A physicist carefully examined the way R2D2 flies in Attack of the Clones, and has come to a startling discovery. Examining the thrust of R2's flight, then adding in gravity and resistance, he discerned that R2's mass is 100 grams.
Rhett Alain, a physicist at Southeastern Louisiana University, first turns R2's flight into a free body diagram, pictured here. Then he solves for F-thrust, assuming Earth gravity and some atmospheric resistance (you can see all his equations here). Then he reaches the fun part, which is figuring out R2's mass.
Writes Allain, as he solves his equation for mass:
* rho = 1.2 kg/m3
* Area: Wookieepedia says that R2 is 0.96 meters tall. Using tracker video on an image of R2, I am going to approximate it as a rectangle that is 0.42 meters by 0.62 meters for an area of 0.26 m2
* Wikipedia lists the drag coefficient for a smooth sphere as 0.1. It has a smooth brick with a coefficient of 2.1. A skier has a coefficient of 1.0. Wikipedia does not list the drag coefficient for R2, but a value of around 1.0 seems reasonable.
* For the velocity, I took it a little far. I was just going to ballpark guess at his speed, but I didn't. I used Tracker to look at R2's motion in Clone Wars where he flies to rescue Padme. From this, I get a speed of 2.3 m/s.
* I already said I would assume Earth-like gravity. So, g will be 9.8 N/kg
* Theta is about 35 degrees (although it could be as high as 45 degrees).
Using these values, the mass of R2 is 0.1 kg. Yes, 100 grams. How do I know I am correct? I know because Wookieepedia doesn't list R2's mass or weight. They know it is silly, so they left it off.
If this mass is so low, I think R2 doesn't even need thrusters. He would just float (which would actually change my calculations above - I left off the buoyancy force). By my estimations, R2 is about .42 meters in diameter. This would put its volume at about 0.1 m3 and R2's density would be:
I was originally thinking that maybe R2 was made of styrofoam - but that has a density of about 40 kg/m3. So there.
So basically R2 doesn't need thrusters, and is made of spiderwebs. Makes perfect sense!
You really must read the whole post to get the full awesomeness - via Dot Physics