BIZOMAT MAKEOS · Mechanics
Inclined Plane and Friction
What force pushes, holds or lowers a load on this slope?
Force parallel to an incline needed to raise, hold and lower a load with sliding friction, with efficiency and a self-locking check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load mass | kg | Mass of the load including any carrier or pallet. |
| Incline angle | ° | Slope of the plane from horizontal. |
| Coefficient of sliding friction | Sliding (kinetic) friction coefficient for the two surfaces, measured or from a supplier; use static friction for break-away. |
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: Load mass
- What it is
- The mass of everything that slides on the slope: the load plus any pallet, carrier or sled. The tool turns it into a weight using standard gravity.
- 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 200 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every force result rises in proportion to the mass.
- Get it right
- Enter mass in kg, not a weight in newtons.
What this means: Incline angle
- What it is
- The slope of the plane, measured from horizontal: 0° is level and larger angles are steeper.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 89.9°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from horizontal, not from vertical. A slope given as a percentage or ratio must be converted to degrees first.
What this means: Coefficient of sliding friction
- What it is
- The coefficient of friction between the load and the surface it slides on: friction force divided by the force pressing the surfaces together.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction raises the force to push up and decides whether the load holds by itself on the slope.
- Get it right
- Use the sliding (kinetic) value for steady movement and the static value for the force to start it moving; both come from tests or supplier data.
Method and formulas
- Weight W = m g with g = 9.80665 m/s².
- Raise: F = W(sin θ + μ cos θ). Hold: F = W(sin θ − μ cos θ). Lower: F = W(μ cos θ − sin θ).
- Self-locking when μ ≥ tan θ. Efficiency raising = sin θ ÷ (sin θ + μ cos θ).
- Example: 200 kg on a 15° slope with μ = 0.3 needs 1,076 N to push it up.
Limitations
- Force parallel to the plane; rolling resistance and acceleration forces are not included.
- Friction coefficients vary widely with surface condition and lubrication.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a pusher, winch or cylinder for a ramp
- Check whether a load slides on a chute
- Estimate efficiency of a sliding lift
Who it is for
- Design engineers
- Maintenance engineers
- Technicians
What you get
- Force to push up the slope
- Force to hold the load
- Force to pull it down
- Efficiency raising
- Self-locking or not
Interpreting the result
- Use the break-away (static) coefficient to size a drive that must start the load.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 165–171. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Worked example · BIZOMAT original book
Internal and wall friction: what a shear test tells you
In Bulk Solids Flow by the Numbers
What it covers: Yield loci, effective angle of internal friction, unconfined yield strength and the flow function from a shear test, wall friction and the tilt test, and why the wall coupon must match the wall.
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