PHYSICS OF THE ROCKET*)

Howard S. Seifert, Mark M. Mills
and Martin Summerfield

II. LIQUID ROCKETS

LIQUID PROPELLANTS

22. Advantages of Liquid Propellants

A propellant that is not in the solid but in the liquid state has two principal advantages. First, most such substances can be placed in a tank of small weight and low strength and from it be fed gradually into the combustion chamber. The latter, although it must withstand high pressure and temperature, need be only large enough to contain the simultaneously burning quantities of substance. The result is a considerable saving in weight. Second, the inflow of liquid can be regulated at will, whereas an engine with a solid propellant, in which the entire charge is placed in the combustion chamber, cannot easily be stopped after it has been started. The disadvantage of liquid rockets, of course, is their greater complexity.

23. Principal Properties of Liquid Propellants

Since the properties of the liquid used determine the design of the engine, it is advisable to begin with a consideration of the properties of propellants. Any liquid composition capable of releasing a large but controllable amount of energy immediately upon entering the combustion chamber is suitable as a propellant. However, chemical reactions of a detonation character are unsuitable for the “constant-pressure” process we are considering. For best engine operation the substance must release the maximum energy, and the combustion products must have the smallest average molecular—

) Continued. For the beginning see UFN, 34, 34 (1948). Howard S. Seifert, Mark M. Mills and Martin Summerfield, Amer. Journ. of Physics 16*, 2 (1947). Translated by M. L. Antokolsky.

weight \(M\) and heat-capacity ratio \(\gamma\). In addition to these basic requirements, the working substance must satisfy such a large number of practical restrictions that the search for suitable substances is one of the chief problems of research work in the field of rockets, and the peculiar properties of these liquids are the source of a considerable part of the difficulties encountered.

A liquid working substance must possess the following properties:

a) The heat of combustion must be maximal, in order to ensure the highest temperature in the combustion chamber.

b) The molecular weight of the combustion products must be minimal, in order to obtain the maximum velocity of their flow.

c) The liquid must be resistant to shocks and temperature fluctuations, i.e., it must not decompose or detonate under the influence of mechanical actions or of moderately high temperature.

d) The rate of reaction must be high, so that the volume of the combustion chamber will be small.

e) The components of the working substance must ignite readily a short time after being brought into contact with each other or with the igniting device.

f) The density of the liquid must be high, since under this condition it requires a smaller tank volume and is more easily pumped. A smaller tank volume reduces air resistance.

g) The vapor density must be low, to avoid loss of liquid and the necessity of careful thermal insulation, and also to improve pumping conditions.

h) The heat capacity and thermal conductivity must be high if the liquid simultaneously serves also as a coolant.

i) The freezing point must be low if the liquid is intended for use under any geographical conditions.

The following additional properties are also of practical importance:

k) corrosive properties; l) toxicity; m) flammability, especially in the vapor phase; n) availability; o) cost.

24. Typical Working Substances

Satisfactory with respect to most of the listed points is a rather limited number of liquids. Not one of them is ideal, and the search for better substances is still continuing. Some substances consist of a single liquid—we call them homogeneous. Others consist of two liquids; the latter normally are a fuel and an oxidizer. The ratio of the mass flow rate of the oxidizer to the flow rate of the fuel is called the mixture ratio \(r\). This coeffi-

coefficient sometimes differs from the stoichiometric value, if the aim is to attain a lower reaction temperature or a lower molecular weight of the products. Table III lists ten typical working substances, classified according to the type of oxidizer.

Table III

Typical liquid working substances

Each working substance has its own distinctive properties, some of which are described below. Quantitative data on them are given in Table IV.

Liquid oxygen—ethyl alcohol. The advantage of this classic combination is its high specific impulse. In addition, its components are nonpoisonous, noncorrosive, and do not detonate. However, liquid oxygen has a high vapor density at ordinary temperatures, which makes its storage difficult and makes it of little value as a coolant (see Section 32). In the “V-2” rockets the Germans used as fuel a mixture of 75% ethyl alcohol ($\mathrm{C_2H_5OH}$) and 25% water. This “water ballast” lowers the reaction temperature and the average molecular weight. As a result, cooling of the motor is achieved more easily, without a noticeable decrease in the quality of its operation.

Liquid oxygen—carbon-free fuel. The exclusion of carbon from the fuel is intended to reduce the molecular weight of the combustion products, since such a fuel may consist mainly of nitrogen and hydrogen. An example is ammonia ($\mathrm{NH_3}$)—a readily available substance which, as calculation shows, gives high efficiency. It is poisonous and must be stored under pressure in order to remain liquid at ordinary temperature. A more convenient fuel is hydrazine ($\mathrm{N_2H_4}$), liquid at room temperature and giving high efficiency at an unusually low combustion temperature (see Table IV). Neither of these liquids is a good coolant—ammonia because of its low

Table IV

The theoretical efficiency of the principal types of liquid propellants

All values of the exhaust velocity \(c\) are referred to a chamber pressure of \(21\ \mathrm{kg/cm^2}\) and expansion to 1 atmosphere. To obtain experimental values of \(c\), \(c^*\), and \(J_{sp}\), the theoretical data should be reduced by 10%.

the boiling temperature, while hydrazine because it decomposes at comparatively low temperatures.

Liquid oxygen—liquid hydrogen. Liquid hydrogen, in combination with liquid oxygen, gives the greatest efficiency of all available types of fuel. However, because of its extreme volatility (boiling temperature approximately \(-254^\circ\)) and low specific gravity (0.07), as well as its relative expensiveness, it has not so far found application. As a coolant it is even less suitable than liquid oxygen. It is, however, of theoretical interest as a kind of limiting substance giving the maximum efficiency that one can hope to attain.

Nitric acid—aniline. The advantage of this combination is its spontaneous ignition when its components are brought into contact, as a result of which there is no need for a special igniting device. The character of this spontaneous igni-

change is shown in Fig. 18. To increase the rapidity of ignition, nitrogen oxides (NO₂) are dissolved in nitric acid (HNO₃) in an amount of 6 to 14%, which gives the so-called “red fuming” nitric acid. In addition, the water content must apparently be not

a)          b)

c)          d)

Fig. 18. Sequential photographs (at intervals of 1/64 sec.) of the self-ignition of aniline and red fuming nitric acid brought into mutual contact.

more than 2–3%. Nitric acid is corrosive and must be kept in tanks made of stainless steel or aluminum. Its vapors are poisonous. These disadvantages are largely counterbalanced by its high specific gravity (1.55) and its resistance to impact and heating.

To lower the freezing point of aniline (C₆H₅NH₂), 20% furfuryl alcohol is usually added to it. Aniline is poisonous, but in other respects presents no difficulties in handling. It has a high boiling point and is an excellent coolant.

Nitric acid—furfuryl alcohol. This combination also possesses the property of self-ignition, and the time required for ignition is somewhat less than in the case of aniline. In this case the acid does not require an admixture of NO₂ and may be the so-called “white acid.” Furfuryl alcohol (C₄H₃O·CH₂OH) has a low freezing point-

...and is nonpoisonous. In efficiency this combination is equivalent to the preceding one and is more convenient for pumping, since the low density of nitric-acid vapors, in comparison with fuming acid, reduces the difficulties caused by cavitation.

