Compound engine configuration (Woolf type): In a Woolf type compound steam engine, what is the usual angular relationship between the high-pressure and low-pressure cranks?

Introduction / Context:
Compounded steam engines expand steam in stages. The Woolf type is a classic arrangement historically noted for its direct HP-to-LP connection. Recognizing crank phasing clarifies torque characteristics and valve timing.

Given Data / Assumptions:

• Woolf type indicates direct coupling of HP exhaust to LP admission without a large external receiver.
• Often constructed in tandem with a common piston rod and a single crank.
• Goal: smooth expansion with minimal receiver volume.

Concept / Approach:
In the Woolf type, the HP and LP pistons are mechanically aligned such that both move together; effectively the cranks are coincident. This corresponds to 0° phase difference. The arrangement simplifies flow between cylinders and reduces inter-stage storage volume, affecting pressure diagrams and avoiding pulsations associated with widely phased cranks.

Step-by-Step Solution:
Identify Woolf type → typically tandem construction.Common piston rod and single crank → same angular position for both cylinders.Therefore, crank angle difference = 0°.Select the option “0° to each other”.

Verification / Alternative check:
Engineering texts contrast Woolf (0°) with cross-compound (90°) for smoother torque but with a receiver.

Why Other Options Are Wrong:
180° and 90° commonly describe multi-cylinder phasing for balance, not the Woolf tandem arrangement.

“None of these” is unnecessary because 0° is explicitly listed.

Common Pitfalls:
Confusing “Woolf” with “receiver type” where a receiver allows other crank phasings (e.g., 90°).

Final Answer:
0° to each other