Examples
Examples
Try the starting example
- Thin rim/tyre ring mass (kg)
- 1
- Ring and rolling radius (m)
- 0.3
- Solid hub-cylinder mass (kg)
- 0.2
- Hub radius (m)
- 0.03
- Total uniformly radial spoke mass (kg)
- 0.3
- Ground speed (m/s)
- 10
- Ideal rotational inertia (kg m²)
- 0.10008
- Equivalent translational mass I/r² (kg)
- 1.112
- Rotational kinetic energy (J)
- 55.6
- Total entered wheel mass (kg)
- 1.5
Try another scenario
- Thin rim/tyre ring mass (kg)
- 1
- Ring and rolling radius (m)
- 0.3
- Solid hub-cylinder mass (kg)
- 0
- Hub radius (m)
- 0.03
- Total uniformly radial spoke mass (kg)
- 0.3
- Ground speed (m/s)
- 10
- Ideal rotational inertia (kg m²)
- 0.09999
- Equivalent translational mass I/r² (kg)
- 1.111
- Rotational kinetic energy (J)
- 55.55
- Total entered wheel mass (kg)
- 1.3
Calculation method
Calculation method
Ideal rotational inertia (kg m²)
Ring mr² + solid hub mrh²/2 + radial spokes ms×(r²+r rh+rh²)/3.
Equivalent translational mass I/r² (kg)
Divide inertia by rolling radius squared.
Rotational kinetic energy (J)
0.5×I×(ground speed/radius)² under rolling without slip.
Total entered wheel mass (kg)
Sum entered ring, hub and spoke masses.
Symbols and units
- a
- Thin rim/tyre ring mass (kg)
- b
- Ring and rolling radius (m)
- c
- Solid hub-cylinder mass (kg)
- d
- Hub radius (m)
- e
- Total uniformly radial spoke mass (kg)
- f
- Ground speed (m/s)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- An idealised mass-distribution comparison: a thin ring, solid hub cylinder and uniformly distributed radial spoke mass. Real spoke angles, tyre deformation, bearings and aerodynamic losses are excluded.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: Euclidean geometry and trigonometric identities ↗
Background reading; this does not imply endorsement or independent review of SumFizz.