Hydrogen peroxide. Hydrogen peroxide in 80–90-percent concentration is an excellent oxidizer, but is rather unstable with respect to heating and very sensitive to impurities, especially metal oxides, which act as catalysts of exothermic decomposition:

\[ 2\mathrm{H_2O_2}\to 2\mathrm{H_2O}+\mathrm{O_2}. \]

Concentrated hydrogen peroxide decomposes explosively at temperatures only slightly exceeding the boiling point of water. The freezing point changes from \(-23^\circ\) to \(-12^\circ\) as the concentration increases from 80 to 90%. The liquid can be stored for a long time, provided it is chemically pure (the amount of impurities not exceeding several parts per million) and kept in vessels of corresponding purity. Vessels of pure aluminum are best suited, although nickel, stainless steel, and vinyl plastics are also permissible.

A regulated process of decomposition of \(\mathrm{H_2O_2}\) is usually carried out by adding a solution of potassium permanganate (at a concentration of several percent), acting as a catalyst, or by passing the peroxide through a layer of a substance containing permanganates or lead compounds. With such decomposition it serves as a working substance with a low reaction temperature and gives a specific impulse approximately equal to one half that given by other standard working substances, at a reaction temperature amounting to only one quarter of the reaction temperature of these substances. Thus, it can serve as a convenient gas generator for turbine-action engines.

Nitromethane (\(\mathrm{CH_3NO_2}\))—the simplest of the nitroparaffins—contains in one molecule all the components necessary for combustion. It can, therefore, be used as a monopropellant. To initiate combustion, external ignition in the presence of oxygen is required. In the presence of a catalytic additive it burns steadily, developing a pressure almost twice as high as the standard value of \(21\ \mathrm{kg/cm^2}\), and requiring a combustion-chamber volume several times larger than the usual volumes employed for other working substances*).

Nitromethane is noncorrosive, nonpoisonous, insensitive to contamination, and has a low vapor density. Owing to the use of only one liquid, the system of tanks and pipelines is simplified. However, it decomposes explosively at temperatures above \(288^\circ\) and can detonate from mechanical shocks. As a coolant it must therefore be used with caution.

*) For \(\mathrm{CH_3NO_2}\) typical values are: \(p_c=38.5\ \mathrm{kg/cm^2}\), \(L^*=875\ \mathrm{cm}\). See the definition of \(L^*\) in Section 28.

When nitromethane is used in combination with hydrogen peroxide, in the form of a bipropellant, the reaction occurs at lower pressures (21 kg/cm²) and volumes ($L^* = 250$ cm) than when nitromethane alone is used. Moreover, this eliminates the need to add a catalyst, while ignition is easily accomplished without the aid of a flame or spark, by initiating the decomposition of hydrogen peroxide with a catalyst in the form of a small amount of permanganate. This combination represents a propellant that is very convenient to handle, owing to the non-toxicity and absence of corrosive action of its components. It may be useful in cases where strong preliminary heating of the propellant components is not required.

“C-Stoff.” In their Me-163B rocket-powered fighter aircraft the Germans used a fuel designated “C-Stoff.” It consisted of 30% hydrazine hydrate ($N_2H_4 \cdot H_2O$), 57% methyl alcohol, and 13% water. Owing to the hydrazine-hydrate content it is hypergolic with $H_2O_2$ and at the same time is sufficiently stable that it can serve for cooling the rocket engine.

25. Limiting Efficiency of Chemical Propellants

The data presented in Table IV on the efficiency and other parameters of all the propellants considered show that, despite their great variety, the greatest difference in their efficiency does not exceed 50%. Sometimes the hope is expressed that the efficiency of a rocket can be greatly improved by the discovery of a new propellant. But thermodynamic calculations, based on the known properties of all possible liquid propellants, indicate a theoretical upper limit for specific impulse that exceeds the best result achieved so far by only about 80%. This limitation is fundamental in character and is determined by the fact that any substance consisting of the elements H, C, O, and N gives combustion products that dissociate at temperatures above 2500° K and in so doing absorb energy so strongly that the combustion temperature cannot exceed 3500°. Since this limitation is determined by the nature of the combustion products, no changes in the kind of propellant can produce a significant increase in specific impulse. The theoretical maximum specific impulse that can be obtained, for example, from liquid oxygen and hydrazine is about 260 sec. Liquid hydrogen in combination either with liquid oxygen or with liquid fluorine can give up to 350 sec., which may be regarded as the chemical limit of rocket efficiency. Since liquid hydrogen has a specific gravity of only 0.07, it greatly reduces the impulse per unit volume of any propellant of which it is a constituent.

A gain of 25% or 50% in the specific impulse \(J_{sp}\), which can be expected in the near future, is in any case of sufficiently great value to justify the expenditure of effort to attain it. But nothing indicates the possibility that some miraculous propellant will appear on the horizon, giving an increase in \(J_{sp}\), for example, by a factor of 10 over present values. One may conclude that the choice of propellant in the future will be dictated more by operating conditions than by efficiency.

The appearance on the energy scene of the atomic nucleus may alter this assertion. However, if the necessity of a working fluid is nevertheless retained, and if the heat reserve in it is limited by temperature requirements, then it will prove impossible to increase \(J_{sp}\) by more than one order of magnitude compared with present experimental values (see Section 46). Thus, for example, \(\mathrm{H}_2\), heated to \(4000^\circ\mathrm{K}\) and expanding adiabatically, produces a specific impulse of 700 sec. If \(\mathrm{H}_2\) is dissociated into \(2\mathrm{H}\), this value will rise to approximately 1000 sec. These predictions may prove too pessimistic if some other method of reactive propulsion at high velocities turns out to be possible. In any case, the problem of using atomic-nuclear energy for rocket propulsion is extremely complicated, and years will be required for its solution.

PRINCIPLES OF THE LIQUID-PROPELLANT ROCKET ENGINE

26. Mechanical design

A typical thrust device using a liquid propellant—what we shall henceforth call an engine—is shown in Figs. 19 and 20, in which the three principal parts are visible. These three parts are: the propellant injector, the combustion chamber, and the nozzle. The engine shown was designed on the basis of the theory set forth in Part 1, and is characterized by the following data:

Characteristics of the engine (at sea level)

The engine is made of a special type of stainless steel possessing comparatively high thermal conductivity. It is furnished with dis—

with an evaporative compensator, rigidly welded to the outer shell and designed for the high operating temperature of the inner shell. The aniline coolant is routed spirally around the nozzle and the combustion chamber before entering the injector tube (regenerative cooling). The inside of the motor is chrome-plated to protect against corrosion and erosion.

Fig. 19. Photograph of the chamber of a rocket motor of 678 kg, showing the cooling channels.

Fig. 20. Section of a motor of 678 kg; from top to bottom—the injector, combustion chamber, and nozzle.

27. Relation of the rocket’s purpose to its design

Among the requirements that determine the design of a rocket motor to the greatest extent are the following: a) magnitude of the thrust force; b) duration of continuous operation; c) one-time

ness or repeated use; c) flight altitude; d) permissible motor weight.

a) Magnitude of thrust. In motors designed for thrust of less than 45 kg, a difficulty arises because of the possibility of clogging the small injector openings. At thrusts above 450 kg, the ratio of length to diameter decreases, as is seen, for example, from a comparison of Figs. 19 and 21. Since, with provision of proper cooling, a shell can be made that withstands both compressive and tensile stresses of the order of 35 kg/cm², there apparently exists no fundamental upper limit for the dimensions of a rocket motor. Thus, for example, a motor developing a thrust of the order of 500 tons would have a throat diameter of about 1.5 m.

