frac{219.96-219.67}{2}=\frac{0.29}{2}=0.145\ \text{mm}, \]

the mean error in the determination of $\delta$ being

\[ \pm \sqrt{0.0047^2+0.03^2}=\pm 0.0304\ \text{mm}, \]

or $21.0\%$ of the value of the clearance. The piston stroke is $H = 321$ mm. The length of the piston is 440 mm; its lateral surface is $3040\ \text{cm}^2$; the weight of the piston together with the crosshead and the connecting-rod head is 63.8 kg.

The specific pressure due to the weight of the piston on the horizontal projection of the cylinder was computed by us from the expression

\[ p_n=\frac{P_n}{(H-nh)D} =\frac{63.8}{(44-5.1,2)22} =0.076\ \text{kg}/\text{cm}^2 . \]

In this expression $n$ is the number of piston rings, and $h$ is the height of a ring. We assumed the specific pressure from the rings to be the same over the entire circumference, although the actual distribution must be different, since the thickness of the rings varies along the circumference. In view of the fact that we need to know only the mean pressure, the assumption of a uniform distribution of pressure does not impair the correctness of our subsequent conclusions.

We determined the pressing force of the rings in the following manner: we wrapped the ring with an indicator cord and tightened it to the diameter of the piston, the upper end of the cord being fixed, while weights were suspended from the lower end, Fig. 3. Let the specific pressure be $p_1$; then the pressure on an infinitely small arc $ds$ will be equal to $dshp_1$, and the component of this pressure parallel to the bisector of the angle $2\alpha$ will be equal to

\[ dshp_1 \cos\alpha = rhp_1 \cos\alpha\, d\alpha . \]

Fig. 3.

§ 3. SPECIFIC PRESSURE FROM THE FORCE PRESSING THE RINGS

Consequently, the resultant $Q$ of all the pressures on half of the ring will be equal to

\[ Q = 2 \int_{0}^{\frac{\pi}{2}} r h p_1 \cos \alpha \, d\alpha = 2 r h p_1. \]

Since $Q$ may be replaced at the joint of the ring by a force twice as small, then

\[ Q = 2 P_k; \]

therefore,

\[ p_1 = \frac{P_k}{r h}. \tag{22} \]

From experiment, as the mean value, we found $P_k$ equal to 6.2 kg; consequently, $p_1 = 0.47$ kg/cm$^2$. The total pressure of all the rings is 195 kg, i.e., almost three times greater than the weight of the piston.

In addition to these pressures, normal pressures are transmitted to the walls of the cylinder. These pressures are caused, first, by accelerating and retarding forces, which reach their maximum at the extreme positions of the piston and, in our machine at 200 revolutions, are expressed as 376 kg and 532 kg; and, second, by the pressures of compression and rarefaction, which in the extreme positions of the piston in our experiments reach 213 kg and 124 kg. The forces of inertia of the moving parts are opposite in action to compression and rarefaction, and therefore after subtraction the force acting in the direction toward the shaft will be equal to 252 kg, and in the opposite direction equal to 319 kg. The normal component of the force, as is known, depends on the angle of inclination of the connecting rod to the axis of the cylinder; it increases with increasing angle and decreases with decreasing angle; consequently, it must increase toward the middle of the piston stroke and become zero at its extreme positions. Since in the middle of the stroke the forces of inertia change their sign and become zero, the normal forces are not large and, according to calculations in our experiments, fluctuate from +31 kg to −28 kg over the entire surface of the piston. The negative forces unload the piston, while the positive ones add to its weight. Since the action of these forces is alternating and since it is not large, we neglected them in all subsequent conclusions.

The compressor of the “Rud.-Meyer” works has two cylinders: high and low pressure. The valve gear of the low-pressure cylinder is forced, while that of the high-pressure cylinder is automatic. Both cylinders are double-acting, cooled by water passing through a jacket, and have a through piston rod, owing to which the piston was in a suspended state. The latter circumstance was of special interest for our work. The distinctive features of this compressor consist in the fact that in it the forced valve gear can be replaced by slide-valve gear and, in addition, the clearance space in the low-pressure cylinder can be varied.

The dimensions of the cylinders and pistons are as follows. The diameter of the low-pressure cylinder is $D'_{\mathrm{c}}=200.53$ mm, with the mean error of the arithmetic mean $\pm 0.011$ mm; the piston diameter is $D'_{\mathrm{p}}=200.29$ mm, with the mean error of the arithmetic mean $\pm 0.013$ mm; the clearance between the surfaces of the cylinder and piston is

\[ \delta'=\frac{200.53-200.29}{2}=\frac{0.24}{2}=0.12\ \text{mm}, \]

the mean error for $\delta'$ being $\pm 0.017$, which in percent amounts to $\pm 14.2\%$ of $\delta'$; the piston length is 224.5 mm, the piston stroke 250 mm, and the lateral surface area 1414 cm$^2$. The diameter of the high-pressure cylinder is $D''_{\mathrm{c}}=100.05$ mm, the mean error $\pm 0.018$ mm; the piston diameter is $D''_{\mathrm{p}}=99.77$ mm, the mean error $\pm 0.013$ mm; the clearance between the surfaces of the cylinder and piston is

\[ \delta''=\frac{100.05-99.76}{2}=\frac{0.29}{2}=0.145\ \text{mm}, \]

the mean error being $\pm 0.022$ mm, which in percent amounts to $\pm 15\%$ of $\delta''$; the piston length is 160 mm, the piston stroke 250 mm, and the lateral surface area 503 cm$^2$.

We cannot calculate the specific pressure due to the weight of the piston, since with a through piston rod it is theoretically equal to zero; the weight of the piston itself is borne by the stuffing boxes.

The rings of both cylinders are not self-springing, but have radial spiral springs; therefore we determined the pressure of the rings in two ways: 1) by tightening the ring with an indicator cord, and 2) by determining the elasticity of each separate spiral spring. For the rings of the large cylinder, by the first method we obtained $P_{\mathrm{k}}=6.5$ kg, which, according to formula (22), gives $p'_1=0.812$ kg/cm$^2$; by the second method we obtained the elasticity of each separate spring as follows: No. 1—6 kg, No. 2—5 kg, No. 3—6 kg, No. 4—6 kg, No. 5—5 kg, No. 6—5.5 kg, No. 7—5 kg, No. 8—6.5 kg, No. 9—5 kg, No. 10—2 kg, No. 11—7 kg, No. 12—7 kg, No. 12—3.5 kg, No. 14—7 kg, No. 15—3.5 kg, No. 16—1 kg, the total pressure being 81 kg; if we distribute this pressure over the area of pressure of the rings, we obtain $p'_1=0.803$ kg/cm$^2$. Both in the first and in the second case, the compression of the rings had to be brought approximately to the diameter of the piston; from this it becomes clear that the accuracy of determining the elasticity of the springs and rings could not be great, as is also evident from the data given above. In exactly the same way we found that for the springs of the small cylinder the specific pressure is $p''_1=1.19$ kg/cm$^2$ and the total pressure is 60 kg. As for normal pressures, they are not transmitted here to the piston, since the engine has a crosshead.

The “Hornsby-Akroyd” engine is built to run on kerosene or petroleum; its power at 200 revolutions is $N_{\mathrm{e}}=25$ h.p.; it is four-stroke, single-acting, and therefore one side of the cylinder is open. We do not reproduce a drawing of this machine here; those wishing to become acquainted with this engine can find a description on p. 112 in Güldner, Internal Combustion Engines, 1907. With respect to inves—

§§ 6, 7, and 8.

Duration of the Experiments

For the study of piston friction this machine is of interest in that the piston and cylinder in it had become run in and, as the measurements given below will show, had become severely worn. It should be noted that this machine was acquired originally for operating purposes and for several years, until an electric station was installed, worked for lighting; subsequently it was transferred to the heat-engine laboratory for student work.

The principal dimensions of the machine are as follows: cylinder diameter $D = 342.68$ mm, mean error of the arithmetical mean $\pm 0.06$ mm; piston diameter $D_p = 342.00$ mm, mean error $\pm 0.22$ mm; clearance

\[ \delta = \frac{342.68 - 342.00}{2} = 0.34\ \text{mm}, \]

mean error $\pm 0.12$ mm, which amounts to $\pm 35\%$ of $\delta$. Such a large inaccuracy in determining $\delta$ is explained by the fact that the magnitudes of the piston and cylinder diameters were taken over the entire length of both, and therefore represent a certain mean value of several diameters. Since this machine is badly worn, the difference of the piston diameters at one and the other end of it is equal to $342.70 - 341.00 = 1.70$ mm. The length of the piston is 507 mm; the total surface of the piston is 5460 cm$^2$; the weight of the piston together with the crankhead of the connecting rod is 124.5 kg.

The specific pressure due to the weight of the piston is $p_n = 0.082$ kg/cm$^2$. The piston has 4 rings; the height of each ring is 16.1 mm; the bearing surface of all the rings is 693.5 cm$^2$. The specific pressure due to the rings, by formula (22), is equal to $p_1 = 0.544$ kg/cm$^2$; consequently, the total pressure due to the rings is 377 kg.
With all eight of the indicated machines we carried out investigations of piston friction by the calorimetric method. As was already indicated above (Introduction, § 2), this method consists in passing water through the jacket of the machine, which removes from the cylinder walls the heat obtained from the friction of the piston.

In carrying out the separate series of experiments we varied the following factors:

1) the number of revolutions of the machine was varied, and consequently also the mean speed of the piston, to which we related the data of the experiments;

2) the lubrication was varied both by taking different lubricating material and by adding kerosene to the usual lubricant;

3) the quantity of lubricant was varied;

4) the temperature of the rubbing surfaces was varied, which was regulated by the quantity of water passed through; and, finally,

5) experiments were performed with piston rings and without piston rings.

The duration of observation in each experiment was not great, from 15 to 25 minutes, and was determined by how the experiment proceeded during the observation. If the temperature of the incoming and outgoing

Chapter II. Arrangement and conduct of the experiments. § 9.

the water during this time changed by no more than $0.2^\circ$, the duration of the experiment was limited to 15 minutes. We allowed fluctuations of $0.2^\circ$ in view of the fact that, even in experiments that had become well established, these fluctuations are noticeable, and are explained by the fact that water from the cylinder jacket enters in separate streams of different temperature. Hence it follows that the preparatory period of observation may be very long and may depend on many causes. For example, on the magnitude of the work of friction, since with small friction the whole machine heats up slowly to a constant temperature. On average, the preparatory period may be taken as about 2 hours, but the author sometimes managed to make observations after some time following a change of conditions; at other times, however, setting up the experiment required 5 hours of preparatory work.

The author made all the observations himself; in doing so it was necessary to observe: 1) the temperature of the incoming and outgoing water, 2) the temperature of the cylinder walls, 3) the water consumption by weighing on scales, 4) the number of revolutions by an armature counter or by some other counter, and 5) the current strength and its voltage on the distribution board.

The temperature of the incoming and outgoing water was measured with thermometers whose divisions were equal to $0.1^\circ$; in taking readings it was possible to determine hundredths of a degree by eye with a possible error of $\pm 0.02^\circ$. For each experiment 4 observations of temperature were made, every 5 minutes. At the same time the temperature of the cylinder walls was also read, with a possible error of $\pm 0.1^\circ$. Greater accuracy was not needed here, since from this temperature we can judge only approximately the temperature of the walls.

The water consumption was determined by weighing, every five minutes; large quantities were weighed on decimal scales with divisions equal to 0.05 kg, while small quantities were weighed on ordinary scales, where an accuracy of $\pm 0.5$ g could be attained. The water coming from the cylinder jacket was collected in a tank or a bucket. Above the tank a funnel was placed, through which, before the start of the experiment, the water flowed into a drainage well. At the moment the experiment began, the funnel was moved aside and the water entered the tank; after five minutes the funnel was put back; all this could be done quickly, whereby accuracy in collecting the water was achieved. When the water consumption was small, the water was collected in a bucket.

Here it is necessary to note that, for the accuracy of calorimetric experiments, it is extremely important that the water consumption remain constant during the experiment. The importance of this may be seen from the fact that, as the consumption increases, the temperature of the discharged water and the temperature of the cylinder walls begin to fall; consequently, as the consumption increases, not only the heat of friction during the observed time will be carried away, but also the heat contained in the mass of the walls. With a decrease in the water consumption—

§ 10. Mechanical method.

...the reverse occurs. In setting up the experiments on the “Otto-Deutz” engine we used water from the Institute’s common mains, in which the pressure often varied, which sometimes forced us to spend extra time preparing the experiments. It was necessary to use only the evening time for setting up the experiments, when the water consumption in the branches of the main either ceased entirely or was very small, and therefore the pressure at that time was constant. This circumstance prompted the construction of a separate pressure water tank for the laboratory, which caused the setup of the experiments with the compressor and the “Hornsby-Akroyd” engine to be delayed by two months.

The number of revolutions was determined by counters. On the “Otto-Deutz” engine an anchor counter was installed, with the motion transmitted from the distributing shaft; consequently, the counter indicated one-half the number of revolutions. On the compressor and on the “Hornsby-Akroyd” engine, a hand counter was fastened to the end of the crankshaft.

The following table presents a sample record.

Experiment I.

23/vш12.

Time	Anchor counter	Difference	Temperature of water, $t$ in	Temperature of water, $t$ out	Time	Weight of water	Difference	Volts	Amps	Remarks
6.11	58135	302	12,3	19,2	6.14	0	29,5	229	21,5	$B=756$.
6.16	58437	302	12,3	19,2	6.24	29,5		228	21,5	$t=18,5$.
6.21	58740	302	12,3	19,2	6.25	29,5	29,6	238	21,5	Oil.
6.26	59043	302	12,3	19,4	6.35	56,1		228	22,0	See 1/1.
6.31	59345		12,3	19,4	—	—	—	227	22,0	In 1 h., 30,4 g.
—	—	302,5	12,3	19,3	—	—	29,55	228	21,7	—

To reduce losses from heat emission, the entire outer surface of the cylinder of the “Otto-Deutz” engine was covered with felt, and a tin disk with a narrow slot for the connecting rod was inserted into the open end of the piston.

In this engine the oil was supplied by a special small pump driven by the distributing shaft. In the compressor and the “Hornsby-Akroyd” engine the oil flowed by gravity onto the rubbing surfaces.

Mechanical method. As indicated above, this method consists in determining the indicated and brake work of the engine, determining the difference between these works, determining the rotations of the flywheels and of the crankshaft, and from all these quantities judging the work of friction of the piston. All that has been said can be expressed by the equation

\[ R_{\mathrm{p}} = N_i - N_i' - N_e - R_{\mathrm{vr}}, \tag{23} \]

where $R_{\mathrm{vr}}$ is the work of rotation of the flywheels, and the remaining quantities are indicated in the introduction (equation 5a).

To obtain all the quantities entering into equation (23), several series of experiments were carried out, the results of which are Tables X and XI. (See below, Chapter III).

All the experiments of Tables X and XI were carried out by the author with students. These experiments were performed not for determining piston friction, but for studying questions concerning the operation of the gas engine as such. In setting up these experiments, two groups of senior-semester students worked, each group having an independent topic and carrying it out as a diploma project. The author took part in all these works not only as organizer, but also as a participant in the observations.

After the completion of all the experiments, the students processed the material independently; in parallel with them, the author also processed the material, and this processing is what entered into the present work.

The duration of the experiments was 25 minutes, each experiment having its own check experiment. Observations were made only after a fully steady state had been reached.

In all the experiments 5 persons took part: the 1st person took indicator diagrams and counted the number of revolutions; the 2nd person took readings from the gas and air meters; the 3rd person recorded the temperature of the water entering and leaving the head and the cylinder jacket, as well as the temperature of the exhaust gases; the 4th person weighed, every five minutes, the water leaving the head and the cylinder jacket; and, finally, the 5th person performed a gas analysis of the exhaust products of combustion.

All readings were taken every five minutes, so that for each experiment six observations were obtained.

The indicator diagrams were taken with a “Maygak” indicator, the springs being taken as follows: 2 mm = 1 atm and 30 mm = 1 atm. First, with the strong spring, a diagram of the working process was taken; then, with the weak spring, a diagram of the suction and exhaust strokes was taken.

The effective power was determined by a self-regulating brake, the construction of which those interested may learn from the work of A. Gramberg¹. The load, reduced to one revolution of the machine, remained constant in all experiments.

The variable factors in setting up all these experiments are: 1) the number of revolutions, 2) the compression ratio, 3) the temperature of the cooling water, 4) the moment of ignition of the mixture by an electric spark, and 5) the composition of the mixture (the ratio of gas to air).

§ 12. WORK OF ROTATION OF THE FLYWHEEL.

For us, in investigating piston friction, two factors are important: the number of revolutions and the temperature of the cooling water.

The variation in the number of revolutions of the machine was achieved by changing the governor springs; springs were available for 200, 175, 150, and 125 revolutions.

As regards the temperature of the outgoing cooling water, it was regulated by the water flow rate at about three points: 20°, 40°, and 60° C. In view of the difficulty of setting these temperatures exactly, it was necessary to be satisfied with a certain approximation, as is evident from Table X. In carrying out all these experiments, water from the Institute’s common supply was used, in which the pressure was continually changing, and therefore the temperature of the outgoing water also varied, which is a shortcoming of the experiments.

The influence of other variable factors on piston friction is not noticeable, and if it did exist, then apparently it was negligible.

The work of rotation of the flywheel, the crankshaft, and the entire distributing mechanism was determined in the following way: the connecting rod with the piston was disconnected from the shaft elbow and the flywheel and shaft were set into rotation. From the amount of electrical energy expended, the work of rotation $R_{rp}$ of the above-mentioned parts of the machine was judged.

The entire arrangement of the experiment and the whole calculation were based on the following principles.

As is known, all electrical losses may be divided into two categories: some of them (strictly electrical) are easily calculated, since they represent losses due to heating of the armature and inductor windings and losses in the brush contacts; the others are difficult to calculate and are determined only by measurement; this category includes mechanical losses, losses due to hysteresis, and Foucault currents. In experiments with a shunt electric motor, it is most convenient to regulate the number of revolutions by resistance in the armature circuit, without at all touching the shunt rheostat; then the current in the armature will vary, while in the inductors it will remain constant. If we neglect losses in the brush contacts as being comparatively small, then in calculating the strictly electrical losses it will be necessary to take only the losses due to heating of the armature winding. As is known, these losses are represented by the product $i^2 r$, where $i$ is the current strength, and $r$ is the resistance in the armature, equal in our case to 0.225 ohm. If we determine, in idle running for a whole series of numbers of revolutions, the electrical energy $W_2$ and the loss due to heating of the armature winding $i_2^2 r$, then the difference $W_2 - i_2^2 r$ will represent the losses of the second category, i.e., the mechanical losses, hysteresis losses, and Foucault currents. If in the same way we determine the electrical energy $W_1$, which is necessary for rotating the electric motor, flywheel, shaft, and distributing mechanism, as well as the losses due to heating of the armature $i_1^2 r$, then the difference $W_1 - i_1^2 r$ will represent,

on the one hand, losses of the second category in the electric motor itself; on the other hand, losses in the belt transmission and the work of rotation $R_{\mathrm{vr}}$ of all the above-mentioned parts of the machine under test.

