Old 24th Nov 2012, 07:30
  #76 (permalink)  
Radu Poenaru
 
Join Date: Jul 2012
Location: Cluj-Napoca, RO
Age: 39
Posts: 23
Gezzs what a blood bath in this thread..

I'm assuming "longer" means dt (more time to) slow down from the same speed

Now stop killing the momentum and inertia, it has nothing to do with our problem!

First let's have Newton in here:
a) Force = Mass * Acc
Now take two airplanes with mass M1 and M2 where M2 is heavier:
b) M2 = 1.3* M1
The lift produced must be just as big aswell:
b) L2 = 1.3 * L1
Now if you want airplane nr 2 to decelerate faster, from (a) and (b), the drag needs to be bigger for the heavier airplaine in respect to it's mass:
c1) F2 = M2/a2 remember that F in our case is Drag
c2) F1 = M1/a1 and because we need
c3) a2> a1 then the drag is automatically:
c) D2 > 1.3 *D1
Now combine (c) and (b) a little bit and you end up with a simple condition
(d) L2/D2 < L1/D1

Lift/Drag ratio needs to be bigger for the second plane. We know that L2>L1 from (b), and we assumed they both start at the same speed, so it's only Alpha that changes to create more lift:
e) Alpha2>Alpha1 (note that we do not know the actual A2/A1 ratio .. it's a matter of wing profile)

So we need a better lift/drag ratio (d) for a higher alpha (e) for airplane nr 2.
Take a look at a polar Cl/Cd graph. This only happens at speeds below max lift/drag ratio, ie below best glide. Above that speed the ligher airplane will slow down faster.
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