The latest investigations show that in large motors a considerable reduction of the relative volume of the combustion chamber can be achieved without great loss in the value of the parameter \(c^*\). This leads to a motor design consisting of a tubular part, followed by a slightly converging throat and then a conical expansion.

b) Duration of continuous operation. A rocket motor of the type shown in Fig. 20 usually reaches thermal equilibrium in about 30 sec. If the motor must operate for a shorter time than this interval, it may have massive uncooled walls whose heat capacity ensures that the permissible operating temperature is maintained. The duration of operation of a cooled motor is limited only by the supply of propellant, since erosion of the nozzle throat—the most vulnerable point, where the most intense heat transfer occurs—usually does not appear before the propellant supply is exhausted. The limiting duration of operation of an aircraft motor is determined by the weight of the propellant supply that it can carry per 1 kg of thrust, and is of the order of 1 hour or somewhat less. If there is no supporting force of the air, as, for example, in the case of a wingless rocket projectile launched vertically upward, then the operating time is, obviously, limited by the requirement that the weight of the propellant be less than the thrust. It is interesting to note here that, in order for a rocket to escape the earth’s gravity, it is necessary to maintain an acceleration of \(2g\) for 10 minutes.

Table V

Duration of operation of rocket motors

For different fields of application of rockets, certain characteristic values of operating duration apply. They are given in Table V.

c) Single use or repeated use. In single use it is often possible to allow a certain degree of erosion and to employ a much lighter motor than that which would be required for repeated operation, especially in flight without passengers, when the safety factor need not be taken into account. If it is not required to stop and restart the motor, then the usual valves are replaced by bursting diaphragms, which leads to a simplification and lightening of the design.

d) Expected flight altitude. As was indicated in Section 9, for each value of the external pressure there exists an optimum nozzle, for which the ratio of the area of the exit section to the area of the throat is such that it produces the maximum thrust. Accordingly, a rigid nozzle can be corrected for only one altitude. Thus, a motor intended for operation at sea level may have an expansion ratio \(\varepsilon=3.5\), while for operation at \(12\,000\) m \(\varepsilon=11.0\). For vertical flight the calculation is made on the basis of the mean altitude. For motors intended to operate outside the atmosphere, \(\varepsilon\) should be taken as large as design limitations permit.

e) Permissible motor weight. In aircraft motors their own weight constitutes a very small part (1–2%) of the total weight of the aircraft, and heavy, strong structures may be used. In projectiles the motor may weigh from 3 to 10% of the total weight, and lighter structures are preferable. At the present level of technology, motors give from 20 to 100 kg of thrust per 1 kg of their own weight.

28. Reduced length \(L^*\) and burning time

The combustion chamber must have such a volume that the propellant has time to undergo sufficiently complete combustion before the combustion products reach the nozzle throat. Unlike the nozzle, it is not possible to specify optimum chamber dimensions. For reasons of manufacturing convenience, chambers are given the form of a cylinder with volume \(V_c\) and length \(l_c\).

It was found experimentally that, in order to ensure proper combustion, the ratio of the volume \(V_c\) to the throat area \(f_t\), which we shall call the reduced length \(L^*\), must not be less than a certain minimum. This value ranges between 60 and 1500 cm, depending on the propellant and the type of injector.

The fact that the burning time \(t_c\), during which the propellant is in the chamber, is proportional to the reduced length of the latter can be shown on the basis of the following simplifying assumptions.

1) The mixing of the components of the working substance is already complete at the end of the cylindrical chamber facing the injector. Directly near the injector combustion is, although not complete, nevertheless sufficient for the substance leaving this region to be regarded as gaseous.

2) The velocity and temperature of the substance that has left the region in the immediate vicinity of the injector are the same throughout the chamber, despite the fact that, as we know, the chemical reaction is still continuing.

The combustion time is

\[ t_c=\frac{l_r}{v_c}, \tag{80} \]

where \(v_c\) is the velocity of the reacting substances in the direction parallel to the axis of the cylindrical chamber. But, according to the equation of continuity [equation (29)],

\[ v_c=\frac{\dot m}{\rho_c f_c}=\frac{\dot m R_s T_c}{f_c p_c}, \tag{81} \]

Fig. 21. Opened tail end of the “V-2” rocket; the outlines of the motor and the complex system of pipelines are visible.

and from (39)

\[ \dot m=\frac{\Gamma f_t p_c}{a_c}. \]

Substituting this value of \(\dot m\) in (81), and the resulting value of \(v_c\) in (80), we obtain, with the aid of equation (52), which defines \(c\),

\[ t_c=\frac{l_c f_c}{f_t}\cdot\frac{a_c}{\Gamma R_s T_c} =\frac{\gamma L^*}{\Gamma a_c} =\frac{\gamma L^*}{(\Gamma)^2 c^*}, \tag{82} \]

where we take \(l_c f_c=V_c\), the effective volume of the chamber. From (82) we see that the time during which the reactants remain in the chamber is directly proportional to the reduced length \(L^*\) and inversely proportional to the characteristic velocity. Thus, for example, a typical acid-aniline motor with a thrust of \(450\ \mathrm{kg}\) has \(c^*=1378\ \mathrm{m/sec}\), \(L^*=1\ \mathrm{m}\), and gives \(t_c=0.0017\ \mathrm{sec}\). With an increase in the size of the motor and of the thrust, the value of \(L^*\) that is necessary does not increase in the same proportion, so that the fraction of the total volume accounted for by the chamber becomes smaller, and that accounted for by the nozzle becomes larger. This is clearly seen from a comparison of the motor designed for \(678\ \mathrm{kg}\) thrust (Fig. 19) with the “V-2” motor designed for \(25\ \mathrm{t}\) (Fig. 21).

29. Typical Engine Design

In designing a liquid rocket engine with regenerative cooling, three groups of data must be determined exactly: the dimensions of the chamber and nozzle, the hydraulic and mechanical parameters of the injector, and the hydraulic and thermal parameters of the cooling passages. Let us begin with the procedure for determining the principal elements of the engine.

The quantities chosen more or less arbitrarily are: the thrust \(F\) \((\mathrm{kg})\), the chamber pressure \(p_c\) \((\mathrm{kg}/\mathrm{cm}^2)\), the external pressure \(p_0\) \((\mathrm{kg}/\mathrm{cm}^2)\), the propellant, and the mixture ratio \(r\). Data concerning the efficiency of the propellant (see Table IV) must be collected beforehand, empirically.

Fig. 22. Dependence of the characteristic velocity \(c^*\) on the chamber pressure \(p_c\) for red fuming nitric acid—aniline and of the nozzle coefficient \(C_F\)—for all propellants; \(r = 2.75\).

From these data we must determine: the throat area \(f_t\) \((\mathrm{cm}^2)\), the nozzle exit area \(f_e\) \((\mathrm{cm}^2)\), the chamber volume \(V_c\) \((\mathrm{cm}^3)\), and the mass flow rate of propellant \(\dot{m}g\) \((\mathrm{kg}/\mathrm{sec})\). This is carried out in the following steps:

1) Having chosen the thrust \(F\), the chamber pressure \(p_c\), and the external pressure \(p_0\), one determines the type of propellant and, if it is composite, the mixture ratio \(r\).

2) With the aid of empirical data obtained in static tests of rocket engines for the selected propellant, and of the values of \(p_c\) and \(r\), in conjunction with thermochemical calculations, one finds the ratio of heat capacities \(\gamma\), the reduced length \(L^*\), and the characteristic velocity \(c^*\). The values of \(\gamma\) for the propellants given in Table IV lie between 1.2 and 1.3, while \(L^*\) usually lies between 125 cm and 250 cm. Typical curves of \(c^*\) as a function of chamber pressure and mixture ratio are given in Figs. 22 and 23. As

show these curves, with changes in \(p_c\) and \(r\), \(c^*\) changes rather slowly.