From all that has been said it follows that, for determining the rotation of the flywheel, shaft, and distributing mechanism, $R_{\mathrm{vr}}$, the following equation may be written:

\[ R_{\mathrm{vr}}=\eta_{\mathrm{r}} \frac{(W_1-i_1^2 r)-(W_2-i_2^2 r)}{736}, \tag{24} \]

where $\eta_{\mathrm{r}}$ is the coefficient of the belt transmission. But this formula is entirely satisfactory only so long as $i_1$ and $i_2$ do not differ greatly; if the difference is large, then the difference will also be large for the losses from hysteresis and Foucault currents, whereas equation (24) was derived on the assumption that these losses remain constant. Equation (24) makes it possible to determine, for any number of revolutions, the work of rotation $R_{\mathrm{vr}}$; but in view of the fact that the data in this equation have to be obtained from two different experiments (at no load and under load), in calculating $R_{\mathrm{vr}}$ one must resort to graphical interpolation, namely, one must first construct the curve $W_2-i_2^2 r$ and then use it to find the corresponding values of the quantity $W_2-i_2^2 r$ in equation (24).

In setting up the experiments it is necessary to install a voltmeter to determine the voltage at the terminals of the machine and an ammeter to determine the current in the armature. It is important to have instruments as accurate as possible, since the possible error of the experiment depends to a significant degree on the inaccuracy of these instruments.

Thus, the determination of $R_{\mathrm{vr}}$ is reduced to carrying out two experiments:

1) determining the work of rotation of the electric motor at no load, and
2) determining the work of rotation of the electric motor, flywheel, shaft, and distributing mechanism of the machine.

The execution of the experiments is extremely simple, but, as we shall see in the following chapter, requires particular care in observation in order to reduce the mean errors in the results of the experiments.

Chapter III.

Processing and Critique of the Experimental Material.

Before proceeding to the conclusions, we consider it necessary to give a critical review of all the experimental material. In order to form an idea of the possible errors in the results of our experiments, arising from inaccuracies of observation and under the influence of secondary causes, we consider it necessary, first, to apply to the computations the theory of errors and, second, to set up supplementary experiments to clarify the influence of extraneous factors¹.

In setting up the calorimetric experiments, the most important thing is exact knowledge of the heat carried away by the cooling water, which, according to equation (2), is expressed by the equality

\[ U_n = (t_1 - t_2) w. \]

The possible error in determining the water consumption is composed of the error in noting the moment of the beginning and end of the experiment, and of the error in weighing. The error in time is possible by no more than one second at the beginning and at the end of the collection of water over 5 min., which amounts to $\pm 0.33\%$ for each reading, while the probable error of both readings is $\pm 0.33\sqrt{2} = 0.46\%$. When weighing on decimal scales, a possible error of $\pm 0.05$ kg is possible, and on ordinary scales $\pm 0.05$ g; these errors must be referred not to the five-minute consumption, but to the whole consumption over the 15 minutes of the experiment, which at large flow rates ranged from 25 kg to 70 kg, and at small flow rates from 6 kg to 20 kg. Consequently, when weighing on decimal scales the error in our case ranged from $\pm 0.07\%$ to $0.20\%$, and the possible error of two weighings is $\pm 0.20\sqrt{2} = \pm 0.28\%$; when weighing on ordinary scales, the error must be referred to 6 kg, since the bucket did not hold more water, and in this case the possible error of two weighings is equal to $\pm 0.01\%$. The mean error for the quantity $w$ will in the first case be $n = 0.46 + 0.28 = \pm 0.74\%$, and in the second $n = 0.46 + 0.01 = 0.47\%$.

The mean errors of the arithmetic means for the temperatures $t_1$ and $t_2$ we computed for the experiments with the smallest $t_1$ and $t_2$, since for these experiments these errors will be the largest, in view of the fact that we did not allow temperature fluctuations greater than $0.2^\circ$. For experiment No. 64, for $t_1$ the mean error is $n = 0.55\%$, and for $t_2$ the mean error is $n = 0.84\%$. Thus the mean total error for $(t_1 - t_2)$ is

\[ n = \sqrt{0.55^2 + 0.84^2} = 1\%. \]

The possible error for $U_h$ will be $n = 1.0 + 0.74 = \pm 1.74$ and $\pm 1.47\%$.

2. If we now turn to the results of the experiments (see the appended diagrams Nos. 3, 4, and 5), we shall see that the errors in reality exceed the computed ones; thus, for example, experiment No. 4 gives a deviation of $10.9\%$ (the “Otto-Deutz” engine), and experiment No. 89 gives a deviation of $9.4\%$ (the Hornsby-Akroyd engine). If we refer all deviations to the mean lines, which are calculated from the mean specific pressure, then we obtain our deviations in percentages. The arithmetic mean of these quantities gives the mean percentage deviation. We obtain, for the experiments of series No. 1, a deviation of $\pm 3.25\%$; for No. 6, a deviation of $\pm 3.69\%$; for No. 13, a deviation of $\pm 2.93\%$; for No. 15, a deviation of $\pm 3.69\%$; for No. 16, a deviation of $\pm 3.79\%$; for No. 17, a deviation of $\pm 3.45$; for No. 14, a deviation of $\pm 5.61\%$, and so on. We have cited here series of experiments relating to the test of friction in the “Otto-Deutz” and “Hornsby-Akroyd” engines, in which the piston design is of one type. The greatest mean deviation is found in series No. 14, and the smallest in series No. 13. Both of these series of experiments relate to the piston of the “Hornsby-Akroyd” engine, operating with rings, but with different lubrication: in the first series there was thick lubrication—a mixture $1/1$; in the second series—machine oil. The conclusion follows that lubrication affects the accuracy of the experiments. This dependence, so obscure at first impression, was noticed by us even when setting up the experiments, and it is explained by the fact that the temperature of the lubricating layer in all these experiments was different, and that the influence of this temperature is more significant with the $1/1$ mixture than with machine oil.

Meanwhile it is impossible, when setting up two experiments, to ensure that the temperature of the lubricant is exactly the same. This circumstance is further complicated by the fact that we cannot achieve the same temperature not only in individual experiments, but also in different parts of the cylinder. The temperature changes from the lower part of the cylinder to the upper; it also changes along the axis of the cylinder, as indicated by the temperature of the walls (see Table VI, columns 10, 11, and 12). Such a difference in wall temperature is explained by the nonuniform motion of the piston in the cylinder and the unequal movement of the cooling water in the individual parts of the cylinder jacket. The difference in the temperature conditions of the individual experiments is explained by the different

§ 3. Influence of Variable Temperature.

the magnitude of the work of friction of the piston, since the velocity in the indicated experiments varied. All this creates such a combination of temperature conditions that it is impossible to expect it to be repeated in any two experiments.

To clarify the influence of the temperature of the lubricating layer on the friction of the piston, we conducted special experiments; but we shall speak of them below, while here we shall indicate what this influence is in the experiments under consideration.

In order to illuminate the question posed more clearly, we shall examine it theoretically and on the basis of the experiments.

Let us turn to the calculation. In column 13 (Table VI) the mean temperature of the cylinder walls is calculated. These calculations were carried out under the following assumptions: first, it was assumed that both the temperature of the walls and the temperature of the water change linearly from bottom to top along the diameter, and that the mean temperature of the walls is lower than $t_2$ by as many degrees as the mean temperature of the water is lower than $t_{\text{out}}$. Undoubtedly, the actual distribution of the temperature of the water and of the walls is different, and the mean temperature deviates from that computed by us; but, in order to have at least some indications concerning the mean temperature conditions of one or another experiment, we decided to compute the mean temperature of the walls, which we have collected in column 13 (Table VI). From this mean temperature the corresponding viscosity was found from diagram No. I, on the assumption that the temperature of the lubricant differs little from the temperature of the walls. In this way the whole of column 18 (Table VI) was obtained. If we now compare the change of viscosity with temperature in the experiments of series No. 1 with the change in the experiments of series No. 6, we shall clearly see what influence the property of the lubricant must have had on the magnitude of the deviation of the work of friction from some mean value. Further, we can see that with temperature the magnitude of friction should have changed for some experiments twofold—for example, in experiments No. 7 and No. 10. In general, on the basis of the theoretical considerations presented, we should have had to come to the conclusion that the inconstancy of the temperature of the lubricating layer must destroy any possibility of judging friction on the basis of the experiments.

Let us turn to the experiments. On the basis of equations (18) and (19) we computed column 22 (Table VI), containing the magnitudes of the specific resistance $f$. This magnitude $f$ depends neither on the velocity $v$ nor on the magnitude of the surface $Q$, but depends on the coefficient of internal friction $\mu$ and the angular velocity $\varphi$ (eq. 21). Consequently, at constant angular velocity $\varphi$, the magnitude $f$ in all experiments of series No. 1 should have been proportional to the viscosity, which in reality is not the case. This can be explained only by the fact that such a change of viscosity as was obtained by us for the experiments under consideration,

on the basis of the considerations given, evidently, did not occur; above all because the temperature of the lubricant is higher than the temperature of the walls, and at higher temperatures the viscosity changes not so sharply as at low ones (see diagram 1); on the other hand, the very calculation of the mean temperature, as we saw above, rests on certain assumptions. Nor can one assume constancy of viscosity, because all the temperature readings—such as the temperature of the entering and leaving water, the temperature of the individual parts of the walls—were different in these experiments, and, consequently, the viscosity was also different. Since a certain constancy of the specific resistance is observed from the experiments, we should have to assume, on the basis of equation (21), that $\varphi$ varies inversely proportionally to the viscosity, although in reality no such strict dependence exists. Consequently, with an increase in the temperature of the layer the viscosity decreases, but in compensation the angular velocity $\varphi$ increases. We cannot express by a formula what the dependence of the angular velocity on viscosity and temperature is; but that this dependence exists is confirmed by the experiments of Tables VI and VII.

On the basis of all that has been said, we may conclude that, in all the experiments indicated, the temperature of the lubricating layer did not have a great influence on the work of friction of the piston, since its fluctuations could not have been considerable in the individual experiments, and since this influence took place through a whole series of phenomena opposed to one another.

In addition to the influence of the temperature of the lubricating layer, two further factors affect the results of the calorimetric experiments: heat exchange¹ with the surrounding air, and compression of the air in the closed part of the cylinder.

Heat exchange with the air may take place both through the external surface and through the internal surface of the cylinder, if one side of the cylinder is open, as is the case in the “Otto-Deutz” and “Hornsby-Akroyd” machines. In these machines the air constantly follows the piston and washes over the entire rubbing surface that is exposed by the receding piston. If the cylinder walls have a temperature higher than that of the surrounding air, then a loss of heat of friction occurs; if lower, then conversely—a part of the heat absorbed by the water will belong to the surrounding air.

Let us make an approximate calculation of the heat exchange in our experiments through the internal surface of the cylinder.

For the calculation we shall use the generally accepted formula

\[ U = aqz(t_{\mathrm{sr}} - t), \tag{25} \]

§ 4. Influence of Internal Heat Exchange

where $\alpha$ is the coefficient of heat transfer in heat units/$\mathrm{m}^2$, $q$ is the surface in $\mathrm{m}^2$, $z$ is the time in hours, $t_{\mathrm{cp}}$ is the temperature of the radiating surface, which for us is the mean temperature of the walls (col. 13 of Table VI), and $t$ is the room temperature.

The coefficient of heat transfer is calculated by the formula¹

\[ \alpha = 2 + 10\sqrt{w}, \tag{26} \]

where $w$ is expressed in meters per second and in our case will be taken equal to the piston speed (col. 15 of Table VI).

Let us calculate the heat exchange for experiment No. 7, whose internal wall temperature differs most from the room temperature.

The coefficient of heat transfer will be

\[ \alpha = 2 + 10\sqrt{2.46} = 17.75 \]

heat units/$\mathrm{m}^2$. The surface washed by the external air is

\[ q = \pi D H = 3.15 \cdot 22.0 \cdot 32.1 = 2226\ \mathrm{cm}^2 \]

or $0.2226\ \mathrm{m}^2$, which constitutes $42.3\%$ of the entire rubbing surface of the cylinder, since the latter is equal to

\[ Q = \pi D(L + H) = 3.14 \cdot 22.0(32.1 + 44.0) = 5260\ \mathrm{cm}^2. \]

We may take any value for the time $z$, but since we reduce all calculations to 1 hour, here $z$ is obtained as equal to 30 minutes; this is obtained in the following manner: the piston alternately opens and closes part of the rubbing surface of the cylinder, and therefore there are points of this surface (the extreme ones) which are closed only for one instant, or opened only for one instant. It is clear that (if the finite length of the connecting rod is disregarded) the sum of the times during which the surface is washed by air will always equal half the time for which we wish to calculate the heat exchange. Consequently, for experiment No. 7 the heat exchange through the inner surface in 1 hour is equal to

\[ U = 17.75 \cdot 0.2226 \cdot 0.5(28.5 - 21) = 15 \]

heat units.

In this experiment the water carried away 2280 heat units; therefore, in percentage terms, the losses through heat exchange are equal to

\[ \frac{15 \cdot 100}{2280 + 15} = 0.65\% \]

of the magnitude of the piston friction. In this calculation, the greatest error we could have made was in calculating the mean wall temperature. It is also probable that the temperature of the lubricating layer was higher than the temperature of the walls, but we cannot suppose that this difference was large, in view of the good thermal conductivity of cast iron, and of the fact that the wall temperature was measured at a distance of $4.5\ \mathrm{mm}$ from the inner surface of the cylinder.

In order to confirm our calculations and to show that the exchange of heat through radiation inside the cylinder is negligible, we decided to open a hatch into the compression chamber of the “Hornsby-Akroyd” machine

and thus obtain heat exchange from the other side of the cylinder. As we shall see below, this also eliminates the heating of the cylinder walls by the heat of compression.

In the “Hornsby-Akroyd” engine the rubbing surface of the cylinder is equal to 1.07 sq. m.; the surface washed by air from the open end of the cylinder is equal to 0.524 sq. m., which amounts to 48% of the entire surface. If we open the hatch, then the surface washed by air becomes twice as large and will be equal to 96% of the entire surface. The experiments of series No. 16 were carried out with the hatch closed, whereby the heat losses through radiation for experiment No. 96 are equal to 53.5 calories, or 2.11% of the heat of the work of friction; the experiments of series No. 17 were carried out with the hatch open, and therefore the heat losses in them should have increased; according to the preceding calculation these losses for experiment No. 104 should be equal to 107 cal., or 3.96% of the heat of the work of friction. We made these calculations taking the difference between the temperatures of the air and of the surface as equal to 10°, for which we have no factual indications, except for analogous experiments with the “Otto-Deutz” engine, where this difference was 7.5° C. Consequently, by opening the hatch, we should expect a reduction in the quantity of heat carried away by the water, first, because we increase the cooling surface for the air, and, second, because we eliminate the transfer of the heat of compression into the cooling water.

If we turn to the experiments, we shall see that the specific resistance of friction is obtained the same for series No. 16 as for series No. 17. The specific resistance of friction $f$ in the experiments of series No. 16 varies$^{1}$ from 0.0144 to 0.0160, with the arithmetic mean $f = 0.0153$; in the experiments of series No. 17 it varies from 0.0143 to 0.0158, with the arithmetic mean $f = 0.0153$. In diagram No. 4 the line $c—c'$ is the mean line indicating the variation of the work of friction both for the experiments of series No. 16 and for the experiments of series No. 17. From this diagram we can see how the individual experiments of the one and the other series deviate from the mean line. Above we have already said that the mean arithmetic deviation for the experiments of series No. 16 is equal to $\pm 3.79\%$, and for the experiments of series No. 17 is equal to $\pm 3.45\%$. In general we may say that neither the one nor the other series of experiments differs in anything essential from the other: their accuracy is the same, and the results of the experiments are quite identical.

This is a somewhat unexpected result, and therefore it is necessary here to give an explanation of this phenomenon. The explanation is, above all, to be found in the difference between the coefficients of heat transfer from the walls to the air and from the walls to the water; the ratio of these coefficients may vary from 25 to 100, depending on the speed of motion of the water. Conse—

$^{1}$ See col. 13 of Table VII.

Consequently, this circumstance alone accounts for the relatively small transfer of heat to the air in comparison with the quantity of heat carried away by the water. We also find a further explanation of this in the following. The particles of air, moving along the lubricated surface of the cylinder, take heat only from the very thinnest layer of lubricant, while the remaining thickness of the layer, owing to the very low thermal conductivity of the oil, does not give up the heat of friction to the air; meanwhile the same heat, owing to the energetic mixing of the oil particles throughout the entire lubricating layer during the process of friction, is readily transmitted to the metallic walls of the cylinder. If, in addition to all that has been said above, we also pay attention to the distribution of the time during which heat transfer to the air and to the walls takes place, then the small losses to the air will become understandable to us. We have already said above that the time for heat exchange is distributed very differently for the separate parts of the surface of the cylinder. The edges of the surface are almost all the time exposed to the action of the air and are covered by the piston only for an instant. The inner parts of the cylinder, on the contrary, are exposed to it only for a single instant. Consequently, we may conclude that the heat of friction at the edges of the cylinder must be almost entirely removed by the air, while inside the cylinder this heat transfer must fall to zero; but, since at the edges of the cylinder friction arises only for a single instant, an infinitely small quantity of heat is developed there as well. Heat is developed chiefly where the process of friction takes place for a longer time, but there is also less time there for heat exchange. On the other hand, more heat is carried off by the water from those parts of the surface where the lubricant particles remain in a mobile state for a longer time, i.e. from the inner parts of the cylinder.

All that has been said explains to us the agreement of the results of the experiments of series No. 16 with the results of the experiments of series No. 17, and we are therefore inclined to think that the actual internal heat exchange is less than was given us by the calculations according to formula 25. These calculations were made on the assumption that the temperature of the inner walls along the cylinder is the same everywhere and is $10^\circ$ higher than the temperature of the air, while the coefficient of heat transfer was taken to be that for cast iron not lubricated with oil.

Let us now turn to the question of heat exchange through the outer walls of the cylinder.

To reduce heat exchange through the outer walls, the Otto-Deutz machine was covered with felt as well as possible; nevertheless, heat transfer could still take place through the projecting parts of the machine, such as through the valve gear, through the frame, and the like. In the experiments with a low mean temperature this heat transfer could not take place to any appreciable extent, because during such experiments the indicated parts of the machine had the temperature of the room. To determine the temperature of these parts, we tied to them

nim with a thermometer covered on the outside with cotton wool. In the experiments with high temperature this heat transfer could occur, but we shall speak of this series of experiments below.

The “Hornsby-Akroyd” engine was not covered with felt, because it was not intended to carry out experiments at high temperature, and for a low one it was considered sufficient to maintain the mean water temperature equal to the room temperature. If we compare the temperature of the room, column 3, Table VII, with the mean water temperature in the experiments with the “Hornsby-Akroyd” engine, column 6, we shall see that the difference between these temperatures is very small; the greatest occurred in experiments Nos. 84, 88, and 103, where it was equal to 2.25°, 2.00°, and 2.25° C., while, with few exceptions, the room temperature was higher than the mean water temperature. Consequently, in these experiments we must expect the transfer of heat by air to the engine. Here it is very difficult to make a calculation with satisfactory accuracy, but, at the risk of making an error of 40–50%, it can be computed.¹ The external surface of the water jacket of this engine is equal to 1.4 sq. m.; the velocity of the surrounding air is 2 m per sec.² The temperature difference is 2.9° C. Under these conditions it follows that 65 calories of external heat, or 2.4%, were carried away by the water. This is the maximum error that we can expect, because we took the experiment with the greatest temperature difference. This error cannot be arithmetically added to the error from internal heat transfer, since in our experiments these errors were mutually opposite.

