KEVOS® MAKEOS · Mechanics
Ramp Traction Check (Axle Loads on a Slope, Tractive Force Needed, Grip, Tipping)
Can this vehicle, truck or AGV drive up the ramp loaded without its driven wheels slipping, and does the uphill axle keep enough load not to lift?
Traction check of a two-axle vehicle climbing a ramp: the load on each axle from the weight, its position between the axles, the height of the centre of gravity and the slope, the force to climb (as the inclined plane tool), to overcome rolling resistance (as the rolling resistance tool) and to accelerate, and the grip of the driven axle from the tyre friction, against the force needed and with a check that the uphill axle stays loaded.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Vehicle mass with load | kg | Mass of the vehicle with its load. |
| Ramp slope | ° | Slope of the ramp. |
| Wheelbase | mm | Distance between the axles. |
| Centre of gravity behind the front (uphill) axle | mm | Horizontal distance of the centre of gravity behind the uphill (front) axle. |
| Centre of gravity height | mm | Height of the centre of gravity above the ground. |
| Driven axle | choice | Which axle drives. |
| Tyre friction coefficient | Friction between tyres and the ramp surface (wet or dusty surfaces are much lower). | |
| Coefficient of rolling resistance | mm | Coefficient of rolling resistance (lever arm, mm). |
| Wheel radius | mm | Wheel radius. |
| Starting acceleration | m/s² | Acceleration when starting on the ramp. |
Method and formulas
- Rear axle load = W (cos θ × a + sin θ × h) ÷ wheelbase; front = W cos θ − rear.
- Climbing force = W sin θ (as the inclined plane tool, no sliding friction); rolling resistance = W cos θ × f ÷ r (as the rolling resistance tool); plus m a.
- Grip = μ × driven axle load; the front axle must stay loaded.
- Example: 3,475.2 N needed against 7,827.2 N of grip; the front axle keeps 8,727.9 N.
Limitations
- Rigid vehicle on a uniform slope; the transition at the ramp foot and crest is worse.
- Front uphill when climbing forwards; reversing up the ramp swaps the axles.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a forklift or AGV on a loading ramp
- Decide front or rear drive for a vehicle on slopes
- Find the steepest ramp a vehicle can climb
Who it is for
- Materials handling engineers
- Vehicle designers
- Safety advisers
What you get
- Axle loads on the slope
- Force needed to climb
- Grip available and decision
Interpreting the result
- Climbing shifts weight to the downhill axle, so rear drive grips better uphill and front drive worse.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 165–171. Topic reference; no source tables or recommended settings are reproduced.
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