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 $. Therefore, there is less need to correct by sharply banking left or right.
Additionally, larger aircraft react to control inputs from the pilots more slowly (for the same reasons), which also makes them look more stable even when the pilots make sudden control inputs.
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$\begingroup$ Forward airspeed also matters, in determining how quickly an aircraft will accelerate in relation to a crosswind gust. In general, the higher the forward airspeed, the more sideforce a given crosswind gust will generate, and thus the more sideways acceleration. $\endgroup$ – quiet flyer Feb 17 at 15:32
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$\begingroup$ Links re above comment -- See aviation.stackexchange.com/questions/70975/… , physics.stackexchange.com/questions/176513/… , physics.stackexchange.com/questions/491600/… $\endgroup$ – quiet flyer Feb 17 at 15:32
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$\begingroup$ @quietflyer Good Point! This is very relevant when comparing with a much smaller plane like e.g. a C172, but for the aircraft mentioned by the OP, it is actually not really relevant. Both the A320/B737 and the A380/B747 have typical approach speeds of around 140 knots. $\endgroup$ – Bianfable Feb 17 at 17:08
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