Question

Could I get some assistance on the following question please.

The undercarriage of an aircraft is comprised of TWO sprung wheel assemblies EACH with 4 springs. The springs are designed to (i) support the weight of the aircraft when stationary on the ground and (ii) absorb the vertical kinetic energy of the aircraft when it touches down.

The mass of the aircraft is 10000 kg. All springs have an identical spring constant of k = 100 kN/m. Ignore effects such as wheel friction and forward velocity.

(i) What is the expected compression (in m) of each spring caused by the weight of the aircraft when stationary on the ground?

(ii) Assume a worst case scenario that the aircraft touches down with a vertical velocity of 1 m/s. Assume the weight of the aircraft is still being supported by lift from the wings and can be ignored.

What is the expected compression (in m) of each spring caused only by the kinetic energy of the landing?

The answer for (i) is 0.1226m and (ii) is 0.1118 m

I first tried to find the kinetic energy KE = 1/2*m*V^2 where V = velocity (m/s) and then use this with the elastic energy EE = 1/2*k*x^2 where k = spring constant and x = compression of spring in (m) to find the spring compression however this did not give me the correct answer. I then tried to make KE = EE and I received an answer that was close which was 0.1238 m however this method must not be correct either.

I am really not sure where to go from here. Any assistance would be greatly appreciated.

Regards

Daniel

Answer 1

Case1

Total number of spring are 8(4in each wheel)

Force exerted by wright of plane is supported my all 8 springs

Spring force =8Kx=weight of plane(Mg)

8*10⁵x=10⁴_*9.81...

X=0.122625 m.......

Case1: total vertical kinetic energy is absorbed by all the 8 springs

In this case weight is supported by lift obtain by wings therefore weight will not compress the springs

Therefore change in kinetic energy = spring elastic energy

1/2MV² = 8(1/2KX²) (total 8 springs elastic energy)

10⁴*1²=8*10⁵*X²

X=0.11180m.........

answered by: anonymous