Calculation
FSt = m·g·sin α
Climbing resistance is the component of vehicle weight along the inclined road and is independent of speed.
Dubbel Kraftfahrzeugtechnik Q 2.1.4: Fst = m·g·sin α, Pst = Fst·v
Vehicle climbing resistance force
Climbing resistance is the component of vehicle weight along the inclined road and is independent of speed.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Climbing resistance force FSt — Additional driving force required solely to overcome the grade.
- Vehicle mass m — Total vehicle mass including payload.
- Gravitational acceleration g — Local gravitational acceleration, about 9.81 m/s² near sea level.
- Grade angle α — Road inclination angle from horizontal.
Example
m=1,500 kg, g=9.81 m/s² and α=10° give FSt≈2,554.6 N.
Assumptions and limits
Constant grade and steady travel; acceleration, rolling resistance, drag and braking on descent must be balanced separately.
Understand Vehicle climbing resistance force
This calculator determines climbing resistance, the third classic driving resistance alongside drag and rolling resistance, from vehicle mass and grade angle.
What does this quantity describe?
On an inclined road, weight force resolves into a component normal to the road and one along it; the latter is climbing resistance FSt=m·g·sin α.
Formula and variables
FSt = m·g·sin α
FSt = m·g·sin α
| Symbol / input | Meaning |
|---|---|
| Climbing resistance force FSt | Additional driving force required solely to overcome the grade. |
| Vehicle mass m | Total vehicle mass including payload. |
| Gravitational acceleration g | Local gravitational acceleration, about 9.81 m/s² near sea level. |
| Grade angle α | Road inclination angle from horizontal. |
Choose the inputs correctly
m is vehicle mass including payload, g gravitational acceleration and α the road's inclination angle.
How to use the calculator
Convert α from grade percentage (α=arctan(p/100)) or use the angle directly; take m as the full vehicle weight.
Worked example
m=1,500 kg, g=9.81 m/s² and α=10° give FSt≈2,554.6 N.
Understand the result and units
Unlike drag and rolling resistance, climbing resistance is speed-independent; on a descent it becomes negative and assists travel.
m is a mass, g an acceleration and α an angle. FSt is output as a force.
Typical applications
Estimating additional drive force and power needed uphill, e.g. for towing or electric-vehicle range planning.
Assumptions, limits and common mistakes
Steady travel at constant grade; acceleration, cornering and varying grade along the route are excluded.
Common mistake: Do not use grade percentage directly as the angle in degrees; at steeper grades the two values diverge noticeably.
Frequently asked questions
What is “Vehicle climbing resistance force” used for?
Estimating additional drive force and power needed uphill, e.g. for towing or electric-vehicle range planning.
Where do the input values come from?
m is vehicle mass including payload, g gravitational acceleration and α the road's inclination angle.
What does the result not cover?
Steady travel at constant grade; acceleration, cornering and varying grade along the route are excluded.