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Old 16th Jan 2008, 00:01
  #34 (permalink)  
Mad (Flt) Scientist
 
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Because the amount of reverse thrust consists of two components: the ram drag (which as usual is a function of the amount of air going in the front end, and its speed) and the gross thrust (which, unusually, is being directly 'vaguely' forwards, with various engines doing so to varying degrees of effectiveness).

The gross thrust term is more-or-less independent of the forward speed, and depends on basic engine parameters. Important here are the amount by which the flow is directed forward - often not much, indeed some designs don't divert the core flow at all. This is one reason why powerback is often a problem (the other being reingestion).

The ram drag term is basically the mass flow into the intake times the forward velocity. Since the mass flow is also dependent on the velocity, this makes it a velocity^2 term. So the ram drag term at 100knots is (10/8)^2= 56% higher than at 80knots, and (10/6)^2=178% higher than at 60knots. Or, if you prefer, if 100knots=100% reverse thrust, then I only have 64% at 80knots and 36% at 60knots.

Since the ram drag term can be a significant proportion of the total reverse thrust, I can easily have lost 50% of my reverse thrust by 60knots or so. That means a potentially significant drop in deceleration.

Next, what really matters in terms of stopping isn't deceleration - that's just a means to the end, which is distance. From the simple equations of motion, distance covered, s, between speeds u and v at a constant acceleration is:

s= (v^2 - u^2) /2a.

Between, say, 110 and 90 knots, the bit in the brackets is -4000.
Between, say, 80 and 60, it's -2800.
So if I could gain, or lose, 10% of my decel, it would be worth 40/28 times more in terms of distance if I could arrange to get the extra decel over the higher speed range. Basically, it's like compound interest; every little counts at the start of the decel run, but by the time you're 'trundling', the distance isn't so sensitive to the exact accel/decel.

So, two things at work:
1. Due to the way most reverse thrust is actually implemented, you get more actual decel at higher speeds; and
2. Any decel at high speed is much more effective in reducing landing roll than the same decel at lower speeds.
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