By Joint Committee’s formula—

B.H.P. = 0·46 × 4 (3 + 4)(3 - 1·18) = 1·84 × 7 × 1·82
= 23·35

By Treasury formula—

B.H.P = 0·4 × 32 × 4 = 0·4 × 9 × 4 = 14·4

Indicated Horse-Power.—The horse-power which an indicator would show as being developed inside the cylinder of a petrol engine, above the piston, would be called the indicated horse-power, and should always work out a greater number than the brake horse-power or power available at the engine flywheel, because some of the power liberated from the combustion of the petrol within the cylinder is lost in friction of the piston and bearings.

The Indicated Horse-Power or I.H.P. = (Pe × A × L x Ne)/33,000.

Where Pe = mean effective pressure from the diagram, in lbs. per sq. inch.
A = area of piston in square inches = 0·7854(diameter of cylinder)2
L = length of stroke of piston, in feet.
Ne = number of power impulses per minute delivered to the crankshaft.

Since a four-stroke engine gives one power impulse to the crankshaft in every two revolutions, it follows that Ne is equal to half the number of revolutions per minute for a single-cylinder engine of that type, and twice the number of revolutions for a four-cylinder engine. A four-cylinder two-stroke engine might be arranged to give either two or four impulses per revolution of the crankshaft—depending upon the arrangement of the cranks.

Example:—A four-cylinder four-stroke engine runs at a speed of 2,000 revolutions per minute and the mean-effective pressure in the cylinders is 75 lbs. per square inch. Calculate the indicated horse-power if the cylinders are 4 in. × 4 in.

I.H.P = (Pe × A × L × Ne)/33,000
= (75 × 0·7854 × 42 × 4/12 × 4000}/33,000
= {75 × 12·56 × 4000}/99,000 = 38

The Indicator Diagram.—At the commencement of this chapter we explained that the work done by a force was measured by multiplying the number representing the magnitude of the force (in pounds) by the distance through which it had acted (measured in feet). This product gave us the quantity of work done in foot-pound units. Thus “quantity of work done” is really the product of two numbers, just as the area of a rectangular floor space is measured by length times breadth. In symbols we write W = F × S where F is the magnitude of the force or resistance in pounds and S the distance through which it has acted, in feet. It is interesting to contemplate this symbolical expression W = F × S together with the expression Area = Length × Breadth, because it gives us a new idea for measuring work. Imagine a diagram of the kind shown in Fig. [68], in which the curved line AB has been obtained by plotting values of F and S for any imaginary case. The diagram is supposed to represent pictorially how the particular force under consideration has varied in magnitude as it has traversed a space represented, to some scale, by the length DC. It is clearly seen that the force has been decreasing in an irregular manner from some large value represented by the height DA to a small value represented by the height CB. We now proceed to show that the shaded area ABCD measures the total amount of work done by this force.

Fig. 68.—Force-space or Work Diagram.