Principles of Flight - Heavy aircraft vs Light aircraft

[yippy ki yay]

Hey guys,

I'm no physicist so thought I'd ask the experts! A friend asked a question which got me thinking...

Question was: why do heavier aircraft take longer to slow down than lighter aircraft?
It may help if you have knowledge of the principles of flight but I was struggling to come up with a watertight answer!

So let's say a 737 obtains its minimum drag speed (Vmd) (ie the greatest difference between lift and drag) at an angle of attack(AoA) of 4 degrees nose up. There are 2 737s. One is 70 tonnes and the other 50 tonnes. Working on the lift formula (L=1/2 x rho x Vsquared x CL x S; whereby CL = angle of attack and S = surface area of the wing) it would follow that to fly level, Lift = Weight. Therefore the heavier the aircraft the more lift required to keep the aircraft level. So at a given AoA, with your wing area (S) fixed the only way for the heavier aircraft to have adequate lift is by increasing its Indicated Airspeed (IAS) which is the 1/2rhoVsquared part of the lift formula.

Now let's say the 2 aircraft are flying at 300kts and want to slow down to 200kts. The heavier aircraft will take longer to reach 200kts but why? I have a few ideas but not sure which one is correct! Is it because:-

1) Let's say Vmd at 70 tonnes is 240kts and at 50 tonnes 210kts. Therefore, initally, the heavier 737 is flying closer to its minimum drag speed, and therefore is subjected to less drag than the lighter 737. It would follow that its rate of deceleration would be less thus it would take longer to reach 200kts. Although once the speed is reduced to 220kts let's say the opposite would be true as the 50 ton 737 would then be closer to its Vmd speed

or

2) It's a question of Momentum. Velocity is constant between the two aircraft so the higher mass 737 has more momentum so would take longer to slow down? However I then think that at given airspeed the heavier 737 will have a higher AoA and therefore be subjected to more induced drag which should slow it down a bit more quickly?

Any ideas welcome - its probably extremely straightforward but I'm just not sure what the correct answer is! I want to say its a combination of both but then I can faults in both theories.

Many thanks in advance!

 

[rcgldr]

Now let's say the 2 aircraft are flying at 300kts and want to slow down to 200kts.

In this case AoA is not the same. Assuming lift versus weight is the same for both aircraft (level flight), then the issue is which aircraft experiences more drag versus weight. As the aircraft slow, in order to maintain lift, AoA will need to be be increased. So the issue is if the lift versus drag related to AoA during deceleration from 300 kts to 200 kts is closer to optimal for the heavier or lighter aircraft.

 

[K^2]

Has nothing to do with weight, really. Not directly.

Two aircraft are traveling at same air speed in level flight. Both cut throttle to idle and maintain altitude by increasing angle of attack as they slow down. Which one slows down faster?

Well, rate of deceleration is by definition drag/mass. We also know that weight/drag is the glide ratio, and weight is mass*g. So we have deceleration = g/glide. So the aircraft with better glide ratio will take longer to slow down.

As OP correctly points out, for identical aircraft, the glide ratio will depend on angle of attack. And at the same air speed in level flight, heavier aircraft will have higher angle of attack. So now the question becomes conditional.

If the two aircraft are flying above V_y, increasing AoA reduces glide ratio, and the heavier of the two will decelerate faster. Bellow V_y, increasing AoA improves glide ratio, and the lighter aircraft will decelerate faster.All of this is only valid for level flight, of course.

 

[yippy ki yay]

Great thanks for the reply - yeah I'm not sure why i mentioned the constant AoA - think I was going in one direction and then decided to go off in another direction but left in that part which I shouldn't have!

Ok - I reckon in practice Vmd is roughly 200kts at 50 tonnes and probably around 220kts at 70 tonnes which is pretty much coincides with the flaps up speed at those weights. Going from 300kts to 200kts would mean that the speed decrease would be in favour of the heavier aircraft until the speed dropped below 210kts? which explains why the heavier aircraft would slow down slower - Thanks!

Could kinetic energy play a part? or is it pretty much redundant in this situation? My initial thought is that its irrelevant

 

[yippy ki yay]

Thanks for reply K^2! trying to get my head around it as I think this goes against what I thought - oops!

 

[K^2]

I can't find the exact values, but rule of thumb is V_y=V₂+20 KIAS for an airliner. That puts it at 160 KIAS and 190 KIAS for the two example you've given. So from 300 KIAS to 200 KIAS, heavier aircraft will slow down faster.