3) On the basis of the heat-capacity ratio \(\gamma\) and the pressure ratio \(p_c/p_0\), the nozzle coefficient \(C_F\) and the nozzle area coefficient \(\varepsilon\) are computed according to equations (49) and (50). Graphs of \(C_F\) and \(\varepsilon\) are shown in Fig. 7. These theoretical values of \(C_F\) must be somewhat corrected to take account of friction and of the divergence of the flow in the nozzle.

4) By means of the fundamental relation

\[ F = C_F p_c f_t \]

[equation (48)] the area of the throat is computed, and from the already known ratio

\[ \varepsilon = \frac{f_e}{f_t} \]

the area of the exit opening \(f_e\).

5) On the basis of the definition of the characteristic velocity \(c^*\), the total mass flow rate is computed:

\[ \dot{m} = \frac{p_c f_t}{c^*}. \]

The mass flow rate of oxidizer \(\dot{m}_0\) and of fuel \(\dot{m}_f\) is then computed from the relation

\[ \dot{m} = \dot{m}_0 + \dot{m}_f, \]

where the mixture ratio is

\[ r = \frac{\dot{m}_0}{\dot{m}_f}. \]

Graph labels: characteristic velocity \(c^*\), m/sec; mixture ratio. Curves: \(C\), \(C'\).

Fig. 23. Dependence of the characteristic velocity \(c^*\) on the mixture ratio \(r\) for nitric acid—aniline.
\(p_c = 21\ \mathrm{kg/cm^2}\).

6) The volume of the combustion chamber is determined,

\[ V_c = L^* f_t, \]

using empirical data on the reduced length \(L^*\).

7) The ratio of the cross section of the combustion chamber \(f_c\) to the throat section \(f_t\) is determined by the conditions of heat transfer and structural strength. Heat transfer increases as \(f_c\) decreases; the stress in the material increases as \(f_c\) increases. A typical compromise value is

\[ \frac{f_c}{f_t} = 6. \]

When this ratio has been fixed, the chamber length \(l_c\) is determined. Taking, as an example, a motor of \(678\ \mathrm{kg}\) thrust, described in Section 26, we obtain for it the following numerical data, arranged in the logical order in which they are obtained.

Initial data

Found data

Design data concerning the injector and the cooling passages for the motor are considered in Section 30.

30. Injector

The purpose of the injector is to deliver the working substance into the combustion chamber and to mix and atomize it as rapidly and uniformly as possible, accompanied by a certain decrease in pressure. With a single working substance, the injector orifices must produce a spray jet giving maximum atomization; with a bipropellant working substance they must produce two streams, with a high flow velocity, directed toward each other and ensuring mixing.

If the pressure drop across the orifice is too small, the result may be improper combustion and even the occurrence of acoustic oscillations. On the other hand, an excessively large pressure drop is also undesirable, since it leads to the necessity of strong tanks for the working substance, capable of withstanding increased pressure. A satisfactory compromise for nitric acid and aniline is provided by the value of the dynamic head \(\left(q=\dfrac{1}{2}\rho v^2,\right.\) where \(\rho\) is density, \(v\) is velocity\()\) of each of the opposing streams, satisfying the condition \(q \geq 0.42\ \text{kg}/\text{cm}^2\). In turbulent flow of liquid through a short tubular nozzle, which corresponds to a typical injector, the pressure drop \(\Delta p\) is related to the dynamic head by the equation

\[ \Delta p = Kq, \tag{83} \]

where \(K\) is the dimensionless nozzle coefficient, whose value ranges from 1.2 to 2.0 depending on the shape of the nozzle and the degree of turbulence. The magnitude of the heat transfer to the chamber wall depends strongly on the geometrical arrangement of the jets issuing from the injector. Since regenerative cooling of a rocket motor entails known difficulties, the position of the nozzles must be set very accurately. A change in their orientation by several degrees may cause local fluctuations in heat transfer of the order of 50–100% and result in an accident due to melting of the chamber walls, since it is not possible to provide a large cooling margin.

Injector with impinging streams. Figure 24 shows a typical injector design with impinging mixing for aniline and nitric acid. This is one of the simplest possible arrangements of the nozzles. The nozzles are made replaceable, so that their hydrodynamic contour and nozzle coefficients can be carefully selected. In this injector, minimum heat transfer to the chamber walls is achieved provided that the direction of motion of the flow after mixing is parallel to the axis of the cylindrical chamber. A typical arrangement of the flows is shown in Fig. 25. The direction of the flow after mixing may also have an indirect effect on the efficiency of operation of the motor—in other words, on the characteristic velocity \(c^*\)—owing to a change in the temperature of the incoming fuel, if the latter is used for cooling. Figure 26 shows the shape of the water jets issuing from a small injector with impinging streams. We give the data for the injector shown in Fig. 24, which is used in the motor described in Section 26, designed for 678 kg of thrust. The number of nozzle pairs is 8; the nozzle diameter for the fuel is 3.28 mm, for the oxidizer 2.43 mm; the nominal value of \(\Delta p\) for the fuel is 4.7 kg/cm\(^2\), for the oxidizer 7 kg/cm\(^2\); the angle \(\beta\) formed by the flow after mixing is \(+5^\circ\) (outward). In this case the pressure losses in the nozzles are taken to be unequal, since in the hydraulic circuit for the fuel there is an additional pressure loss in the cooling passages.

Other types of injectors. An interesting injector for a bipropellant, in which the liquids meet not at discrete points but in an annular space, is shown in Fig. 27. This injector gives somewhat better mixing and combustion efficiency, owing to the fact that in it a liquid stream in the form of a converging cone intersects a stream in the form of a diverging cone. It apparently gives a higher heat transfer to the walls of the motor.

Fig. 25. Diagram of the resultant momentum produced by two impinging injector streams.
Visible labels in the diagram: oxidizer; fuel; \((mv)_i\); \(\theta\); \(\phi\); \(\beta\).

Fig. 26. Water test of the injector nozzles of a motor with a thrust of 90.6 kg.

Injectors whose principal purpose is not mixing but atomization have an entirely different construction, as may be seen from Fig. 28, which shows the injector of a motor developing 90 kg of thrust with a monopropellant—nitromethane. Here a centrifugal atomizer is used, in which the emerging liquid is broken up into the finest droplets by the action of centrifugal force. The amount of heat transfer in this type of injector depends considerably less on their orientation than in the types used for bipropellants.

To the present time, the design of injectors has been of a purely empirical character, since very little is known about the internal processes in liquid rocket motors. Direct determinations of velocity, temperature, density, and chemical composition are extremely difficult because of the high temperature in the chamber.

31. Ignition

The starting of a liquid rocket motor presents a number of serious problems that do not arise in ordinary engines. A prolonged warm-up period, during which the thrust has a reduced value, is inadmissible, since at the high consumption of propellant every second of unproductive operation of the motor is costly in terms of specific impulse per unit weight. In addition, combustion must begin quickly (within a few tenths of a second), since delayed ignition causes an accumulation of propellant that may lead to a dangerous rise in pressure or a “hard start.”

Fig. 27. Section of an injector for a bipropellant, giving two intersecting conical jets of nitric acid and aniline.

Fig. 28. Section of an injector with spark ignition for a monopropellant: the injector gives only an atomized jet owing to the centrifugal effect.