The situation is much worse with surface heat exchange in the compressor. The point is that heat exchange through the external surface does not depend on friction, and therefore the heat exchange can remain the same both at large and at small friction work. In the compressor we have precisely the case of large external heat transfer and very small piston friction.

For the small cylinder, the rubbing surface is 1290 cm², the external surface 6300 cm², the ratio of surfaces 1:4.9; for the large cylinder, the rubbing surface is 2950 cm², the external surface 9400 cm², the ratio of surfaces 1:3.2. The external surface has been estimated by us approximately from the drawing, without taking into account the increase of surface from projecting parts, of which the large cylinder has especially many, owing to the fact that it has two different distributions (slide-valve and valve), brackets for the camshaft, and so forth. This approximate calculation indicates what an unfavorable ratio of the areas of the internal and external surfaces exists in the compressor.

§ 4. Influence of External Heat Exchange

If we calculate, by formula 25, the heat exchange for experiment No. 67 (large cylinder), we obtain that the water carried away 175.5 calories of heat from the external air. Alongside this, experiments were performed to determine the heat transfer from the external air to the cooling water. For this purpose, water was passed through the cylinder jacket for 15 minutes, and the temperature of the incoming and outgoing water was recorded. The results of the experiments are collected in Table V.

Table V.

No. of experiments	Room temperature, $t$	Mean water temperature, $t_{\mathrm{cp}}$	Difference $t - t_{\mathrm{cp}}$	Water consumption in kg per 1 hour	Quantity of heat, heat units
1	26.50	15.20	11.30	52.2	202.0
2	25.00	12.10	12.90	55.8	220.6
3	23.00	12.00	11.00	51.9	206.4
4	22.00	10.45	11.55	118.4	249.0
5	21.00	12.25	8.75	57.0	191.0
6	20.50	14.40	6.10	52.5	176.2
7	20.00	10.00	10.00	162.4	272.2

From this table it is clearly seen that the quantity of heat carried away by the water depends on the quantity of water passing through the cylinder jacket and on the difference between the temperatures of the air and the walls. It is difficult to derive this dependence on the basis of our experiments; in general it is difficult to investigate this process under our conditions, but it is possible to indicate a certain approximate value for taking account of heat exchange in our experiments on piston friction. In all our experiments of series No. 10 we took the heat transfer to be one and the same, namely 205 calories, because the temperature difference for them varied within the limits of 1° C. We took the magnitude of the heat transfer from Table V as the arithmetical mean of the data of experiments 1, 2, 3, and 5. We rejected the results of experiments 4, 6, and 7 in view of the following considerations: in experiments 4 and 7 the water consumption greatly exceeds the consumption in the experiments of series No. 10, in which it varied from 50.0 to 50.5 kg per hour; experiment No. 6 has a small temperature difference, $t - t_{\mathrm{cp}} = 6.1^\circ$ C. The result of the experiment (205 cal.) differs from the result of the calculation (175.5 cal.), but this is always possible owing to the low accuracy in determining the velocity of motion of the surrounding air and in determining the surface of the cylinder, quantities which enter into the calculation formula 25. If we refer the value 205 cal. to the quantity of heat carried away in experiments No. 64 and No. 68, we obtain heat exchange, in percent, equal to 50.7% and 64.4%!

If, as before, we calculate by formula 25 the heat exchange through the surface of the small cylinder, we obtain it equal to 91.3 calories. Alongside this, an experiment was performed. Through the jacket of the small cylinder water was passed for 15 minutes with a temperature of

on average $12.0^\circ$ C.; passing through the jacket, it was heated to $15.4^\circ$. During this time $6.95$ kg of water passed through. The room temperature was $24.5^\circ$ C., and the mean temperature of the water $13.7^\circ$ C. Consequently, the cooling water carried away, as part of the heat of the external air, $94.5$ calories. After 20 minutes, without changing the conditions in the least, the experiment was repeated, and the results obtained were identical. The results of the experiment and the results of the calculation are very close. If we add these $94.5$ calories to the quantity of heat carried away by the cooling water in experiment No. 62, then the heat exchange obtained, in percent, is equal to $56\%$!

For the experiments of series Nos. 9 and 10, all the quantities in column 7 were obtained as the difference between the heat carried away by the water and the heat determined experimentally in the manner indicated above. This quantity $U$ we regarded as the heat which was produced by the friction of the piston. From this quantity we determined the work of friction and all the remaining quantities of Table VII. What, then, is the error of these experiments and calculations? If this question is considered from the point of view of the error of the observations and measurements made during the experiments, then this error could be regarded as insignificant; moreover, the greatest error for the calorimetric experiments may be expected to be equal to $\pm 1.47\%$. The auxiliary experiments were carried out with the same error, and therefore the quantities $U$, Table VII, obtained as the difference of the quantities of two experiments, have a mean error equal to the square root of the sum of the squares of the errors of both experiments. Consequently, the mean error with which $U$ is determined will be equal to $\pm 2.08\%$. If we turn to diagram No. 5, we shall see that the deviations of the experiments of series No. 10 do not exceed this error; the experiments of series No. 9 deviate, but only slightly. But if we take into account that the magnitude of the heat exchange was taken by us in all experiments as the same, and moreover equal to the arithmetical mean of the quantities obtained under conditions that were not identical and not the same (see Table V), it will become clear that the determination of the work of friction of the piston in the compressor cannot be regarded as satisfactory. If, however, the points have nevertheless arranged themselves along a straight line, this must be attributed not to the circumstance that the mean value of the heat exchange was determined correctly, but to the fact that it apparently was constant in all the experiments of series No. 9 and No. 10. Indeed, whatever value of the heat exchange we take, by this we can only change the position of the straight line or curve in the coordinates, but not its inclination or form.

To confirm this, we set up series of experiments No. 12. In these experiments, as also in all the subsequent experiments with the “Hornsby-Akroyd” machine, we began to heat the cooling water in the supply pipe with a special burner¹, and tried to obtain such a temperature of the incoming water that its mean temperature—

§ 5. Effect of the heat of compression.

... in the jacket was approximately equal to the temperature of the room. The arrangement of these experiments proved very difficult; it required much time, attention, and patience. All this was due to the fact that, with a small consumption of water (60–70 kg per hour), its movement through the large-diameter pipes and in the jacket was extremely slow; the mixing of the newly heated water with the water contained in the pipes took place very slowly, and when this did occur it sometimes turned out that the flame had been incorrectly regulated. It was necessary to spend several hours regulating the burner flame, and nevertheless there was no possibility of attaining an absolute agreement of the temperatures (see columns 3 and 6, Table VII). This entire series of experiments is plotted graphically in Diagram 5. From this diagram we can see that this method gives not only larger values of the piston friction in comparison with the experiments of Series No. 10, but also a different dependence on speed, since the lines $a—b$ and $c—d$ of Diagram 5 are not parallel, but intersect when prolonged. The difference at a speed of 1 m/sec was found to be 19 cal., and at a speed of 1.5 m/sec, 76 cal. Since the dependence of friction on speed remained the same, the difference in the results may be attributed to an error in the determination of the heat exchange according to Table V. On this basis we may draw the following conclusions: first, the magnitude of the heat exchange according to Table V was determined by us as too large, on the average by 45 calories; secondly, the heat exchange did not remain constant in experiments Nos. 64–68, but decreased with a decrease in the number of revolutions. The decrease in heat exchange can be explained only by the fact that, with a decrease in the number of revolutions, the velocity of motion of the air caused by the moving parts of the machine decreases.

As regards the heat exchange through the inner wall of the cylinder and the influence of the heat of compression on the magnitude of the errors of the calorimetric experiments, all these causes were eliminated in the compressor by the fact that both dead spaces were connected through the slide-valve box.

In carrying out calorimetric experiments on the “Otto-Deutz” and “Thornycroft-Akroyd” machines, the compression chambers were closed so that air would not circulate through them. For this purpose the valves were disconnected from the camshaft, and the valve disks were pressed against the valve seats by the elasticity of springs; if the spring proved insufficiently elastic, as, for example, was the case with the “Thornycroft-Akroyd” machine, then the valve was drawn to the seat behind the spindle by ordinary hand vises.

After the machine had been set in motion, an indicator diagram was taken with a weak spring and the magnitude of the compression was determined. From Diagrams 4 and 5 we can see that in the cylinders of both the one and the other machine there occurred now compression, now rarefaction of the air. The difference of pressures from the diagrams is obtained for the “Otto-Deutz” machine as equal to 0.97 atm., and for the “Thornycroft-Akroyd” machine as equal to 1.17 atm. The final

compression pressure from the diagrams we have, for the “Otto-Deutz” machine, $p_c = 1.72$ abs. atm., for the “Hornsby-Akroyd” machine $p_c = 2.12$ abs. atm.; with adiabatic compression and with the same initial pressures we would have

Diagram

Fig. 4.

the final compression pressure for the first machine $p_c = 6.0$ abs. atm., for the second machine $p_c = 4.22$ abs. atm.; with isothermal compression, for the first machine $p_c = 3.26$ abs. atm., for the second machine $p_c = 2.74$ abs. atm. What the law of compression and expansion is, we cannot see from our diagrams, because the form of the curves was distorted by leakage of air through the valves. But we can see that the absorption of heat by the walls during compression and their giving up heat during expansion differ little from one another, since otherwise these lines would not lie close to one another. Hence we conclude that in the heat exchange only the surface layer of the walls takes part, which heats up very quickly and cools down quickly. This we can also see in diagram XCV (Fig. 5) of the “Hornsby-Akroyd” machine. In this diagram

Diagram

Fig. 5.

the compression and expansion lines are shown by arrows; at point $a$ they intersect. We can see that from point $a$ the line of expan-

§ 6. Influence of the heat of compression.

...expansion lies above the compression line; this can be explained only by the fact that at this time heat is being vigorously given up to the walls. If this were not so, the expansion line would lie below the compression line, owing to the fact that part of the compressed air had been allowed to pass through the valves. The latter phenomenon may be seen in diagram VI, Fig. 4, relating to the “Otto-Deutz” machine. In this diagram the whole expansion line lies below the compression line, which is due to a considerable extent to the loss of air through the valves, but also to heat transfer through the walls.

Heat transfer could be detected during the experiments in both of the indicated machines by the heating of the compression chamber (head) after prolonged operation. In addition, we carried out the following experiment. In the head of the “Otto-Deutz” machine, which had cooling separate from the cylinder jacket, water was left in the amount of 7.85 kg. This water completely covered the cooled surface. After 5 hours 30 minutes the temperature of the water had risen by $18^\circ$ C. Consequently, during the experiment heat passed into the water at the rate of 25.7 calories per hour; of course, in this process part of the heat was lost by radiation from the outer surface of the head, but this part of the heat could not have been large, because the temperature of the head was not high in comparison with the surrounding air (from $18^\circ$ to $36^\circ$ C.). In general, the conductivity of the walls could have influenced the area of the diagram, as we said above, only in part. The greater part of this diagram was obtained as the work of the suction and delivery stroke of the piston. During the experiments it was impossible to ensure that the valves of the machines did not let air through; at the same time it turned out that in the “Otto-Deutz” machine they let air through to a greater extent than in the “Gornsby-Akroyd” machine. This latter fact may be seen, first, from the indicator diagrams, and secondly, from the temperature curves constructed by us by the well-known graphical method¹), Figs. 6 and 7. Since the compression and expansion lines intersect the atmospheric line at a distance from one another of 5.5% of the entire piston stroke, we consider that approximately the same percentage of the volume described by the piston is passed as air through the valves. The greater rarefaction in the “Otto-Deutz” machine can be explained by the fact that during compression the air was expelled through the valves more readily than in the “Gornsby-Akroyd” machine. If we turn our attention to the temperature curves, Figs. 6 and 7, we shall see that during compression there occurred a strong drop in temperature in both machines, and in the first machine this drop in temperature amounted to $150^\circ$ C., and in the second to $75^\circ$ C.; since we took the initial temperature equal to $+30^\circ$ C., it follows that at the end of compression the temperature was

¹) V. G. Karpenko, “Graphical construction of thermal diagrams of internal-combustion machines.”

In the first machine—120°, in the second—45° C. This, of course, cannot be; such results were obtained only because the temperature curve is constructed under the assumption of the constant quantity of the compressed gas, according to the equation

\[ Pv = RT, \]

Drawing 6.

Drawing 6.

whereas this constancy did not exist, since the valves were leaking. We can now draw the conclusion: since the temperature curves constructed from our indicator diagrams give a strong

Drawing 7.

Drawing 7.

fall of temperature during compression, which ought not to occur, consequently in our experiments part of the compressed air was being lost, and then was again drawn in during rarefaction.

§ 7. Influence of High Temperatures.

This circumstance deprives us of the possibility of calculating the final temperature of compression by the known formulas, since the curves of diagrams, Figs. 4 and 5, cannot give an idea of the polytropic exponent.

In order to investigate the influence of the heat of compression on the results of the calorimetric experiments, we opened the hatch into the compression chamber and carried out experiments which also served to clarify the influence of internal heat exchange. As we have seen above, the results of these experiments proved to be completely identical with the results of the experiments with the hatch closed. This gives us grounds to state the following propositions:

a) the heat of compression cannot have any noticeable influence on the results of the calorimetric experiments if the compression does not exceed one atmosphere;

b) heat exchange through the internal surface does occur, but in percentage terms it is not large.

Clarifying the influence of high temperatures on piston friction is undoubtedly very important, because the usual operating conditions of a piston in heat engines are accompanied by a high internal temperature.

The calorimetric method of investigation, although it encounters here a great obstacle in the form of heat losses, is nevertheless not excluded, as we can see from what follows.

We began the experiments of series No. 2 with the highest temperature that we could attain by means of friction. It turned out that the experiment succeeded only at a wall temperature of 53°–54° C. Raising the temperature higher became difficult because of the very small consumption of water and because of the considerable losses of heat through radiation. To reduce these losses by the external walls of the machine, it was covered with felt. The losses of heat through the internal surface of the cylinder can be approximately calculated by formula (25). The calculation for experiment No. 11 gave a loss equal to 28.6 calories per hour, which amounts to 2.86% of all the heat developed by friction in this experiment.

As for the accuracy of the observations in these experiments, it was no less than that which we calculated above for the calorimetric experiments.

We plotted the results of the entire series No. 2 on diagrams 6 and 7, Figs. 8 and 9. In diagram 6 we laid off along the axis of abscissas the upper temperature of the walls according to the mean thermometer, and in diagram 7 along the same axis we laid off the mean temperature of the walls (col. 13 of Table VI). The first method of plotting the temperatures has the advantage that in this case one has to operate with real quantities taken from the experiment, whereas the mean temperatures of column 13 are calculated under certain assumptions and one cannot vouch for their great accuracy. But, on the other hand, the upper temperature of the walls cannot

Chapter III. Processing and Critique of the Experimental Material. § 7.

fully characterize the temperature conditions of the experiment, because these conditions depend on the temperature of the incoming water, on the speed of its motion in the jacket, etc.; therefore it seems to us that the mean temperatures characterize the experiment better from the temperature standpoint.

Diagram 6.

Fig. 8.

We began the group of experiments Nos. 11–15 with the highest temperature and gradually proceeded to the lowest temperature. All the points in diagram 6 corresponding to these experiments are connected by straight lines; likewise, experiments Nos. 16–19, which were begun with the lowest temperature, are connected with one another by straight lines. The latter experiments lay below experiments Nos. 11–15, although the experiment with the highest temperature, No. 19, almost coinc—

§ 8. Additional experiment.

does not agree with experiment No. 11. It is difficult to find an explanation for this; it is perhaps even possible that this depends on the manner in which the points were plotted, all the more so since in diagram No. 7 these points lay along a single curved line.

Diagram 9.

Fig. 9.

In order to determine the influence of higher temperatures, we set up a special experiment, which only partly rests on calorimetric experiments. From the latter we determined the work of transmission of energy from the distribution board to the piston. For this we made use of experiments Nos. 12—18. In these experiments we recorded the expenditure of energy at the distribution board, and from the removal of heat from the jacket of the cylinder we determined the quantity of energy spent on piston friction. The difference between these quantities is the energy spent on friction in

shafts, for losses in the belt transmission, for losses in the wires and in the electric motor; in these experiments the resistance by the rheostats, of course, was not changed.

The experiment consisted in admitting illuminating gas into the Otto-Deutz machine, whereupon it drove the electric motor as a dynamo machine. When the temperature of the walls reached approximately 80° C and became steady, the supply of gas was stopped, and the machine was then rotated by the electric motor. The machine immediately began to cool from the cooling water, as a result of which the expenditure of energy for its rotation began to increase. During the experiment the temperature of the walls and the volts and amperes on the distribution board were recorded. The results of the records and calculations are collected in Table VIII.

Table VIII.

Nos. of observations	Temperature $t_1$	Temperature $t_2$	Temperature $t_3$	Amperes	Volts	Watts	Correction, watts	Corrected value	h.p.	Work of piston friction, h.p.
1	75,0	77,5	77,5	14,0	226	3163	+6,64	3169,64	4,31	1,24
2	75,0	76,0	76,0	14,0	228	3192	+6,64	3198,64	4,35	1,28
3	71,0	71,5	72,0	14,5	227	3290	+4,61	3294,61	4,48	1,41
4	64,0	64,5	66,0	15,0	226	3390	+2,95	3392,95	4,61	1,54
5	57,5	58,0	58,5	16,0	222	3550	+0,74	3550,74	4,83	1,76
6	53,0	53,0	53,0	17,0	222	3774	0,00	3774,00	5,13	2,06
7	47,0	47,0	47,5	18,0	230	4140	−0,74	4139,26	5,60	2,53
8	43,0	43,0	44,0	19,0	230	4485	−4,61	4480,39	6,07	3,00
9	40,0	40,0	40,0	21,0	228	4790	−11,80	4778,20	6,49	3,42

The results of this experiment were plotted on diagram No. 6, with the readings of the middle thermometer laid off along the axis of abscissas. We can see that the curve begins at higher temperatures than we have in the calorimetric experiments, approaches the curve of the group of experiments Nos. 11—15 near the 12th experiment, and further on merges with it. This shows us that calorimetric experiments are possible, when the influence of temperature on friction is investigated, but only within certain temperature limits. These results make it possible to judge the magnitude of friction under the usual working conditions of the machine.

Let us see with what accuracy the latter curve has been determined, or what is the accuracy of all the data in the last column of Table VIII.

We calculated the error for the first and the last observations, which give the greatest and the smallest piston friction.

