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Difficulty: Very hardEngine Principles and Internal Components

To diagnose a power loss issue, a mechanic manually rotates the crankshaft of a four-stroke engine to verify valve timing. The rotation begins with the piston at Top Dead Center (TDC) precisely at the onset of the intake stroke. After the crankshaft has been turned exactly 540∘540^\circ, what is the camshaft's rotational displacement from its starting position, and what is the mechanical state of the piston and valves?

  1. The camshaft has rotated 270∘270^\circ; the piston has reached Bottom Dead Center (BDC), and the exhaust valve is beginning to open.Answer
  2. B
    The camshaft has rotated 1080∘1080^\circ; the piston is at Bottom Dead Center (BDC), and the intake valve is opening to draw in the air-fuel mixture.
  3. C
    The camshaft has rotated 270∘270^\circ; the piston has returned to Top Dead Center (TDC), and both valves are fully closed for the power stroke.
  4. D
    The camshaft has rotated 540∘540^\circ; the piston is at Top Dead Center (TDC), and the exhaust valve is opening to expel combustion gases.

Answer

The camshaft has rotated 270∘270^\circ; the piston has reached Bottom Dead Center (BDC), and the exhaust valve is beginning to open.
In a four-stroke engine, each stroke requires 180∘180^\circ of crankshaft rotation. A 540∘540^\circ rotation means exactly three strokes have completed: intake (0∘0^\circ-180∘180^\circ), compression (180∘180^\circ-360∘360^\circ), and power (360∘360^\circ-540∘540^\circ). At the end of the power stroke, the piston is at its lowest point, Bottom Dead Center (BDC), and the exhaust valve begins to open to initiate the exhaust stroke. Furthermore, because the camshaft is geared to rotate at exactly half the speed of the crankshaft, a 540∘540^\circ crankshaft rotation mathematically dictates a 270∘270^\circ camshaft rotation.

Step-by-Step Solution

1
Determine the rotational ratio between the crankshaft and the camshaft.
The camshaft rotates at exactly half the speed of the crankshaft (a 1:2 ratio).
This ratio ensures that the valves open exactly once during the complete four-stroke cycle, which takes two full crankshaft revolutions (720∘720^\circ).
2
Calculate the camshaft's rotational displacement.
540∘÷2=270∘540^\circ \div 2 = 270^\circ of camshaft rotation.
Applying the half-speed ratio directly converts the crankshaft degrees to camshaft degrees.
3
Track the engine strokes based on crankshaft degrees starting from TDC intake.
Stroke 1 (Intake): 0∘0^\circ to 180∘180^\circ. Stroke 2 (Compression): 180∘180^\circ to 360∘360^\circ. Stroke 3 (Power): 360∘360^\circ to 540∘540^\circ.
Each internal combustion stroke requires exactly half a crankshaft revolution (180∘180^\circ). 540∘540^\circ completes exactly three strokes.
4
Determine the mechanical state at the 540∘540^\circ mark.
The power stroke has just ended, the exhaust stroke is beginning, the piston is at BDC, and the exhaust valve is opening.
At the end of the downward power stroke (540∘540^\circ), the piston is at the bottom of the cylinder (BDC) and must push gases out, requiring the exhaust valve to open.

Key Concept

Camshaft-to-crankshaft rotational relationship and spatial phase tracking in a four-stroke cycle.
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Topics

Engine Principles and Internal Components

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