If the propellant is self-igniting, as in the case of nitric acid and aniline, upon contact of its components, then the safety of ignition is achieved by the fact that the amount of material supplied

at start-up is made considerably less than the normal feed under fully established combustion. These first portions of the reactant first react at the interface between the two liquids and evolve heat in an amount proportional to the area of contact or to the degree of mixing. The dissipation of this heat is determined by the character of the motion of the liquid and by the shape and initial temperature of the chamber. If the heat balance proves unfavorable, ignition may be delayed until an excess of the working substance has accumulated, the result of which is a “pop.” It is important that the hydraulic system be arranged so as to ensure the simultaneous admission of both components and that the mixture ratio during the initial period of the establishment of combustion not deviate greatly from the stoichiometric value.

Fig. 29. Section of an injector for nitromethane—hydrogen peroxide, in which ignition is effected by a preliminary reaction between the catalyst (permanganate) and hydrogen peroxide.

An initial feed of \(1/6\)—\(1/10\) of the normal value usually establishes the necessary pressure within 2–3 sec., so that during the next 1–2 sec. a transition to the normal feed can be effected. A convenient starting device is provided by burst disks, which partially close the feed pipes and rupture when the delivery pressure reaches a specified fraction of its full value. Since the full pressure in the pipes is established with a delay, this ensures a reduced initial feed.

Catalytic ignition. Hydrogen peroxide decomposes rapidly if a saturated solution of potassium permanganate is supplied along with it through the injector in an amount of 3% of its weight. Sometimes the permanganate is directed in a counter-jet in order to promote spraying. If the peroxide is supplied in combination with the fuel, then the catalyst feed may be stopped after one or two seconds and the reaction continues without its participation. This method of ignition is very reliable. A typical injector for the catalyst, fuel, and peroxide is shown in Fig. 29. Decomposition of the peroxide can also be effected by passing it through a layer of catalytic substance.

Ignition by means of a spark and flame. Working substances incapable of self-ignition, such as nitromethane and various combinations with liquid oxygen, require ignition in the vapor phase by means of a spark or flame. The ignition device must therefore be positioned so that it is not flooded with liquid; we note, by way of example, the arrangement of the spark ignition device in Fig. 28. Spark ignition is convenient for small

engines, since it permits repeated starts, although its disadvantage is the relatively rapid burning of the contacts. In large engines, such as, for example, the “V-2,” pyrotechnic devices are used, placed inside the engine and developing large quantities of heat; otherwise the ignition flame may be extinguished.

Nitromethane has the unfavorable characteristic that increased pressure or a “sharp start” caused by “delayed ignition,” or, finally, thermal decomposition in the cooling passages, may produce a detonation wave in the feed pipe, capable of reaching even the fuel tank. For this reason the spark-ignition circuit is provided with a breaker that opens the circuit after a definite interval of time, beginning from the moment the liquid enters the chamber. It is interesting to note that nitromethane ignites with difficulty in the absence of gaseous oxygen, although after combustion has begun, oxygen is not required. “Detonation traps” have been developed, which prevent the detonation wave from passing beyond a specified point in the feed pipe by destroying the pipe and spraying its contents when the detonation wave approaches.

32. Heat Transfer in Rocket Engines

a) Typical values of thermal parameters.

A rocket engine operates under more severe conditions with respect to temperature and heat influx than any other heat engine. For this reason the problem of heat removal is among the most important and acute in engine design. All engines may be roughly divided into two classes: in some, the heat transmitted by the stream of hot gases is absorbed by the material of the engine itself (the uncooled type); in others, the working substance is used partly or wholly for this purpose (the cooled type). The latter type, in turn, may be subdivided into one in which the cooling liquid absorbs heat while circulating in special passages around the engine (the type with regenerative cooling), and one in which part of the cooling liquid is directed into the working chamber itself in such a way that it forms a cooling film on the inner surface of the walls (film cooling). At first glance one may doubt whether the flowing working substance is capable of absorbing the heat transmitted through the walls while still remaining in the liquid phase. Measurements of the total heat flow show that often absorption of this heat is possible without heating the coolant to boiling. Cooling conditions vary appreciably with the dimensions of the rocket. The amount of coolant increases linearly with an increase in thrust, whereas the cooled surface of the engine grows less rapidly. Thus,

there may be cases when a given working substance is suitable as a coolant for large motors and unsuitable for small ones.

It is useful, for orientation, to give typical numerical values of the thermal parameters of regeneratively cooled rocket motors. The heat of combustion, for example, for red fuming nitric acid and aniline is approximately equal to \(1\ \text{kcal}/\text{kg}\). At sea level, at \(p_c = 21\ \text{kg}/\text{cm}^2\), less than 50% of this energy is converted into the kinetic energy of the issuing jet, and almost all the remaining part remains in the rocket in the form of thermal energy. In a motor, from 2 to 3% of the heat produced by combustion passes through the walls of the combustion chamber and nozzle to the coolant and then, in a regenerative cooling system, returns again to the chamber. The magnitude of the heat transfer is determined by the heat-flux density \(q\); it is of the order of \(0.04\ \text{kcal}/\text{cm}^2\) in the chamber and \(0.10\)—\(0.12\ \text{kcal}/\text{cm}^2\) in the nozzle throat, where it has its maximum value. In industrial furnaces with the highest temperatures, heat transfer reaches values no more than one tenth of those encountered in a rocket motor. Figure 30 shows the distribution of heat-flux density along the direction of the axis of a rocket motor with a thrust of \(90\ \text{kg}\), with an aluminum chamber and a copper nozzle.

Fig. 30. Distribution of heat-flux density along the direction of the axis of a rocket motor.

Heat transfer in the motor may be reduced by a factor of two to four with the aid of refractory liners. However, known refractory materials under rocket-motor conditions have a limited lifetime.

For a mixture of red fuming nitric acid—aniline, the temperature of the gases in the combustion chamber reaches \(2500^\circ\text{C}\) and falls to \(1700^\circ\text{C}\) in the nozzle throat and to \(1100^\circ\) or less at the nozzle exit. Most usable metals melt at considerably lower temperatures. Therefore uncooled motors, even for very brief operation, are possible only because of the existence of a transition layer with a very large temperature gra-

gradient between the main gas flow and the walls of the engine. The equilibrium temperature \(T_{WG}\) of the inner surface of the walls washed by the hot gases, in an engine with regenerative cooling, lies, for steel alloys, between 420 and \(720^\circ\text{C}\). This temperature is determined mainly by the wall thickness \((0.25—0.5\ \text{cm}\) for steel alloys) and the thermal conductivity of the material. The temperature of the surface washed by the coolant, \(T_{WL}\), must not exceed a value lying somewhat below the boiling point of the latter; for example, for aniline at a pressure of \(35\ \text{kg}/\text{cm}^2\), this is \(329^\circ\text{C}\). In the boundary layer between the cooled wall and the main mass of coolant there is also a sharp drop in temperature. A typical value of the mean temperature of the liquid \(T_L\) after it has absorbed heat is \(130^\circ\text{C}\).

All the temperatures mentioned are shown in the graph of Fig. 31, and typical values of the thermal parameters are brought together in Table VI.

Fig. 31. Temperature distribution over a section of the combustion chamber. Large temperature gradients in the gas and liquid “films” at the solid wall.

The temperature of the engine walls for a specified gas temperature in the chamber is determined chiefly by the temperature of the coolant near the wall. Therefore the drop in the transition layer \(T_{WL} - T_L\) must be as small as possible. The thermal conductance \(h\) of this film, which we define as the density of the heat flux through the film for a temperature difference of one degree, increases with increasing coolant velocity, and the temperature drop across the film may vary from \(12—20^\circ\) to several hundred degrees. It is therefore advantageous to have the greatest possible velocity of coolant flow for which the pressure loss in the cooling passages remains acceptable. In modern designs the coolant velocity lies between 4.5 and \(15\ \text{m}/\text{sec}\). The velocity is usually increased near the throat. The total pressure loss in the cooling passages is kept to a value on the order of \(3.5\ \text{kg}/\text{cm}^2\).

