[Question] Running against gravity?

[Murazor]

I have tried (and failed) to calculate just how fast a human(oid) would have to be running in a circular wall, parallel to the floor, without falling down to the ground.

If someone could answer this doubt for me, or explain how I might calculate this, I'd be grateful.

[Darth Wong]

All you need to do is figure out the centripetal acceleration for any given velocity and radius of curve, and then make that equal to g.

[Howedar]

Well, that's true in Physics Experiment Land. In real life, said fellow will need to be running somewhat faster than that. He needs to be pushed down by the wall to some degree (that is to say, a normal force must be exerted) in order for there to be any friction between his feet and the wall. Obviously, if there's no friction then he can't apply force to the wall to continue running.

[Darth Wong]

Well, that's true in Physics Experiment Land. In real life, said fellow will need to be running somewhat faster than that. He needs to be pushed down by the wall to some degree (that is to say, a normal force must be exerted) in order for there to be any friction between his feet and the wall. Obviously, if there's no friction then he can't apply force to the wall to continue running.

Only for the split-second that he is actually at the very top of the curve. At every other point along that curve, his radial acceleration will exceed the radial component of g.

PS. Of course, if you figure that he needs the same downforce that he normally has when walking on the ground, then he would need something between 0 and 2g radial acceleration depending on his point on the curve. I suppose we'd have to plot the sine wave for his velocity curve in order to get it just right, but I suspect that's going beyond what Murazor was asking for.

[Howedar]

Technically he only needs >1g at the extreme top of the curve, yeah, but I don't think the few dynes of normal force he's going to get before the crest are going to cut it when he needs the power (in the literal meaning of the word) from his legs to continue up the crest.

I agree that we can easily continue past the point where Murazor cares.

[Darth Wong]

I agree that we can easily continue past the point where Murazor cares.

I think we already have

Murazor, just look up the formula for centripetal acceleration. Its terms will be the velocity and radius of curvature. If you want to get any fancier than that, get back to us.

[aerius]

I'm not quite clear on this, are we talking about a vertical loop such as a rollercoaster or a horizontal loop like one of those amusement park rides that spins real fast and sticks you to the walls of a rotating cylinder?

[Jawawithagun]

You mean like the Wall of Death? Usually it's done with a motorcycle though.

[Darth Servo]

You mean like the Wall of Death? Usually it's done with a motorcycle though.

The Wall of Death looks like its perpendicular to the ground. The wall in this thread is parallel to the ground.

[Jawawithagun]

The Wall of Death looks like its perpendicular to the ground. The wall in this thread is parallel to the ground.

But a wall parallel to the ground is just another floor, or a roof.
To me at least the OP reads that not the wall but the runner has his body parallel to the ground.

[Darth Servo]

But a wall parallel to the ground is just another floor, or a roof.
To me at least the OP reads that not the wall but the runner has his body parallel to the ground.

I read it to mean the wall was a roof and the runner was running against gravity.

With a wall perpendicular to the ground, wouldn't it just be a matter of creating enough friction to prevent falling?

[raptor3x]

The answer is going to be a function of the radius of the circle, gravitational acceleration, and the coefficient of static friction between the wall surface and shoe/foot. I get a minimum velocity of v = sqrt(g*r/mu_s). BTW, when you say the circle is parallel to the floor I'm assuming you mean the area vectors are parallel.

[Howedar]

Not quite, there's also some angular issues involved. Of course, you need your sums of forces and sums of moments to be zero (in your own non-inertial frame).

[Murazor]

You mean like the Wall of Death? Usually it's done with a motorcycle though.

Yes, I actually mean like the Wall of Death. I wrote the OP in a hurry and failed to clear that it is the runner who has to be parallel to the floor. Nonetheless, many thanks to Mr Wong, Howedar and all those who have replied.

raptor3x, that equation might be the answer to my question. Can you please elaborate upon it a bit so that I may understand it (I've never had more than a high school knowledge of physics and, to be sincere, that was several years ago)?

[raptor3x]

Howedar, do the actual math. Unless you're assuming that there is an incline to the wall then the angle of the runner relative to the wall ends up not mattering.

[raptor3x]

Also, if you want to know what the resulting angle is between the runner and the wall, it's phi = arctan(1/mu_s).

[Surlethe]

Suddenly, the conversation at the top of the thread makes so much more sense: they were talking about a vertical loop.

raptor3x, that equation might be the answer to my question. Can you please elaborate upon it a bit so that I may understand it (I've never had more than a high school knowledge of physics and, to be sincere, that was several years ago)?

