Energy Storage
in a rotating wheel

T   
here was a picture of a Hitachi hard drive in Wired Magazine this month with a submission form for a patent. The ad's point was that you could invent something to do with the ever smaller hard drives they are making ... yada, yada, yada.

Well, just how much energy can you store in a wheel? Why doesn't anyone patent an energy storage device with a wheel? They probably have, so my question is then ... why don't we see electrical storage devices using rotating wheels? What's the trouble?

Let's get some elementary math together

I want a replacement for the car's gas tank capable of storing the energy of, say, 10 gallons of gas.

energy released by one gram of 
gasoline = 5.o x 104 joules

one gallon of gas is 2620 grams

So, ten gallons of gasoline releases about

2620 x 10 x 5 x 104 = 1,310,000,000 joules

Now, I want to put all that energy in the rim of a rotating wheel, so I can use simply mv2 for the energy in a rotating wheel because I'm just going to do a ballpark calculation for the rim of the wheel. It's not totally accurate but 90% accuracy is good enough here.

The size of the wheel is critical here. About two feet in diameter is about as big as I'm willing to go. The wheel will have to rotate inside of a sphere so that the wheel can precess 360o every day with the earth's rotation. If not, the car might just flip over on its back every day ... not too good for control in traffic. So, whatever energy is put into the wheel must be extracted with electrical pickups and magnets, etc. ... that would seem do-able so we needn't get into that at this stage of inquiry.

Now, the mass of the wheel is important. More mass and we can have more energy stored per gram ... but ... more mass means more centrifugal force trying to tear the wheel apart. Therein lies the goal of this page. What kind of force is there that will bust this thing apart thereby making it not feasible?

Let's go with fifty kilograms or a little over one hundred pounds.


50 kg 
So that,
v2 = 1.31 x 109 joules 
       50 kilograms
then,

v = about 5000 meters per second  

Well, that's about five kilometer per second. Pretty fast. Let's see what kind of force that will yield on 1 of, say, 10 spokes about 1/4 meters long inside the wheel.

The centrifugal force will be


mv2/r
so that yields

50 kg x (5 x 103)m2  =  ~5 x 109 Newtons
       .25 m
Which in pounds is ... about a billion pounds. Now we can further cut that down to a tenth since we've postulated ten spokes ... so, it's about

one hundred million pounds per spoke.

... roughly equivalent to the weight of American Airlines entire fleet ... I think

Well, that's why we don't see energy contained in a rotating wheel for cars as a replacement for that gas tank. We don't have anything to hold that kind of force in a confined space to make it useful. There has been some talk about very large wheels to store electrical power for cities. One can imagine a much larger and heavier wheel with a lower speed being used as a temporary storage device. If the centrifugal force were held down to reasonable levels, that could be a help in smoothing out the supply-demand problems in the electrical supply. But it's a no go for automobiles as far as I can see ... for any foreseeable future.



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