Yes, Happy Star Wars Day! (May the 4th Be With You - get it?)
For this year's Star Wars Day, I am going to look at C-3P0. You know, the droid? Really, this started when I was wondering when we would all have robot servants to do the stuff that we don't want to do - like mow the lawn. When will that day come? Oh, sure, there are robot mowers now. That's not what I am talking about though. These lawnbots ONLY mow the lawn. I want C-3P0, a droid that understands Bocce and the binary language of moisture vaporators but ALSO can mow the lawn.
The problem we have today might be batteries for these androids. What kind of battery would they need? How big would they be? Could I just run my robot on a whole bunch of AA batteries? Oh, notice that I am using the terms: robot, android, droid all interchangeably. I am pretty sure in the international convention for artificial intelligence, these names mean different things. Sorry about that.
How Much Energy?
Of course I am going to have to make some guesses here. How much energy in one day would an android need? My first estimate is to compare the android to human. Really, isn't that essentially where the word android comes from? Then the question becomes: how much energy does a human use in one day? A good first approximation is 1000 calories a day. This is 1000 food calories. Oh, you didn't know there was a difference? There is.
When people talk about food, they normally use units of "large" calories. In chemistry, the unit is the "small" calorie where 1000 small calories equals 1 large calorie. Who uses chemistry calories? Yep, chemists. I like energy units of Joules. One chemistry calorie is equal to 4.2 Joules. Back to the energy in a day. This means that 1000 calories a day would be:
4.2 million joules will be my starting point for an estimate. Really, I think I will just go with this value for the energy used by an android like C-3P0 each day. Let me list a couple of reasons why I shouldn't use this value.
- It's C-3P0! What does this guy do but just stand around all day? How much energy does it take to stand around?
- He is probably made of metal or something. My guess is that he would be a bit heavier than a human so that he would use more energy to move than a human.
- Heart. What about a heart and lungs? He doesn't have those so he won't need to use energy to keep them running.
- What about his computer processor? Typically, the faster the processor the more energy it uses. It seems that most laptops use around 60 Watts. 60 Watts of power for a full day is about 5 x 106 Joules, so...
I am sticking with 4.2 million joules a day. What about power? Recall that power is the energy used per unit of time. I can calculate C-3P0's power as:
I guess since this is just an estimate, it wouldn't hurt to just call this 50 Watts.
A Star Wars Battery
In order to estimate the type of battery that C-3P0 uses, I need to first make two guesses. How long does this battery last (how long between recharging)? How big is the battery?
So, how long can C-3P0 go in between charges? Who knows? We just need to guess. In all of the episodes, did we ever see C-3P0 being recharged? When Luke Skywalker acquired him, he gave him a bath but I didn't see him being recharged.
Perhaps C-3P0 rarely needs to be charged. If he was my droid, I would want him to at least last longer than my phone. How about 1 week? That seems like a good enough time for him to last on one charge. If he uses 50 Watts of power, then the energy required for one week would be 30 million Joules.
Now, how big is C-3P0's battery? (I have to admit that I am getting rather tired of typing C-3P0. It isn't the easiest thing to type.) For some reason, I always thought this thing on his back was a battery.
If I assume 3P0 is average human height, this this battery thing would be about 25 cm by 15 cm and maybe 10 cm deep. Really, it doesn't look that deep but I am estimating on the large side. This would give a battery volume of 3.75 x 10-3 m3. What about the energy density (energy per unit volume)? Let me call this ρ even though that probably isn't the standard symbol for energy density. For this battery, it would be:
If I write this in units of MegaJoules per liter, it would be 8 MJ/L. Now I can compare that to the materials on Wikipedia's energy density page. One material on there is the zinc-air battery. It has an energy density of 6 MJ/L. These are essentially non-rechargeable cells that are used in hearing aids and stuff (according to Wikipedia). I guess this wouldn't work for C-3P0 though. I suspect he doesn't carry around disposable batteries. What about a laptop battery? These usually use something like a Lithium-ion battery and have energy densities up to 2.23 MJ/L.
I guess there could be some battery from long long ago that had an energy density up to 9 MJ/L. Also, it is possible that the battery for C-3P0 is much bigger than what I estimated.
C-3P0 Powered by AA Batteries
What if I purchased a C-3P0, but it said on the side of the box "batteries not included"? How many batteries would I need? Would they fit inside C-3P0? Why choose the AA battery? Obviously, I already have data on AA batteries - see my post on the energy in a battery. From this, a good battery - like a Duracell there is about 10,000 Joules of stored energy. If I need 30 x 106 Joules, that would be (30 x 106 Joules)/(104 Joules per battery) = 3000 AA batteries.
How much space would 3000 AA batteries take? Let's look at some AA batteries. I just happened to have a few. If I stack them in a nice arrangement, it would look like this:
This stack of 16 batteries seems to take up a space that is 5.5 cm x 5.5 cm x 5 cm. This would give an effective volume per battery of 9.45 x 10-6 m3. This means that 3000 AA batteries would have a volume of 0.028 m3. If I arranged this in a cubical fashion, each side would be 30 cm on a side. Hmmmm... That isn't quite as large as I thought it would be. Still, it would obviously stick out and is 7 times bigger than the estimated battery from above.
Here is approximately what C-3P0 would look like if he were powered by AA batteries.
Not crazy big - but noticeable. Yes, remember I made some assumptions and estimations. Yes, I know Star Wars isn't real. Yes, have a happy Star Wars Day.
