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Vehicle Axle Loads depend on Hitch loads Aerodynamic drag Inertia Force ( a x W/g) Slope/grade (θ ) Rolling resistance Vehicle geometry (towing/towed) L, c, b, h, h h, h b, h a

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Fundamental rule of vehicle dynamics Control forces act on the tires’ contact patches (i.e. accelerate, brake, turn)

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Find Axle Loads W r and W f θ c WfWf F xf R xf WrWr F xr R xr x z haha DADA W/g a x Wcos θ Wsin θ W h R hx R hz h L dhdh b A B

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Solving for Axle Load W f Taking moments about point B, we can similarly find W r What happens to axle loads for changes in: 1.Grade? 2.Hitchloads? 3.Acceleration? 4.Drag?

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Trailer (with boat/ATV/payload) FBD θ f x z h ab D Ab W b /g a x W b cos θ W b sin θ WbWb hbhb R xtr WtWt e R hxh R hz A

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Solving the system of eqn’s Let’s rearrange the equations… To obtain: Two steps: 1. Calculate R hx and R hz, then 2. Substitute R hx and R hz into axle load formulas for W r, W f Solve this eqn first

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Gradeability… ability to climb grades Ability to climb is a function of: Need friction between towing tires and surface Traction forces = f(μ, axle weights) Traction force ≥ downhill weight = W total sinө

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Forces in x-direction Assume no hitch and drag forces, constant velocity, then But remember maximum traction is limited by friction available at surface!

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Vehicle towing trailer uphill at constant velocity FWD RWD 4WD Let drag, rolling, & inertia forces = 0 Let’s do some examples…

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What grade can a vehicle climb? Friction limited Power limited Anything else? http://www.youtube.com/watch?v=OS5b_cuDVhs

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First, what is “slope and grade?” Slope: Angle θ Slope: Grade (%)

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Vehicle towing trailer uphill at constant velocity Will a 4WD, FWD or RWD have enough traction to climb grade?

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Which drive will be “grade-able?” (4WD, FWD or RWD) Recall…force to overcome…. 824 lbs. FWD and RWD will slip!

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Automate calculations with a spreadsheet…. Connect ot course website at: http://coen.boisestate.edu/reggert/ME485/ME485.htm Click on… GradeabilityS09 (*.xls)

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Gradeability (Ford E150 plus ATV and trailer)

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1 Zissimos P. Mourelatos, Associate Prof. Daniel N. Wehrwein, Graduate Student Mechanical Engineering Department Oakland University Modeling and Optimization.

1 Zissimos P. Mourelatos, Associate Prof. Daniel N. Wehrwein, Graduate Student Mechanical Engineering Department Oakland University Modeling and Optimization.

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