In view of the fact that only \(2—3\%\) of the heat released in the chamber passes through the wall, and that the absorption of this small fraction by the coolant is not complete, any factor affecting the transfer of heat through the wall has great significance in the design-

Table VI

Thermal parameters of a typical regenerative-cooling engine operating on the mixture red fuming nitric acid—aniline and with aniline cooling

regulation. As was already indicated in Section 30, the magnitude of the heat transfer is very sensitive to small changes in the form of the flow of the substance in the chamber. It was found experimentally that small deviations in the dimensions of the injectors during their manufacture can cause fluctuations both in the value of \(c^*\) and in the heat-flux density by 50–100%.

A promising improvement in the regulation of the heat flow through the walls of a rocket engine, as applied by the Germans in the V-2 rocket, is the introduction into the chamber of small quantities of liquid through a series of small holes. The liquid introduced in this way spreads over the wall in the form of a film and evaporates. The essential advantage of this method, which has received the name “film cooling,” is that the protective film can evaporate, which increases many times its ability to absorb heat, as compared with the usual method, in which the coolant must remain in the liquid phase. A further advantage is that the heat does not have to pass through the wall, which makes it possible to save considerably in the thickness and weight of the latter. In an ideal engine with film cooling the wall requires no external cooling and is not heated to a temperature exceeding the boiling point of the coolant.

A logical development of the film-cooling system is the unlimited increase in the number of holes admitting the coolant, in other words—the use of porous walls. The coolant then seeps uniformly over the entire surface. This method is sometimes

called “sweat cooling” (literally, “perspiration” cooling—sweat cooling).

The cooling film may be formed either by the working mixture itself or by one of its components, or by some special liquid, which may be either inert (for example, water) or take part in combustion. An example of the successful application of film cooling is the “V-2” engine, in which about 3% of the total mass flow was accounted for by the cooling film of alcohol. About half of this amount took part in combustion and thus did not remain unused.

b) Mechanism of heat transfer. The hot gases communicate heat to the engine walls mainly by convection and radiation. Transfer by direct thermal conduction may be neglected. Theoretical calculations*) of heat transfer lead to the conclusion that up to 30% of the heat absorbed by the chamber walls is due to radiation. In the nozzle, where the temperatures are lower and the dimensions smaller, radiation plays no substantial role. The situation may change when it becomes possible to attain considerably higher temperatures in the chamber.

The principal amount of heat communicated to the walls by convection is difficult to calculate accurately. The density of the convective flux \(q_c\) through the boundary layer of hot gas, or through the film, is proportional to the temperature difference at the boundaries of the film:

\[ q_c = h_G \Delta T . \tag{84} \]

\(h_G\) is called the coefficient of the gas film, or its thermal conductivity, and is expressed in units of \(\mathrm{kcal}/(\mathrm{sec}\cdot\mathrm{deg}\cdot\mathrm{cm}^2)\), \(\Delta T = T_c - T_{WG}\), where \(T_c\) is the temperature of the gases in the chamber, and \(T_{WG}\) is the temperature of the inner surface of the wall. The highly questionable assumption is made that the same conditions of convective transfer exist in the chamber as in a long straight tube, which permits application of the equation obtained by Kármán\(^{7}\) with the aid of the analogy between fluid friction and heat transfer. This equation gives:

\[ h_G = \frac{q_c}{\Delta T} = C_H c_p \rho_c v_c, \tag{85} \]

where \(c_p\) is the heat capacity at constant pressure, \(\rho_c\) is the density of the combustion products, \(v_c\) is the velocity of the gases in the chamber, and \(C_H\) is a dimensionless coefficient of heat transfer. With the aid of the continuity equation, (85) may be reduced to a more convenient form:

\[ h_G = C_H c_p \frac{\dot m}{f_c}, \tag{86} \]

*) These calculations, however, contain a number of doubtful assumptions concerning the radiating capacity of the hot gases and the distribution of velocities in the combustion chamber.

determining the dependence of heat transfer on mass flow rate and cross-sectional area. The coefficient \(C_H\) depends on the flow conditions, the Reynolds number, and the surface roughness. It varies greatly for different sections of the chamber. A rough estimate gives for it the value \(0.0022\), but the error of this estimate may reach \(100\%\).

The heat-flux density is determined mainly by the thermal conductivity \(h_G\), since this quantity is much lower than the thermal conductivity of the other sections of the heat-flow path, just as the current in an electric circuit with elements in series is determined mainly by the section with the highest resistance. A typical value of \(h_G\) is \(0.000021\ \text{kcal}/\text{sec}\cdot\text{deg}\cdot\text{cm}^2\).

In practical calculations of motor wall temperatures it is necessary first to have empirical data on the heat-flux density \(q\). If this quantity is known, then all the temperature values given in Table VI can be computed successively.

1) Knowing the chamber surface \(A\), the coolant flow rate in weight units \(w_f\), the heat capacity \(c_p\), the temperature of the surrounding space \(T_a\), and the heat flux at each point of the surface \(q\), the mean coolant temperature \(T_L\) is calculated by the formula:

\[ T_L = T_a + \frac{1}{w_f c_p}\int_0^A q\,dA. \tag{87} \]

2) For characteristic cross sections of the motor, such as the nozzle throat and the region of maximum \(T_L\), the coolant velocity is specified and the thermal conductivity of the liquid film \(h_L\) is calculated; from this one can determine the temperature \(T_{WL}\) at the boundary between the wall and the liquid by the formula:

\[ T_{WL} = T_L + \frac{q}{h_L}. \tag{88} \]

If this temperature is too far above the coolant boiling point corresponding to the pressure assumed at the given point, it may prove necessary to change the coolant velocity, the area, or the flow rate in the stream. A typical value of \(h_L\) is \(0.00035\ \text{kcal}/\text{sec}\cdot\text{deg}\cdot\text{cm}^2\).

The calculation of \(h_L\) is made by a semiempirical formula obtained on the basis of dimensional analysis. A typical form of this formula is the following\(^8\):

\[ \left(\frac{h_L D}{k}\right) = 0.023\left(\frac{vD\rho}{\mu}\right)^{0.8} \cdot \left(\frac{\mu c_p}{k}\right)^{0.4}, \tag{89} \]

where \(h_L\) is the thermal conductivity of the film for a round tube, \(D\) is the tube diameter, \(k\) is the thermal conductivity of the liquid, \(\rho\) is the density of the liquid, \(v\) is its velocity, \(\mu\) is the viscosity, and \(c_p\) is the heat capacity. The terms in parentheses

are dimensionless numbers bearing the names (successively from left to right) of the Nusselt, Reynolds, and Prandtl numbers. Some of the quantities entering into the equation are not known with complete accuracy for the liquids included in the working mixtures; such, for example, are the thermal conductivity and viscosity. A correction for the curvature of the cooling channels along arcs of relatively small radius must also be introduced into the value of $h_L$. This correction has not been determined accurately, but may reach 25–50%.

3) The thickness $d$ of the chamber and nozzle walls necessary to withstand the acting stresses at the expected temperatures is estimated. Then, knowing the thermal conductivity $K$ of the wall material, the temperature $T_{WG}$ at the wall–gas boundary is calculated by means of the ordinary equation for heat flow through a plate. The nozzle throat usually proves to be the critical section. The equation has the form

\[ T_{WG}=T_{WL}+\frac{qd}{K}. \tag{90} \]

If $T_{WG}$ proves to be such that the material cannot withstand the developing stresses, then a new choice is made of the wall thickness, the material, or the value of $T_{WL}$, and the calculation is repeated again.

c) Pressure loss in the cooling channels. Since the pressure in the feed pipes affects the total weight of the rocket, it is necessary that the pressure drop in the cooling channels not be large. If the coolant velocities obtained from the above calculation lead to an excessively large pressure loss, they must be changed, and the entire calculation corrected accordingly.

