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Old Apr 2nd 2014, 10:23 PM   #1
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energy from falling object.

Hi guys,

Lets assume we have a wind turbine (used to generate electricity) which has a rope and a 1000kg ball attached to one of its propellers in the 9'oclock position. The propellers are 100m above the ground. If this ball is dropped to the ground, in effect spinning the turbine, how many kw of power would be generated from this event.

I have done the following calculations,given that it will take 2.25s to hit the ground and withstanding any resistant forces:

- velocity: v = √2gh = √2x9.8x100 = 44.27
- Kinetic energy: KE = 1/2mv² = 1/2 x 1000 x 44.27² = 980000J
- Power (w): P = E/t = w = J/s w = 980000 / 2.25 = 435555.5w (435.5KW)

My confusion is whether the energy is of that on impact, or of that generated during the fall.

Thanks.
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Old Apr 3rd 2014, 04:32 AM   #2
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Your calculation of the ball's kinetic energy is correct, though could have been simplified using:

Change in potential energy = mgh = gain in KE

This is the gain in KE attained by falling 100 meters. Power is a measure of change in energy per unit time. The trick is: what value of time to use? You've used 2.25 seconds, which assumes that all the energy of the ball falling goes into the turbine at a steady rate. The implication is that the ball falls at a steady speed, not gaining any KE as it falls, since all of its energy is going into the turbine. So - how did you calculate 2.25 seconds? It would actually take longer than that, so the power produced during that fall is less than what you've calculated.

On the other hand if the ball is allowed to free fall, then all that energy is expended in the split second of impact with the ground. The power generated at impact is significantly greater, but lasts for a much shorter time.
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Old Apr 3rd 2014, 05:12 AM   #3
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Thanks ChipB.

Yes i think i have made an error. The 2.25 seconds is the time it takes for an object weighing 1000kg to hit the ground as gravity attracts it to the earth, withstanding friction / drag etc.

How could i calculate the energy generated in such a scenario?

I will try and simplify it. A wind turbine is stagnant. A 100kg object tied to a rope is tied to one propeller which is in the 9oclock position. The 100kg object falls 10m in turn spinning the turbine. How much energy would the object have generated. Or if possible how much energy has the spinning turbine produced. I assume the latter and possibly the former would be impossible to calculate given no torque measure can be provided.

So what would be the relevance of torque in the scenario? Moreover would greater torque in the turbine equal greater energy generated albeit the object falls at a slower speed?

Isn't this how the big wind turbines in Europe incorporate gear ratios to spin the big turbine slower whilst the generator spins faster to generate electricity?
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Old Apr 3rd 2014, 06:39 AM   #4
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The energy produced by a falling object is equal to mgh. A 100 Kg weight falling 10m can produce (100Kg)(9.8m/s^2)(10m) = 9,800 Joules of energy. The torque produced is irrelevant to this calculation. Alternatively if you know the moment arm (length) of the propeller you could use torque times angle traversed, where torque = mgR and angle traversed is h/R, where h is your 10 meters. Note the R terms cancel, so the answer for energy produced is the same.

Your next question is how much of that energy could be actually converted to electrical energy? I assume you're thinking about the inefficiences and losses in the generator itself. A generator is typically about 80% efficient, meaning about 20% of the input energy is lost through friction, resistance in the windings, etc.

As for gear reductions to change torque on the generator and spin at a higher or lower rate - in theory it's a wash with respect to power production. Given torque T and rotational speed w the power produced by the genertor is P=Tw. If you double T but cut w in half the power is the same. Consider how the gears on a bicycle work - in a lower gear w is reduced, and so if you pedal with the same amont of power the torque that the bicycle tire puts down on the road surface goes up, allowing you to climb that hill. However, a wind turbine must spin at a standard rate in order to synchronize its voltage wave form with the power grid - at 60Hz in the US and 50Hz in Europe and elsewhere. So I suspect that wind turbines deploy their gear trains to give that specific frequency of output when the blades are turning at a desirable speed. In fact the power grid essentially forces the turbine to spin at that precise rate - if the turbine tries to spin faster it puts energy into the grid, which causes a counter torque on the turbine, preventing it from speeding up. And if the wind is calm so that the turbine isn't spinning fast enough on its own it consumes energy from the grid to speed up. That's why all the wind turbines in a wind farm all turn at the same rate - the grid forces it.

Last edited by ChipB; Apr 4th 2014 at 05:54 AM.
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Old Apr 3rd 2014, 02:23 PM   #5
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Thanks ChipB.

Your explanation is awesome!
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Old Apr 4th 2014, 05:54 AM   #6
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Thanks mryeh - you are most welcome!
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