# B Why do tightrope walkers carry a rod?

1. Jul 8, 2016

### alba

Intuitively I guess that what matters is
a) the position (lowers CoM)
b) the weight ( probably weight equal to the body is best)
c) length of the rod (larger L)
d)...
but I can't say why point c helps or if thereare other factors

Can you give some technical explanations on all points?

Last edited: Jul 8, 2016
2. Jul 8, 2016

### rootone

The long rod acts a stabiliser resisting forces acting immediately close to the walker.
A slight mis-step that could cause loss of balance is compensated for.
Long story - angular momentum.

3. Jul 8, 2016

### alba

That is intuitive and obvious, can you expand and quantify? suppose the man's weight is 70 Kg, the rod's 20 Kg, can you explain in details? a 4 m rod has a larger L, but L can be increased by mass? How does acually the rod help him?

Last edited: Jul 9, 2016
4. Jul 9, 2016

### rcgldr

The walker can apply a torque to the rod, which rotates the rod in one direction, rotates the walker in the other direction. A Newton third law pair of forces exerted at the wire shifts the center of mass of walker and rod back over the wire. A bit of over correction is used in order to restore the rod back to a horizontal orientation.

See post #14 for a better explanation.

Last edited: Jul 9, 2016
5. Jul 9, 2016

### alba

Thanks, aren't there other factors?
Lowering CoM makes him more stable?
Simply shifting the rod sideways shifts CoM restoring balance? etc

6. Jul 9, 2016

### malawi_glenn

larger moment of inertia- The bigger moment of inertia - the slower angular acceleration. If the angular acceleration is lower, then you have more time to adjust position of the feets and the body as a whole.

It is easier to balance a long rod on its tip on your finger tip than a pencil- for the same reasons

7. Jul 9, 2016

### alba

What you say is surely true, but difference in time is really tiny, isn't it? what about the sideways shift to compensate CoM out of the vertical? that can really happen a lot quicker.
Also, if you hold the rod above youre head, you are less stable even with a longer rod

8. Jul 9, 2016

### rcgldr

The height of the rod doesn't make much difference, other than they are heavy enough to be fatiguing if not held with arms down. The angular momentum of the long rod is high, so just applying a torque results in rotations (rod one way, walker other way), and the rotation of the walker shifts the center of mass of both walker and rod. When applying a torque, the high angular momentum of the rod means it's angular acceleration is slow, but relatively low angular inertia of the walker means the angular acceleration of the walker is relatively high, and rotation of the walker results in a shift of center of mass, since the wire is mounted to resist lateral motion.

Trying to shift the rod side to side doesn't have as much effect, it's much lighter than the walker, and lateral motion is limited.

update - I forgot to mention that the walker also has to exert a side force onto the wire when exerting a torque onto the rod. The wire exerts and equal and opposing force onto the walker, which shifts the center of mass of walker and rod.

See post #14 for a better explanation.

Last edited: Jul 9, 2016
9. Jul 9, 2016

### Staff: Mentor

So often on PF, the OP would be better off by first reading the Wikipedia article first.

Now for my own follow up: The rods are flexible and the ends droop down. Think of a rod bent into the shape of a U or a V. With the point of the V resting on the wire it is unstable. A straight rod (with no human) is also unstable resting on the wire. But an inverted V with the point up, resting on a wire is stable. Now a real walking pole does not bend as much as a V, but some added stability is better than none.

10. Jul 9, 2016

### sophiecentaur

Reducing the height of the total CM has to be relevant, but I can't see it is a sufficient explanation.
Holding a long horizontal rod gives the tightrope walker an extra dimension to work with. He (she) can move the pole side to side and also rotate it. This allows him to keep his CM above the wire by using the effective difference in MI, with and without the pole. This is a much more effective way than if he just waved his arms around. An alternative method involves using an umbrella that can be moved from side to side and used to provide a varying correcting moment, depending on the 'perpendicular distance' from the wire (pivot).

11. Jul 9, 2016

### rcgldr

To clarify, moving the rod side to side has little effect on center of mass, since the system is mostly free to rotate about the pivot point due to the relatively low angular inertia of the walker, especially if the walker is laying down on the wire (a common trick). So moving the rod left will move the walker right, but the center of mass of rod + walker hasn't moved much.