The arithmetic mean for the magnitude of the losses in the transmission of energy is equal to 3,07 h.p., with the mean error $m = \pm 0,1$ h.p. The possible error in readings on the ammeter is $\pm 0,5$ amp.; consequently, for observation No. 1, $n = \pm 3,57\%$, and for observation No. 9, $n = \pm 2,38\%$; the possible error in readings on the voltmeter is $\pm 1$ volt, which consti-

§ 8. Supplementary Experiment.

for both observations $ \pm 0.44\%$; the mean error of the quantity $W - ei$ for observation No. 1 is $n_1 = \pm 4\%$, for observation No. 9 $n_9 = \pm 2.8\%$, or, respectively, for the one and the other $m_1 = \pm 126.5$ watts, or $\pm 0.172$ h.p., and $m_9 = \pm 136.0$ watts, or $\pm 0.184$ h.p.

During the experiment the current varied from 14 amps to 21 amps; as a result of this, the losses due to heating of the armature winding, the conductors, and the rheostats that were included in the circuit also varied; consequently, the magnitude of the losses in the transmission of energy did not remain constant (3.07 h.p.). We introduced a correction which proved to be smaller than the accuracy of determination of the quantity 3.07 h.p.; but, so that there should be no objections to us on this score, we decided to show it.

The relative mean error of this correction comes out very large if referred to the correction itself. For the first observation,

$n_1 = \pm 35.2\%$, which amounts to 7.3 watts, or 0.1 h.p.; for the last observation $n_9 = \pm 27.0\%$, which amounts to 3.2 watts, or 0.004 h.p.

If we now compute the absolute mean error in the determination of the work of piston friction (last column of Table VIII), then for the first observation it is expressed as

\[ m_1 = \pm \sqrt{0.100^2 + 0.172^2 + 0.099^2} \simeq \pm 0.2 \ \text{h.p.}, \quad \text{or } \pm 16\%, \]

for the last observation

\[ m_9 = \pm \sqrt{0.100^2 + 0.184^2 + 0.004^2} \simeq \pm 0.2 \ \text{h.p.}, \quad \text{or } \pm 5.8\%. \]

In diagram No. 6, on both sides of the curve $a—b$, upward and downward, the possible magnitude of the error ($\pm 0.2$ h.p.) is laid off; the points thus obtained are joined by dotted lines. If we pay attention to the fact that the points taken from the experiment are located near the very curve $a—b$, then we must come to the conclusion that the possible error calculated by us, if it occurred, did so with the same sign in all 9 observations of Table VIII. Indeed, the error made by us in calculating the arithmetic mean for the losses in the transmission of energy entered the last column of Table VIII with some one sign. This error constitutes only half of what we calculated (0.1 h.p.); the other half of the error follows from the inaccuracy of readings on the ammeter and voltmeter; but, owing to the fact that these readings were made only at the moment when the ammeter needle indicated a quite definite value, the results of the readings came out better than we expected. We are therefore inclined to think that in fact, in obtaining the curve, we could have made an error of no more than 0.1 h.p.

All the experiments considered up to the present time for determining the influence of high temperatures on piston friction still do not give us the right to draw any conclusions about the friction occurring during the process of combustion, because at that time inside the cylinder there arises

temperature is $1800^\circ$—$2000^\circ$C. In order to be able to judge this, we carried out a series of experiments by the mechanical method. We spoke of the arrangement of these experiments in the preceding paragraph; now let us see how close we came in these experiments to the true value of the friction.

The results of these experiments are collected in Tables X and XI. Table X contains all the experiments relating to the investigation of the influence of the cooling water on the operation of the machine. In these experiments the number of revolutions and the load of the machine were not changed. Table XI contains the experiments carried out to clarify the influence of the number of revolutions on the operation of the machine; here the temperature of the cooling water was kept the same. The constancy of the indicated factors is of relative importance. It was especially difficult to obtain, in all the experiments of Table XI, the same mean temperature of the cooling water. The inconstancy of the indicated factors affects the results of the conclusions, but it is impossible to indicate this influence and the error resulting from it by means of calculations; this may be judged from the results of the experiments, from those deviations from the mean value which are observed for the individual experiments. But in order to judge to what extent a given deviation may be due to the non-constancy of the indicated factors and to what extent to the accuracy of the observations and calculation, we have computed the mean possible error in determining the work of piston friction; we shall now pause over the calculation of this error.

When using a self-regulating brake¹, the magnitude of the load suspended from the brake cannot change, and therefore the magnitude of the effective work $N_e$ can be calculated from the equation

\[ N_e = An,\quad \text{where } A=\frac{2\pi RG}{60\cdot 75}. \]

The weight $G$, expressing the load, consists of two quantities: the weight of the load $G_1$ and the counterbalancing weight of the brake $G_2$. The weight $G_1=17.235$ kg was determined with a possible error of $\pm 0.5$ g; the weight $G_2=10.6$ kg was determined with a possible error of $\pm 20$ g; consequently, the mean error in determining the brake load is

\[ m=\pm\sqrt{20^2+0.5^2}=\pm 20\text{ g}, \]

or the relative error is $n=\pm 0.072\%$. In determining the radius of the brake, an error of $\pm 1$ mm, or $\pm 0.082\%$, is possible. The mean relative error in calculating $A$ is composed of the relative errors of all measurements plus the possible error on the slide rule, $\pm 0.02\%$. Thus we have $A=0.048$ with relative error $n=0.174\%$². The possible error in finding the number of revolutions $n$ depends on the time, if we take the error in the time readings to be

§ 11. Mean Error in the Determination of Indicated Power.

within ±1 sec., this will amount to ±0.067%, and for two observations

\[ \pm 0.067\sqrt{2}=\pm 0.095\%. \]

The mean relative error in determining the effective power will be equal to ±0.27%.

The indicated work was calculated by us from the equation

\[ N_i = Bp_i n, \]

where

\[ B=\frac{\pi D_1^2 H}{4\cdot 60\cdot 75}, \]

the error of this numerical coefficient being equal to the sum of the errors of $D^2$ and $H$, plus the possible error on the slide rule, which in our case amounts to $2\cdot 0.14+0.16+0.02=\pm 0.46\%$. As for the possible error in determining $p_i$, according to the indications of Prof. Meyer¹ and Prof. Malyshev² we take it as ±2%. The possible mean error in determining $n$ was calculated by us as ±0.095%.

Thus the mean error in calculating $N_i$ is equal to

\[ n=0.46+2.0+0.095=\pm 2.56\%. \]

The indicated work of the suction and delivery strokes, or the work of the machine as a pump $N_i'$, was determined from the same equation by which the positive work was calculated; therefore the mean errors of the numerical factor $B$ and of the number of revolutions $n$ remain the same. As for $p_i'$, it was determined with a large possible error. This depended chiefly on the magnitude of the area of the indicator diagram, which in turn depended on the magnitude of the vacuum of the suction stroke. The point is that in the Otto-Deutz machine the regulation is quantitative; consequently, the governor of this machine, by changing the valve lift, changes the magnitude of the charge drawn in. For individual tests the area of the indicator diagram varies two or three times; as for the diagram of one and the same test, these fluctuations reach ±10%. If we take the possible planimetering error as ±0.2%³, the error in determining the length of the diagram as ±0.16%, and the mean error of the spring scale as ±0.55%, then the possible error in determining $p_1'$ is equal to

\[ n=10.0+0.2+0.16+0.55 \simeq \pm 11\%. \]

The mean error in determining the work of the pump is

\[ n=11+0.46+0.095 \simeq \pm 11.6\%. \]

If this error is referred to the work of the cylinder $N_i$, of which $N_i'$ constitutes 0.1, then this error will amount to ±1.16%.

We shall now see with what mean error the work of rotation of the flywheel, shaft, and distributing mechanism was determined by us.

We shall carry out the calculation for a certain average number of revolutions; for a larger number of revolutions the relative accuracy, of course,

will increase, and for a smaller one will decrease. Let us take observation No. 9 for the no-load running from Table IX. To calculate $W_2-i_2^2 r$ (see Eq. 24), it is necessary to know the resistance of the armature winding $r$; this quantity $r$ was determined by us with an average relative error of $\pm 1.76\%$ and is equal to $0.225$ ohm. The instrument readings were $6.4$ amperes and $173$ volts. Since the accuracy of these instruments is $\pm 1$ volt and $\pm 0.1$ ampere, the possible relative error in reading the current will be

\[ n=\pm \frac{0.1\cdot 100}{6.4}=1.56\%, \]

and the possible relative error in reading the voltage

\[ n=\pm \frac{1\cdot 100}{173}=0.578\%; \]

the average relative and absolute errors in calculating $W_2=ie$ will be $n=1.56+0.578=\pm 2.138\%$, or $m=\pm 23.66$ watts; the average error in calculating $i^2r$ is $n=2\cdot 1.56+1.76=\pm 4.88\%$, or $\pm 0.45$ watt; the average error in calculating $W_2-i^2r$ will be

\[ m=\pm \sqrt{23.66^2+0.45^2}=\pm 23.7\ \text{watts} \]

and $n=2.17\%$.

Table IX.

Observation No.	No-load running of the electric motor. Number of revolutions $n$	No-load running of the electric motor. Current, amp.	No-load running of the electric motor. Voltage, volts	No-load running of the electric motor. Energy, watts	No-load running of the electric motor. Losses $i_2^2 r$	No-load running of the electric motor. Difference	Observation No.	Loaded running of the electric motor. Number of revolutions $n_1$	Loaded running of the electric motor. Number of revolutions $n_2$	Loaded running of the electric motor. Current, amp.	Loaded running of the electric motor. Voltage, volts	Loaded running of the electric motor. Energy, watts	Loaded running of the electric motor. Losses $i_1^2 r$	Loaded running of the electric motor. Difference
1	840	8.2	231	1895	21.3	1873.7	1	769	203	9.0	205	1845	18.2	1827.0
2	800	8.0	220	1760	20.2	1739.8	2	830	219	10.0	227	2270	22.5	2247.5
3	735	7.2	199	1434	11.7	1422.3	3	698	184	8.8	185	1628	17.4	1610.6
4	612	5.9	157	926	7.8	918.2	4	626	165	7.9	160	1265	14.0	1251.0
5	550	5.3	138	732	6.3	725.7	5	489	129	6.4	116	742	9.2	733.0
6	440	4.3	103	443	4.2	438.8	6	360	95	5.4	73	394	6.6	387.5
7	305	3.2	50	160	2.3	157.7	7	220	58	5.0	25	125	5.6	125.0
8	800	7.8	220	1715	13.7	1701.3	8	345	91	6.0	67	402	8.1	394.0
9	660	6.4	173	1107	9.2	1097.8	9	550	145	7.2	138	994	11.5	983.0
10	490	4.7	120	564	5.0	559.0	10	656	173	8.8	181	1592	17.4	1575.0
11	250	2.8	34	96	1.8	94.2	11	808	213	10.5	221	2320	24.8	2295.0

From diagram No. 8, drawing 10, it is seen that all the points obtained by observation lie from the mean curve $a-b$ by less than $23.7$ watts, i.e. the observations were made satisfactorily.

If we calculate the average errors in computing $W_1-i_1^2 r$ (see Eq. 24) for observation No. 4 under loaded running (Table IX), we obtain $m=\pm 20.9$ watts and $n=\pm 1.88\%$. Examining the position of the points relative to the curve $c-d$ (diagram 8), we can see that the points at low speeds lie no farther than 20 watts, while at higher speeds strong deviations from the curve are observed. Thus, for example, observation No. 2 deviates by $4\%$, observation No. 1 by $9.8\%$, and observation No. 10 by $9.5\%$. This unsatisfactory character of the observations is explained by the fact that the voltage of the electric network from which we took current fluctuated somewhat during the experiment, as a result of which there occurred now an increase, now a decrease in the number of revolutions;

therefore occurred, then the flywheel absorbed live force, then returned live force to it. This could also be noticed during the observation, since the pointer of the ammeter oscillated. The greater

Fig. 10.

the number of revolutions of the machine, the more difficult it became to read the current, and it was necessary to take a certain mean value around which the ammeter pointer oscillated.

When determining the mean error of the expression $(W_1 - i_1^2 r) - (W_2 - i_2^2 r)$, the magnitude of the error for $W_1 - i_1^2 r$ must be taken from diagram 8 as the arithmetic mean of all errors (deviations from the curve drawn by eye), equal to $\pm 54.5$ watts; for $W_2 - i_2^2 r$ one may take the previously computed value $23.7$ watts, because the errors of the individual observations do not exceed this value. Consequently, the mean error of the entire expression will be

\[ m = \pm \sqrt{23.7^2 + 54.5^2} = 59.4 \]

watts; this value, referred to the difference $(W_1 - i_1^2 r) - (W_2 - i_2^2 r)$, at 600 revolutions gives a relative error of $\pm 22.5\%$.

The following diagram 9 represents the curve of variation of the work of resistance to rotation of the flywheel, crankshaft, and valve gear. This curve is calculated from equation (24). To compute the mean error in determining the work of rotation $R_{\mathrm{vr}}$, it is necessary to know what error is introduced by adopting the belt-transmission coefficient equal to $0.95$, but this, unfortunately, we cannot

Diagram 9.

Figure 11.

know; therefore we confine ourselves to the assumption that the mean relative error will be the same as for the expression

\[ (W_1 - i_1^2 r) - (W_2 - i_2^2 r), \]

i.e. $\pm 22.5\%$.

If we apply this error to the largest and smallest $N_i$, then we obtain a possible error of $\pm 0.52\%$ and $\pm 1\%$.

We can now compute the mean error in determining the work of the piston. Since we have

\[ R_n = N_i + N_i' - N_c - R_{\mathrm{vr}}, \]

the possible mean error in determining $R_n$ will be

\[ n = \pm \sqrt{2.56^2 + 1.15^2 + 0.27^2 + 1.00^2} \simeq \pm 3.0\% \]

of the indicated work of the machine $N_i$. Since this indicated wo...

§ 14. Mean Error in Determining Piston Friction

the work varied, for all the experiments of Table X, from 14.0 h.p. to 15.4 h.p.; therefore we may take the absolute mean error to be equal to 0.46 h.p. Consequently, the relative mean error in determining the work of friction is equal to ±12.1% and up to ±15.4% of $R_{\mathrm{п}}$.

If we now turn to Table X, we can see that the fluctuation of the work of friction in the majority of individual experiments can be explained by a possible error in the observations and calculations. Those experiments which deviate in one direction or the other from the mean value by more than 0.46 h.p. are marked by us with plus and minus signs; moreover, experiments deviating from the mean value of friction in the direction of increase are marked with a plus sign, and in the direction of decrease with a minus sign.

Table X.

No. of experiments	Water temperature, inlet $t_1$	Water temperature, outlet $t_2$	Water temperature, mean $t_{\mathrm{cp}}$	Work of friction $N_{\mathrm{mp}}$	No. of experiments	Water temperature, inlet $t_1$	Water temperature, outlet $t_2$	Water temperature, mean $t_{\mathrm{cp}}$	Work of friction $N_{\mathrm{mp}}$
1st series					1st series
1	1.8	19.3	10.5	3.96	35	3.1	42.4	22.8	3.67
2	2.2	19.4	10.8	3.98	36	3.0	42.8	22.9	+3.93
3	2.0	19.7	10.8	3.60	37	3.3	44.9	24.1	3.28
4	1.8	20.0	10.9	3.96	38	3.0	46.0	24.5	−2.74
5	2.1	20.0	11.0	3.97	39	3.0	46.6	24.8	3.77
6	1.9	20.7	11.3	3.60	40	3.0	46.8	24.9	3.30
7	2.2	20.4	11.3	−3.15		3.0	39.5	21.2	3.29
8	2.2	20.5	11.4	3.68	3rd series
9	2.2	21.0	11.6	3.90	41	9.0	35.2	22.1	2.24
10	2.3	21.3	11.8	4.01	42	7.0	37.8	22.4	2.60
11	2.2	21.3	11.8	3.50	43	7.0	37.8	22.4	2.93
12	2.2	21.5	11.9	3.97	44	9.5	35.6	22.5	2.27
13	1.7	22.3	12.0	3.86	45	9.0	36.3	22.6	2.53
14	2.2	22.3	12.2	−3.29	46	9.5	35.9	22.7	2.81
15	2.2	22.3	12.2	4.00	47	7.3	39.0	23.2	2.40
16	1.8	22.9	12.4	3.85	48	7.3	39.5	23.4	2.78
	2.1	21.0	11.5	3.77	49	9.5	37.3	23.4	2.77
2nd series					50	7.2	40.0	23.6	2.90
17	3.0	31.0	17.0	−2.12	51	9.5	39.4	24.5	2.55
18	3.0	31.0	17.0	2.83		8.4	37.6	23.0	2.62
19	2.8	31.5	17.2	−2.66	4th series
20	3.1	34.5	18.8	−2.28	52	2.5	55.0	28.8	3.48
21	2.2	36.7	19.3	3.07	53	2.5	55.6	29.0	3.47
22	3.5	35.7	19.6	3.61	54	2.4	56.0	29.2	3.36
23	2.2	37.5	19.9	3.00	55	2.5	57.3	29.9	3.43
24	3.0	37.0	20.0	3.55	56	2.8	58.2	30.5	3.35
25	3.0	37.8	20.4	3.40	57	2.5	58.7	30.6	3.11
26	2.6	38.8	20.7	3.14	58	3.8	60.5	32.1	−2.76
27	2.6	39.2	20.9	3.24	59	3.5	61.0	32.2	3.10
28	3.7	38.3	21.0	3.71	60	2.7	63.0	32.8	3.32
29	2.7	40.3	21.5	+3.87	61	2.7	63.0	32.8	3.28
30	3.0	40.7	21.8	−2.60	62	3.7	62.2	33.0	3.31
31	3.2	40.9	22.0	2.97	63	3.3	63.3	33.5	3.58
32	3.1	41.3	22.2	−2.68	64	2.5	65.6	34.0	3.17
33	2.8	42.0	22.4	3.25		2.9	60.0	31.4	3.30
34	3.2	42.0	22.6	2.80

All the experiments of Table X are divided by us into 4 series depending on the temperature of the cooling water. We can see that this temperature of the cooling water within each series of experiments was not constant. The effect on friction of this change in temperature is difficult to note because of the low accuracy of the experiments; but if we calculate the mean values of the friction for each series, then the influence of the water temperature on friction is revealed.

The mean errors in determining the arithmetic means were obtained by us as follows: the value 3.77 l. s. is determined with a mean error $m=\pm 0.07$ l. s.; the value 3.29 l. s. with a mean error $m=\pm 0.10$ l. s.; the value 2.65 l. s. with a mean error $m=\pm 0.06$ l. s.; and, finally, the value 3.30 l. s. with a mean error $m=\pm 0.06$ l. s. All the values of the errors are considerably smaller than the difference that was obtained between the mean values of friction of the separate series. This gives us grounds to regard this difference as arising from the temperature conditions of the experiments.

In Table XI are collected the experiments set up to investigate the influence of the number of revolutions on the work of the “Otto-Deutz” engine. We

Table XI.

