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When watching heavy crosswind video compilations, I noticed heavy aircraft like the A380 an B747 have a more stable approach compared to the B737 or A320 where the plane banks left and right on approach more frequently.

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A constant crosswind affects all aircraft equally. A crosswind gust will however affect a lighter aircraft more than a heavy one due to lower inertia. The acceleration $a$ felt from the gust is

$$ F = m \times a \;\; \Leftrightarrow \;\; a = \frac{F}{m} $$

where $F$ is the force from the gust and $m$ is the total mass of the aircraft. The force is roughly proportional to the area that the wind sees, which scales with the scale factor squared: $ F \sim s^2 $. The mass however is proportional to the volume, which scales with the scale factor cubed: $ m \sim s^3 $. This results in less sideways acceleration from a wind gust for larger aircraft: $ a \sim s^2 / s^3 = 1 / s $. Therefore, there is less need to correct by sharply banking left or right.

Additionally, larger aircraft react to control inputs from the pilots more slowly (for the same reasons), which also makes them look more stable even when the pilots make sudden control inputs.

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