Realization about centrifugal gravity

[Terralthra]

While doing some cogitation about physics in a rotating inertial frame where ostensible "gravity" is being created by centrifugal/centripetal forces, I realized something that startled the shit out of me, and I'm not sure if I'm waaaaay behind everyone else (who already thought of this) or waaaay ahead (because no one else has ever mentioned it), or just plain wrong.

In a frame as described above (e.g. O'Neill Island III Hab, Ringworld, colony ship, etc.)...you can't jump, practically speaking. I mean, you literally can jump, but if you do, once you stop touching the inside of the rotating surface, you no longer have any force acting on you to push you down against it. The force you feel as gravity is centrifugal force, the reaction force of centripetal force which in this case is being exerted by the structure itself. Once you stop touching the "floor", you are effectively weightless, and leisurely sail upwards at 2-5 m/s until you hit the ceiling (or equally likely, the floor on the other side of the cylinder). On Terra, you jump and immediately start decelerating because gravity doesn't stop working on you because you're 1m from the ground. On a hab as described, it seems you'd jump and just kinda float away.

So...am I wrong? If so, how?

This obviously has all sorts of more complex effects (and more serious ones than simply making basketball dunking easy for anyone), if I'm right, but I really am curious about what the deal is here. If I'm wrong, where's the force pushing you back to the floor? If I'm right, how come no one else seems to have noticed this?

[Grumman]

No, you're correct. However, in order to produce this "gravity" the ring will have considerable angular velocity, which means you aren't going to hit the other side of the cylinder - you'll hit the cylinder ahead of your jumping off point.

[jwl]

While doing some cogitation about physics in a rotating inertial frame where ostensible "gravity" is being created by centrifugal/centripetal forces, I realized something that startled the shit out of me, and I'm not sure if I'm waaaaay behind everyone else (who already thought of this) or waaaay ahead (because no one else has ever mentioned it), or just plain wrong.

In a frame as described above (e.g. O'Neill Island III Hab, Ringworld, colony ship, etc.)...you can't jump, practically speaking. I mean, you literally can jump, but if you do, once you stop touching the inside of the rotating surface, you no longer have any force acting on you to push you down against it. The force you feel as gravity is centrifugal force, the reaction force of centripetal force which in this case is being exerted by the structure itself. Once you stop touching the "floor", you are effectively weightless, and leisurely sail upwards at 2-5 m/s until you hit the ceiling (or equally likely, the floor on the other side of the cylinder). On Terra, you jump and immediately start decelerating because gravity doesn't stop working on you because you're 1m from the ground. On a hab as described, it seems you'd jump and just kinda float away.

So...am I wrong? If so, how?

This obviously has all sorts of more complex effects (and more serious ones than simply making basketball dunking easy for anyone), if I'm right, but I really am curious about what the deal is here. If I'm wrong, where's the force pushing you back to the floor? If I'm right, how come no one else seems to have noticed this?

If you're in a sealed environment, no, because you and the air inside are still going at the same speed. A bit like how a sealed truck of chickens won't speed up due to lost mass if all the chickens inside take flight.

[Terralthra]

If you're in a sealed environment, no, because you and the air inside are still going at the same speed. A bit like how a sealed truck of chickens won't speed up due to lost mass if all the chickens inside take flight.

I don't think the air is going to push you back down from a jump. I'm not a fluid dynamics expert, but it seems unlikely that there would be enough force in the flow of air (which would generally be out from the center of the cylinder, yes) to act as any real brake on upward movement.

[GrandMasterTerwynn]

While doing some cogitation about physics in a rotating inertial frame where ostensible "gravity" is being created by centrifugal/centripetal forces, I realized something that startled the shit out of me, and I'm not sure if I'm waaaaay behind everyone else (who already thought of this) or waaaay ahead (because no one else has ever mentioned it), or just plain wrong.

In a frame as described above (e.g. O'Neill Island III Hab, Ringworld, colony ship, etc.)...you can't jump, practically speaking. I mean, you literally can jump, but if you do, once you stop touching the inside of the rotating surface, you no longer have any force acting on you to push you down against it. The force you feel as gravity is centrifugal force, the reaction force of centripetal force which in this case is being exerted by the structure itself. Once you stop touching the "floor", you are effectively weightless, and leisurely sail upwards at 2-5 m/s until you hit the ceiling (or equally likely, the floor on the other side of the cylinder). On Terra, you jump and immediately start decelerating because gravity doesn't stop working on you because you're 1m from the ground. On a hab as described, it seems you'd jump and just kinda float away.

