[MSN Spaces] Urinary lawn sprinklers and escape velocities.

So, as you know, I've been reading The Dilbert Blog. His entry on March 10th, 2006, entitled Nature's Jet Pack, asked us "If you lived on a planet with almost no gravity, would you be able to fly just by peeing?" Once I recovered from laughing and picked myself up off the floor, I started reading through the comments. It's surprising, and a little disconcerting, the level of ignorance of physics some people exhibit. I'm not going to go into that; instead, I want to point out some of the better (and funnier) comments. And so, I present the following:

From Rick Ellis:

All the people with shy bladders would have to walk though.

From Tom B:

Perhaps more importantly, if I take a point mass and apply an acceleration to it, it will move in the direction of the acceleration. However, you (unless you are very tiny) are not a point mass.

If you peed and we assume your center of gravity is actually about ten to fourteen inches higher up, you'd actually create a torque that would tend to rotate you around your center of mass. So instead of doing a lot of flying in a linear direction away from your rudder, you might do a certain amount of rotating in place. Sort of like a Roman Candle sparkler, only less sanitary. More of a urinary lawn sprinkler, if you ignore the pun.

From Steve:

First of all, define "almost no gravity". The amount of inertial change to a 70 kg man by ejecting 100 ml (about 100 g) of urine at typical urinary speeds would be fairly miniscule. Assuming a fairly high pee rate of 2 m/s, the end speed of the peeing individual would be about 3 mm/sec in zero gee with no resistance. Which is literally a snail's pace (some snails go considerably faster, up to 13 mm/sec, according to http://hypertextbook.com/facts/AngieYee.shtml). With a gravity of any more than 0.0014 gee, the man would not be able to achieve liftoff, even if he peed the entire 100 ml load in one second (a difficult task. Try it). He could, however, probably achieve escape velocity by jumping.

If the man is in microgravity, he would have other problems. He wouldn't have enough traction to walk, and there would be no oxygen (1/700 of a gee is not enough to hold on to any atmosphere), so he'd have to be wearing a space suit. So if he was to undo his fly to take his willy out, he'd die of suffocation. Although the velocity of the air rushing out of his zipper would help him achieve his propulsion objectives.

On the other hand, the center of force would be close to the center of gravity, so the flight would be relatively stable. Especially if the man allowed his arms and legs to lag behind his direction of travel, which would place his center of gravity behind his center of thrust, a very stable configuration (ignoring the visibility issues). A woman using this propulsion system would be more unstable, since her thrust system is at right angles to a man's, and she has no way of getting her center of gravity behind the center of thrust, apart from wearing heavy shoes. On the other hand, this would make women more maneuverable. And women would probably be better at takeoff and landing, since their feet are in line with their urinary path.

Just what kind of pee velocity would give a man liftoff in Earth-like gravity?

Well, assuming a man can pee 50 ml/second, and weighs 70 kg, he'd have to pee a stream at 13,720 m/s [ -ed.] just to counteract his weight. This is fast enough that if he peed upwards, his urine would achieve orbit (escape velocity is 11200 m/s).

However, pee traveling at that speed would create serious heat due to air friction, so the pee would probably boil off into steam. Which would eventually form into clouds and rain down on some unsuspecting bystander.

Probably a good thing we can't do it.

That is all.