Ok, so the windmill concept is rather simple, and it has served mankind well long prior to electrical generation. Fine. Now, introduce electricity. Ever hand-cranked a generator to light one or two 60 watt bulbs in a science museum? You need some SERIOUS rpms to get those babies lit!
Yet, these modern windmills make lazy circles at (perhaps deceptively) low rpms. And, they generate MW of power? Not to mention overcoming the inertial mass of the wheel (I) [of a significant radius] to keep these puppies spinning? Makes me wonder if wind power is boasting some gross figure when I wager the net figure may not be all that we think it is. What’s the SD on wind power?
Extra Credit: Why do I often find one windmill by itself adjacent a cluster? I WAG this was a pilot windmill to see if the whole, full-blown proposed project was worthwhile? (Sometimes, the one by itself is smaller than its cluster of cousins.)
You don’t need RPM to light a bulb; you need power. Power is the product of rotational speed and torque. The windmill has a lower rotational speed than your hand crank, but that’s OK, since it has a heck of a lot more torque.
And you don’t need to overcome inertia to keep something moving. Inertia is what keeps things moving to begin with. You need to overcome inertia to get it started moving, but you get paid back for that in that the inertia also keeps it moving for a bit after the wind dies.
You do need to overcome friction, of course, but there are various ways to minimize that.
There’s plenty of energy in wind. Easily enough to generate a MW of power at a single turbine. The blades move slowly, but the generator is geared to spin much faster. See here for some of the economics: Wind power - Wikipedia
Just because the rotor is turning at a low angular velocity doesn’t mean that the generator is. A transmission system can be in-between to step up the rotation.
Of course, as Chronos notes, the rotation speed is not directly connected to power.
Science museum generators are often based on 2 or 4 pole DC motors intended for high speed service. By putting more poles, and more turns of wire you can make the voltage at lower speed.
Also, there are these things called gears that convert low speed, high torque motion to high speed with lower torque motion, and other things called transformers that can convert low-voltage/high current, to high-voltage, low-current. In small sizes they cost more power and dollars than they are worth, but on the big, really slow turbines gearheads and/or transformers will allow a much more economical, light weight, and efficient generator to be used.
While I understand the math, the practical application doesn’t work the way I would picture it. Somewhere, my mental model is wrong with anything with gears. Foremost, isn’t Torque (Tau) = Inertia (I) * rotational acceleration (alpha), analogous to F = ma? So, say a constant wind creates a constant omega (rads/s or rpms). Then, alpha = zero so torque = zero. Am I wrong so far? Maybe you can find where my mental image is corrupt.
But the wind does not make a constant omega, it makes a constant tau (that is, if it is constant wind). The generator pushes back with a compensating torque as it bleeds off rotational energy to create electricity.
The RPMs are low, but the blade tips are moving at high speed. Take the E-126, for instance. Diameter of 127 m, so a circumference of 399 m. Peak RPM is 11.7, which comes out to a tip speed of 77.8 m/s, or 174 mph. As others have said, there’s a ton of torque.
Hmm, I can only picture that a constant wind (at v = k) perhaps parlays into the source of constant tau you suggest above from the “velocity pressure” of the airstream? Also known as “impact pressure”, I suggest this pressure (applied over the area of the windmill blade tip) relates to a force (likewise, wind impact relates to impulse which equates to F * dt)…and that force, applied at the blade tip of a windmill * radius (r) (i.e., length of windmill blade) results in the tau of which you speak? Perhaps, that is how it all the pieces fall into place?
When the windmill is at speed, it has zero angular acceleration, and therefore zero net torque. The net there is important. It still has a torque from the wind, but it’s balanced out by an opposite torque produced by the magnets in the generator.
And while most manufactured generators are designed to be run at low torques and high angular speeds (thus requiring a gearbox between the windmill and the generator), this can be varied by the number of windings of wire. I’ve heard that they’ve started making generators with enough windings that they don’t need a gearbox, thus reducing the number of moving parts and hence the need for lubrication and other maintenance (good for offshore windfarms, which aren’t easily accessible).
I think your analysis confirms my suspicion there is more to the story. Yes, the blade tip is booking along at a constant linear speed (omega) at only 11.7 rpms (assumed sustained, for this argument) So, delta omega = 0, so alpha = 0, thus Tau = 0. So far, a kinematics analysis alone is not the answer. This little exercise fortifies my suspicion we have to consider momentum as well, the impulse (Fdt) of the wind velocity pressure converts to the source of torque (Tau = Ialpha). The torque (Tau) is held in check by the resistance from the generator (as transferred through the transmission of the windmill)…and frictional losses.
