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# Thrust to weight ratio and Weight Problems

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1) If a 22450lb (total gross weight) airplane develops 8160lbf thrust from each of its two engines and has a wing area of 312ft2 and wing-span of 53.5ft. And a empty weight of 11770lbf. Determine the thrust to weight ratio and the wing loading of this aircraft?

2) Consider an ordinary, helium-filled party balloon with a volume of 2.2ft3 . The lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. Using this
fact, Archimedes Principle can be derived, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. Assuming the balloon is at sea level, standard atmospheric conditions, calculate the maximum
weight that can be lifted by the balloon.

Note: the molecular weight of air is 28.8 and that helium is 4. What if the helium is replaced by hydrogen, molecular weight of 1?

##### Solution Summary

The weight and thrust to weight ratios are calculated in the solution.

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Problem 1

If a 22450lb (total gross weight) airplane develops 8160lbf thrust from each
of its two engines and has a wing area of 312ft2 and wing-span of 53.5ft. And a
empty weight of 11770lbf. Determine the thrust to weight ratio and the wing loading
of this aircraft?

Solution:

The thrust to weight ratio can be computed by dividing the total thrust provided by both engines to the gross weight of the airplane:
T = 2*8160 = 16320 lbf (total thrust)
G = 22450 lb (total gross weight)
--> T/G = 16320/22450 = 0.727 (it is a dimensionless feature)

The wing loading will be computed in the same way, by dividing the total gross weight of the airplane to the wing area:
S = 312 ft2 (total wing area)
--> G/S = 22450/312 = 71.96 lb/ft2

Problem 2

Consider an ordinary, helium-filled party balloon with a ...