Using a stack of pancake rare earth magnet motors, to produce 100hp, how many watts hrs per kilogram would it take? If using Li-ion batteries at 5.0Ahr each, how many would it take? That is if each cell came in at 300Wkg.
There are loads of possible issues here, but these are some rules of thumb:
For doing early estimates, you can consider both permanent magnets motors and batteries to be 100% efficient. This is not actually true, with motors being about 90% efficient for very good ones, and batteries varying in efficiency depending on how quickly current is drawn from them. But to simply get a feel for how many batteries would be required for a certain hp motor, leaving out efficiencies (at first) can allow you to very quickly decide that a project is worth pursuing or not.
Also, my personal preference is to round things off to make it easy to do the calculations without a calculator, computer or pen and paper. So, 100 hp is about 75 kilowatts. Therefore, if you want to run this motor for one hour at 100 hp, you would need 75 KWh of batteries. In large scale production, Li Ion batteries can be estimated at about $200/kWh, (we think) so you could estimate a cost of $15,000 for batteries. (My eyes are tearing up, already.)
As you probably know, motors can run at many different voltages. For a given power output, lower voltage requires higher current (amperage). Higher current requires larger, heavier wires, so there is an advantage to using higher voltage. Let's say you decide to use 200 volts. If you selected 14 volt Li Ion batteries, then you would need about 14 of these to give you 200 volts. One such battery pack would be 1 kWh. (200 volts x 5 Ah) So you'd need about 75 of these packs, in parallel, to give you 75 kWh. So 75 x 14 would be about 1050 batteries.
Li Ion batteries are available in many voltages, so you can play around with the math to get the number of batteries required for your application -- but it all balances out in the end: you need more lower voltage batteries, fewer higher voltage ones, etc.
The constant is the cost ($200 per kWh) and energy density (150 Wh/kg), so from that, you can make quick estimates. Your pack would weigh about 500 kg (1100 lb) (which squares pretty well with the 900 lb weight of the Tesla's 56 kWh pack.)
The Tesla car has about 6000 Li Ion batteries in its battery pack, and individual cell monitoring so that if one fails, it is automatically bypassed. (Some might say, "What a nightmare.")
The $15,000 I mentioned is an estimate for large scale production. Not long ago, I was given a quote by a supplier of a highly-hyped (with very desirable properties, if they pan out) Li Ion batteries of $2/Wh. I'm hoping you are seated. That's $150,000 for a 75 kWh pack for a prototype.
But perhaps in your application, you don't need 100 hp for one hour. There are loads of small cars that can go slightly over 100mph on 100 hp, so you would have 100 mile range at that speed (and probably double that at 50 or 60 miles per hour). Again, as a rule of thumb, the Tesla gets about 200 miles per charge, if conservatively driven, on its 56kWh pack.
If you are building a small, lightish, motorcycle for drag racing, then you'd only need 100 hp for 15 seconds at a time. That would cut the size and cost of your battery pack dramatically. In that case power density (and your figure of 300 W/kg could be reasonable for Li solid polymer) becomes important. Then, you'd need 250 kg of batteries.
BTW: re a stack of motors: the last motor in the stack would transfer the torque of all the motors combined, so it's output shaft (key, splines, etc.) and attachments could easily be sheared off, it not designed for this application.
Sounds like an interesting project. Have fun.
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Wattage usage
Re: Wattage usage