Say you had a habitat that was a mile (1.6 km) wide rotating fast enough to simulate a single Earth-gravity. Any given point on the habitat wall will be moving at better than 88 m/s. If you had a basketball player accelerate to a vertical velocity of 5 m/s, this will be on top of his pre-existing 88 m/s velocity tangential to the surface of the hab. His effective velocity vector will be one going slightly faster than the hab's rotational speed at an angle of a couple of degees (with respect to his original angular velocity.) Since the inside of the habitat is curved, and his the angle of his trajectory is so slight ... he will intersect with the ground again.

Interestingly, though, instead of looking like he's jumped straight up and down (like he would in normal gravity); our hypothetical basketball player will actually land slightly offset in the direction of the hab's rotation (per above,) and at a bit of an angle toward the direction of the hab's rotation.

[Elheru Aran]

So, basically one's jumping would kind of go in a crooked direction versus a straight-ish line? I can buy that, although it does strike me that if you jumped from a sufficient altitude you might have issues. Say you have a habitat a mile in diameter, you build a tower a quarter-mile tall (half a radius)-- we've done that already so it's not impossible, just a little silly-- what would jumping off said building do, though? Because obviously you'll have less gravity the closer you get to the middle of the cylinder...

[Formless]

No, you're correct. However, in order to produce this "gravity" the ring will have considerable angular velocity, which means you aren't going to hit the other side of the cylinder - you'll hit the cylinder ahead of your jumping off point.

Which, if I understand correctly, should be the same point on the ring that you started at (unless you jumped "forward"), because it is moving with you underneath your feet the whole time. It would be a weird experience the first time you did it, and in a small enough centrifuge you might end up "falling" on your face because of the rotation. But on a large colony, you would probably get used to it and learn to adjust pretty quickly.

[Simon_Jester]

Basically yes. Jumps and other ballistic trajectories will look sort of like normal gravity in a rotating reference frame, but only sort of. Anyone trying to throw a ball, or aim a gun in the rotating reference frame will have to compensate, to an extent that increases as the distances involved grow. They make very little difference at low speed and point blank ranges, but lots of difference if you're aiming at a point a quarter of the way around the cylinder.

So, basically one's jumping would kind of go in a crooked direction versus a straight-ish line? I can buy that, although it does strike me that if you jumped from a sufficient altitude you might have issues. Say you have a habitat a mile in diameter, you build a tower a quarter-mile tall (half a radius)-- we've done that already so it's not impossible, just a little silly-- what would jumping off said building do, though? Because obviously you'll have less gravity the closer you get to the middle of the cylinder...

Well, you might fall off the building due to the 'crooked' effect, for one.

[Terralthra]

Ok, essentially I underestimated the angular speed of the hab's interior surface, relative to the vertical speed a human can achieve.

So, you'd intersect the ground again, with the proviso that you'd land offset slightly and at an angle slightly, with both the offset and the angle dependent on how long you were in the air. If you were to jump high enough (or off something high enough) that might mean that theoretically you could jump vertically and land flat on your back/belly.

The offset also means that the angle you land at is proportional to the change in vector of velocity of the ground where you land. IE, your vector becomes static when you leave the ground, but the ground you land on - though the same ground you left from - does not, due to angularity. It's still moving at the same speed as you, but not in the same direction, leading to some very interesting results once air time exceeds trivial. Basically, the main point here is that when you jump in gravity, your speed goes from max positive y, decelerating constantly to max negative y by the time you hit the ground. In a rotational frame, your speed stays at +y + ω for the whole jump until you intersect with the ground again, which will still be moving at ω, but when translated into a non-rotating frame of reference, may be rather painfully not the same vector(x,y,z) it added to your initial jump.

Does this line up?

Also, while this is fine for jumping humans, any number of things humans do might lead to other interesting results. A pitched baseball's thrown speed is (in professional leagues) up around 40 m/sec, a significant proportion of the angular speed of the hab's surface. A bullet's speed (note: I do not recommend firing bullets in a space habitat) exceeds the angular speed in basically every case. Depending on the direction fired, this interaction of vectors would have some very strange effects on such things.

It's essentially a weird and much more noticeable coriolis force, yeah?

[GrandMasterTerwynn]

So, basically one's jumping would kind of go in a crooked direction versus a straight-ish line? I can buy that, although it does strike me that if you jumped from a sufficient altitude you might have issues. Say you have a habitat a mile in diameter, you build a tower a quarter-mile tall (half a radius)-- we've done that already so it's not impossible, just a little silly-- what would jumping off said building do, though? Because obviously you'll have less gravity the closer you get to the middle of the cylinder...

