Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
右上がりの坂を右へ動かす例です。重力の一部が進行を妨げます。
θは坂と水平面の角度です。質量m、摩擦μ、加速度aと進行方向をそろえます。
移動する質量 m
100 kg
進行方向の勾配 θ（下りは負）
5 °
動摩擦係数 μk
0.1
静摩擦係数 μs（始動用）
0.15
進行方向の加速度 a（減速は負）
0.2 m/s²
進行速度 v
0.5 m/s
駆動系の効率 η
80 %
駆動輪・ドラムの半径 r
50 mm
橙のFは坂に沿う駆動力です。下りなどで負になれば、その方向の走行に制動が必要です。
走行中の必要駆動力 F（負は制動）
203.164 N
正方向へ動き始めるための力（加速分なし）
232.011 N
正方向駆動の必要入力動力
126.977 W
The load moves right up a slope. Part of gravity opposes travel.
θ is measured from horizontal. Match mass m, friction μ, acceleration a and travel direction.
Moving mass m
100 kg
Route slope θ (negative downhill)
5 °
Kinetic friction coefficient μk
0.1
Static friction coefficient μs (breakaway)
0.15
Acceleration a (negative when decelerating)
0.2 m/s²
Forward speed v
0.5 m/s
Drive efficiency η
80 %
Drive wheel / drum radius r
50 mm
Orange F is drive force along the slope. A negative value, such as on a descent, indicates braking is needed.
Required running drive force F (negative: brake)
203.164 N
Positive breakaway force (excluding acceleration)
232.011 N
Required positive-drive input power
126.977 W
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
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2. Example inputs
Moving mass mWhat goes here?
This is mass, including fixtures or loads that move with it where required. Kilograms describe mass; newtons describe force.
100 kg
Route slope θ (negative downhill)What goes here?
Match the field symbol to the diagram and check dimensions, specifications or operating conditions. Replace example numbers with your actual conditions.
5 °
Kinetic friction coefficient μkWhat goes here?
A dimensionless ratio of friction to normal force. With μ=0.1 and a 100 N normal load, the model gives 10 N friction.
Static friction concerns breakaway; kinetic friction concerns sliding. Match lubrication, surfaces, speed, temperature and seal resistance. Comparison values are not material standards. Use product data or measured resistance divided by normal force. Do not transfer rolling-guide values to sliding contacts.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
A dimensionless ratio of friction to normal force. With μ=0.1 and a 100 N normal load, the model gives 10 N friction.
Static friction concerns breakaway; kinetic friction concerns sliding. Match lubrication, surfaces, speed, temperature and seal resistance. Comparison values are not material standards. Use product data or measured resistance divided by normal force. Do not transfer rolling-guide values to sliding contacts.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
0.15
Acceleration a (negative when decelerating)What goes here?
Change in velocity per time. Check signs for acceleration along travel versus deceleration.
0.2 m/s²
Forward speed vWhat goes here?
Distance travelled per time. Check whether the field asks for initial, final or constant speed.
0.5 m/s
Drive efficiency ηWhat goes here?
The fraction of input delivered as useful output. η=80% means 0.8 with 20% loss. Check whether the input unit is percent or fraction.
There is no universal recommended efficiency. Use curves or measurements at the actual load, speed and temperature. For a combined train, use consistent input/output boundaries and ηtotal=η1×η2…; do not count losses twice.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
80 %
Drive wheel / drum radius rWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
50 mm
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Required running drive force F (negative: brake)
203.164 N
Positive breakaway force (excluding acceleration)
232.011 N
Required positive-drive input power
126.977 W
Check degrees versus percent grade: 5° differs from 5%. Negative running force means braking is required during positive-direction travel.
4. Which formula is used?
N = mg cosθ, F = ma + mg sinθ + μk N, Fstart = max(0, mg sinθ + μs N), Pdrive = Fv/η (F≥0), Pbrake = −Fv (F<0), Twheel = Fr
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
Straight positive-direction travel with drive force parallel to the surface. Switch between degrees, radians and grade percent (5% is not 5°). Enter coefficients for the actual contact; this model requires μs≥μk. Breakaway is the static-friction threshold without acceleration; running force uses kinetic friction. Negative drive force requires braking during forward travel. Regeneration efficiency, wheel rolling resistance, drag, rotational inertia and gearing are excluded. Torque is at the drive wheel, not the motor shaft.
