F. W. Roberts has kindly sent us this data for checking the output of an engine without recourse to a dynamometer. Although quite as accurate results should be obtainable from Tapley meter readings, Mr. Roberts’s method has the topical advantage that the car need not necessarily be driven on the road – so, to our mathematically-inclined readers we have pleasure in presenting his calculations. – Ed.
Most enthusiasts would like to know the power output of their engines and to find out what effects any alterations and modifications have had. Few have access to professional testing machines, but the method given here enables anyone to obtain an approximate idea of his engine’s capabilities. It is not necessary to disturb the car at all; indeed, the method is such that the car is run on the road in the normal way. Observations can therefore often be made while going about one’s usual business, although in these days it is perhaps not in the public interest to try for the maxima speeds.
It is proposed to divide these notes into two parts. First, a general picture of what apparatus is needed and what figures are to be recorded. Second, how to turn these figures into the b.h.p. output of the engine.
Required are:– (a) Stopwatch; (b) accurate speedometer; (c) known laden weight of car as driven.
If (b) is doubtful, it can be calibrated at various speeds over a measured 1/4 or 1/2 mile using the stopwatch; (c) can be found for sixpence at any public weighbridge; (a) is indispensable. Beyond pencil and paper, and perhaps a passenger of known weight to operate the stopwatch, the only other thing needed is a straight level stretch of road, and the absence of any appreciable wind.
The method of testing is to time the maximum acceleration possible over a number of short ranges of speed in top gear on a level piece of road. The time to decelerate freely without touching the brakes over the same piece of road in the same direction over the same speed range is also measured. If this coasting is carried out with top gear in, the i.h.p. of the engine – i.e., the power developed in the cylinders – will be measured. If the car coasts in neutral, the b.h.p. at the clutch will be found. The difference is due to considerable piston friction and the power consumed by various auxiliaries and the valve gear.
More accurate results are obtained by taking several pairs of acceleration and deceleration figures and using the average value; this minimizes personal errors. In all cases, for simplicity in calculation, the time in seconds to increase or decrease speed by exactly 10 m.p.h. should be noted.
After performing the following simple calculations, the results should be plotted on ordinary graph paper and the smoothest possible curve drawn among the points:–
M is total weight (including driver, etc.) of car in pounds.
t1 is the time to accelerate 10 m.p.h. in seconds.
t2 is the time to decelerate 10 m.p.h. in seconds.
V is the higher speed reached in m.p.h.
U is the lower speed reached in m.p.h.
Then firstly V-U must be 10, since all times are measured for a change in speed of 10 m.p.h.
M x (V + U) x (t1-t2) b.h.p. = ….(1)
1500 x t1 x t2
The above includes an allowance of 10 per cent. for the rotational inertia of the rotating parts.
The b.h.p. calculated above for each speed range (V to U) should be plotted against the mean speed of that range, i.e.
V + U / 2 m.p.h.
The method is simplified if two tables are first drawn up, one to use while taking the figures, the second to use when calculating.
The worked out figures show, for example, the results obtained with a 7-h.p. car; lack of time prevented further observations being made. Mathematically-minded readers can derive torque-speed curves and estimate b.m.e.p. curves in the usual way from the power output graph thus obtained.
If present-day restrictions have laid up the car, it is still possible that readers may have some performance figures available. By guessing at the quantities opposing motion, it is still possible to estimate the power-curve, although accuracy becomes doubtful. These resistances are in general the sum of tyre drag and air resistance. The first is proportional to the weight on the tyres and is best represented by the curves given in Fig. 1, page 165, for three typical tyre sections. The second is more complicated, being dependent on the speed, frontal area of the car, and its shape. The formula is usually quoted as:–
R=kxAx(m.p.h.)2 pounds drag..(3) where A is frontal area in square feet. Values of “k” are tentatively suggested as being as follows:–
Veteran very square cars……k=0.0022 to 0.0028
1925-1935 tourers……k=0.0018 to 0.0022
1925-1935 saloons……k=0.0017 to 0.0018
1935-1940 rounded tourers……k=0.0017
1935-1940 rounded saloons……k=0.0015
Modern well streamlined saloons……k=0.0011 to 0.0013
Extremely streamlined saloons……k=0.00006 to 0.00009
Theoretically flat plate……k=0.0032
Incidentally the power consumed by these resistances is easily calculated since:
h.p. = m.p.h. x drag in pounds / 375 ….4
The calculations are now different from, and more difficult than, the preeeding ones, and are as follows:–
(A) Calculate for 10, 20, 30. etc. m.p.h. the tyre drag and air resistance using Fig. 1 for tyres and equation (3) for air resistance; a value for “k” can be taken from the table given.
(B) Add these two resistances together and plot them as a graph of pounds total drag against m.p.h. This represents all the losses against which the rear wheels are working, the road being assumed level and the wind speed zero.
(C) if any maxima speeds are known, then for these speeds the corresponding total resistances can be read froin the graph and converted to h.p. by equation (4). This gives points on the power-speed curve if m.p.h. are turned into r.p.m. by using equation (2).
(D) If any hill climbing data are available work these out as follows:
Pull to climb a hill of 1 in x is approximately:–
P= M/x pounds (x not smaller than 6)
To this must be added the total tractive resistance found in (B) above. The sum of all these can be converted to h.p. again as before, although care must be used if the hill was not climbed in top gear.
(E) If acceleration data such as time in seconds to accelerate from 10 to 30 m.p.h. are available proceed according to the following equation which allows 10% for rotational inertia:–
Pounds to accelerate = M x (V-U) / t x 20
M, V, U are as in Part I; “t” is time to raise speed from U to V in seconds. To the pounds effort so obtained add the total pounds drag from (B) above, and convert to h.p. by equation (4). The result can then be plotted to a base of r.p.m.
Conclusion.– The results obtained according to know performance are passably accurate since the coasting period takes care of tyre resistances, air resistance, rear axle losses, gearbox drag, etc. If the coasting is performed in gear, the extra engine losses are also included. and in that case the b.h.p. obtained is not at the clutch shaft but is an approximation to the i.h.p. in the cylinders. Results from “gestimated” performance data are much less accurate since they depend upon an estimate of losses outside the car; rear axle losses are neglected and the data available for working out sections C, D, and E are usually very meagre. It might be helpful to note the following:
1 gallon or water = 10 lb.
1 gallon of petrol = 8 lb
Average passenger = 120-200 lb.
r.p.m. x torque in lb.-ft.
b.h.p.= / 5,250
Effective tyre radius = Ordinary diameter x 0.478.