It’s been too long, so I have forgotten often such problems are solved by a simultaneous energy and momentum analysis…akin to solving a “ballistic pendulum” problem or the dynamics of a satellite changing orbits. An energy analysis alone won’t cut it. I bet therein lies the answer to the source of the torque from a constant wind.
The wind simply exerts a force on the rotor blade, and the rotor blade is at an angle to the wind so that a portion of that force is pushing it “sideways” (the rest of the force being canceled by rigid-body forces in the windmill). Since the sideways force is at a distance for the centre of rotation, there is a non-zero torque applied.
This torque would cause the rotor to have an angular acceleration if not for counter-torque provided by friction and the generator mechanism.
Well, I’m not really sure what kind of answer you’re looking for.
One way of looking at it is that you’re converting the kinetic energy of the air into electrical energy. It’s straightforward to calculate an absolute peak: for the E-126 in a 10 m/s wind, we get 1.2668e4 m^2 of swept area, 1.2668e5 m^3/s of air volume, 1.5521e5 kg/s mass flow rate, and 7.76 MW power (assuming we extracted all the kinetic energy from the air).
Already this is looking pretty close to the nameplate rating, but there is the additional factor of Betz’ law. Simply put, the law means you can never extract more than 59% of the kinetic energy from the air. So, at 10 m/s our E-126 is only making 4.59 MW at most, and in practice there are additional inefficiencies.
If we instead assume 7.5 MW to start with at 40% efficiency and work backwards, we get a required wind speed of 13.4 m/s. Still not unreasonable.
Jinx ol’ buddy, you’re not decomposing the problem correctly.
As Chronos said the net torque of the whole system is zero. Not the torque, the *net *tourque.
As explained just above, the windmill blades are generating megawatts of power & vast amounts of torque on the shaft where the blade hub connects. That torque is sent down the length of the shaft to where the generator rotor is. (and maybe through some gears along the way but let’s ignore that for now).
A generator connected to a load provides a massive resistance to being turned. In other words a torque in the direction opposite of rotation.
So …
Yes, when the whole system is at a steady state RPM there is no net torque on the system. But that’s because the blade hub is exerting umpteen million ft-lbs of torque on the shaft in one direction, whereas the generator is exerting the same umpteen million ft-lbs of torque in the opposite direction. So the shaft’s RPM is constant, but it’s under considerable torsional stress the whole time. (And therefore exhibits some minor but non-zero torsional strain the whole time too).
There is NOTHING different about this analysis for a windmill versus a steam turbine in a coal, natgas, or nuclear plant, nor a water turbine in a hydropower dam.
In all cases the generator and the turbine are in equilibrium in torque, with the working fluid injecting power into the turbine and the generator injecting power into the power output wires. And the shaft is subject to massive opposing torsional forces which are managed by its strength.
During spin-up or spin-down the net torque is higher or lower respectively at the input end of the shaft. But once we’re at operating RPM the earlier explanation is correct.
If the shaft severs under load, the blade hub will immediately accelerate to destructive speeds (ignoring any control ssystem intervention). That’s the proof the blades are delivering nno-zero torque to the shaft.
This. If the generator stops providing the countertorque that holds the RPM’s down…and the parking brake fails…the turbine blades can spin so goddam fast that the whole thing destroys itself. In this video the turbine is spinning so fast that the frame rate of the camera can’t really depict rotation; as soon as the whole thing comes unglued you can get a sense of the massive scale from how long it takes things to fall to the ground.
Bottom line: the video shows that when the blades are spinning slowly, the wind is still applying a lot of torque to them. The only reason the turbine doesn’t accelerate to Ludicrous Speed is because of the countertorque from the generator.
Yes, you’re right, with your powers of observation and deduction, you’ve seen through the ruse: it’s all a scam. When the Big Four shut off wind wheels because they generate too much power and the net is already full (and they don’t want to shut off nuclear power plants for political reasons)? Must be imagination. All those hours of power produced by wind wheels, measured not only by the group owning them, but by the energy provider they’re selling it, all those Euros earned by the group members when the energy provider converts hours fed into the net to cash? All not true. Good for you to pointing this out.
Well, there are several possible reasons depending on the individual circumstances, so the easiest way would be to ask the group that owns/ built them. Oh but way, you don’t trust what they say.
Well, in that case, a cluster of wind wheels can get very lonely on long nights, so they cuddle close together and when they love each other enough, a smaller wind wheel is born …