Series	Experiment Nos.	Number of revolutions	Work of friction	Series	Experiment Nos.	Number of revolutions	Work of friction	Series	Experiment Nos.	Number of revolutions	Work of friction
1st series	1	122.8	1.69	2nd series	20	152.0	1.90	3rd series	41	176.0	2.00
1st series	2	126.0	1.83	2nd series	21	152.0	2.00	3rd series	42	176.0	2.00
1st series	3	126.8	1.54	2nd series	22	152.4	1.92	3rd series	Mean	173.1	2.41
1st series	4	127.2	1.94	2nd series	23	152.4	1.94	4th series	43	192.8	2.77
1st series	5	127.5	1.48	2nd series	24	152.7	1.89	4th series	44	193.2	2.53
1st series	6	127.6	1.94	2nd series	Mean	151.0	1.95	4th series	45	195.7	—2.24
1st series	Mean	126.4	1.74	3rd series	25	169.5	2.41	4th series	46	196.0	2.53
2nd series	7	146.7	2.06	3rd series	26	170.8	2.56	4th series	47	196.5	2.90
2nd series	8	148.8	1.84	3rd series	27	171.1	2.35	4th series	48	196.5	2.81
2nd series	9	148.8	1.97	3rd series	28	171.2	+2.93	4th series	49	196.8	2.27
2nd series	10	150.2	1.98	3rd series	29	171.4	2.65	4th series	50	197.6	2.78
2nd series	11	150.3	1.78	3rd series	30	171.7	2.60	4th series	51	197.6	2.93
2nd series	12	150.8	2.06	3rd series	31	171.8	2.17	4th series	52	198.0	2.40
2nd series	13	151.2	1.94	3rd series	32	172.0	+2.96	4th series	53	198.0	2.98
2nd series	14	151.3	2.14	3rd series	33	173.2	—1.78	4th series	54	198.4	2.60
2nd series	15	151.5	1.91	3rd series	34	173.8	2.05	4th series	55	198.3	3.71
2nd series	16	151.6	1.74	3rd series	35	174.0	2.57	4th series	56	199.2	3.61
2nd series	17	151.6	2.34	3rd series	36	174.0	2.71	4th series	57	200.0	—2.12
2nd series	18	151.8	1.92	3rd series	37	174.2	2.43	4th series	58	200.0	2.66
2nd series	19	152.0	1.79	3rd series	38	174.6	2.33	4th series	59	200.0	2.28
				3rd series	39	174.6	2.46	4th series	60	201.0	2.83
				3rd series	40	175.5	2.44	4th series	Mean	197.6	2.72

made use of these experiments to investigate the influence of speed on piston friction. All the experiments are divided into series according to the different numbers of revolutions. Within each series the numbers of revolutions dif-

§ 17. Friction in the connecting-rod mechanism.

of individual experiments fluctuated, owing to changes in the operating conditions of the machine, within 5–6 revolutions. In our conclusions about the mean values of the work of friction, we do not take into account this influence of the fluctuation in the number of revolutions, and assume constancy of conditions within each series of experiments. If, however, there was in fact no constancy, nevertheless these variable factors did not exert an influence greater than the possible error (0.46 h.p.) from measurements, observations, and calculations¹. We calculated the mean errors on general grounds. The calculations gave the following results: for the arithmetic mean 1.74 h.p., the mean error $m=\pm 0.08$ h.p.; for the arithmetic mean 1.95 h.p., the mean error $m=\pm 0.03$ h.p.; for the arithmetic mean 2.41 h.p., the mean error $m=\pm 0.07$ h.p.; for the arithmetic mean 2.72 h.p., the mean error $m=\pm 0.07$ h.p. We also calculated the arithmetic mean values for the numbers of revolutions, but the mean errors of these quantities are of little interest to us, and therefore we do not give them.

We must also point out one inaccuracy which is involved in determining the friction of the piston by the method indicated. This is the friction in the journals of the crankshaft and in the crosshead of the connecting rod. This friction can be determined exactly only experimentally; therefore in the tables for friction we entered figures containing not only the friction of the piston, but also the friction in the connecting-rod mechanism. In any case, this friction is insignificant and cannot appreciably change the results of our experiments. Indeed, we can see that the work of rotating the flywheel, shaft, and valve gear amounts to 0.5 h.p. at 200 rev. Since the area of the crank journal is equal to $1/5$ of the surface of the bearings, we may expect that the work of friction in the journal will be approximately one fifth of the work of rotation of the shaft, i.e. 0.1 h.p. This quantity cannot change the differences of the mean values in Table X, because it enters all these quantities equally and with the same plus sign. It enters the mean values of Table XI differently, but it cannot appreciably affect the ratio of these quantities, because it is subject to almost the same dependence on the number of revolutions as that to which the work of friction of the piston is also subject.
In conclusion of this chapter we shall make a brief review of the experimental material in Tables VI and VII. Here we shall point out certain details concerning these tables which we did not have occasion to mention above.

In the first series of experiments in Table VI, the material concerns the investigation of the influence of speed on the magnitude of friction with a lubricant consisting of machine oil No. 6 with cylinder oil No. 1. In columns 17–20 are collected data on the properties of the lubricant and on its quantity. In col—

§ 18 gives the viscosity during the experiment; this value was obtained on the basis of the mean wall temperature (column 13) and does not differ with great accuracy, because the mean wall temperature was not determined exactly; this column was introduced in order to show, at least approximately, what we may expect with respect to the change of viscosity with temperature. Columns 21 and 22 give the values of the total resistance and of the specific resistance. The total resistance was computed on the basis of the data of columns 8 and 15 by the formula

\[ F=\frac{A_R}{v_m}; \]

the specific resistance $f$ was obtained by dividing the total resistance by one and the same value of the total lateral surface of the piston (3040 cm$^2$); therefore this value $f$ always remains proportional to $F$, so long as we are dealing with one and the same machine. In column 16 the work of friction is reduced to one and the same speed or to one and the same number of revolutions (220 revolutions). The correction was introduced on the basis of the assumption that the work of friction is proportional to the speed. As we shall see below, this assumption of ours is entirely correct.

The second series contains experiments relating to the investigation of the influence of temperature changes on piston friction. The lubricant remained the same as in the first series.

The third, small series (Nos. 20–23) was carried out with the object of determining the influence of the quantity of lubricant. These experiments have significance only for the given machine and at a low temperature of friction. The matter is that, in the “Otto-Deutz” machine, the lubricant is supplied approximately to the middle of the cylinder, under pressure by a special pump; therefore an excess of lubricant may result, which is squeezed out of the clearance between the rubbing surfaces, accumulates at the edges of the piston, and increases not only the resistance to motion, but also the internal friction in the layer of lubricant. With lubricants of low specific viscosity this excess has no noticeable effect; with viscous lubricants and at low temperatures this effect is noticeable. As for the other machines, the “Hornsby-Akroyd” and the compressor, there the influence of the quantity of lubricant is in general scarcely noticeable, because in these machines the oil was supplied by gravity or by the difference between atmospheric pressure and the rarefaction in the cylinder. In the “Hornsby-Akroyd” machine the lubricant passed from the oil cup through a gutta-percha tube into an opening made at the open edge of the cylinder. If we turn to the experiments, we shall see that the least friction is obtained for abundant kerosene lubrication (experiment 22), but this experiment must be assigned to the next series No. 4, where the influence of viscosity was investigated; in this same series it fell, in setting up the experiments, because of the necessity of freeing the cylinder from the large excess of lubricant that had accumulated from the preceding experiment. The following experiment, No. 23, was conducted with the smallest quan—

§ 18. Review of calorimetric experiments.

of the amount of lubricant, and the friction in it proved to be considerably less ($f = 0.0262$) than in experiments No. 6 ($f = 0.0364$), No. 20 ($f = 0.0406$) and No. 21 ($f = 0.0440$). We are inclined to explain this favorable result of experiment No. 23 by the influence of the preceding experiment—namely, by the influence of the kerosene that had become mixed with the lubricant from the preceding experiment and had somewhat reduced its viscosity. It is nevertheless beyond doubt that the quantity of lubricant has an influence, and therefore we conducted all experiments with the more viscous oils with the same oil consumption, in one part.

Series 4 was arranged to investigate the influence of the viscosity of the lubricant on the magnitude of piston friction. Initially the author associated another idea with these experiments as well—namely, to detect the influence of temperature on friction. It was proposed to prepare a series of mixtures with kerosene (see Chapter I on this) and thus obtain lubricants of different viscosity; from this viscosity, using diagram No. 1, the temperature conditions were to be found under which ordinary lubricant (a mixture of machine oil with vaseline) would have the same viscosity. It was intended, therefore, by experiments at low temperatures to create in the machine friction conditions corresponding to high temperatures. In practice this could not be carried out, because the viscosity of the oils underwent further change during the experiment depending on its temperature conditions; therefore it was necessary to determine the temperature from diagram No. 1, taking into account not the viscosity determined at $20^\circ$ C, but the assumed viscosity at the mean temperature of the walls (column 18). This method could not give satisfactory results, and therefore it remained to consider these experiments only with respect to the viscosity of the lubricant.

Series 5 was arranged to clarify the influence of temperature change when lubricating with machine oil. The results of the experiments are plotted on diagram No. 7 (curve $c—d$).

Series 6 was arranged to determine the influence of speed on the magnitude of friction when lubricating with machine oil. The results of the experiments are plotted on diagram No. 3.

Series 7 and 8 were arranged to determine friction without piston rings. In order to show that the piston rings do not influence the law of variation of friction with speed, we carried out experiments at various numbers of revolutions. The results of these experiments are plotted on diagram No. 3.

Table VII collects the experiments on investigating piston friction in the compressor and in the “Hornsby-Akroyd” engine. In view of the fact that the number of revolutions has a great influence on the magnitude of the work of friction, in order to characterize piston friction better we did not confine ourselves to a single definite speed, but varied it within the possible limits for each machine.

Chapter III. Processing and Critique of the Experimental Material. § 18.

Owing to the fact that, on these machines, it was impossible to measure the temperature of the cylinder walls, the corresponding columns of data are absent from Table VII. In order to judge the temperature conditions of the experiment, we introduced column 6, the mean water temperature. In this table we also lack information on the properties of the lubricant; this absence is explained by the fact that, in carrying out all the experiments of Table VII, only two kinds of lubricant were used: a mixture of machine oil No. 6 in half quantity with cylinder oil No. 1, and machine oil No. 6 alone. The properties of both lubricants remained constant, and they may be seen in Table VI.

Series Nos. 9, 10, 11, and 12 refer to experiments with the compressor. In all the experiments of these series the number of revolutions was varied. All the experiments were made at a low temperature, and in the first two series the incoming water was not heated. The lubricant in all the experiments was machine oil. The piston rings were removed only in series No. 11. In this series it was necessary to confine ourselves to only three experiments, owing to the difficulty of carrying them out. All the results of these experiments with the compressor are collected in diagram No. 5.

Series Nos. 13, 14, 15, 16, and 17 refer to experiments with the “Hornsby-Akroyd” machine. In all the experiments of these series the number of revolutions was varied. The first two series were carried out with piston rings; the remaining ones were carried out without rings. Machine oil was used in series Nos. 13 and 15, while in series Nos. 14, 16, and 17 a mixture was used. In series No. 17 the rear cavity was connected by a hatch with the air; in the remaining series the hatch was closed, the volume of the compression chamber being equal to $23780\ \mathrm{cm.^3}$. All the results of these experiments are collected in diagram No. 4.

Chapter IV.

Results of the Experiments.

On the basis of all the experimental material considered in the preceding chapter, in this chapter we shall draw the corresponding conclusions.

When we spoke of the friction of lubricated bodies, we established that the work of friction depends on the pressure, on the magnitude of the surface, on the velocity of motion, on the temperature of the lubricating layer, on the internal properties of the lubricant, and on the magnitude of the clearance between the rubbing surfaces. In order to ascertain the influence of any one of the indicated factors, it is necessary to arrange the experiment so that, with one factor varying, the others remain constant. In investigating piston friction we encountered two difficulties: first, we cannot vary all the factors at will; second, we cannot make all the factors constant. The question of piston friction is, with respect to investigation, in the most unfavorable position, owing to the great technical difficulties of varying certain factors and conditions of the experiment; for example, in one and the same machine we cannot vary the pressure per unit of surface to any appreciable extent for the purpose of changing the magnitude of the friction; a different pressure can be obtained only by passing from one machine to another; in the same way we can achieve a change in the magnitude of the rubbing surface and a change in the magnitude of the clearance; but the transition from one machine to another is connected with a change in certain other factors affecting friction, for example, with a change in the quality of the machining of the surfaces. On the other hand, it is impossible to achieve constancy of such factors as the temperature conditions of the experiment. Owing to such difficulties, the experimental investigation of piston friction does not make it possible to investigate the question from all sides. But the solution of the question of piston friction, in the narrowly special sense, does not require an exhaustive answer; thus, for example, the question of the specific pressure for piston friction is of no significance, because the possible fluctuations of pressure for different pistons are not large, and its influence on friction is negligible.

The specific pressure from the weight of the piston in our experiments varied from 0 in the compressor to 0.076 kg/cm² in the Otto-Deutz machine and to 0.082 kg/cm² in the Hornsby-Akroyd machine. Comparable are

only the last two machines, because the piston designs in them are the same; but with the difference in specific pressure that exists for these machines, there is no need to speak of the influence of pressure. Consequently, on the basis of our experiments we cannot draw a conclusion as to the influence of pressure on friction; we shall therefore confine ourselves here to a summary of the views of various authors on this question.

In the opinion of Hirn (1854) and N. Petrov (1886), the frictional force of well-lubricated bodies is proportional to the square roots of the pressures $P$; in the opinion of Tower (1885) and Dettmar (1899), the coefficient of friction is inversely proportional to the specific pressures $p$, and therefore the frictional force does not depend on the total pressure. In the opinion of later authors, Stribeck (1902), Lasche (1902), Heimann (1905), and Pinegin (1911), the coefficient of friction falls to a transition load and then begins to rise again, while the law of the fall may be different in each case. Since the transition load lies far beyond the limits of possible pressures from the weight of the piston and from the pressure of the rings, we believe that a possible change of pressure cannot cause an excessive increase in piston friction, or even exert a substantial influence.

Much more noticeable from the experiments is the influence of the piston rings. The following Table XII shows how much the work of friction decreased at one and the same speed ($v_m = 2.5$ m.) after the rings had been removed from the piston.

Table XII.

Machine	Total pressure from the weight of piston and rings	Total pressure from the weight of piston	Machine oil: rings fitted	Machine oil: rings removed	Mixture: rings fitted	Mixture: rings removed
Otto-Leitz . . . . . .	258.8	63.8	3.20	2.31	3.78	2.70
Ratio . . . . . .	—	—	1.39	1	1.40	1
Hornsby-Akroyd . . . . . .	701.5	124.5	3.38	1.84	4.70	2.78
Ratio . . . . . .	—	—	1.84	1	1.69	1

The magnitudes of the work of friction entered in this table were taken from diagrams No. 3 and No. 4. For greater clarity, this table also shows the ratio of the works of friction with piston rings and without them. From this table we can judge the influence of the piston rings on friction only for each machine separately; in order to make the results of the experiments on both machines comparable with one another, we compiled two other tables, XIII and XIV.

In Tables VI and VII we have two columns (21 and 22 of Table VI, and 13 and 14 of Table VII) in which are shown the resistance of the piston to motion $F$ and the specific resistance $f$, which was obtained by dividing the first quantity by the entire lateral surface of the piston. The quantities $F$ cannot

§ 2. Influence on the Friction of Piston Rings

...be compared for different engines, because they relate to different magnitudes of the friction surfaces; but $f$ also is inconvenient for comparison in the form in which we have computed it, because in this computation the ratio of the areas of the rings and of the piston itself has not been taken into account. In order to allow for this, one must proceed as follows: determine the mean value $F_1$ from the experiments with piston rings and subtract from it the mean value $F_2$, determined from the experiments without piston rings; then the difference will express the magnitude of the frictional resistance of the rings. All this may be expressed by equation (27)

\[ F_k = F_1 - F_2 . \tag{27} \]

Such a calculation introduces the assumption that the friction of the piston itself does not change and remains constant both with piston rings and without them, whereas the layer of lubricant, under the influence of the scraping action of the rings, will in the two cases be different, and consequently the friction will also differ. In addition, when calculating the resistance of the rings, the result is affected both by the mean error in the computation of $F_1$ and by the mean error in the computation of $F_2$. These circumstances led us to abandon the computation, separately for each experiment, of the specific frictional resistance for the rings and for the piston.

In the following table we have collected all the magnitudes of the frictional resistance, and alongside them the mean errors are indicated.

Table XIII.

Machine	Mixture: $F_1$, kg	Mixture: $\pm m_1$, kg	Mixture: $F_2$, kg	Mixture: $\pm m_2$, kg	Mixture: $F_k$, kg	Mixture: $\pm m_k$, kg	Machine oil: $F_1$, kg	Machine oil: $\pm m_1$, kg	Machine oil: $F_2$, kg	Machine oil: $\pm m_2$, kg	Machine oil: $F_k$, kg	Machine oil: $\pm m_k$, kg
Otto-Deutz	113.64	4.80	81.30	6.03	32.34	7.77	94.53	5.77	69.9	6.31	24.63	8.54
Hornsby-Akroyd	142.03	11.98	83.40	3.85	58.63	12.60	99.75	3.82	54.16	2.20	45.59	4.88

On the basis of these data we have compiled the following Table XIV, in which the specific frictional resistances are collected. In computing the specific frictional resistance of the piston without rings, its lateral surface was taken into the calculation after subtracting the area of the grooves for the rings.

Table XIV.

Machine	Mixture: specific resistance of the piston, $f$	Mixture: $\pm n\%$	Mixture: specific resistance of the piston, $f$	Mixture: $\pm n\%$	Machine oil: specific resistance of the piston, $f$	Machine oil: $\pm n\%$	Machine oil: specific resistance of the piston, $f$	Machine oil: $\pm n\%$
Otto-Deutz	0.0309	7.4	0.0780	24.6	0.0265	9.0	0.0600	34.6
Hornsby-Akroyd	0.0175	4.6	0.0846	21.5	0.0114	5.9	0.0658	10.6

In this same table are shown the mean errors in the determination of $f$, referred to these quantities themselves.

The accuracy of determining the specific resistance is not great, but it is especially unsatisfactory for the specific resistance of the rings. In comparing the specific resistance of the piston of one machine and the other, we may state that it is smaller in the “Hornsby-Akroyd” machine and larger in the “Otto-Deutz” machine. The possible errors are smaller than the difference between the specific pressures. We explain this difference by two causes: first, the “Otto-Deutz” machine is new, whereas the other had worked a great deal for operating purposes; consequently, in it the piston had worn itself in to the cylinder; secondly, owing to wear, the clearance in the “Hornsby-Akroyd” machine had become so considerable that the upper part of the piston surface does not participate in the friction; therefore, in calculating the specific resistance of friction, it would have been necessary to take into account not the entire lateral surface, but, after subtracting, a certain part of it. Unfortunately, for quite understandable reasons, we cannot do this.

In comparing the specific resistance of the rings, the reverse is observed. The specific resistance of the rings in the “Hornsby-Akroyd” machine is greater than in the first machine. What this may be explained by, we find it difficult to say—whether it is explained by peculiarities of the material or by a possible error in determining the quantity $f$; but, in any case, not by that difference in specific pressure which is revealed from the difference in the elasticity of the rings.

