Flywheel Kinetic Energy and Speed Fluctuation
The rotational kinetic energy stored in a spinning flywheel and how much its speed swings under a pulsing load.
Example
You enter
- Flywheel weight (lb) 100
- Radius of gyration k (ft): disk r/1.414, rim ~r 1
- Speed (rpm) 1000
- Energy pulse per cycle (ft-lb, 0 to skip) 2000
You get
- Stored kinetic energy 17042 ft-lb
- Speed fluctuation 5.87 % swing
Details, formula, and sources
The number a millwright or machine builder uses to size a flywheel for a punch press, shear, or engine. KE = 1/2 I omega^2; in US units I = (weight/32.174) x k^2 (k = radius of gyration: disk r/sqrt(2), rim ~ r -- rim flywheels store far more per pound, so real ones put mass outside), and omega = rpm x pi/30. A 100 lb flywheel with a 1 ft radius of gyration at 1,000 rpm stores ~17,000 ft-lb. When the machine draws an energy pulse per stroke, the flywheel slows: the coefficient of fluctuation (fractional speed swing) = pulse / (I omega^2) = pulse / (2 KE), so a 2,000 ft-lb draw swings this flywheel ~5.9%. Machines target a Cs from ~0.002 (AC generators) to ~0.2 (punches/shears) and size the flywheel until the swing is small enough. A sizing aid; the actual inertia from the geometry, the load's energy profile, and the drive/prime mover govern.
I = (weight_lb / 32.174) x radius_of_gyration_ft^2; omega = rpm x pi/30; kinetic_energy_ftlb = 0.5 x I x omega^2; speed_fluctuation_pct = 100 x energy_fluctuation_ftlb / (I x omega^2) = 100 x pulse / (2 x KE).
Flywheel stored rotational kinetic energy and coefficient of fluctuation (machine-design first principles; Machinery's Handbook flywheel practice), by name; the actual moment of inertia from the flywheel geometry, the load's real energy profile, and the drive and prime mover govern the design.
The rotational-energy relation (one-half I omega squared) is public physics; the flywheel weight, radius of gyration, speed, and the load's energy pulse are the machine's values.
Estimate. AHJ and licensed professional govern.
Field names used by the API: weight_lb, radius_of_gyration_ft, rpm, energy_fluctuation_ftlb, kinetic_energy_ftlb, speed_fluctuation_pct
- Rotational KE KE = 1/2 I omega^2; I = (W/g) k^2 (g = 32.174 ft/s^2); k = radius of gyration (disk r/sqrt(2), rim ~ r); omega = rpm x pi/30machine-design first principles
- Coefficient of fluctuation Cs = energy pulse / (I omega^2) = pulse / (2 KE); target ~0.002 (AC generators) to ~0.2 (punches/shears)Machinery's Handbook flywheel practice