# Effect of Size on Thermal Efficiency of Motors.*

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The Council of the Institution of Automobile Engineers appears to be determined to put before the members as much information relating to the design of internal-combustion motors, scientifically considered, as it is possible to do, and Prof. H. L. Callender's paper on the above subject, forms a most valuable addition to the information at the designer's command.

After pointing out the sources of loss of heat, the author considered the case of an ideal engine, and the air-standard efficiency, and made some remarks relating to the relative efficiency of an actual engine, the properties of the working fluid, and the variation of efficiency with size. The author then proceeded to describe some experiments with a small motor. As our space is somewhat limited, we are able only to print extracts from this, and other parts of the paper.

Experiments with a Small Motor.

In order to study this question from a theoretical point of view, I undertook a series of experiments about three years ago with a very small motor, 2.36 inches bore. A number of these experiments were described in " Technics " for April, July and August, 1904. The motor was fitted with an indicator capable of working with a high degree of accuracy up to a speed of 2,500 revolutions per minute. A number of thermocouples were inserted in the walls of the cylinder, as in my experiments with Professor Nicelson on the steamengine (Proc.Inst.C:E. 1898), for observing the temperatures and estimating the losses in different parts of the cylinder. Fans were arranged for regulating the temperature, and electric and mechanical brakes for measuring the load. There were several advantages in employing a motor of this type. Owing to its small size, the losees to be investigated were greatly exaggerated, and were therefore rendered easier of detection and measurement. The conditions could be very easily and quickly varied through a very wide range as regards speed, load, etc. There was no water-jacket to equalise artificially the temperatures of different parts of the cylinder, or to interfere with free access to anything. Many reliable experiments were available for comparison on other types of motors, but the small petrol motor afforded a comparatively new field.

Variation of Heat-Loss with Speed and Temperature It is very commonly assumed in considering loss of heat from a gas to a surface that the rate of loss is proportional to the temperature-difference and to the surface exposed. This is true for static conditions and small differences of temperature, but is not even approximately correct in the problem under discussion. As a matter of fact, the conductivity of a gas increases very rapidly with temperature, which makes the heat-loss at high temperatures much greater than in simple proportion to the temperature-difference, and explains the loss of efficiency with increase of flame-temperature. Part of the heat-loss is due to the fact that a layer of gas close to the surface cannot burn immediately. This would mean a nearly constant loss per explosion. Again, the transmission of heat from a gas to a surface is largely affected by the velocity of motion of the gas, which becomes the principal factor in determining the heat-loss in the cylinder of a gas-engine during combustion, where the motion is turbulent and the velocity high. Since the velocity of motion of the gases in a given engine, other things being equal, varies nearly as the speed in revolutions per minute, it is clear that, on this account, the heat-loss per explosion should be more nearly independent of the speed, and that there should not be any marked increase of mean pressure with increase of speed. For very low speeds, the effects of leakage and static cooling tend to reduce the efficiency. For very high speeds ignition lag and gaseous inertia produce the same effect. In any case there will be a very flat maximum value of the efficiency at some particular speed which is not in general far removed from the normal speed of the engine. Variation of Heat-Loss with Size.

Assuming on the above grounds that the greater part of the heat-loss per explosion for a given diagram and flametemperature is independent of the speed to a first approximation over a wide range, it should be simply proportional to the surface exposed and independent of the time of exposure. In other words, the loss Of relative efficiency in similar engines of different size under equivalent conditions of running should vary inversely as the linear dimensions. The loss of efficiency may be taken to vary as A/D, where D is the diameter, and A an appropriate coefficient depending on the form of the surface, which remains constant so long as the form is the same. It is well known that any change in the form or extent of the surface of the combustion chamber produces a very marked effect on the efficiency. Amongst the best available data for testing a formula of this type are the recent trials by a Committee of the Institution of Civil Engineers of three similar engines L, R, X, varying in size from 6 to 6oi.h.p. These are compared with the small motor already referred to, which is denoted by C, in the following table, taking the value of the constant A as equal to unity, when D is taken in inches.

