Question

Find the angle of inclination with respect to the vertical of a two wheeler negotiating a turn. Given combine of mass of the vehicle with rider is 250kg. Moment of inertia of engine flywheel 0.3kg/m2. MR of each wheel is 5 times that of the road wheels and in the same direction with that of centre of gravity of the rider with vehicle is 0.6m, vehicle speed 90km/h and wheel radius is 0.3m and radius of turn 50m. [15]

Answer 1

Determine the gyroscopic couple:

$$C_g=\frac{v^2}{Rr}(2I_W+GI_e)\cos\theta=145.8\cos\theta.$$

The centrifugal couple:

$$C_c=\frac{mv^2}{R}·h\cos\theta=1875\cos\theta.$$

Obtain the total overturning couple is

$$C_O=C_1 +C_2=2020.8\cos\theta.$$

Find the balancing couple:

$$C_B=mgh\sin\theta=1471.5\sin\theta.$$

Remember the condition of equilibrium? Me too:

$$C_0=C_B,\\\space\\ \tan\theta=\frac{2020.8}{1471.5},\\\space\\ \theta=53.94°.$$