From all that has been set forth we may conclude that the work of friction of the rings constitutes a considerable part of the work of friction of the piston; in our experiments it reaches, in individual cases, up to 45% (see Table XIII) of the entire friction of the piston. Such an increase of friction from the rings may be explained not so much by their pressing force as by their scraping off the lubricating layer. With a decrease in the thickness of the layer, the conditional velocity $\varphi$ increases, and, consequently, the magnitude of the friction also grows.

As regards the influence of the magnitude of the surface on the magnitude of the friction force, on this matter too, on the basis of our experiments, we can say nothing. Our theoretical conclusions and the opinions of all the authors cited above (except Hirn) converge on one conclusion: that the friction force is proportional to the rubbing surface.
As regards the influence of velocity on friction, various authors arrive at different conclusions. Hirn and Petrov consider the friction force of machine parts proportional to the velocity of the relative motion of solid bodies; Tower and Dettmar consider it proportional to the square root of the velocity; all the remaining authors come to the conclusion that at first, with an increase in velocity, the friction force rapidly decreases, then begins to grow approximately up to 4 m/sec.; above this velocity the friction force does not increase (Lasche)¹.

¹ All the cited authors draw their conclusions with respect to the coefficient of friction; but since the friction force at constant pressure is proportional to the coefficient of friction (equation 15), the replacement of one concept by the other does not distort the meaning.

§ 4. The Influence of Speed on Piston Friction

Let us now see what conclusions we can draw, on the basis of our experiments, concerning the influence of speed on piston friction. In diagrams Nos. 3, 4, and 5 (see the appendix at the end of the book) we plotted along the axis of abscissas the mean piston speed $v_m$. The mean piston speed is proportional to the number of revolutions, as is the circumferential speed at the journals, but the phenomena occurring in the two cases are different. In one case the displacement of the layer of lubricant takes place in only one direction; in the other case the displacement changes its direction. The latter circumstance is probably connected with a loss of energy. The motion of the piston is alternately accelerated and retarded; consequently, we must expect corresponding displacements of the particles of lubricant under the influence of their kinetic energy. Since, for each revolution of the shaft, the piston twice comes into a dead-center position, we therefore also have to do with static friction. To what extent all the indicated factors influence the magnitude of piston friction, we can speak only conjecturally. There is no doubt that one cannot speak of homogeneity of the phenomenon of friction at journals and at pistons, but it is also beyond doubt that those laws of friction of lubricated bodies which are found at journals must also manifest themselves in piston friction.

In the chapter on the friction of lubricated bodies we said that the force of friction does not depend on the speed of relative motion if the magnitude of the clearance between the rubbing bodies is sufficient for the layer of lubricant to be able to increase. This proposition gave us the possibility of assuming that the force of piston friction also should not vary with the number of revolutions, since the magnitude of the clearance between the cylinder and the piston is sufficiently large (see on this in Chapter II); but then, according to equation (19), in our experiments we should obtain work of friction proportional to the speed $v$. Indeed, we can fully convince ourselves of this on the basis of our experiments. Let us turn to the experiments of Table XI. If from this table we take the ratio of the mean values of the numbers of revolutions, we may write the following series of ratios:

\[ 126{,}4 : 151.0 : 173{,}1 : 197{,}6 = 1 : 1{,}19 : 1{,}37 : 1{,}56. \]

The ratio of the corresponding magnitudes of friction, however, is represented by the series:

\[ 1{,}74 : 1{,}95 : 2{,}41 : 2{,}72 = 1 : 1{,}12 : 1{,}38 : 1{,}56. \]

Comparison of both series of ratios shows an almost complete proportionality between the numbers of revolutions and the work of friction. Such a result of the experiments might also not have been obtained under the influence of the possible mean error, but this influence is nevertheless not so great as to conceal the proportionality completely. If we add or subtract the possible mean errors in the determination of the work of friction, we obtain the following two series of ratios:

1) from increase

\[ 1.82 : 1.98 : 2.48 : 2.79 — 1 : 1.09 : 1.36 : 1.53 \]

2) from decrease

\[ 1.66 : 1.92 : 2.34 : 2.65 — 1 : 1.16 : 1.41 : 1.60. \]

Comparing these two series of ratios with the series expressing the ratio of the numbers of revolutions, we can see that they present a greater deviation from proportionality with it than the series obtained directly from the experiment, but nevertheless the proportionality is evident. In the series of ratios obtained from the experiment, the second term of the series has the greatest deviation from proportionality, but it too is corrected if an error is introduced into this one term.

If we turn to diagrams No. 3 and No. 4, we shall see that the dependence of the work of friction on speed is expressed by straight lines passing through the origin of the coordinates. Each line corresponds to a definite series of experiments. As soon as we had noticed the proportionality between the work of friction and the speed, we calculated, on the basis of all the experiments of the series, the mean value of the specific resistance and from it determined the direction of the straight line. Individual experiments deviate noticeably from the straight lines, and these deviations fluctuate on the average by about 3.5% for the individual series. Since these deviations of the experiments from the straight line occur in both directions, we consider it possible to express by a straight line the actual dependence between the work of friction and the speed, which analytically may be represented thus: $A_{\mathrm{R}} = kv$. If it is assumed that the force of friction is proportional to the speed (Hirn, Petrov), then, with constant thickness of the layer, the work will be proportional to the square of the speed, $A_{\mathrm{R}} = kv^2$; if the force of friction is assumed proportional to the square root of the speed, then the work will be proportional to the 1.5 power of the speed, $A_{\mathrm{R}} = v^{1.5}$. In diagram No. 3 we have constructed dotted curves expressing all the indicated dependences of the work of friction on speed; likewise a curve has been constructed expressing the dependence

\[ A_{\mathrm{R}} = \sqrt[1.5]{v}. \]

From a comparison of our results with these curves, we clearly see that the friction of the piston does not obey any of the above-indicated dependences. Consequently, we may suppose that the work of friction of the piston varies proportionally to the first power of the speed, i.e. linearly, or else proportionally to some power very close to unity $(0.95—1.05)$. Since, with the aid of our calorimetric experiments, it is impossible to indicate this dependence more precisely, it will be truest to express it linearly, especially since this fully agrees with the results of the experiments in Table XI.

If we now turn our attention to diagram No. 5, on which the results of the experiments with the compressor are plotted, then there the dependence

§ 4. The Influence of Speed on Piston Friction.

the work of friction on speed is different. Although we expressed this dependence by straight lines, we did so only because the accuracy of the experiments is not sufficient for one to judge from them the form of the curves. It is possible that this dependence does not obey the law of a straight line, but is some curve; all the more so because these straight lines, first, do not pass through the origin of coordinates, and second, lie between curves whose law of variation is expressed by the equations $A_k = kv^2$ and $A_k = kv^{1.5}$. The fact that the lines do not pass through the origin already indicates a lack of proportionality between the work of friction and the speed; and the fact that these lines lie between the curves gives us grounds to suppose that this dependence can be expressed by a curve of the same name as those indicated. The accuracy of the experiments with the compressor is not great (the possible errors in these experiments were indicated by us above), and therefore we consider it possible to make also the supposition that the dependence between the work of friction and the speed may be expressed even by one of the indicated curves. In particular, we may say this with respect to the experiments of series No. 12, which we can easily represent by the curve $A_k = kv^2$, shifting it on the drawing to the right.

All this indicates that the friction of the piston in the compressor stands in a different dependence on speed than in the Otto-Deutz and Hornsby-Akroyd engines; but these results were not unexpected for us.

We expect proportionality between the work of friction and speed in those cases when the clearance between the rubbing bodies is sufficiently large for the thickness of the layer to increase with speed; otherwise, with an increase in the relative speed $v$, the angular speed $\varphi$ will increase, consequently the specific resistance of friction $f$ will increase, and the work of friction will grow in proportion to some power of $v$ greater than unity. If we pay attention to the magnitude of the clearance in the compressor, we shall see that it is somewhat smaller than the clearance in the Otto-Deutz engine; therefore there is no need to seek the cause of the phenomenon indicated above in the magnitude of the clearance. Here we find the cause in another circumstance, which immediately attracted our attention when inspecting the piston. It turned out that one side of the piston was badly worn. This indicated that the piston does not run centrally in the cylinder, but is pressed by one side against the surface of the cylinder. This occurs because the cylinder covers are poorly centered, as a result of which the axis of the through piston rod does not coincide with the axis of the cylinder. It is difficult to say what this pressing force is; it may be that it is not so great, because otherwise it would have attracted attention during the construction of the compressor; but undoubtedly the clearance here is small and, moreover, cannot increase under the influence of hydrodynamic pressure.

Chapter IV. Results of Experiments. § 4.

Consequently, in the compressor we have the case where the thickness of the layer either does not change at all or changes very little. The result of this is an increase in the angular velocity $\varphi$ and in the specific resistance $f$. In diagram No. 11 (Fig. 12) the curves of the variation of $f$ with the velocity $v$ are plotted. From the diagram it is difficult to determine the dependence between $f$ and $v$; whether these lines will be straight or curved is unknown; apparently, they will not all pass through the origin of coordinates if they are

Fig. 12.

represented in the form of straight lines. For the experiments of series No. 12, the straight line passes through the origin of coordinates, i.e. the relation between $f$ and $v$ is such that $f = kv$; this is what we should have expected, since the work of friction for these experiments is proportional to the square of the velocity $v$, as we saw above.

To investigate the influence of the viscosity of the lubricant on the friction of the piston by the walls, experiments of series No. 4 were carried out.

In order that the dependence of friction on viscosity could be seen more clearly, we constructed diagram No. 10. (See the appendix at the end of the book.) On this diagram we plotted the viscosity of the lubricant not at $20^\circ$ C, but that which corresponds to the mean temperature of the experiment, i.e. we used

with the viscosity of column 18 of Table VI. How accurately this curve expresses the indicated dependence, we do not venture to assert anything positively about this; but one thing is beyond doubt: there is no proportionality between viscosity and the work of friction, nor is there such proportionality with respect to the specific resistance of friction, which we might have expected on the basis of equations (18) and (19).

The following Table XV clearly shows how far viscosity and specific resistance deviate from proportionality.

Table XV.

Nos. of experiments	Viscosity	Specific resistance	Nos. of experiments	Viscosity	Specific resistance
22	1.00	1.53	31	25.43	2.07
24	1.56	1.08	32	50.90	2.79
25	4.24	1.00	33	8.06	1.83
26	4.81	1.18	34	6.84	1.90
27	4.47	1.86	35	5.17	1.83
28	30.00	2.48	36	3.41	1.66
29	4.78	1.69	37	2.81	1.44
30	13.16	1.87	38	2.01	1.15

For greater clarity, in this table we have expressed viscosity and the specific resistance $f$ not by their actual magnitudes, but by numbers proportional to them, taking their smallest values as unity.

We see from the table that, with an increase of viscosity by 5 to 10 times, the specific resistance increases two or three times (experiments Nos. 25, 31, and 32). We find the explanation for this in the fact that the thicker the lubricant is, the thicker the lubricating layer will be, and the smaller the angular velocity. The magnitude of the specific resistance $f$, according to equation (21), is expressed through the angular velocity $\varphi$ and the coefficient of internal friction

\[ f=\mu \varphi . \]

With an increase in viscosity, and consequently in the coefficient of internal friction $\mu$, $\varphi$ decreases, if only $f$ changes little. If these quantities were inversely proportional to one another, then the value of $f$ would remain constant for all lubricants; but since this is not the case, we conclude that the thickness of the layer, which reduces the angular velocity, is determined not only by the internal cohesion and friction of the particles, but also by other internal properties of the oil. Here we adhere to the opinion that the angular velocity $\varphi$ is one of the characteristic features of every lubricant. The value of $\varphi$ cannot be reduced artificially without changing the lubricant itself, because for this it would be necessary, at a constant relative velocity $v$, to increase—

to increase the thickness of the lubricating layer, which is determined only by the internal properties of the lubricant. On the other hand, we can always increase $\varphi$ by reducing the clearance between the rubbing surfaces.

If we return to Table XV, we can also see that, with a decrease in viscosity as compared with experiment No. 25, the specific resistance increases in experiments Nos. 22, 24, 36, 37, and 38. In experiments 24 and 38 this increase may be attributed to inaccuracy in determining $f$, but in the remaining experiments this increase is beyond doubt, and it is explained by direct contact of the metallic parts as a result of the lubricant being squeezed out. By this is meant such a reduction in the thickness of the lubricant layer when projecting particles of one surface, in large numbers, come into direct contact with the other surface. The thinner the layer becomes, the greater the number of particles that will come into contact, and the more strongly the property of friction of solid bodies will manifest itself, and the greater the specific resistance will become.

6. As regards the influence of temperature on friction, most authors indicate no dependence whatever in this respect. Most of them consider this dependence to be complex and to have the character of a change in viscosity, but Dettmar and Tower indicate a dependence that may be expressed as follows: $\eta T = const.$ This enabled Dettmar to derive also the following dependence: $p\eta T = const.$ We do not agree with such a categorical conclusion, but we do not deny that there is some basis for such a view.

The specific resistance of friction $f$ will have the same dependence on temperature as has the coefficient of friction, and therefore we may write, by analogy, that $fT = const.$ and also, consequently, $A_kT = const.$ We expressed the latter dependence by curves in diagrams Nos. 6 and 7. (See above). In diagram No. 6 the curve $A_kT = const.$ in its lower part almost coincides with the curves of our experiments, but in diagram No. 7 we observe a considerable deviation; moreover, the only difference in these diagrams is that in diagram No. 6 the higher cylinder temperature is plotted on the abscissa axis, while in diagram No. 7 the mean cylinder temperature is plotted. Hence we see that the agreement of the curves in diagram No. 6 is not yet proof of the proposition $A_kT = const.$, and that the difficulty in determining the mean temperature of the experiment deprives us of the possibility of verifying this dependence.

Reviewing the results of our calorimetric experiments, we come to the conclusion that, with an increase in temperature, the specific resistance of friction and the work of friction decrease, but not as rapidly as the viscosity changes. The change in specific resistance differs for different lubricants, as we can see from diagram No. 12 (drawing 13), where curve $a—b$ corresponds to experiments with

§ 6. The Influence of Temperature on Piston Friction

with a lubricant mixture of $1/1$, and curve $c—d$ corresponds to the experiments with lubrication by machine oil.

$Diagram No. 13: graph of piston friction versus temperature, with curves $a—b$ and $c—d$.$

Fig. 13.

From the experiments of Table X we can see that the greatest friction of the piston of the “Otto-Deutz” machine is found in the experiments with a low mean water temperature (1st series); with normal cooling¹ (2nd series) and in the experiments with a high temperature (4th series), the friction in both series remains the same at one and the same temperature of the incoming water. The third series of experiments also has normal cooling, but differs from the second series in the temperature of the incoming water. This difference has a strong influence on friction. The mean value of the friction of the third series is $0.67$ h.p. less than the mean value of the second series. In general, the influence of cooling on friction is noticeable and beyond doubt. This circumstance gives us an important indication that the temperature of the process of internal-combustion engines ($1800—2000^\circ$ C.) does not have an exclusive influence on piston friction, and that, notwithstanding such a temperature of the internal process, the viscosity of the lubricant nevertheless depends strongly on the temperature of the cylinder walls. We adhere to the opinion that the surface layer of the metallic walls of the cylinder is not strongly subjected to the influence of variable temperatures, owing to the poor thermal conductivity of the lubricant, and that their temperature is maintained at a definite level depending on the cooling of the cylinder.

As regards the work of piston friction of the “Otto-Deutz” machine, we can obtain an idea of this both on the basis of diagram No. 6 and on the basis of Table X.

Chapter IV. Results of the Experiments. § 7.

If we turn to Table X, we shall see that the work of friction in the experiments with the temperature of the entering water $3^\circ\text{C}$ and of the outgoing water $39.5^\circ\text{C}$ was equal to 3.29 h.p., while in the experiments with the temperature of the entering water $8.4^\circ$ and of the outgoing water $37.6^\circ\text{C}$ it was equal to 2.62 h.p. In individual cases, however, one may expect the work of friction to reach 3.5 h.p.

In order to make use of diagram No. 6, we first compiled Table XVI, in which is shown the relation between the temperature of the leaving water and the temperature of the walls. Since the temperature

Table XVI.

Temperature of the outgoing water	Temperature of the outgoing water	Temperature of the cylinder walls	Temperature of the cylinder walls	Temperature of the cylinder walls
from the head	from the jacket	$t_1$	$t_2$	$t_3$
50	40	52	54	49
70	50	66	62	58
80	80	92	89	85

of the water leaving the cylinder during operation of the machine is maintained at about $40^\circ$, then on the basis of Table XVI we may take the mean highest temperature of the walls to be $52^\circ\text{C}$, to which, according to diagram 6, there corresponds a piston-friction work of 2.1 h.p. at an entering-water temperature of $15^\circ$—$16^\circ\text{C}$.

On the basis of all that has been said, we may draw the conclusion that the work of friction of the piston of the “Otto-Deutz” machine varies, depending on the temperature of the cooling water and in general on the temperature conditions of the experiment, from 2 h.p. to 3 h.p., and sometimes even up to 3.5 h.p.^1)

One of the practical conclusions from the results of the experiments on the investigation of piston friction is an indication concerning the cooling of internal-combustion engines. In view of the fact that the temperature of the entering water has a strong influence on piston friction, excessively cold water must be avoided. The best temperature will be $15^\circ$—$20^\circ\text{C}$; therefore in winter the water should be heated to the indicated temperature by the heat of the products of combustion, or else circulating cooling should be employed^2). Water should also be supplied not from below the cylinder, but from above, because then the temperature of the lower and upper layers will not differ so greatly. When, however, the water is supplied from below, a sharp difference is obtained between the temperature of the lubricant at the bottom and at the top of the cylinder; and since the viscosity of the lubricant increases very rapidly with decreasing temperature, much more rapidly than the temperature falls, the lower cold layers greatly increase piston friction.

1) All these data refer to piston friction when lubricated with a mixture of machine oil and cylinder oil. At the present time we have switched to more viscous lubricants, and therefore the piston friction in this machine has greatly diminished.
2) G. Güldner, ibid., p. 367.

§ 8. Practical conclusions from the experimental results.

In view of the fact that viscosity changes more sharply with temperature in thick oils, one should use a lubricant that is not viscous, but has a high flash point.

When the present article had been submitted for typesetting, samples of special oils for lubricating internal-combustion engines were received at the Laboratory of Heat Engines of the T. T. Institute from the firm T-va Br. Nobel. We determined the specific gravity, the viscosity by Engler at 50° C., and the flash point of these oils. Here, as in all our work, we use the specific viscosity as obtained by Engler, without taking into account the influence of the specific gravity of the oil being tested on the magnitude of the viscosity; therefore, in order to find the actual specific viscosity, our viscosity data must be multiplied by the corresponding specific gravity of the oil, taking temperature into account. The specific gravity of the oils is given by us at 20° C., and not at 15° C., as is often encountered, in view of the consideration that the room temperature with us was at all times about 20° C., and therefore during the testing of the oil we kept the indicated temperature constant. From our data it is easy to pass to the specific gravity at a temperature of 15° C.; for this our readings must be increased by 0.0007 · 5 = 0.0035, since it is known that the specific gravity increases or decreases by 0.0007 when the temperature changes by 1° C. The determination of specific gravity was carried out with an areometer. The flash point was determined in an open crucible.