Great attention must be paid to the proper choice of the dimensions of the cooling channels and to the exact observance of these dimensions in manufacture. Indeed, for a circular tube, for example, at constant flow rate the pressure loss varies inversely proportional to the fifth power of the diameter.

Helical bending of the cooling channels, for moderate radii of this bending, leads to an increase in pressure loss of approximately 30%. For the 678 kg motor described in Section 29, the head loss, on the basis of the most reliable data from hydraulics, was calculated to be 2.8 kg/cm², and this figure was later confirmed experimentally.

33. Characteristic of the Jet Emerging from the Rocket

a) Shock waves*). The most striking feature of the jet issuing from the rocket nozzle is the presence of sharply distinguishable oblique shock waves, numbering up to six or more, similar

* See ³, also ⁹.

those which are visible in Fig. 32. They are regions in which a sharp, almost discontinuous change occurs in the pressure, density, velocity, and entropy of the flowing gas.

Shock waves occupy a position fixed relative to the nozzle and have no effect on the thrust, provided only that they are not inside the nozzle itself, which can happen only with an excessively expanding nozzle. As was shown by Prandtl,^10 the intervals \(d\) between these shock waves are related to the thrust \(F\) in kg by the simple relation:

\[ d\;(\text{cm})=\sqrt{\frac{F(\text{kg})}{12}} . \tag{91} \]

The total length of the visible flame of the rocket in typical cases may be roughly estimated by the formula

\[ l\;(\text{cm})=\frac{\sqrt{F(\text{kg})}}{6}. \tag{92} \]

In the case of acid—aniline, the luminous flame behind the tail of the rocket can be almost eliminated by adding \(6\%\) \(KNO_3\) to the acid.

b) Increasing the thrust. If the jet of gases is discharged directly into the atmosphere at normal pressure, then part of its kinetic energy is not utilized. If the gases of this jet are made to mix with the air in such a way as to impart to the air a directed velocity, then the motion of this additional mass increases the quantity of motion, or thrust. For this purpose the nozzle is placed in a tube in which the aforementioned mixing takes place.

This device has been given the name “thrust augmenter” (augmentor) (Fig. 33).

Analysis shows that with the aid of such a tube an increase in thrust of up to \(35\%\) can be obtained for a stationary rocket. When the system is in motion this increase rapidly falls and becomes equal to half its initial value when the velocity of the system relative to the atmosphere reaches \(5\%\) of the gas outflow velocity. In prac-

Fig. 32. Exhaust jet of a rocket at 90 kg of thrust; stratification of the glow caused by oblique shock waves is visible.

...the cylinders needed for this prove somewhat bulky, which hinders their use in operating types of rockets.

Fig. 33. “Thrust augmenter” (augmentor)—a device for increasing thrust force. It increases the total momentum at the expense of the kinetic energy of the initial jet.

LIQUID ROCKET SYSTEMS AND THEIR APPLICATION

34. Principal Component Parts

The moving part of the rocket includes, in addition to the motor itself, a device for controlling the inflow of the working mixture, a supply of its components in the corresponding tanks, and a device for pressurization. Fig. 34 shows a typical pressurizing device. A strong cylinder contains nitrogen at a pressure of 140 kg/cm². During operation this pressure falls to approximately 42 kg/cm². The nitrogen passes through a

Fig. 34. Typical hydraulic feed diagram of a liquid rocket by means of compressed gas.

reducer, which maintains a constant pressure of 35 kg/cm². The pressure thus regulated is transmitted to both components through a hydraulically or pneumatically actuated valve and predo-

a safety valve with one-way passage, preventing the connection of the two components of the working mixture through the pipes feeding the nitrogen, which could have catastrophic consequences.

Access of the injected liquids into the motor is opened by means of hydraulically actuated valves (or, sometimes, burst diaphragms), placed as close as possible to the motor itself, in order to ensure the simultaneous admission of both liquids into the motor. In some systems the motor feed valves are opened simultaneously with the valve of the nitrogen cylinder, so that the first portions of the propellant enter at a gradually increasing pressure, as a result of which the gas pressure in the chamber does not rise too abruptly. In this connection it is of interest to note that, when nitromethane is used as a homogeneous propellant, its too rapid inflow into the injector tube should not be permitted, since adiabatic heating of the mixture of air and vapor may entail an explosion.

The manufacture of tanks for the propellant mixture and of the gas cylinder must be carried out with the aid of the highest-grade technique, since they are required to have low weight and must withstand large destructive forces, while possessing a very small margin of strength.

35. Injection technique

For short-duration systems, a cylinder of compressed gas is usually used, having the temperature of the surrounding space and a pressure of from 150 to 200 kg/cm². If it is assumed that no heat is imparted to the gas during its expansion from the initial pressure \(p_0\) to the final pressure \(p_r\), and that the gas from a cylinder of volume \(V_0\), through a reducer, passes into the liquid tanks of volume \(V_p\), having the constant pressure \(p_r\), then, as analysis shows, the equation

\[ \frac{V_0}{V_p}=\frac{\gamma p_r}{p_0-p_r}, \tag{93} \]

holds, where \(\gamma=\dfrac{c_p}{c_v}\) is the ratio of heat capacities for the gas in the cylinder. In practice, during the operation of the rocket (of the order of 1 minute) the gas absorbs a noticeable amount of heat, as a result of which \(\gamma\) must be replaced by a smaller “effective” value \(\gamma'\), determined empirically. Thus, for nitrogen, with \(\gamma=1.40\), \(\gamma'\) may fall to 1.25.

A very considerable saving in weight could be achieved if the injected gases were generated as the result of some chemical reaction throughout the entire operation. In this case the vessel for the reagents could be small and withstand only the injection pressure, and not the much higher pressure of the stored gas. Moreover, the generated gases usually turn out to be hot, with an absolute temperature several times exceeding the temperature of the gas compressed in the cylinder. This leads to a reduction, by the same factor,

density and the mass flow rate of the gas consumed. For generation, ordinary rocket propellants, both liquid and solid, may be used. However, before this valuable method of reducing weight can find practical implementation, much work still remains to be done on its technical improvement.

As the duration of the rocket’s operation is increased, the required weight of the compressed-gas cylinder also increases. When a certain critical value, of the order of 1 min., is reached (it is the smaller, the greater the thrust), pressurization by means of a small turbine centrifugal pump proves more advantageous, in terms of total weight, than the use of a compressed-gas cylinder.

It is not possible here to describe these pumps in detail. Gas turbines with a speed of about 10,000 revolutions per minute, consuming from 2 to 3% of the rocket propellant, burned in a special gas-generator chamber, are being successfully used. The technical difficulties in developing pumps that deliver such liquids as nitric acid or liquid oxygen are very numerous. Small pumps are driven by turbines placed at the exit of the rocket nozzle and acting like a windmill. It should be noted here that, whereas chemical gas generators, while saving the weight of the cylinder, do not reduce the weight of the tanks for the propellant, the pump-feed system also reduces the weight of the latter, which are transformed into light vessels designed for low pressures.

