In the design ofall-terrain vehicles, itis necessary to considerthe failure ofthe

Chapter 2, Problem 29

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In the design ofall-terrain vehicles, itis necessary to considerthe failure ofthe vehicle when attempting to negotiate two types of obstacles. One type offailure is called hang-upfailure 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 [Bekj, shows the components associated with the nosein failure of a vehicle. In that reference, it is shown that the maximum angle a that can be negotiated by a vehicle when f is the maximum angle at which hang-up failure does nut occur satisfies the equation A sin a cos a + B sin2 a C cosa sin a = 0, where A=lsinf\, B=lcosfi\, C= (h + 0.5D) sin O.SDlan f\, and = (/; + 0.5Z))cos/li 0.5D. a. Itis stated that when I = 89 in., h = 49 in., D = 55 in., and /l) = 11.5, angle a is approximately 33. Verify this result. b. Find a for the situation when /, h, and are the same as in part (a) but D = 30 in.