Piston Speed Comparison — Single-Acting vs Double-Acting Engines For the same stroke length and the same crankshaft speed, the mean piston speed of a double-acting steam engine is __________ the mean piston speed of a single-acting steam engine.

Introduction / Context:
Mean piston speed is a basic kinematic quantity used for comparing engines and estimating friction, lubrication needs, and allowable speed. It depends on stroke and rotational speed, not on whether an engine is single-acting or double-acting in thermodynamic sense.

Given Data / Assumptions:

• Stroke length L is the same in both engines.
• Crankshaft speed N (revolutions per minute) is the same.
• Definition of mean piston speed used in practice: V_mean = 2 * L * N (ensure consistent units).

Concept / Approach:
In one revolution, the piston completes one double stroke, travelling a distance of 2 * L. Therefore, the average linear speed over time is 2 * L * N. This formula is purely kinematic and does not depend on whether the engine admits steam on one side or both sides of the piston. Double-acting affects power output for a given size but does not change piston travel per revolution.

Step-by-Step Solution:
Write mean speed relation: V_mean = 2 * L * N.Hold L and N constant for both engines.Conclude V_mean(single) = V_mean(double) → equal.

Verification / Alternative check:
Kinematic diagrams show that crank–slider motion is identical for single- and double-acting layouts; only thermodynamic admission differs.

Why Other Options Are Wrong:
twice/three times/four times: would imply different travel per revolution, which is incorrect for the same stroke and rpm.

Common Pitfalls:
Confusing mean piston speed with indicated power; double-acting engines can produce roughly double power at similar size because steam acts on both sides, but piston speed stays the same.

Final Answer:
equal to