36. Auxiliary Devices for Takeoff and for Boosting the Flight Performance of an Airplane

The greatest demands on an aircraft engine are made during takeoff, when it must, in a short time, impart to its load the maximum possible acceleration in order to reach flying speed and overcome, in doing so, the drag. Additional thrust from a rocket motor proves very useful. The following examples show the advantages achieved by increasing the thrust by 30–50% with the aid of a rocket.

1) The takeoff run at normal load may be reduced to \(^{2}/_{3}\) of its usual value. This is important for small airfields and for aircraft carriers.

2) With the normal takeoff run, the load may be increased by 20%. This is important for long-distance flights requiring large fuel reserves, or when it is necessary to dispatch an overloaded airplane.

3) The takeoff run at an altitude of 3000 m, which without a rocket reaches almost twice the length of the run at sea level, is made, with the aid of a rocket, approximately the same as at sea level. This is important for high-altitude airfields.

4) The rate of climb can be almost doubled. This increases safety in the first moments of flight and helps the aircraft, after carrying out an attack, to avoid pursuit and antiaircraft-artillery fire.

5) The speed of horizontal flight can be increased by 25%. This is important for the same reasons as those indicated in item 4.

Fig. 35 depicts the takeoff of a small airplane with the aid of an auxiliary rocket of 68 kg. The considerable increase in the takeoff angle in comparison with the usual one is clearly visible. Another application of JATO (auxiliary rockets) is the takeoff and landing of “supersonic,” ultra-high-speed airplanes, which often have such small wing surfaces that they cannot take off and land without the aid of auxiliary and braking rockets. The rockets used may operate either with a solid (Fig. 16) or with a liquid (Fig. 36) propellant, depending on the duration of operation,

Fig. 35. Takeoff of a light airplane with the aid of a small rocket with a solid propellant. A large takeoff angle is visible.

Fig. 36. A typical auxiliary rocket for takeoff, approximately 450 kg of thrust. It is intended for permanent mounting on the aircraft engine nacelle.

and may be either jettisonable or permanently installed on the airplane. Both types have already found practical application. Typical data on the weight of a liquid JATO rocket, designed for a thrust of 590 kg for 60 sec., are as follows: propellant—180 kg, pressurizing gas—11.3 kg, cylinders—54 kg, pipelines and frame—34 kg, motor—22.5 kg, total—300 kg.

37. Rocket Airplanes

A rocket motor is very suitable for propelling an airplane at very high altitudes and at speeds exceeding the speed of sound, when propellers operate inefficiently. The duration of operation in this case is so great that only liquid rockets with pump feed are suitable. This duration in typical cases ranges from 10 minutes to 1 hour.

The rocket engine is especially suitable for aircraft of the “flying laboratory” type, intended for the study of the aerodynamics of flight at sonic and even supersonic speed. Rockets that received the name RAFT (Rocket airfoil tester) have already been launched with small models of an airplane wing fixed on the nose, and transmitted by radio data on the aerodynamics of flight at supersonic speed, recorded by a registering apparatus located on the ground.

Fig. 37. Diagram of a “turborocket,” in which the liquid propellant is forced by pumps with a turbine drive.

One of the systems of rockets with pump feed, called a “turborocket,” is shown in Fig. 37. In it the liquid is forced by pumps driven by a gas turbine. The gas turbine may operate on the combustion products of the same propellant as the rocket motor, or, as in the German “V-2,” on the decomposition products of a special liquid, such as, for example, hydrogen peroxide. If the propellant of the rocket itself is used, it sometimes has to be diluted with some admixture in order to reduce the temperature of the gases produced to such a value that it does not cause damage to the turbine blades.

The turborocket system was used by the Germans in the Me-163-B rocket fighter. Its power plant produced a thrust of 1500 kg for takeoff for 3 minutes and then, by throttling, operated at a thrust of 450 to 600 kg during flight. It provided

attained maximum speed, approaching the speed of sound, and the total flight time was limited to 10–20 minutes. At takeoff approximately 50% of the airplane’s weight was propellant, which was a combination of hydrogen peroxide and “C-Stoff.”

Another interesting German rocket airplane, known under the name “Viper” (“Natter”), was launched vertically upward and reached an altitude of 12,000 m in approximately 1 minute. It then released, against an approaching formation of bombers, a barrage of about two dozen independent rockets. At the next moment the pilot, by means of a mechanical device, separated and discarded the nose section of the airplane, while at the same time a parachute opened in the tail section. The sharp braking that resulted caused the pilot to be torn away from his cockpit, and, in conclusion, the latter descended on his own personal parachute, accompanied by not a single part of the peculiar disintegrating airplane. Truly, only a completely jaded pilot would have found service in such aviation “monotonous”!

Fig. 38. German “V-2” rocket at the White Sands Proving Ground, New Mexico, prepared for a night flight.

38. Rocket Projectiles and High-Altitude Rockets

The Germans developed a multitude of rocket projectiles, beginning with antiaircraft-defense projectiles 10 cm in diameter and 150 cm long, called “Typhoon,” and ending with the massive “V-2,” which weighed about 14 t (Fig. 38). It is not possible to describe all these types here. It is enough to confine ourselves to the sadly famous “V-2” in order to gain an idea of these projectiles. It was propelled by liquid oxygen and ethyl alcohol with water and was stabilized at the beginning of its flight by graphite vanes placed in the exhaust flame. The rocket motor, made of ordinary mild steel about 0.6 cm thick, had several annular rows of small openings through which a small fraction of the fuel component flowed into the chamber, forming a protective film on the inner wall. The design of the “V-2” is shown in Fig. 21, and some quantitative data are given in Table VII.

The first American rocket for reaching altitudes comparable with those attained by the “V-2” was developed in our laboratory

Table VII

Main data of the “V-2” rocket*

and was named “WAC-Corporal.” This rocket is relatively small, carries a payload of 11 kg, and was originally intended for sounding measurements in the upper layers of the atmosphere. It has no stabilizing vanes in the gas jet and maintains a vertical position thanks to the aerodynamic stability of its stabilizer. It is launched from a 30-meter vertical tower with the aid of an auxiliary rocket with a solid propellant (ballistite), originally developed for the navy under the name “Tiny Tim.” The latter was rebuilt for a thrust of 22.5 t, developed over 0.5 sec. Such a large initial throw is necessary in order to attain an aerodynamically stable velocity before separation of the auxiliary rocket. The night photograph shown in Fig. 39 shows the interval between the burning of the auxiliary rocket, which gives a broad flame, and the ignition

Fig. 39. Night launch of a high-altitude rocket with the aid of an auxiliary solid-fuel rocket for launching.

Fig. 40. The WAC-Corporal high-altitude rocket, which reached an altitude of 70 km.

Fig. 41. Tower for launching rockets at the White Sands range, from which the WAC-Corporal rocket was launched. In the background is the observation room. The rocket descended vertically from an altitude of about 70 km near this room.

of the main rocket and the subsequent separation of the paths of both rockets. The design of the rocket is shown in Fig. 40, and its data¹¹ are given in Table VIII.

Table VIII

Data of the WAC Corporal high-altitude rocket

Fig. 41 shows a view of the launch tower of the WAC-Corporal rocket.

CITED LITERATURE

1. Th. von Karman, The analogy between fluid friction and heat transfer. Trans. Am. Soc. Mech. Eng. 61, 705—710 (1939).
2. W. H. McAdams, Heat transmission. McGraw-Hill, 1942, p. 168.
3. A. Stodola, Steam and gas turbines. McGraw-Hill, 1927, v. I, 83—84, v. II, 1006—1016.
4. L. Prandtl, Phys. Zeits. 5, 593 (1904).
5. Engineering and Science. July, 1946.

(Conclusion in the next issue)