The top of your ludicrously tall tower would be moving slower than the base, so if your jumper jumped with just enough velocity to clear the tower, his overall velocity vector will be one in the direction of the habitat's rotation, except slower than the speed with which the 'floor' of the habitat is moving.

Your jumper will land somewhere anti-spinward of the base of the tower at a velocity of some 44 m/s pointing directly into the ground. The air, being dragged along at the same 88 m/s as the floor of the habitat, will attempt to impart some acceleration in the direction of rotation, meaning he won't land quite as far away from the base of the tower as he would in a vacuum.

It'll still hurt, though. A lot.

[Dass.Kapital]

Actually.... people could 'step off' in the very center of the cylinder with extra large 'swim fins' on their feet (Or something analogous to 'wings)and hence sort of 'swim' about in effectively micro gravity.

Arial synchronized acrobatics any one?

There's also an interesting idea possible for a 'floating' (Albeit moving VERY quickly) kind of monument within the cylinder as well. Since something NOT moving along with the rotation will still be in effective micro gravity UNTIL it comes in contact with the surface of the spinning hab.

Just some thoughts.

Much cheers to all

[Elheru Aran]

Actually.... people could 'step off' in the very center of the cylinder with extra large 'swim fins' on their feet (Or something analogous to 'wings)and hence sort of 'swim' about in effectively micro gravity.

Arial synchronized acrobatics any one?

I believe either Asimov or Clarke had something along these lines in one of their books. I know for sure Clarke had a sort of "sky bicycle" pedal-powered ultralight aircraft for use in the center of a cylindrical habitat in Rendezvous with Rama. The general idea was you could achieve sufficient velocity by jumping off a high point, then pedal to the center where you have the least gravity, and 'hover' there. As you're not going to be exactly centered you'll drift one way or another eventually but you'll be able to pedal back to where you were. Fun little notion.

[bilateralrope]

I'm not sure if I'm waaaaay behind everyone else (who already thought of this) or waaaay ahead (because no one else has ever mentioned it), or just plain wrong.

You're not the first to think of it.

[jwl]

If you're in a sealed environment, no, because you and the air inside are still going at the same speed. A bit like how a sealed truck of chickens won't speed up due to lost mass if all the chickens inside take flight.

I don't think the air is going to push you back down from a jump. I'm not a fluid dynamics expert, but it seems unlikely that there would be enough force in the flow of air (which would generally be out from the center of the cylinder, yes) to act as any real brake on upward movement.

No, what I'm saying is the air doesn't affect you because it is moving at the same speed as you. So you don't suddenly stop moving and lose the fictional force on you. It is true that you'd, as people said, land forward of where you started, but I would expect that the small angles involved in a flat-looking ground would render that negligible.

[jwl]

OK, lets quantify this.
Lets say we have a centrifuge of radius x. Drop a ball from a height of 1m and, to an outsider, it will carry on going in a straight line from its momentum until it hits the outside of the centrifuge. This means you create a right-angled triangle between the point dropped, the centre, and the point it hits the side of the centrifuge. Using the angle from the centre, this means the hypotenuse will be x and the adjacent will be x-1. This means the opposite (which is the distance the ball will travel) will have a length of (x^2-(x-1)^2)^0.5, and the angle will be arccos((x-1)/x). The length of the arc is equal to the radius multiplied by the angle, so this means the distance the centrifuge will have to move to catch up will be x(arccos((x-1)/x)). This means, in the frame of the ball, it will move x(arccos((x-1)/x))-(x^2-(x-1)^2)^0.5 horizontally whilst falling. Plug this into here between 0 and 10000, and you'll see that the distance moved reduces with increasing radius, and goes below 1cm at about 2km radius.

[Ultonius]

This simulator is quite useful for understanding motion in a rotating habitat.

[gigabytelord]

This simulator is quite useful for understanding motion in a rotating habitat.

I can't use that because it's causing Java to have an stroke.

[Ultonius]

I can't use that because it's causing Java to have an stroke.

When I open the page in Firefox, I click where it says 'Activate Java Platform SE 7 U', then click 'Allow now' in the small window that appears, and then it works fine for me.

[Enola Straight]

I always wondered about that scene in 2001 where Dr. Poole was jogging within the centrifuge module onboard the Discovery...was he jogging spinward, thus increasing the G force and increase the effectiveness of his workout, or anti-spinward and enjoying low-G on demand?