In the design of all-terrain vehicles, it is necessary to consider the failure of the vehicle when attempting to negotiate two types of obstacles. One type of failure is called hang-up failure and occurs when the vehicle attempts to cross an obstacle that causes the bottom of the vehicle to touch the ground. The other type of failure is called nose-in failure and occurs when the vehicle descends into a ditch and its nose touches the ground.
The accompanying figure, adapted from [Bek], shows the components associated with the nosein failure of a vehicle. In that reference it is shown that the maximum angle α that can be negotiated by a vehicle when β is the maximum angle at which hang-up failure does not occur satisfies the equation
A sin α cos α + B sin2 α ˆ’ C cos α ˆ’ E sin α = 0,
Where
A = l sin β1, B = l cos β1, C = (h + 0.5D) sin β1 ˆ’ 0.5Dtan β1,
And E = (h + 0.5D) cos β1 ˆ’ 0.5D.
a. It is stated that when l = 89 in., h = 49 in., D = 55 in., and β1 = 11.5—¦, angle α is approximately 33—¦. Verify this result.
b. Find α for the situation when l, h, and β1 are the same as in part (a) but D = 30 in.

Transcribed Image Text:

D/2 βι