Ratio of Net Thrust to Weight during a Climbing Flight

[runstreet]

I came up with two solutions as shown in the picture.
I knew the one on the left is wrong, but I couldn't figure out why?

Can someone please clarify?? Thanks in advance.

 

[BAretired]

I'm no expert in dynamics, but the jet is climbing, so it is overcoming gravitational acceleration. Your equations ignore the vertical acceleration of the plane.

BA

 

[runstreet]

Do you mean the lift of the aircraft??

 

[BAretired]

Hi runstreet,

Yes, I mean lift. The plane weighs W. Your equation sinθ(T - R) = W says that the sum of vertical forces is zero. That is true in statics. An object weighing W resting on the ground has a reaction of W. What force is required to give it an upward velocity of Vsinθ where V is the velocity of the plane measured along the slope theta?

BA

 

[BAretired]

I would like to modify my earlier comments as follows:

In order to arrive at a constant velocity, the jet plane must accelerate and there would be forces associated with that acceleration. However, once a constant velocity has been reached, there is no acceleration, which means the system is in equilibrium.

I now believe that the correct answer to the question is 1/sinθ, as you have shown on the solution at the left.
EDIT: But wait a minute...that can't be correct, because as θ approaches zero, i.e. level flight, W/sinθ increases without limit. If the jet plane is in equilibrium after it reaches constant velocity, then T - R = 0 and the answer to question 4. is 0.

Don't hang your hat on this analysis. I think we need the help of an aeronautical engineer to solve this problem. I believe I flunked the exam. Help!!!

BA

 

[BAretired]

What? No more comments?

BA

 

[IRstuff]

Thrust is still required to climb at constant velocity -- the gain in potential energy comes from the work produced by the thrust; with zero thrust, the plane becomes the classic ballistic projectile in a parabolic trajectory.

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[BAretired]

Well, I am not sure how you would express that in a way that would solve the problem, but I will mull it over in my poor old brain for a little longer. Maybe, while I am doing that, someone will come up with the answer to the problem.

BA