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Old 1st Nov 2017, 09:51
  #42 (permalink)  
PaulisHome
 
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Oh, good - a physics problem.

Let's get rid of all the ideas that 'the momentum' of an aircraft somehow reduces its susceptibility to turbulence. Momentum has no effect on how an aircraft moves given an external force. Mass, on the other hand does (ie inertia). But that's not the same as momentum.

To first order:

1. Take the equation for lift (proportional to v^2, wing area, CL). Again to first order, CL is proportional to angle of attack.
2. In level flight lift = mass * gravity
3. Now consider what happens when your aircraft moves from air that's not going up or down into air that is (eg a thermal). Effectively, the angle of attack changes, and so the lift from the wing changes, accelerating the aircraft vertically. That's your turbulence.

Solve the equations above, and you find that the extra 'g' experienced by the aircraft is proportional to velocity and wing surface area, and inversely proportional to mass - or if you like proportional to velocity and inversely proportional to wing loading.

That all makes intuitive sense. For otherwise identical aircraft - if you fly faster you get more 'g' from turbulence (hence manoeuvring speeds), and if you add weight you get less (at higher speeds, the angle of attack is less, by a factor of V^2; the change in angle of attack due to the thermal is less too, but only by a factor of V). Likewise for aircraft of equivalent weight and speed, the one with the bigger wing is effected more, since it starts off with a lower angle of attack.

Of course, in the real world, the linear assumption about lift and angle of attack doesn't quite hold, but I think it's good enough for this exercise.

As a sanity check, putting a few numbers in the formulae above, suggests that a B747 with a wing area of 525 m^2, max weight of 400,000 kg, flying at 200 kts (100 m/s), has a vertical acceleration due to a vertical thermal about a fifth of my glider (wing area 11.6 m^2, weight 500kg, speed 30 m/s).

Paul
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