A treadwheel can produce shaft rotation when a person, animal or other load acts with a horizontal offset from the axle. This calculator models only the gravity moment of an entered point-mass idealization.
Tread Mill Interactive Calculator
Enter point-mass value, wheel diameter and horizontal gravity-line offset from the axle. Outputs are a static gravity moment, an equivalent rim-tangential force and the offset/radius ratio—not power or usable machine output.
Equation Used
- Standard gravity g0=9.80665 m/s² converts entered mass to weight force.
- The mass is represented as a point load with the entered horizontal moment arm.
- Wheel radius is D/2 and the equivalent rim force is purely tangential.
- No gait, contact, motion, acceleration, inertia, friction, power, efficiency, fatigue or load transmission is modeled.
- Offset/radius above 100% flags an entered geometry outside the wheel radius; it is not a design utilization.
Gravity Moment About a Treadwheel Axle
For a downward weight force, the moment about the axle equals that force multiplied by the perpendicular horizontal distance from the axle to the force line of action. NASA describes torque or moment as force multiplied by perpendicular distance to the pivot.
A real treadwheel adds moving contact, stepping, wheel inertia, bearings, drive components and a load. None of those are represented by the static point-mass calculation.
What This Calculator Represents
The tool converts entered mass to standard weight force and multiplies by an entered horizontal offset. It then expresses the same moment as an equivalent tangential force at the entered wheel radius.
This equivalence is useful for understanding moment arms. It does not predict sustainable operator torque, shaft power, hoisting capacity or safe construction.
Static Moment and Rim-Force Equivalent
static gravity moment = mg0 d
equivalent rim force = mg0 d/(D/2)
offset/radius = 100d/(D/2)
g0 is 9.80665 m/s², m is kilograms, d and D are metres, moment is N·m and equivalent force is newtons.
Worked Static Example
For m=30 kg, D=1.0 m and d=0.17 m, weight force is about 294.2 N and static gravity moment is about 50.0 N·m. At the 0.5 m wheel radius, the equal-moment tangential force is about 100.0 N. The offset is 34% of radius.
Model Boundary
- Calculated: weight at standard gravity, one static moment, an equal-moment rim force and a geometry ratio.
- Not calculated: treadwheel motion, gait, available human or animal effort, torque ripple, starting, braking, inertia, bearing friction, drive ratio, rope drum, load, power, efficiency, structural strength, ergonomics or safety.
Frequently Asked Questions
Does the moment output predict continuous shaft torque?
No. It is a static point-mass moment at the entered offset.
What does equivalent rim force mean?
It is the tangential force at wheel radius that produces the same moment.
Why can offset/radius exceed 100%?
The controls are independent. A result above 100% means the entered offset lies beyond the entered radius and is not an internally consistent point location within the wheel.
Does wheel diameter change the gravity moment?
No. It changes the equivalent rim force and geometry ratio, while moment depends on mass and horizontal offset.
Is power calculated?
No; angular speed is not an input.
Can this tool size a treadwheel or hoist?
No.
References
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