Power of four-stroke engines — indicated power formula For a single-cylinder four-stroke engine, which expression gives the indicated power in watts (P in N/m^2, L in m, A in m^2, N in revolutions per second)?

Introduction / Context:
Indicated power represents the power developed inside the engine cylinder based on the indicated mean effective pressure. For exam problems, students must recall how engine stroke cycle timing affects the number of power strokes per unit time. This is especially important for distinguishing two-stroke from four-stroke engines.

Given Data / Assumptions:

• Single-cylinder, four-stroke engine.
• P = indicated mean effective pressure (N/m^2).
• L = stroke length (m).
• A = piston area (m^2).
• N = crankshaft speed (revolutions per second).

Concept / Approach:
Work done per cycle equals P * displacement volume. Displacement volume per cycle is L * A. For four-stroke operation, one power stroke occurs every two revolutions, so power strokes per second are N / 2. Indicated power equals work per cycle multiplied by cycles per second.

Step-by-Step Solution:
Work per cycle = P * (L * A).Power strokes per second (four-stroke) = N / 2.Indicated power IP = P * L * A * (N / 2).Therefore, IP = P * L * A * N / 2.

Verification / Alternative check:
Dimensional check: P has units N/m^2 and LA is m^3, so P * L * A gives Nm, which is joules per cycle. Multiplying by cycles per second (1/s) yields watts, confirming consistency.

Why Other Options Are Wrong:
Using P * L * A * N assumes a power stroke every revolution, which matches a two-stroke, not a four-stroke. The factor 2 * P * L * A * N doubles the already incorrect result. Dividing by 4 underestimates power by another factor of 2.

Common Pitfalls:
For multi-cylinder engines, multiply by number of cylinders; for two-stroke, remove the division by 2. Do not confuse indicated power with brake power, which accounts for mechanical losses.

Final Answer:
P * L * A * N / 2