Here we will look at a problem centred around the angular momentum of a airplane wheel during retraction of the landing gear.
You will need a compliant scientific calculator for your exams. I have listed a few here if you need one. I used An Engineering Data Book to help me solve this problem.
The image shows an airplane landing gear assembly. Shortly after take-off, each landing gear is retracted into the wing by rotation about the axis A-A. Throughout it is assumed that the wheel continues to spin at constant rate as it is being retracted.
1.The wheel has a radius of 0.5 m and a take-off speed of 55 m/s. Compute the wheel angular speed, Ω, at take-off.
From the equation: v = aΩ , we can rearrange to Ω =v/a. Plugging in the numbers from the question gives: Ω = 55/0.5 = 110 rad/sec
2. If the wheel has a mass of 40 kg and its radius of gyration about axis C-C is 0.37 m. Compute the airplane wheel angular momentum about its centre of mass.
Icc = m(Kcc)2 = 40 x (0.37)2 = 5.476 kg.m2
L = IccΩ = (5.476)x(110) = 602.36 kg.m/s
3. If the angular speed of retraction ω is 2 rad/s, compute the kinetic energy of the wheel during retraction.
Ke =0.5mv2 + 0.5IccΩ2 = (0.5 x 40 x ((4.5 – 0.5) x 2))+(0.5 x 5.476 x(1102)) = 33.29 KJ
4. If the angular speed of retraction ω is 2 rad/s, compute the torque in the structure A-B due to the gyroscopic effect of the spinning wheel.
Torque N is equal to the rate of change of angular momentum N = L.= ω x L = ω x Icc x Ω = 2 x 5.476 x 110 = 1204 Nm.
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During my revision I found it extremely helpful to have an Engineering Data Book. The one I used, and still use now, is found here.
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