Windage, the drag of air on a spinning wheel, rises with the cube of the rim speed, so it dominates the losses of a fast flywheel on good bearings: a rough estimate puts it near 1.4 kW for a 1.2 m wheel with a 0.15 m wide rim at 94.2 m/s, against under 116 W for ball bearings. Cut the rim speed first, since halving it cuts drag by 8 times; thinning the air in a sealed housing cuts it in proportion to the pressure, but a vacuum housing then carries about 156 kN of atmospheric load on a 1.4 m lid.
Part of Flywheel Energy Storage
How much power the air takes from a spinning wheel, and the options for reducing it: lower speed, smoother surfaces, thinner air.
The Estimate, With Its Weak Point Named
Treat the rim as a cylinder dragging air at its surface speed v. The drag power is the skin-friction force times the speed:
P = C_f × ½ × ρ_air × v² × A × v
Inputs: air density 1.2 kg/m³ (a handbook value for room temperature, not from the corpus); rim surface area A = π × 1.2 m × 0.15 m = 0.565 m² (the rim of the wheel in Rim-Weighted Design); skin-friction coefficient C_f = 0.005 (an assumed order-of-magnitude value for turbulent flow on a rough surface, not from the corpus and uncertain by a factor of two or three).
- At v = 94.2 m/s: ½ × 1.2 × 94.2² = 5,324 Pa; × 0.005 = 26.6 Pa; × 0.565 m² = 15.0 N; × 94.2 m/s = 1,418 W.
- At v = 74 m/s: 0.73 kW (the ratio (74 ÷ 94.2)³ = 0.485).
- At v = 47.1 m/s (half): 177 W (one eighth).
The two side faces of the wheel, any bolt heads, spoke edges and keyways add to this. The number is an estimate for ranking the remedies, not a measurement. Measure your own wheel’s loss with a coast-down in a calm pit and compare it with the bearing figures in Bearings & Friction.
What 1.4 kW Means
The wheel stores 2.2 MJ. A steady 1.4 kW would empty it in 2,221 ÷ 1.418 = 1,566 s, about 26 min. In practice the loss falls steeply as the wheel slows, because it follows speed cubed, so the wheel loses its speed quickly at first and slowly later. Compare it with the ball-bearing figure of 8 to 116 W: on a fast wheel the air takes more power than the best bearings. The reverse holds at low tip speed: a slow, heavy wheel with plain bearings is bearing-limited.
Remedies In Order Of Effect
- Lower the rim speed. Power goes as v³ but stored energy as v². Halving v cuts drag 8 times and energy 4 times; the wheel loses a smaller fraction of its energy per hour. The cheapest remedy is a bigger, slower wheel of the same mass, but that raises the rim area.
- Thin the air. Gas density is proportional to pressure at a fixed temperature, so at one tenth of an atmosphere the drag is about one tenth: 1,418 ÷ 10 = 142 W. This needs a sealed housing, a shaft seal that does not itself add large friction, and a pump (a hand pump will do only if the seal is good and the pump is run often).
- Smooth the surface. Fill the gaps between spokes with a solid web or covers, and remove protruding bolt heads, so the wheel does not churn the air like a fan. How much this saves cannot be sourced here.
- A close housing. An ordinary casing round a wheel in normal air changes the flow but this page cannot give a sourced drag figure for it; the housing’s firm value is containment, not drag reduction.
The Price Of A Vacuum
A housing at low pressure has atmospheric pressure pressing on every face. For a lid 1.4 m in diameter: area = π × 0.7² = 1.54 m², force = 101,325 Pa × 1.54 m² = 156 kN, the weight of about 16 tonnes. The lid and its seal must be built as a pressure part. Run the vacuum only after the structure has been checked, and fit a vacuum-break valve, because a sudden leak sends air in at high speed against a spinning wheel.
Other costs: heat from the bearings can no longer leave through air, so a hot bearing may overheat sooner; the shaft seal becomes the largest friction source; and a person standing on a lid over a vacuum pit has a structural-failure hazard below them.
Common Mistakes
- Chasing bearing friction before windage. On a fast wheel the air is the main loss.
- Believing “enclose it” alone cuts the drag. Air inside a casing is still air.
- Sizing a vacuum lid as a hatch cover. It is a pressure vessel in reverse.
Safety
A vacuum housing is a hazard of its own
The 156 kN load on a 1.4 m lid can collapse a light hatch or crush a person standing on it. A sudden loss of vacuum puts a gale across a spinning rim. Do not combine a vacuum housing with an untested wheel, and keep the containment function (see Housing) separate from the sealing function.
What’s Next
- Learn next: Motor-Generator Set — how the wheel is charged and drawn down
- Combine with: Speed vs Mass Trade-offs — why a slower wheel is the cheapest cure