“Motor oil T,” for medium and large heat engines and for worn ones (in case gases pass by the piston from the cylinder). Specific gravity 0.905 at 20° C., viscosity 8.6, flash point 215° C.

“Motor oil M,” for medium and large petroleum (Diesel), kerosene, and gas-generator engines. Specific gravity 0.902, viscosity 6.0, flash point 200° C.

“Motor oil L,” for low-power heat engines—(with the exception of the Diesel engine). Specific gravity 0.895, viscosity 2.6, flash point 180° C.

In addition to the oils indicated, T-va Br. Nobel manufactures thicker oils for automobile engines, which have a comparatively small piston surface and a high cooling-water temperature, and sometimes are cooled by air.

“Avtol T.” Specific gravity 0.912, viscosity 22.5, flash point 265° C.

“Avtol M.” Specific gravity 0.910, viscosity 10.0, flash point 225° C.

“Avtol L.” Specific gravity 0.905, viscosity 8.0, flash point 205° C.

If we compare the indicated samples, with respect to their properties, with the common mineral oils of the same company (see Table XVII), then we can see that “Motor oil T” in viscosity comes close to “Machine oil No. 8,” but has a higher flash point; “Motor oil M” in viscosity is similar to “Machine oil No. 6,” but likewise has a higher flash point; “Motor oil L” has a viscosity lower than the existing machine oils, but has a comparatively high flash point. In color these oils differ from machine oils by a darker coloration.

Table XVII.

Mineral oils of the Nobel Brothers Co.*)

Name of oil	Specific gravity at 20° C	Viscosity	Flash temperature
Machine oil No. 4	0.897/0.902	4.0 at 50° C	180°
Machine oil No. 6	0.902/0.906	6.0—7.0 at 50° C	190°
Machine oil No. 8	0.908	7.5—8.5 at 50° C	200°
Machine oil No. 10	0.910	10.0—11.0 at 50° C	210°
Cylinder oil No. 2	0.910/0.916	1.5—2.5 at 100° C	220°
Viscosine No. 3 or cylinder oil No. 1**)	0.908/0.916	3.0—4.0 at 100° C	240°
Viscosine No. 5	0.918	5.0—6.0 at 100° C	255°
Viscosine No. 7	0.922	7.0—8.0 at 100° C	300°
Viscosine No. 10	0.930	10.0 at 100° C	330°

As for automobile lubricants, by their properties they fall within the series of viscosines, and therefore there is no need to use them for internal-combustion engines. Only in cases of badly worn pistons or insufficient cooling can they be used.

Almost simultaneously with the samples from the Nobel Brothers Co., samples of oils from the Vacuum Oil Company were obtained, but in quantities of 100 cm³ each, which is insufficient when testing oils for viscosity by Engler, since the viscometer requires not less than 240 cm³. Owing to the insufficient quantity of oil, the results of the viscosity determinations obtained by us were somewhat inaccurate, and, as follows from theoretical considerations, the viscosity came out greater than it should be according to Engler standards. Nevertheless, we give the test results in the following table, since comparative experiments showed that the increase in viscosity is insignificant; thus, for example, in testing turbine oils of the Nobel Brothers Co. at 20° C, we obtained the viscosity of “Turb. oil L” at 100 cm³ as 12.8, and at 240 cm³ as 12.5; the viscosity of “Turb. oil M” at 100 cm³ as 22.5, and at 240 cm³ as 22.0.

Table XVIII.

Samples of oils of the Vacuum Oil Company.

Name of oil	Specific gravity at 20° C	Viscosity at 50° C	Flash temperature
Gargoyle Mobil Oil A	0.904	6.5	210°
Gargoyle Mobil Oil B	0.887	22.0	270°
Gargoyle Mobil Oil E	0.890	3.0	190°
Gargoyle machine oil Etna	0.895	21.0	200°
Gargoyle Gas Engine Oil	0.867	2.7	190°
Gargoyle Engine Oil Naphthal	0.902	5.0	210°
Gargoyle DM	0.896	5.3	185°
Gargoyle OV	0.896	5.3	185°
Gargoyle E N	0.897	6.5	205°

) This table was compiled on the basis of the firm’s own data.
*) The latter name, according to the old nomenclature, has been preserved in practice to the present time; therefore we have used it in the exposition of our article.

§ 8. Practical conclusions from the results of the experiments.

Unfortunately, we do not have instructions from the firm itself as to the purposes for which it produces one or another grade of oil. We know only that “Gargoyle Mobile Oil A” is recommended by the firm for multi-cylinder gas engines with water cooling, and is also recommended as an automobile oil; “Gargoyle Mobile Oil B” is recommended as a special oil for motorcycles and for water-cooled machines in the hot season; on the other hand, “Gargoyle Mobile Oil E” is recommended for water-cooled machines in the winter season.

As regards the other oils in the table, we consider all of them quite suitable for internal-combustion engines. They may all be used for lubricating the cylinder, but depending on the type of cooling.

The properties of the “motor oils” of the Nobel Brothers Company, as well as the oils of the Vacuum Oil Company, show that both these firms are on the right path in producing special lubricants for the cylinders of internal-combustion engines. Our investigations of piston friction show that motor oils should have a low specific viscosity and, if possible, a high flash point, although the author knows of a case in which mazut was used for lubricating the cylinders of gas-producer engines of 1000 h.p., whereas it is known that the flash point of mazut is not more than 140° C. The submitted samples of oils compare favorably in this respect both with ordinary machine oils (in flash point) and with a series of viscosins (in viscosity). Viscosins should not be used for lubricating the cylinders of internal-combustion engines; their purpose is for superheated steam. The author knows of a case in which a 5-horsepower kerosene engine completely refused to run in winter so long as viscosin lubricant was used at a low temperature of the incoming water. The engine began to run as soon as the indicated conditions were changed.

In concluding this addendum on the properties of the oils of the Nobel Brothers Company and the Vacuum Oil Company, we cannot refrain from expressing our wish that these firms themselves would provide information on viscosity, flash point, and specific gravity. In view of the enormous influence of viscosity on the piston friction of internal-combustion engines, it would even be desirable that the catalogues and prospectuses distributed by these firms should include curves of the viscosity of the oils with temperature (see Diagram 1). We think that then every engineer, and indeed every practitioner, would easily find his bearings in the choice of lubricant, depending on the given cooling conditions.

The second practical conclusion is an indication concerning the magnitude of the clearance. We have already said more than once above that the clearance must be sufficient for the unobstructed increase of the lubricant layer. We found the clearance in the tested machines to be sufficient; consequently, in practice the indicated condition is fulfilled, but irregularities of form are overlooked. As a result, in individual parts of the cylinder and piston an excessively small clearance is obtained. It is also necessary to keep in mind the non-uniform change of the piston’s form due to temperature influences, and, consequently, the reduction of clearance and increase of friction. In general, the clearance must be provided for, and it must be the greater, the more viscous the lubricant used. Particular attention must be paid to the clearance in machines with a through piston rod, because the slightest non-coincidence of the axes of the cylinder and the piston causes a great increase in friction. In such cases

...in cases, as we saw with the compressor, the work of friction increases in proportion not to the first, but to the second power of the speed.

Finally, the third practical conclusion is an indication concerning the size of the piston surface. It must not be too large, because the work of friction is proportional to the surface. By increasing the piston surface in those machines in which the piston serves as a slide, they intend thereby to reduce the wear of the cylinder, as a very expensive part; but by this they greatly increase friction and lower the mechanical efficiency of the machine. The wear of the piston is thereby reduced little, since with an increase in the piston surface the rubbing surface increases and, consequently, so does the wear. By increasing the surface, they also think to obtain a better tightness of the piston around its circumference¹, but up to a certain limit this is better achieved by increasing the number of rings. In calculating the advantage of one or the other increase, one may adhere to the indication that the specific resistance of the rings is approximately four times greater than the specific resistance of the piston.

It is necessary to point out one more practical conclusion. Our experiments on the investigation of piston friction have shown that the thermal conductivity of the cylinder walls is very great; so great that the temperature of the lubricating layer depends to a greater degree on the cooling water than on the temperature of the process; in the calorimetric experiments, despite both ends of the cylinder being open, the heat of friction is carried away almost entirely by the water, with a small difference between the temperatures of the cooling water and the lubricant. This gives us grounds to think that, from the side of cooling, no obstacles to increasing the power of internal-combustion engines are to be expected, because it is always possible, by an appropriate consumption of water and by a corresponding choice of lubricant, to attain satisfactory operation of the machine.

In some cases it is necessary to determine the work of friction of the piston of one or another machine, even if not very precisely, without carrying out a preliminary experimental investigation. In view of these considerations, we venture to give some empirical coefficients for the approximate calculation of the work of piston friction in internal-combustion engines, but we warn that such a calculation may give an error of 50%.

The calculation formula may be the equation

\[ N_{\mathrm{п}}=\frac{T_0(f_1Q_1+f_2Q_2)v_m}{75T}, \tag{28} \]

where $f_1$ and $f_2$ are the specific friction resistance for the surface of the piston and for the rings, $Q_1$ and $Q_2$ the lateral surface of the piston and the rings, $T_0$ the mean

temperature at which we determined $f_1$ and $f_2$; $T$ is the mean temperature of the experiment under study, and $v_m$ is the mean piston speed.

On the basis of Table XIV we have: for a lubricant with viscosity 130 at $20^\circ\text{C}$, the specific resistance for the piston surface of a new machine is $f_1=0.03\ \text{kg}/\text{cm}^2$, for the piston surface of a run-in machine $f_1=0.018\ \text{kg}/\text{cm}^2$, and for the surface of the rings $f_2=0.08\ \text{kg}/\text{cm}^2$; for a lubricant with viscosity 38, the specific resistance for the piston surface of a new machine is $f_1=0.026\ \text{kg}/\text{cm}^2$, for the piston surface of a run-in machine $f_1=0.011\ \text{kg}/\text{cm}^2$, and for the surface of the rings $f_2=0.06\ \text{kg}/\text{cm}^2$. All this was determined at a mean temperature of the cooling water $T_0=18^\circ\text{C}$.

Let us give examples of calculation for our tested machines.

For the “Otto-Deutz” machine, $Q_1=2625\ \text{cm}^2$, $Q_2=415\ \text{cm}^2$, the mean speed $v_m=2.2\ \text{m/sec}$; the temperature of the incoming water $t_{\text{in}}=4^\circ\text{C}$, $t_{\text{out}}=40^\circ\text{C}$; consequently, the mean temperature is $T=(40+4):2=22^\circ\text{C}$. Substituting all this into equation (28), we obtain

\[ N_n=\frac{18(0.03\cdot 2625+0.08\cdot 415)2.2}{75\cdot 22}=2.67\ \text{h.p.} \]

For the “Hornsby-Akroyd” machine, $Q_1=4760\ \text{cm}^2$, $Q_2=693\ \text{cm}^2$, the mean speed $v_m=2.9\ \text{m/sec}$, and the mean temperature of the cooling water is $20^\circ\text{C}$. With all these data, from equation 28 we have the work of piston friction $N_n=4.74\ \text{h.p.}$

CONCLUSION.

We shall now make a summary of all the conclusions on the basis of our experiments.

Data on the friction of the tested machines.

1) The work of friction in the “Otto-Deutz” machine may vary, depending on the temperature conditions of the experiment, from 2 to 3.5 h.p. when lubricated with a mixture of machine oil No. 6 and cylinder oil No. 1 in half volume; this amounts to from 15% to 25% of the indicated power of the machine and from 20% to 35% of the useful power.

2) For the “Hornsby-Akroyd” machine we have experimental data at low temperature conditions; therefore we can give an indication of the piston friction of this machine on the basis of comparison with the preceding machine. We think that we shall not make a large error if we take the fluctuations of friction with the same lubrication to be from 4.5 h.p. to 6.5 h.p., which in percentages will amount to a fluctuation from 15% to 22% of the indicated power.

3) The work of friction of the piston of the large cylinder of the compressor, when lubricated with machine oil No. 6, is equal to 0.32 h.p. at 150 revolutions, which amounts to 4%–5% of the indicated work of this cylinder. Such losses to friction, comparatively small in relation to the preceding machines, ...

are explained by: 1) the lower viscosity of the lubricant, 2) the comparatively smaller surface of the piston, and 3) the fact that the indicated work of the compressor is relatively 4 times greater, since it is performed for each stroke of the piston, whereas in the preceding machines it occurs once in 4 strokes.

Directions for the investigation of piston friction.

I. When applying the calorimetric method of investigation, the principal errors arise not from measurements and observations, but from the influence of various incidental causes; therefore, in setting up these experiments, the following must be observed:

1) a completely established state of the experiment, namely, when for 15—20 minutes the temperature of the outgoing water neither rises nor falls, but fluctuates about some mean value by $\pm 0.2^\circ\text{C}$;

2) the temperature of the incoming water must be constant;

3) the mean temperature of the water must be equal to the temperature of the room, although here only a certain approximation can be attained;

4) the water consumption must be strictly constant;

5) there must not be too great compression of the air in the cylinder; and

6) the heat exchange with the air of the room must be reduced as far as possible and studied by supplementary experiments.

The investigation of friction at high temperatures is best carried out by means of a supplementary experiment; in view of this it is necessary to use instruments on the distribution board that are as accurate as possible, both for determining the expenditure of energy during the calorimetric experiments and during the supplementary experiment.

II. When applying the mechanical method of investigation, the principal error is introduced by the various measurements and observations; therefore, in carrying out these experiments, the following must be observed:

1) everything that is required for the accurate determination of the indicated works, both of the working cylinder and of the pump;

2) in determining the work of rotation of the flywheels, it is necessary to use instruments on the distribution board that are as accurate as possible;

3) it is necessary that the voltage of the network from which the current is taken should not fluctuate; to achieve this, accumulator batteries must be used.

Advantages and disadvantages of each method.

Among the disadvantages of the calorimetric method must be counted:

1) that it is applicable only to those machines which have a water jacket;

2) that it gives quite satisfactory results only under low-temperature conditions, which differ greatly from the ordinary operating conditions of the machine;

§ 10. Conclusion.

3) that it may introduce a large error into the results as a consequence of heat exchange in those machines whose external surface is large and whose work of friction is small.

These shortcomings are offset by the following advantages:

First, this method is flexible in its application to the investigation of various questions of friction, for example, to the investigation of the influence of speed, of various lubricants, both liquid and viscous; as for temperature effects, they can easily be investigated by means of an additional experiment;

second, it is simple in its arrangement, in the calculation of results, and does not require additional investigations, which introduce one or another error into the final results of the investigation.

Among the shortcomings of the mechanical method must be included:

1) that, in the final result, it does not give only the single value of the friction of the piston, but gives the sum of the values of the friction of the piston and the friction in the connecting-rod mechanism;

2) that this method consists of a whole series of observations and separate experiments, whose errors, when summed, may give a considerable value of error in the final result (up to 15%);

3) that this method is not flexible in its application to the investigation of various questions of friction, because it is bound up with the arrangement of experiments under the usual working conditions of the machine, which do not allow all the factors under investigation to be varied, for example, the use of liquid and volatile lubricants.

Among the unquestionable advantages must be included:

1) that the investigations are carried out under those friction conditions under which the piston usually works;

2) that, by means of this method, one can calculate the friction of the piston for any experiment with the machine on the basis of the data of the experiment itself, and not make use of average data from an entirely different investigation;

3) that it is applicable to all kinds of piston machines.

On the influence of these or other factors on piston friction.

1) The work of friction of the piston varies proportionally to the number of revolutions or to the mean speed of the piston; consequently, the specific resistance of friction does not depend on the relative velocity $v$.

2) The specific resistance of friction depends on the angular velocity of displacement $\varphi$.

3) The magnitude of the clearance influences the friction of the piston; with an increase in clearance the friction decreases.

4) Friction increases with the viscosity of the lubricant, but not proportionally; rather, to a lesser degree.

5) Friction decreases with an increase in the temperature of the lubricant.

6) Piston friction depends to a greater degree on the temperature of the cooling water than on the temperature of the internal process.

7) The temperature not of the water leaving the cylinder, but of the water entering it, has the greater influence on friction.

8) Friction is proportional to the surface area of the piston.

9) Piston rings increase the work of piston friction for two reasons: first, because they increase the specific frictional resistance; second, because with their edges they scrape off the layer of lubricant and reduce its thickness.

Practical conclusions.

It follows:

1) that a sufficient clearance should be provided between the surfaces of the piston and the cylinder,

2) that the lateral surface of the piston should be made as small as possible, but not to the detriment of tightness,

For internal-combustion engines:

3) that the engine should be cooled with water that is not too cold, with a temperature not below 15°C,

4) that in winter the water should be warmed by the heat of the products of combustion, or circulation cooling should be employed,

5) that the cooling water should be supplied not from the bottom of the cylinder, but from the top,

6) that oils which are not too viscous should be used.

Diagram No. 3

L.C.

Diagram No. 4.

Diagram No. 10.

l.s.

Machine “Otto-Deutz.”

