DETERMINATION OF THE POWER OF AN INTERNAL COMBUSTION ENGINE OPERATING ON A MOULINETTE

V. K. NECHAEV, V. P. BELTYUKOV

Air brakes (moulinettes), in a number of cases used as load brakes in testing internal combustion engines, compare favorably with brakes of other types by the simplicity of their design and the great steepness of their characteristic. However, a serious drawback of these brakes is the dependence of the power they absorb on atmospheric conditions. If, under normal atmospheric conditions \((P_0 = 760\ \text{mm Hg}\) and \(T_0 = 288^\circ K)\), the power absorbed by the moulinette at a certain speed \(n_{\text{n}}\) is determined by the formula [1]

\[ N_{0m} = A \frac{P_0}{T_0} n_{\text{n}}^3 , \tag{1} \]

then under new atmospheric conditions \((P, T)\) and a new speed \(n\), the moulinette will absorb the power

\[ N_m = A \frac{P}{T} n^3 = N_{0m}\frac{PT_0}{P_0T}\left(\frac{n}{n_{\text{n}}}\right)^3 . \tag{2} \]

Here \(A\) is a coefficient depending on the shape and dimensions of the moulinette.

Using formula (1), one can construct the moulinette characteristic (a cubic parabola) for normal atmospheric conditions.

The power developed by an internal combustion engine also depends on atmospheric conditions, but this dependence is different from that for the moulinette. Therefore, if under normal atmospheric conditions the engine power was determined by point \(B_0\) (Fig. 1), the intersection of the engine and moulinette characteristics, then under changed atmospheric conditions it will be determined by point \(B\), the intersection of the same characteristics for the new atmospheric conditions. In this case, the established speed \(n_{\text{n}}\) of the engine and moulinette will change to some new value \(n\).

Fig. 1

The difference \(n_{\text{n}} - n\) is determined both by the “sensitivity” of the moulinette and engine to changes in atmospheric conditions, and by the dependence of engine power (at unchanged \(P\) and \(T\)) on its speed \(n\).

During prolonged tests the atmospheric conditions change repeatedly. Naturally, the question arises as to the possibility of using

characteristics of the moulinette, constructed for normal conditions, under other atmospheric conditions.

To reduce the power of an internal-combustion engine to normal conditions, GOST [2] recommends the formula

\[ N_{o\,dv}=N_{dv}\,\frac{P_0}{P}\,\frac{530+t}{545}. \tag{3} \]

To take into account the dependence of \(N_{o\,dv}\) on \(n\), we introduce into the right-hand side of formula (3) the additional factor \(\left(\frac{n_n}{n}\right)^x\), where \(x\) is a coefficient determined by the form of the engine speed characteristic in the interval \(n_n-n\). Now, instead of (3), we have

\[ N_{o\,dv}=N_{dv}\,\frac{P_0}{P}\,\frac{530+t}{545}\left(\frac{n_n}{n}\right)^x . \tag{4} \]

From formula (4), the engine power under conditions differing from normal ones is determined by the expression

\[ N_{dv}=N_{o\,dv}\,\frac{P}{P_0}\,\frac{545}{530+t}\left(\frac{n}{n_n}\right)^x . \tag{5} \]

At point \(B\) (Fig. 1), according to (2) and (4),

\[ N_{dv}=N_m \]

and

\[ N_{o\,dv}\,\frac{P}{P_0}\,\frac{545}{530+t}\left(\frac{n}{n_n}\right)^x = N_{o\,m}\,\frac{P}{P_0}\,\frac{T_0}{T}\left(\frac{n}{n_n}\right)^3 . \tag{6} \]

Hence, with the obvious equality (at \(n_n\))

\[ N_{o\,dv}=N_{o\,m} \]

we have

\[ \left(\frac{n_n}{n}\right)^{3-x} = \frac{T_0}{T}\,\frac{530+t}{545} \]

or finally

\[ n_n=n\sqrt[3-x]{\frac{288}{545}\cdot\frac{530+t}{273+t}} . \tag{7} \]

Thus, the speed regime of an internal-combustion engine operating on a moulinette does not change when the barometric pressure changes and is determined only by the change in the ambient temperature and by the value of \(x\), the exponent in expression (4).

Using formula (7), it would be possible, knowing the value of \(x\), the air temperature \(t\), and the number of revolutions of the moulinette (and of the engine) \(n\), to determine its number of revolutions \(n_n\) under normal atmospheric conditions, and from it, on the basis of the main characteristic of the moulinette (Fig. 1), the point \(B_0\) and its ordinate—the engine power reduced to normal atmospheric conditions. However, the value of \(x\) varies at different points of the engine speed characteristic.

Let us consider the following special cases (Fig. 2):

1) the engine power is directly proportional to its revolutions (point I—the regime of maximum torque), \(x=1\)

\[ n_n = n \sqrt{\frac{288}{545}\cdot\frac{530+t}{273+t}}; \]

2) the engine power does not depend on revolutions (point II—the regime of maximum power), \(x=0\)

\[ n_n = n \sqrt[3]{\frac{288}{545}\cdot\frac{530+t}{273+t}}; \]

3) the engine power is inversely proportional to revolutions (point III), \(x=-1\)

\[ n_n = n \sqrt[4]{\frac{288}{545}\cdot\frac{530+t}{273+t}}. \]

Fig. 2

When working in the laboratory, the air temperature may vary within the range from \(+10^\circ\mathrm{C}\) to \(+30^\circ\mathrm{C}\). In the most unfavorable first case, the deviations of the revolutions of an engine operating on a moulinette from the revolutions under normal atmospheric conditions will then be:

\[ n_n' = n \sqrt{\frac{288}{545}\cdot\frac{530+10}{273+10}} = n\sqrt{1.009}=1.005\,n, \]

\[ n_n'' = n \sqrt{\frac{288}{545}\cdot\frac{530+30}{273+30}} = n_0\sqrt{0.979}=0.991\,n_0. \]

Thus, in the most unfavorable case, the deviation of the engine revolutions from the nominal values is less than \(1.0\%\), i.e., less than the error when measuring revolutions with an electric tachometer [3]. Therefore, the dependence of the speed regime of an internal combustion engine operating on an air brake (moulinette) on atmospheric conditions during operation indoors may be disregarded, and the engine power may be determined from the moulinette characteristics constructed for normal atmospheric conditions.

REFERENCES

1. Mechanical Engineering. Encyclopedic Handbook, vol. 10, GONTI, Moscow, 1948.
2. GOST 491—55. Automotive and Tractor Engines. Methods of Bench Testing. Official edition, Moscow, 1955.
3. Gorbachev F. A., Melkobrodov E. A. Physical Principles of the Design and Operation of Aircraft Instruments, Oborongiz, Moscow, 1953.