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How far can a Model S travel on one AA battery?

My 12 yr old son asked me this question today.

How far can a Tesla Model S travel on one fresh AA battery?

I really have no idea how to answer this, so I tried a back-of-the-envelope calculation. The AA power output varies by brand, but a reasonable figure seems to be about 2.4 W/h (based on a 1.5V to 0.9V voltage drop and 2 amps/h over that time; it's roughly linear so we don't need calculus). An 85D gets (supposedly) 270 mi of range from a full 85 kW/h charge. So the 85D battery is the equivalent of about 35,417 AA batteries and the range per AA is about

(270*5280)/(35417) = 40.25 ft.

That's more than I would have expected, honestly. And the batteries used in a real Model S are better than the average AA alkaline cell you buy at the store.

Of course one AA could not move a Model S from a stop... the power needed to overcome the inertia is going to be more than a small battery could provide, but it could (theoretically) move an already-rolling Model S for 40 feet. Theoretically.

Ok, electric car experts... did I do it right? :)
The only thing that jumps out at me is that the full 85 kWh is not all usable. Estimates of usable kWh are between 75 and 81. So it could actually be more than 40 feet because you'd be using 100% of the AA battery.
Good question. It may help you check your answer to know that my 85D gets 323 Wh/mi on average. It can get as low as 300 wH/mi in right conditions (right temperature, medium traffic on a commute, etc.). If you're trying to exaggerate the results, use the Wh/mi averages for an S60 instead ... I think they can regularly get into the 270s.

- K
Keep in mind you'll have to discharge that AA at something like 0.1W to get that 3Wh of capacity. :p

Edit: Some real data. Apparently I was pretty optimistic with my discharge rate.


At a 25mA discharge (1/100C !) it says it will get 2.5Ah, which would be 3.75Wh. Unfortunately, 1/100C is ridiculously slow discharge. That would be just over 1 horsepower for an 85 kWh pack of AA's (almost 23,000 AA's). lol.
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It won't go anywhere. A single cell doesn't provide enough voltage or current to turn the motor to overcome friction.

Here's a question to get your son thinking: If you connected your 85KWh pack to a flashlight (assuming you have a 400V bulb in your flashlight :smile: ), how long would it stay lit?
I think this would actually be a fun science project: Get an EV to move using a few AA's.

Basically would need a decent boost converter with some super capacitors. Drain the AA's into the caps while bumping the voltage with the boost converter. Then hook the contraption up to like a Leaf or something and get it to move.

A 24-pack of AA's and the aforementioned device should get a Leaf to go about 1/4 mile. :p

Could potentially drive an inverter and charge a Model S from a bunch of AA's in a similar fashion.
I'm sure this is both inappropriate and impossible, but I want to use my model S to shift all my home electrical usage to "off-peak". Basically making the car a powerwall.

Feel free to insult my lack of knowledge at your convenience.

Tesla probably doesn't/won't allow that because you could just make daily trips to a SC and then unload at night. Free power indefinitely. Or until you get a nastygram.
I'm sure this is both inappropriate and impossible, but I want to use my model S to shift all my home electrical usage to "off-peak". Basically making the car a powerwall.

Feel free to insult my lack of knowledge at your convenience.

Neat idea. At TMC 2015, Tesla staff confirmed during a panel talk that this is not possible because there is no hardware in the car that allows for the serving of power from the battery to any other source than the car itself.

Separately, there is also analysis out there right now that taking into account the battery pack degradation/life expectancy loss and performance lossfrom cycles, you would need electricity to be at $0.24/kWh or above to be worth the wear and tear on your battery. This was done using PowerWall pricing, not Tesla car battery pricing, which is unknown.

I am sure you can Google these forums faster than I can find the source for this analysis. :) It was quite detailed.

- K
This particular son has a bright future I say.
As has been mentioned, there is only about 77kWh usable and power of a sngle AA cell is insuficient to do anything in practice so one can choose the best discharge rate for maximum energy output for this fun gedankexperiment.

For lolz one coud take some tens of thousands of AA cells and wire them up in say 250 series strings, and mount them on a three axle trailer :)
What such experiments demonstrate is the absurdity of "driving without AC, radio and lights to improve range in an EV".
People comprehend what one gallon of fuel means, but they have no clue what one kWh would be. They understand that lights, AC radio run on electricity so it must help to turn them off. Yes, you get 50m more range ...
Driving a bit slower does not occur to anyone as a prudent solution in dire circumstances.
I really have no idea how to answer this

First, buy two 18650 cells from amazon here. These are slightly bigger than AA cells. The Model S 85 kWh has 7104 of these cells. Then when the cells arrive, show your son the pictures in wk057's topic and tell him he is very clever because he correctly guessed how the car works. Then give him one of the 18650 cells as a gift so he can show it to his friends. Then explain that the car can go 400 km with 7104 cells and let him calculate how many metres it would go on one cell.