svetz
Works in theory! Practice? That's something else
Wind power, in general, is awful... details: see: www.solacity.com/small-wind-turbine-truth/
Basically, the problem is most areas have low wind average speeds near ground level. The power formula for the maximum theoretical power from wind using a turbine blade is: P = π/2 r² v³ * ρ; usual efficiency is around 40% of the max. Where P is power, r the radius, v the wind speed, and ρ the air density. The two biggest factors are the wind speed (a cube) and the radius (a square). So for sea level:
So, as you can see, those gentle 3 mph breezes most people have on average don't generate any power. Most wind turbines don't even show power until you're over 8 mph. It's the cube that kills you at low speeds, and does wonders at high speed.
Magnus Effect
But there is another force that can make use of low wind speeds (or slow tidal currents); that's the Magnus effect. Basically a rotating body in a stream creates a force. It's how golf balls get lift and follows F/L = ρv 2πr²ω, where r is the radius of the cylinder and ω is the cylinder rotational speed. Everything here is linear except the radius (which is independent of wind speed).
It's been used in a variety of ways over the years, here's an example a "Flettner ship", basically those cylinders rotate and create thrust as the breeze flows across the ship.
So, if the cylinders had a 1.5' radius, then for 1m cylinder length at sea level the power is:
So, four cylinders rotating 1 per second in a 3 mph breeze should have a maximum of 588 W. Or, assuming the same 40% efficiency, ~5 kWhr per day (assuming a constant 3 mph breeze). Think of this as a conventional wind turbine with the blades replaced with 4 spinning cylinders and re-geared so the whole assembly spins slowly.
Conventional bladed air turbines with their cube to the wind speed win hands down in fast winds. But most places don't have fast winds 24 hrs a day and conventional wind turbines have problems in high winds (but with the Magnus effect you can just slow the cylinder RPM to decrease the force. Or, you could adjust the RPM to get the power output you want, great for handling peak loads).
Conventional wind turbine blades require high precision and strength; if they get dirty they're less efficient. A cylinder for the Magnus effect is relatively cheap, and the rougher the better; They should be a lot cheaper to produce; but they do have more moving parts.
It's been tried a few times, but even though the theory is valid I haven't heard of a successful device. Hopefully someone will crack this one day. The US Navy did a report on it here: apps.dtic.mil/dtic/tr/fulltext/u2/a165902.pdf.
See also: https://diysolarforum.com/threads/tidal-power-the-magnus-effect.27/
Basically, the problem is most areas have low wind average speeds near ground level. The power formula for the maximum theoretical power from wind using a turbine blade is: P = π/2 r² v³ * ρ; usual efficiency is around 40% of the max. Where P is power, r the radius, v the wind speed, and ρ the air density. The two biggest factors are the wind speed (a cube) and the radius (a square). So for sea level:
wind, mph | wind m/s | power, W, radius of 1m |
1 | 0.44704 | 0.2 |
2 | 0.89408 | 1.4 |
3 | 1.34112 | 4.6 |
5 | 2.2352 | 21.5 |
10 | 4.4704 | 171.9 |
25 | 11.176 | 2,686.0 |
So, as you can see, those gentle 3 mph breezes most people have on average don't generate any power. Most wind turbines don't even show power until you're over 8 mph. It's the cube that kills you at low speeds, and does wonders at high speed.
Magnus Effect
But there is another force that can make use of low wind speeds (or slow tidal currents); that's the Magnus effect. Basically a rotating body in a stream creates a force. It's how golf balls get lift and follows F/L = ρv 2πr²ω, where r is the radius of the cylinder and ω is the cylinder rotational speed. Everything here is linear except the radius (which is independent of wind speed).
It's been used in a variety of ways over the years, here's an example a "Flettner ship", basically those cylinders rotate and create thrust as the breeze flows across the ship.
So, if the cylinders had a 1.5' radius, then for 1m cylinder length at sea level the power is:
Code:
power W, cylinder revolutions per second
wind, mph wind m/s 1 2 3 4 5 6 7 8
1 0.44704 49 98 147 197 246 295 344 393
2 0.89408 98 197 295 393 491 590 688 786
3 1.34112 147 295 442 590 737 884 1032 1179
5 2.2352 246 491 737 983 1228 1474 1719 1965
7 3.12928 344 688 1032 1376 1719 2063 2407 2751
10 4.4704 491 983 1474 1965 2456 2948 3439 3930
So, four cylinders rotating 1 per second in a 3 mph breeze should have a maximum of 588 W. Or, assuming the same 40% efficiency, ~5 kWhr per day (assuming a constant 3 mph breeze). Think of this as a conventional wind turbine with the blades replaced with 4 spinning cylinders and re-geared so the whole assembly spins slowly.
Conventional bladed air turbines with their cube to the wind speed win hands down in fast winds. But most places don't have fast winds 24 hrs a day and conventional wind turbines have problems in high winds (but with the Magnus effect you can just slow the cylinder RPM to decrease the force. Or, you could adjust the RPM to get the power output you want, great for handling peak loads).
Conventional wind turbine blades require high precision and strength; if they get dirty they're less efficient. A cylinder for the Magnus effect is relatively cheap, and the rougher the better; They should be a lot cheaper to produce; but they do have more moving parts.
It's been tried a few times, but even though the theory is valid I haven't heard of a successful device. Hopefully someone will crack this one day. The US Navy did a report on it here: apps.dtic.mil/dtic/tr/fulltext/u2/a165902.pdf.
See also: https://diysolarforum.com/threads/tidal-power-the-magnus-effect.27/
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