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A 180 degree setup will allow for two power pulses per revolution, and thus a smoother power delivery. Additionally, there would be lower side loading on the crank due to the counterbalancing effect of one cylinder travelling the opposite direction from the other at all times.

A 360 setup will give a larger power pulse half as often, similarly to a large-displacement single cylinder engine (commonly referred to as a "thumper"). This can be advantageous in soft ground for avoiding wheelspin.

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EDIT:

The original answer above is true only for 2-stroke engines, however I feel the original question may have been referring to 4-stroke.

For 4-stroke, it takes 720 degrees to complete the entire cycle in 4-stroke engine. Therefore, the effects would be the opposite. 360 setup would have beats equally timed apart. 180 setup would have more inherent vibrations but would have closely timed 2 beats, resulting in bigger momentarily 'kick', 'hook' or 'bite in the dirt" followed by longer 'recovery', which may or may not be advantageous depending on applications.

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order of phases:

0-180 degree

180-360

360-540

540-720

4-stroke, 360 degree setup:

(occurring in #1 cylinder)

- intake

- compression

- SPARK & POWER

- exhaust

(occurring in #2 cylinder)

- SPARK & POWER

- exhaust

- intake

- compression

4-stroke, 180 degree setup:

(occurring in #1 cylinder, same as above in 360 setup)

- intake

- compression

- SPARK & POWER

- exhaust

(occurring in #2 cylinder)

- exhaust

- intake

- compression

- SPARK & POWER (right after #1's SPARK & POWER)

_____________

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Q: What advantage in a parallel twin-cylinder motor does a 180 degree crank have over a 360 degree one?
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