TABLE IV.

| No. of experiment | Barometer, pressure $B$ | Room temperature $t$ | Thermometer, water: inlet to pipe, bulb $t_{\mathrm{in}}$ | Thermometer, water: outlet from pipe, bulb $t_{\mathrm{out}}$ | Oil consumption per hour $W$ | Quantity of heat $U$ | Work, kg·m/sec | Work $N$, hp | Temperature of cylinder walls: near head $t_1$ | Temperature of cylinder walls: middle of open end $t_2$ | Temperature of cylinder walls: near open end $t_3$ | Mean temperature $t_{\mathrm{av}}$ | Number of revolutions $n$ | Mean piston speed $v_m$ | Mean working pressure $p$ | Viscosity at 200° | Oil consumption in grams of oil | Coefficient $\mu$ | Oil consumption per hour, g | Total friction force $F$ | Specific resistance $f$ | Specific piston-friction work | Relative coefficient |
|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| Series 1. ||||||||||||||||||||||||
| 1 | 756 | 18.5 | 12.30 | 19.30 | 177.3 | 1240 | 147.0 | 1.96 | — | — | — | — | — | 1.30 | — | — | 130.4 | — | 0.905 | 30.4 | 113.0 | 0.0372 | 0.076 | 0.47 |
| 2 | 756 | 19.0 | 12.50 | 21.30 | 169.5 | 1492 | 177.0 | 2.36 | — | — | — | — | — | 1.56 | — | — | " | " | " | 28.6 | 113.5 | 0.0373 | " | " |
| 3 | 756 | 19.0 | 12.60 | 22.20 | 163.5 | 1570 | 186.0 | 2.48 | — | — | — | — | — | 1.70 | — | — | " | " | " | 30.4 | 109.5 | 0.0360 | " | " |
| 4 | 756 | 21.5 | 12.70 | 20.30 | 144.8 | 1096 | 130.5 | 1.74 | — | — | — | — | — | 1.03 | — | — | " | " | " | 28.6 | 126.7 | 0.0417 | " | " |
| 5 | 756 | 22.0 | 12.60 | 20.90 | 224.1 | 1860 | 220.5 | 2.94 | 32.0 | 35.0 | 30.0 | 30.0 | 180.0 | 1.92 | — | — | " | 30.0 | " | 30.4 | 114.8 | 0.0378 | " | " |
| 6 | 756 | 22.5 | 12.70 | 21.18 | 223.0 | 2030 | 241.0 | 3.21 | 35.5 | 36.0 | 30.0 | 30.0 | 204.0 | 2.18 | 3.40 | 55 | " | " | " | 30.4 | 110.6 | 0.0364 | " | " |
| 7 | 759 | 21.0 | 12.88 | 22.10 | 274.0 | 2280 | 271.0 | 3.61 | 31.0 | 33.0 | 28.5 | 28.5 | 230.4 | 2.46 | 3.44 | 55 | " | " | " | 30.4 | 110.2 | 0.0363 | " | " |
| 8 | 759 | 22.5 | 14.34 | 20.08 | 76.8 | 441 | 52.3 | 0.69 | 26.0 | 26.0 | 23.0 | 23.0 | 42.8 | 0.46 | — | 98 | " | " | " | 28.6 | 113.6 | 0.0374 | " | " |
| 9 | 759 | 23.0 | 13.82 | 21.06 | 84.8 | 611 | 72.7 | 0.97 | 26.0 | 27.0 | 23.5 | 23.5 | 58.6 | 0.63 | — | 143 | " | " | " | 28.6 | 115.4 | 0.0380 | " | " |
| 10 | 759 | 24.0 | 14.00 | 22.60 | 84.9 | 730 | 86.5 | 1.15 | 24.0 | 26.0 | 22.0 | 22.0 | 75.8 | 0.79 | — | 169 | " | " | " | 25.4 | 109.1 | 0.0359 | " | " |
| Series 2. ||||||||||||||||||||||||
| 11 | 755 | 23.5 | 18.00 | 51.50 | 28.3 | 949 | 112.5 | 1.50 | 53.0 | 54.5 | 55.0 | 38.0 | 224.0 | 2.40 | 1.47 | 27.0 | 130.4 | — | 0.905 | 28.6 | 46.9 | 0.0154 | 0.076 | 0.47 |
| 12 | 755 | 21.5 | 15.88 | 48.60 | 38.4 | 1257 | 149.2 | 1.99 | 51.5 | 53.0 | 53.0 | 36.0 | 217.0 | 2.33 | 2.01 | 30.0 | " | " | " | 30.4 | 64.0 | 0.0211 | " | " |
| 13 | 765 | 22.5 | 14.50 | 40.72 | 66.0 | 1731 | 205.4 | 2.74 | 44.5 | 46.0 | 32.5 | 32.5 | 222.8 | 2.38 | 2.70 | 38.5 | " | " | " | 28.6 | 86.3 | 0.0284 | " | " |
| 14 | 765 | 24.0 | 13.40 | 27.74 | 157.5 | 2258 | 268.0 | 3.57 | 33.5 | 37.5 | 30.5 | 30.5 | 217.6 | 2.33 | 2.61 | 45.5 | " | " | " | 28.6 | 115.0 | 0.0378 | " | " |
| 15 | 765 | 23.5 | 13.10 | 21.36 | 281.4 | 2324 | 276.0 | 3.68 | 30.0 | 35.0 | 30.0 | 30.0 | 216.9 | 2.32 | 2.73 | 47.5 | " | " | " | 30.4 | 118.9 | 0.0391 | " | " |
| 16 | 767 | 20.0 | 12.80 | 21.16 | 151.0 | 2018 | 237.0 | 3.16 | 38.0 | 38.0 | 31.5 | 31.5 | 215.4 | 2.31 | 2.26 | 44.0 | " | " | " | 30.4 | 102.6 | 0.0338 | " | " |
| 17 | 757 | 22.0 | 14.04 | 33.26 | 79.2 | 1678 | 199.0 | 2.65 | 39.5 | 43.0 | 32.6 | 32.6 | 220.0 | 2.35 | 2.65 | 38.5 | " | " | " | 28.6 | 84.7 | 0.0279 | " | " |
| 18 | 757 | 23.5 | 16.04 | 44.82 | 47.4 | 1365 | 162.0 | 2.16 | 47.5 | 49.0 | 34.5 | 34.5 | 218.0 | 2.33 | 2.18 | 33.0 | " | " | " | 30.4 | 69.5 | 0.0229 | " | " |
| 19 | 757 | 24.0 | 18.48 | 50.44 | 30.5 | 944 | 112.5 | 1.50 | 52.5 | 54.0 | 38.0 | 38.0 | 221.6 | 2.37 | 1.49 | 27.0 | " | " | " | 30.4 | 47.5 | 0.0150 | " | " |
| Series 3. ||||||||||||||||||||||||
| 20 | 760 | 21.5 | 12.02 | 21.00 | 257.6 | 2430 | 288.0 | 3.81 | 30.0 | 34.5 | 35.0 | 30.0 | 217.0 | 2.32 | 3.86 | 45 | 130.4 | — | 0.905 | 54.5 | 123.3 | 0.0406 | 0.076 | 0.47 |
| 21 | 760 | 22.0 | 12.00 | 21.66 | 271.0 | 2618 | 310.0 | 4.14 | 30.0 | 36.5 | 37.0 | 31.5 | 217.7 | 2.32 | 4.20 | 44.0 | " | " | " | 262.0 | 133.8 | 0.0440 | " | " |
| 22 | 760 | 23.5 | 12.82 | 19.30 | 160.0 | 1068 | 126.7 | 1.69 | 22.0 | 25.0 | 25.0 | 22.0 | 225.0 | 2.41 | 1.65 | 1.1 | " | " | 0.828 | — | 52.6 | 0.0173 | " | " |
| 23 | 760 | 23.5 | 12.88 | 20.04 | 207.0 | 1585 | 188.0 | 2.51 | 25.0 | 29.0 | 30.0 | 27.0 | 221.0 | 2.36 | 2.50 | 63.0 | " | " | 0.905 | 16.5 | 79.7 | 0.0262 | " | " |
| Series 4. ||||||||||||||||||||||||
| 24 | 754 | 22.0 | 12.62 | 18.52 | 124.8 | 736 | 87.5 | 1.17 | 20.0 | 25.0 | 22.0 | 22.0 | 221.0 | 2.36 | 1.16 | 1.78 | 1.78 | 0.853 | 140.7 | 37.2 | 0.0122 | 0.076 | 0.47 |
| 25 | 754 | 23.0 | 12.75 | 17.92 | 131.2 | 677 | 80.5 | 1.07 | 19.5 | 20.5 | 21.5 | 20.0 | 218.0 | 2.33 | 1.08 | 4.88 | 4.88 | 0.871 | 82.5 | 34.4 | 0.0113 | " | " |
| 26 | 754 | 23.5 | 13.15 | 20.18 | 172.0 | 788 | 93.8 | 1.25 | 21.0 | 24.0 | 24.0 | 20.0 | 218.0 | 2.33 | 1.26 | 5.60 | 5.60 | 0.878 | 40.8 | 40.3 | 0.0133 | " | " |
| 27 | 754 | 22.5 | 12.40 | 21.60 | 140.0 | 1288 | 153.0 | 2.04 | 27.0 | 29.0 | 29.0 | 24.5 | 223.0 | 2.39 | 2.01 | 6.65 | 5.10 | 0.876 | 95.8 | 64.0 | 0.0210 | " | " |
| 28 | 754 | 25.0 | 12.75 | 21.82 | 188.2 | 1706 | 202.0 | 2.70 | 26.5 | 28.5 | 28.5 | 24.0 | 222.0 | 2.37 | 2.67 | 37.5 | 34.00 | 0.902 | 57.9 | 85.2 | 0.0280 | " | " |
| 29 | 747 | 22.5 | 12.65 | 19.37 | 167.2 | 1124 | 133.5 | 1.78 | 24.0 | 25.0 | 26.0 | 23.0 | 215.0 | 2.30 | 1.82 | 6.37 | 5.40 | 0.859 | 46.0 | 58.1 | 0.0191 | " | " |
| 30 | 747 | 22.5 | 12.65 | 19.87 | 179.2 | 1294 | 153.7 | 2.05 | 25.0 | 26.5 | 27.5 | 24.0 | 216.0 | 2.31 | 2.08 | 18.2 | 15.0 | 0.884 | 88.4 | 66.6 | 0.0211 | " | " |
| 31 | 747 | 23.0 | 12.90 | 22.25 | 152.0 | 1420 | 168.6 | 2.25 | 27.0 | 29.0 | 30.0 | 26.0 | 222.0 | 2.37 | 2.23 | 46.4 | 52.0 | 0.899 | 54.0 | 71.2 | 0.0234 | " | " |

TABLE VII.

No. of experiment	Barometric pressure, $B$	Room temperature, $t$	Water temperature: entering pipe, $t_{w1}$	Water temperature: leaving pipe, $t_{w2}$	Mean water temperature, $t_{cp}$	Water consumption, $w$	Quantity, $V$	Pump work, kg·m/s	Pump work, hp	Number of revolutions, $n$	Mean speed, $v_m$	Total resistance, $R$	Specific friction, $f$	Quantity of lubricant, g	Excess pressure: at entrance, kg/cm²	Excess pressure: at end, kg/cm²

								Compressor.
								Small cylinder.
Series 9.
59	761.0	22.0	13.43	21.30	17.36	30.20	169.0	20.0	0.267	175.5	1.46	13.70	0.0272	87.0	0.0	1.19
60	761.0	22.5	13.76	21.12	17.44	30.00	127.0	15.8	0.201	151.5	1.26	12.50	0.0249	90.0	0.0	1.19
61	761.0	22.5	14.08	20.15	17.32	29.84	99.1	11.8	0.157	121.6	1.01	11.80	0.0235	61.0	0.0	1.19
62	761.0	24.5	12.06	18.62	15.34	25.60	74.0	8.8	0.117	106.2	0.89	9.90	0.0197	87.0	0.0	1.19
63	761.0	24.5	13.00	19.26	16.13	25.00	62.6	7.4	0.099	96.0	0.80	9.25	2.0184	70.0	0.0	1.19
								Large cylinder.
Series 10.
64	751.0	25.0	10.20	18.20	14.20	50.50	199.0	23.6	0.315	174.6	1.46	16.16	0.0114	60.0	0.0	0.803
65	751.0	25.0	10.65	18.65	14.65	50.40	199.0	23.5	0.313	171.5	1.43	16.43	0.0116	67.0	0.0	0.803
66	751.0	26.0	11.03	18.65	14.84	50.10	177.0	21.0	0.280	157.0	1.31	16.04	0.0114	54.0	0.0	0.803
67	756.0	26.5	11.43	18.38	14.91	50.00	143.0	17.0	0.226	136.0	1.13	15.05	0.0107	58.0	0.0	0.803
68	756.0	26.5	12.00	18.37	15.19	50.00	113.7	13.5	0.180	120.0	1.00	13.50	0.0095	62.0	0.0	0.803
Series 11.								Large cylinder. Water was heated by a burner. Rings removed.
69	752.0	24.5	23.20	26.60	24.90	41.15	129.2	15.4	0.206	177.0	1.48	10.40	0.0074	57.0	0.0	0.0
70	758.0	21.0	21.15	23.20	22.18	41.52	83.0	9.8	0.131	137.0	1.14	8.60	0.0061	60.5	0.0	0.0
71	758.0	21.0	21.00	22.45	21.72	41.00	59.4	7.1	0.094	108.0	0.90	7.89	0.0056	63.0	0.0	0.0
Series 12.								Large cylinder. Water was heated by a burner.
72	767.0	24.5	21.77	25.56	23.66	75.50	286.0	34.0	0.453	181.3	1.51	22.50	0.0159	62.5	0.0	0.803
73	767.0	24.5	22.24	25.42	23.83	64.30	204.5	24.3	0.324	154.0	1.28	18.98	0.0134	61.0	0.0	0.803
74	767.0	24.0	20.95	24.96	22.96	64.50	258.0	30.6	0.408	165.2	1.37	22.32	0.0158	60.5	0.0	0.803
75	766.0	22.8	20.92	23.10	22.01	63.75	139.0	16.5	0.220	128.0	1.07	15.42	0.0109	65.5	0.0	0.803
76	766.0	23.5	20.90	22.77	21.84	62.35	116.5	13.8	0.184	111.4	0.93	14.85	0.0105	64.0	0.0	0.803
77	766.0	23.6	21.12	23.59	22.36	61.70	152.5	18.1	0.241	131.6	1.10	16.46	0.0117	64.5	0.0	0.803
								“Gorison-Akroyd” machine
Series 13.								Lubrication with machine oil.
78	759.0	23.5	17.00	30.00	23.50	189.3	2460	292.0	3.89	176.2	2.86	102.10	0.0187	86.0	0.082	0.544
79	759.0	24.0	16.67	32.72	24.69	198.6	3000	361.5	4.82	214.0	3.46	104.50	0.0192	83.0	0.082	0.544
80	753.0	23.0	16.78	24.87	20.83	129.2	1042	123.7	1.65	78.5	1.27	97.40	0.0179	84.0	0.082	0.544
81	753.0	24.5	17.00	27.78	22.39	139.5	1505	178.5	2.38	111.2	1.80	99.20	0.0182	84.0	0.082	0.544
82	753.0	25.2	16.91	31.10	24.00	134.1	1904	225.8	3.01	144.0	2.33	96.90	0.0178	85.0	0.082	0.544
83	759.0	23.5	17.28	29.10	23.19	200.7	2370	281.2	3.75	176.2	2.86	98.40	0.0181	88.0	0.082	0.544
Series 14.								Lubrication with a mixture of machine oil and cylinder oil.
84	761.5	23.7	12.80	29.55	21.18	259.8	4350	517.0	6.89	210.0	3.40	152.00	0.0279	56.0	0.082	0.544
85	761.5	23.7	14.70	34.70	24.70	171.6	3432	407.2	5.43	178.5	2.89	141.00	0.0259	56.0	0.082	0.544
86	761.5	24.5	14.70	35.20	24.90	158.4	3245	385.5	5.14	179.5	2.91	132.50	0.0243	58.0	0.082	0.544
87	763.0	23.0	14.00	29.95	22.00	200.1	3190	378.8	5.05	156.5	2.54	149.20	0.0274	58.5	0.082	0.544
88	763.0	24.0	14.10	28.10	21.10	194.7	2720	324.0	4.32	131.0	2.12	152.80	0.0280	57.0	0.082	0.544
89	763.0	24.0	17.65	33.00	25.33	126.0	1930	229.6	3.06	110.8	1.80	127.50	0.0234	58.0	0.082	0.544
90	763.0	24.5	[[unclear]]	29.10	23.50	123.6	1385	164.2	2.19	73.0	1.18	139.20	0.0255	59.0	0.082	0.544
Series 15.								Lubrication with machine oil. Rings removed.
91	765.0	22.0	19.30	28.90	24.10	168.0	1614	191.2	2.55	214.5	3.48	55.0	0.0101	82.0	0.082	0.0
92	765.0	22.0	19.17	28.00	23.59	156.6	1384	164.2	2.19	178.5	2.89	56.8	0.0104	84.0	0.082	0.0
93	765.0	22.5	19.50	26.80	23.15	149.4	1090	129.7	1.73	143.0	2.32	55.9	0.0103	83.0	0.082	0.0
94	763.0	22.0	20.50	24.50	22.50	189.0	756	90.0	1.20	108.4	1.76	51.1	0.0094	83.0	0.082	0.0
95	763.0	22.5	21.00	23.70	22.35	189.0	510	60.8	0.81	72.4	1.17	52.0	0.0095	82.0	0.082	0.0
Series 16.								Lubrication with a mixture of machine oil and cylinder oil. Rings removed.
96	760.0	21.5	15.65	25.30	20.48	256.8	2479	294.0	3.92	208.7	3.38	87.0	0.0160	55.0	0.082	0.0
97	760.0	20.0	15.30	22.70	19.00	258.0	1910	225.8	3.02	177.2	2.87	78.6	0.0144	55.5	0.082	0.0
98	760.0	18.5	15.15	22.15	18.65	210.0	1470	174.6	2.33	132.8	2.15	81.2	0.0149	56.0	0.082	0.0
99	760.0	17.0	14.58	19.80	17.19	204.0	1065	126.8	1.69	88.6	1.44	88.0	0.0161	56.0	0.082	0.0
100	760.0	15.0	14.50	19.00	16.75	171.3	771	91.5	1.22	69.2	1.12	81.7	0.0150	54.0	0.082	0.0
Series 17.								Lubrication with a mixture of machine oil and cylinder oil. Rings removed. Manhole open.
101	752.0	25.0	21.50	26.32	23.91	220.2	1062	126.0	1.68	92.6	1.50	84.0	0.0154	54.0	0.082	0.0
102	752.0	25.0	19.55	26.56	23.55	204.6	1435	170.3	2.27	134.5	2.18	78.0	0.0143	54.5	0.082	0.0
103	752.0	25.0	17.40	28.10	22.75	197.4	2111	250.5	3.34	179.3	2.91	86.1	0.0158	52.0	0.082	0.0
104	752.0	22.5	15.90	28.60	22.25	196.0	2490	295.5	3.94	212.4	3.44	85.9	0.0158	53.0	0.082	0.0

G. Güldner. Internal-Combustion Engines. 1907, p. 239. ↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩
V. Malyshev, “Experimental Investigation of Two-Stroke Machines.” P. 106. ↩↩↩↩↩
Gramberg, “Technical Measurement.” P. 37. ↩

Submission history

[v1] 1913

	Page
1. Methods of investigating piston friction	1
2. Calorimetric method	2
3. Mechanical method	4

Temperature of the outgoing water	Temperature of the outgoing water	Temperature of the cylinder walls	Temperature of the cylinder walls	Temperature of the cylinder walls
from the head	from the jacket	\(t_1\)	\(t_2\)	\(t_3\)
50	40	52	54	49
70	50	66	62	58
80	80	92	89	85

On the Question of Piston Friction: with 4 tables

Full Text

On the Question

of Piston Friction.

Preface

Contents

Introduction

Chapter I

On the Internal Friction of Lubricant

On the Friction of Lubricated Bodies

Contents

Chapter II.

Arrangement and Execution of the Experiments.

Chapter III.

Processing and Critique of the Experimental Material.

Contents

Chapter IV

Results of the Experiments

INTRODUCTION.

Methods for Investigating Piston Friction.

Introduction

§ 2.

§ 2. Calorimetric Method

Introduction

Chapter I

On the Internal Friction of Lubricants

Chapter I. On the Internal Friction of Lubricant. § 5.

On the Friction of Lubricated Bodies.

§ 11. Dependence of the Specific Resistance on \(\varphi\).

Table IV.

Chapter I. On the Friction of Lubricated Bodies. § 11.

Chapter II.

Arrangement and execution of the experiments.

Duration of the Experiments

Chapter III.

Processing and Critique of the Experimental Material.

§ 4. Influence of Internal Heat Exchange

§ 7. Influence of High Temperatures.

§ 8. Additional experiment.

§ 8. Supplementary Experiment.

Chapter III. Processing and Critique of the Experimental Material. § 18.

Chapter IV.

Results of the Experiments.

§ 2. Influence on the Friction of Piston Rings

§ 4. The Influence of Speed on Piston Friction

Chapter IV. Results of Experiments. § 4.

§ 6. The Influence of Temperature on Piston Friction

Chapter IV. Results of the Experiments. § 7.

Table XVII.

Table XVIII.

CONCLUSION.

TABLE IV.

Submission history

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