It's the torque applied by the walker to the rod that is used to shift the center of mass of walker and rod. The angular orientation of the rod doesn't have a direct effect on the center of mass, but the angular orientation of the walker holding the rod does have a significant effect on the center of mass. If the balance rod is angled, the walker can apply torque to the rod (initially to further increase angular orientation of the rod) to offset the center of mass a bit, so that the torque related to gravity can be countered with torque applied to the rod, correcting the orientation of both rod and walker.

update - I forgot to mention that the walker also has to exert a side force onto the wire when exerting a torque onto the rod. The wire exerts and equal and opposing force onto the walker, which shifts the center of mass of walker and rod.

See post #14 for a better explanation.

Last edited: Jul 9, 2016
12. Jul 9, 2016

### wrobel

it would be a good exercise to write equations of motion of this system in the linear approximation near the equilibrium and to describe strategy of rotating of the rod

13. Jul 9, 2016

### sophiecentaur

If all the walker does is rotate the rod to counter the effect of perturbation then the overall effect will not change (Conservation of angular momentum). There has to be some linear motion of the CM of the rod as well as a rotation. The walker has the force of his weight and the weight of the rod plus any temporary torque he can get from the rod. The high MI of the rod is what makes it so effective.

14. Jul 9, 2016

### rcgldr

I didn't fully explain this before (I updated my prior posts to refer to this post), the linear force is exerted at the wire (pivot point). If the center of mass is offset to the left, the walker exerts a left force onto the wire, which exerts a right force and a counter clockwise torque onto the walker. At the same time the walker has to exert a counter-clockwise torque to the rod which exerts a clockwise torque onto the walker so that the net torque on the walker is close to zero. The center of mass is shifted right, and the rod ends up displaced at some angle. To correct the rod's orientation, the walker could shift the rod laterally and let gravity correct, or the walker could deliberately offset the center of mass a bit so that the correction process ends up with the rod returned to horizontal.

Angular momentum is conserved, but not angular orientation, for example, an astronaut "hovering" in the space station can windmill his arms and stop to change the direction faced, but the angular momentum is zero before and after the maneuver.

Last edited: Jul 9, 2016
15. Jul 10, 2016

### sophiecentaur

Is this correct? The force of the foot on the wire will be to the right, surely. The wire will then be pushing the foot to the left. There will be a torque due to the weight and horizontal displacement The rod has to be rotated to produce a correcting torque but there will be an angular acceleration. How do you deal with (eliminate) the final angular velocity of the rod except with an equal and opposite torque, applied later? You are saying, I guess, that the CM will end up on the other side of the wire and that resulting torque can be used to stop the rod. If the MI of the rod is greater than the MI of the walker, control will be easier.
There is another thing which I (we?) have been ignoring. The walker can always apply a fore and aft torque due to the baseline of his feet and that would allow him to use a precession torque by rotating the rod horizontally which would restore verticality around the wire. That would make things a lot easier, I think. (Don't ask me to demonstrate it over Niagra Falls, though!) But it has to be true that moving the rod through other dimensions than the axis of the wire can produce the required correcting force / torque.

16. Jul 10, 2016

### rcgldr

If the center of mass is to the left and no corrective action has been taken, then yes, the walker is oriented a bit counter clockwise, and exerts a right force onto the wire, which exerts a left force onto the walker, while gravity acts at the center of mass opposed by the wire which exerts an upwards force at the pivot point which results in a counter clockwise torque exerted onto the walker, making the situation even worse, an unstable situation.

If the center of mass is offset to the left, then the corrective action is to exert a counter clockwise torque onto the rod, which coexists with the rod exerting a clockwise torque on the walker, and at the same time, with the walker exerting a left force onto the wire, which coexists with the wire exerting a right force and counter clockwise torque onto the walker. The corrective action is somewhat instinctive, since it corrects the lean sensed by the walker.

The angular velocity of the rod after a correction could be an issue, but the walker also has linear momentum, so after the initial correction, the applied torque on the rod and the force exerted on the wire is reversed to stop both the rod's angular velocity and walker's linear momentum. If the walker gets it's it just right, there's not a lot of over correction.

Last edited: Jul 10, 2016
17. Jul 10, 2016

### Staff: Mentor

I second @wrobel s suggestion. These verbal narratives are becoming overwhelming. The language of physics is math.

18. Jul 10, 2016

### rcgldr

or a free body diagram, but I don't have drawing tools.

19. Jul 12, 2016

### sophiecentaur

Free drawing and painting software is available for PC. Try it.
Personally, I use (Apple) Powerpoint for simple drawings. Sledgehammer to crack a nut but it gets results.