Since my previous post on R2-D2 flying was so popular, I thought I would follow it up. I was going to add these two points in the comments, but a separate post seems to make more sense.
Point 1 - R2 flies at a constant speed
Well, he obviously doesn't always have to fly at a constant speed. However, in the clip I was looking at there are two important things in the analysis. What angle is R2's thrusters at? Is R2 flying at a constant speed? I found a much better quality version of the flying R2 from Billy Brook's site. That helped out a lot. So, on to Tracker Video Analysis (I always call it Tracker Video Analysis, but I think officially it is just Tracker). The scene I analyzed was this one:
A pretty good clip for video analysis. The camera does move, but I can set the origin to something in the background. I have to admit, the scale was kind of a guess. I know how big R2 is supposed to be, but the shot is from an angle. I did my best. However, the point is that he is moving at a constant speed. Here is the data I got from Tracker.
Here the x-axis is in the direction of R2's motion. Call it what you want, but I would call this constant velocity with a magnitude of about 2.3 m/s (I previously said 2.2 m/s).
Point 2 - Angle of thrusters
Ok, this one is more difficult. However, it would be difficult to claim that the thrusters are pointing down. Here is a shot from the clip.
And here is the image I made of flying R2-D2 (in Apple's Keynote).
That looks like a fair representation. Measuring the angle in Keynote, the thruster is 43 degrees from the vertical. I thought this might be a little large, so I used 35 degrees. Just because.
There was a good shot at the end of R2's flight. As R2 is landing, it looks like this:
This also presents a problem. It looks like the thrusters are mostly vertical. In order to slow down the thrusters should face forward. Actually, this is a good analogy for the way people think. Most people think of of forces and motion the way Aristotle thought. This is "Aristotle's Law of Motion:"
Aristotle: A constant force makes an object move in constant motion. If there is no force, there is no motion.
It is ok if you think about forces this way - like I said, this is the way most people think. Here is Newton's Law of Motion:
Newton: A constant force makes an object CHANGE its motion. If there is no force, there is no CHANGE in motion.
And this is why no one complains about Star Wars errors. Everything looks fine. That is, unless you are very familiar with physics. Aristotle thought the same way, if you want a cart to keep moving, you have to push it.
What should it look like?
If you go with the assumption that R2 is flying with rockets, and not some anti-gravity thingy like the land speeder, then it should look similar to the rocket flying guy. It was difficult to find an appropriate video, but this one seems to show some shot of a rocket-pack guy. If you want to skip to about the 3-minute mark, you can see some flying.
The problem is that these guys rarely go at a constant speed. However, here is a shot that appears constant-y speed.
Notice that he is oriented vertically. This is the way R2 should do it.
Cool post! I especially like the observation of how R2's landing physics make him seem as light as a feather to slow down that way.
Those R2 problems remind me of the Watchowski bros' Speedracer film, which was highly criticized for being to CGI heavy. In my opinion the problem was that the cars CGI looked like they had no mass, and I bet this kind of analysis would show that.
Thanks for going through all this! Very interesting, indeed.
Very nice post...at first glance I tought nothing was wrong! Aristoteles thinking!
You're awesome, guy.
Maybe the thrusters use thrust vectoring independent of the angle of R2's "legs", or whatever those things are called, because the legs have to be at a specific angle for the landing, or because they don't move fast enough to stabilize R2 in flight.
Have you tried solving for R2's mass by finding an equilibrium point between his thrust vector and apparent buoyancy? A balloon that large could support at least a few kilograms, maybe that's what's going on?
Perhaps R2 units have a factory-set neutral buoyancy, and most of the time, he's too overloaded to lift off? Maybe this can be adjusted manually to keep the droid on the ground in different atmospheres?
I feel this deserves a more detailed analysis. There may be lost droids floating around in the upper atmospheres of star wars planets.