The numbers in the last line are obtained by dividing the observed value of the relative efficiency of each engine by the fraction (i—i D) which it ought to realise if the losses under consideration vary as iJD. Observing that the whole loss for engine X does not exceed it per cent., one might be led to infer that the losses in question were comparatively unimportant; but it is obvious from the table that this is not the case in dealing with motors of a small size such as are employed in automobiles. The losses may vary from 20 to 40 per cent. They are far from negligible, and must evidently be taken into account in comparing motors of different sizes.

It should be remarked that the values of the relative effi,;-ciency given in the table in reality include the variation, if any, of the mechanical efficiency. The relative efficiencies of engines R and X, deduced from the indicator diagrams taken at the trials, were 0.70 and 0.65 respectively, in place of o.65 and 0.69, which were obtained from the B.H.P. by assuming a mean value of the mechanical efficiency. Since the B.H.P. values are in all cases the most reliable and the most easily determined, and since the formula appears to represent them satisfactorily, we must assume that the variable part of the mechanical efficiency can be represented by the same type of formula as the variable part of the thermal losses.

Application to a Rating Formula.

The considerations above discussed have an important bearing on the question of a rating formula. For general descriptive purposes it may be admitted that the rating formula adopted by the Royal Automobile Club, namely :—

Nominal B.H.P. = 0.40 D2 per cylinder, (A.C.) provides all, or nearly all, that is required. This formula is equivalent to assuming a normal piston speed of i,000 feet per minute, and a mean effective pressure of 67.2 lbs. per square inch per explosion as corresponding to the B.H.P. But if such a formula is applied to the award of prizes in competitions, it may lead to undesirable departures from good design, since considerable advantage may be obtained by varying factors of which no account is taken in the formula. The principal factors unaccounted for in the A.C. rating are, (t) Variation of mean pressure with compression-ratio. (2) Variation of mean pressure with size. (3) Variation of piston-speed with ratio of stroke to bore. It is interesting to consider how far account may be taken (1,f these factors, without unduly complicating the formula.

Effect of Compression-Ratio on the Mean-Pressure.

It is generally admitted that the thermal efficiency-and consequently the mean effective pressure for a given rate of fuel consumption-varies with cdmpression-ratio. It would be easy to take account of this in the rating formula by substituting for the constant 0.40 in the A.C. formula the value E of the air-standard efficiency corresponding te the actual compression-ratio in the engine. The value 0.40 for the air-standard efficiency corresponds to a compressionratio of 3.5, which is not uncommon in petrol motors, giving a compression-pressure of 7olb. above atmospheric. By increasing the compression ratio to 5.0, the factor E would be increased to 0.48, giving an advantage of zo per cent. in point of power, of which the A.C. rating takes no account. But this advantage is obtained at the expense of increasing the compression-pressure to I r8lb. Apart from the economy of fuel, there are many objections to excessive increase of compression-ratio, and a formula like the A.C. rating, which directly encourages such increase, is therefore to be deprecated.

Effect of Size on the Mean Pressure.

As already explained, the variation of the thermal and mechanical efficiency with size, is such as to make the mean pressure equivalent to the b.h.p. vary approximately in the proportion given by the factor (1 'ID), for similar engines. This factor may also readily be included in the formula, which then becomes,

Efficiency Rating B.H.P. = C D (D /). (P.C.) In order to give a rough comparison of this formula with the A.C. rating, the value of C in the following table is taken to be equal to 1/2, which makes the two formulx agree for a cylinder five inches in bore. I have added a column giving the rating in terms of cylinder-capacity, assuming the stroke equal to the bore. This basis has, I believe, been adopted in Germany for purposes of taxation, and has often been employed in competitions. It has the merit of giving some advantage to small engines as compared with large, but it is not •a strictly scientific method, and favours undue distortion in the direction of shortening the stroke.

