Quote:
Originally Posted by kidicarus5897
I'm bored. Anyone know what the average tail-down force the horizontal stabilizer produces in cruise flight is? I say average because it varies with CG loading and speed. Or, I guess more specifically, how much does the down force change with a forward versus and aft CG in cruise flight?
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I'm more bored than you. and I went to riddle.
here are the assumptions, I made up the numbers since I don't have the real ones:
airplane weight 48000 lbs
total lift produced in level flight 48000 lbs at the cg.
cp location 1 foot behind cg
tail cp location 49 feet behind cg
the forces at the cp (of the wing and of the tail) are creating torque around the cg. torque is force (weight or lift) times distance (from cg)
the two torques (lift and tail down) cancel each other (or else the nose would go up or down)
so:
lift produced at cp + lift produced at tail cp = lift at cg = 48000 lbs
cp torque - tail cp torque = 0
lift at cp = X lbs
torque at cp = X lbs x 1 ft = 1X ftlbs
lift at tail cp = Y lbs
since it's down force as opposed to (up) lift, it's -Y lbs
torque at tail cp = -Y lbs x 49 ft = -49Y ftlbs
all lifts add up to airplane weight
X lbs + (-Y) lbs = 48000 lbs
therefore Y = X-48000
the two torques cancel out
X+(-49Y)=0
substitute X-48000 for Y
X+(-49(X-48000))=0
X-49X+2352000=0
-48X=-2352000
X=2352000/48=49000
since X+Y=48000
Y=-1000
so the wing produces 49000 lbs, and the tail -1000 lbs, to lift the 48000 lbs plane at the cg. obviously since these numbers (the 1 ft and the 49 ft) aren't real, the result isn't either, but you can see the relationship between lift at the wing and down force at the tail is proportional to the distance from cg to cp and the distance from cg to tail cp, with both forces adding up to the weight of the airplane.
other notes:
trim for t/o is designed to give you somewhere between v2 and v2+15. you can try it! (but please don't except in the sim) it works regardless of how many engines are running.
concorde has a rear fuel tank because in supersonic flight the cp travels so far aft that full up trim isn't enough to counter the mach tuck, so instead the cg has to be moved aft and this is done by transferring fuel to the rear tank. this new cg would be too aft for subsonic flight. so this fuel has to be transferred back to the wings (it can't be burnt!) while slowing down.
still bored?
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