1. 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

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

3. 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

4. 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?

5. 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

6. 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

7. 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

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

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

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

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

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

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

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

15. Gradeability (Ford E150 plus ATV and trailer)