BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Vehicle mass with load
- What it is
- The total mass of the vehicle with its driver and load as it climbs the ramp.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2500 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All forces scale in direct proportion.
- Get it right
- Include the heaviest load and any attachment.
What this means: Ramp slope
- What it is
- The angle of the ramp surface from horizontal.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A steeper slope raises the uphill pull needed and moves load onto the rear axle.
- Get it right
- Enter degrees, not percent grade: a grade in percent is 100 × tan of the angle.
What this means: Wheelbase
- What it is
- The distance between the front and rear axle centres.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the vehicle data sheet.
What this means: Centre of gravity behind the front (uphill) axle
- What it is
- The horizontal distance from the front (uphill) axle back to the centre of gravity of the loaded vehicle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 900 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must lie between the axles; it can be found by weighing each axle on level ground.
What this means: Centre of gravity height
- What it is
- The height of the loaded vehicle’s centre of gravity above the ground.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher centre of gravity moves more load to the rear axle on the slope.
- Get it right
- A raised load moves it up; use the height with the load as carried on the ramp.
What this means: Driven axle
- What it is
- Which axle’s wheels are driven and so can provide grip for climbing.
- Units and format
- Choose one of 3 options from the list: Rear (downhill) axle; Front (uphill) axle; Both axles.
- Example
- The form opens with “Rear (downhill) axle” selected as a worked example. Choose the option that matches your case.
- Get it right
- Rear drive gains grip on a slope as load shifts back; front drive loses it.
What this means: Tyre friction coefficient
- What it is
- The friction coefficient between the driven tyres and the ramp surface, which limits how much pull the wheels can give.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Available grip rises in direct proportion.
- Get it right
- Use the value for the worst surface condition, such as wet, oily or dusty, from tyre or surface data.
What this means: Coefficient of rolling resistance
- What it is
- The rolling resistance coefficient expressed as a lever arm: how far ahead of the wheel centre the ground reaction acts as the tyre deforms.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rolling resistance rises in direct proportion.
- Get it right
- This is a length in millimetres, not the dimensionless rolling coefficient.
What this means: Wheel radius
- What it is
- The rolling radius of the wheels, from axle centre to the ground.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger wheel lowers rolling resistance.
- Get it right
- Radius, not diameter: halve the tyre diameter.
What this means: Starting acceleration
- What it is
- The acceleration you want when starting off up the ramp, which adds to the pull needed.
- Units and format
- Enter a number in m/s²: metres per second squared. The form accepts 0 m/s² to 5 m/s². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 m/s² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The extra pull needed rises in direct proportion.
- Get it right
- Enter m/s²; 0 checks a steady climb only.
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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