In a nutshell, if you've got an object traveling in a circular path along a wall as you envision it, it's going to have three forces acting on it: the centripetal force pulling it against the wall, gravity pulling it down, and the force of friction pushing it up against gravity. The way friction works is that it resists movement along a surface; since gravity's pulling the object down along the surface of the wall, the friction will resist that.

Friction is a function of how hard the object is being pushed against the wall (think about it: the harder you press your hand against a tabletop, for instance, the harder it is to slide your hand along that tabletop), and a constant, called the static coefficient of friction, that depends on the surfaces involved.

I can't recall the math off the top of my head, but I can sketch out a sort of pseudo-solution for you. We'll call your velocity v, the centripetal force w, the force of friction F, and the gravitational force g. To start, you want him running and not falling, so the force of friction has to at least equal g -- that is, F = g. Now, F(w) (that is, F is a function of w, as I explained above). w(v), however, so we actually have F(v) = g. You can solve this for v, which is what I believe raptor3x did to arrive at his formula.

Howedar, do the actual math. Unless you're assuming that there is an incline to the wall then the angle of the runner relative to the wall ends up not mattering.

I think Howedar means that while he's not touching the wall (since he's running), the runner will fall, so even if he's going fast enough, his path will look like a spiral down the inside of the wall. EDIT: This is why, I guess, performers use bikes: constant contact means constant friction, so angle wouldn't matter (until the bike slipped, just as you slip when you lean into a turn too much).

[drachefly]

Well, since the force you're applying is not straight down, you're going to be falling whenever you're not touching the wall, but you're going to be pushing yourself back up whenever you are. On the net, you can be arranged to maintain a constant height.

However, in any vaguely realistic wall-running case, that radius is going to be so small that the step size will approach the diameter and the approximation of circular motion is really bad.

One could make a larger case work in really low gravity, I suppose. Even in zero gravity it's hard to stay near the wall until you get up to speed (if the wall is spinning, then that gets you up to speed right away)

[SCRawl]

Well, since the force you're applying is not straight down, you're going to be falling whenever you're not touching the wall, but you're going to be pushing yourself back up whenever you are. On the net, you can be arranged to maintain a constant height.

Well, no, not really. You can't use friction to push yourself up -- only to keep yourself from falling down.

[Surlethe]

Well, since the force you're applying is not straight down, you're going to be falling whenever you're not touching the wall, but you're going to be pushing yourself back up whenever you are. On the net, you can be arranged to maintain a constant height.

I think that pushing yourself back up are the "angular issues" to which Howedar was referring.

[SCRawl]

Well, since the force you're applying is not straight down, you're going to be falling whenever you're not touching the wall, but you're going to be pushing yourself back up whenever you are. On the net, you can be arranged to maintain a constant height.

I think that pushing yourself back up are the "angular issues" to which Howedar was referring.

I think I see your meaning -- the runner would be running at an angle a little above the horizontal, in order to keep himself from falling. This means that I owe drachefly an apology....

[Howedar]

Howedar, do the actual math. Unless you're assuming that there is an incline to the wall then the angle of the runner relative to the wall ends up not mattering.

Yeah, I was responding to Darth Servo (see the post times). I should have been more clear.

[drachefly]

Well, since the force you're applying is not straight down, you're going to be falling whenever you're not touching the wall, but you're going to be pushing yourself back up whenever you are. On the net, you can be arranged to maintain a constant height.

Well, no, not really. You can't use friction to push yourself up -- only to keep yourself from falling down.

What the FUCK are you talking about?

[SCRawl]

Well, since the force you're applying is not straight down, you're going to be falling whenever you're not touching the wall, but you're going to be pushing yourself back up whenever you are. On the net, you can be arranged to maintain a constant height.

Well, no, not really. You can't use friction to push yourself up -- only to keep yourself from falling down.

What the FUCK are you talking about?

Yeah, see a couple of posts ago -- I owe you an apology.

See, I thought that you were trying to suggest that someone running in this theoretical circular path -- parallel with the horizontal, and therefore perpendicular to the direction gravity is pulling this runner -- could avoid falling downwards. (He can't take a horizontal path because of the times when his feet aren't in contact with the track, and therefore exerting no normal force against it. But you know that already.) Obviously, such a runner can't avoid this by taking a horizontal path; he would have to take a path with a slight upward angle.

In short, I misinterpreted your meaning, and I have apologized for calling you on it.

[drachefly]

Sorry for missing your apology two days after you issued it.