It will be observed that the P.C. rating gives values intermediate between the capacity and the A.C. ratings, but nearer the latter, especially for large engines. The last column gives the rating according to the old formula for the nominal h.p. of a steam-engine given by Bourne (Steam-Engine, 1872, p. 120), which has been applied by Remington to petrol engines. The value of the constant in this formula has been taken as 4.3-in place of 5 as given by Remington-in order to give the same value as the other formuke for an engine of 5 inches bore. Reming-ton's formula, thus modified, agrees very well over the experimental range from 3 to 6 inches bore with the P.C. rating, but gives values which appear to be excessive for large engines. It was designed to allow for the effect of variation in stroke on piston-speed, but it also includes an allowance for the effect of size.

Application of the P.C. Formula.

A formula of this kind, in which account is taken of the effect of size, is most useful in comparing the performances of small engines with large, or of muticylinder engines with single-cylinders of equal power. An Obvious objection to the P.C. type of formula is that the B.H.P. of an engine of 1 inch bore and stroke would be zero. According to the A.C. rating it should be 2/ribs of a horse-power. Another objection that has been urged against the formula is that the dimensions are not homogeneous. This is incorrect, because the figure i in the formula stands for x inch, and represents a length. If the bore is measured in millimetres the formula would read, B.H.P. = D

(D 25.4)11290.

The effect of size on the thermal efficiency of small engines, according to the P.C. rating, is nearly as great as that of compression-ratio. The effect of increase of bore from 2 tO 4 inches is to increase the thermal efficiency so per cent. To produce a similar effect would require an increase of compression-ratio from 3 to 5, and of compressionpressure from 511b. to 1181b. If it is thought desirable to take account of compression-ratio in consumption trials, the effect of size should also be allowed for. Both are included in a comparatively simple manner in the P.C. formula. For this reason it may be called the Petrol-Consumption (P.C. Rating, because it gives the relative power for corresponding rates of consumption, i.e., at equal piston-speeds. It takes no account of piston-speed, which obviously should not be included in a fuel-efficiency rating. Corrected for compression the P.C. rating becomes-

B.11.P. = 2.5ED(D 0/2.

The author then discussed the variation of efficiency with ratio of stroke to bore; the variation of piston-speed with ratio of bore to stroke; hill-climb or speed-test ratios, and the relation of power to weight, the full text of which we regret that we are unable to find space for.

Prof. H. L. Callender concluded a highly interesting and instructive paper with the following : Summary of Formulae.

It will be evident from the previous discussion that no single rating formula can be applied universally. The factors of which account is to be taken, and the data available for comparison, will differ in different cases. Any proposed formula should be capable of modification to suit the requirements of the case to which it is to be applied. I have, therefore, endeavoured to show how the formula should be modified to take account of different factors. Assuming that the primary object of a rating formula is to encourage efficiency irrespective of size, the necessary effect of size on the efficiency should always be allowed for in comparing similar engines of different sizes. This is represented by the factor

i/D), but between the limits 3" and 6' bore the cube root of the diameter may be taken with an appropriate change in the constant. the piston-speed may be taken to

vary as the factor r X/(2D L), or as the cube root of the ratio L/D. This factor should be employed for powerrating in hill-climbing competitions, but not for estimating power in terms of fuel consumption.

The formulee are here summarised with reference to the factors of which account is taken in each.

D = bore, L = stroke, X = L D, all measured in inches.

E = Air-standard efficiency = m (r/r)-4, where r = compression ratio.

Efficiency rating. (P.C.).

Bore only, D(D 1)/2, or DI .c," 15/4.3. Bore and stroke, D(D 11/2 + X/6. Compression and bore, 2.5E D(D 1)/2.

Piston-speed.

Piston-speed = x,000 (s X/(20 + L)), 1,000 Power rating. (H.C.)

Bore and piston-speed, (2D + L) (D 1)/6, or D2 i7f/4.3. Bore, stroke, and speed, D(L + 2D 3)/6, or D(D 0/2 XD/6.

The formulx may be multiplied by 2.5E to allow for compression, and by the number of cylinders in multicylinder engines.