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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 lets 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!!!

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# Principles of Flight - Heavy aircraft vs Light aircraft

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