# Why do heavier people go further on a zipline?

1. May 6, 2017

### pkc111

Hi

I was on Camp recently and noticed that heavier people go further on a zip line even though they all start at the same point. I would have thought if anything heavier people would have not gone as far due to increased friction.. clearly not! I have done some reading and found some theories about less air resistance, less rolling resistance and different shape of the line (heavier people make the middle of the line hang lower) but I am not sure which ones of these are having the major difference. Is there a way to work it out?

Many Thanks

2. May 6, 2017

### pkc111

Oh.. and WVU gives the following empirical data for "losses" as a function of mass on the zip line... Why does the curve go down and not up?

3. May 6, 2017

### pkc111

A typical "zip line" or "flying fox" set up (from WVU)...

4. May 6, 2017

### Daniel Gallimore

It may be that a larger mass begins with more potential energy. I assume we can neglect air resistance because the speed is relatively slow. I also assume we can neglect anything having to do with the harness or the connection to the line itself since this should not change for a wide range of masses (it's not like you're throwing a towel over the zip line; you're probably working with a rigid connector and bearings). Lastly, I assume the line will not significantly deform until you are close to it's minimum.

In order for the zip line to slow you down, it must do work on you in the opposite direction you are travelling. While you are travelling down the stiff portion of the line, virtually no work will be done by the line to oppose your motion so no energy is lost. Travelling down this section of the line is analogous to a block sliding down a frictionless (slightly curved) ramp.

As you approach the minimum of the line, however, the line will begin to deform so that your angle of descent decreases (i.e., becomes shallower) much faster than if the line had remained rigid. This deformation takes energy, and that energy comes from the person causing the deformation. However, the line will only be able to deform so much (for a reasonable range of masses), so the energy it takes from a large person should be roughly equal to the energy it takes from a slightly smaller person. Thus, the person who started with more potential energy (the large person) would retain more kinetic energy and go farther.

Just a shot in the dark on my part, but it's fun to think about.

5. May 6, 2017

### Randy Beikmann

You need to look at the ratio of the summed forces (F) acting on the person, to the person's mass (m). Then the acceleration (a) of the person equals F/m. Whichever person maintains the highest acceleration will reach the highest speed, and their momentum will carried them the furthest. The forces are gravity, friction, air resistance, and forces that might arise from the cable changing its angle.

You're right that a larger person has more potential energy, but they also have a larger mass to accelerate, so those two factors would cancel out. As small as air resistance and friction might seem, they are often significant when the only accelerating force comes from gravity (think soapbox derby racing). Air resistance is proportional to frontal area - roughly proportional to the square of a person's height, but mass depends on volume, which is roughly proportional to the cube of their height. So mass increases faster than air resistance, and heavier people will accelerate faster and travel further. The line hanging lower (as the OP mentioned) probably also plays a role.

6. May 7, 2017

### JBA

It appears to me that the change of cable angles due to the increased weight would have little beneficial effect because apply a point loading to the cable beyond the top cable connection point, the accelerating region, increases the cable angle behind that point load but also reduces the downward angle between that point and the bottom apex of the cable and past that bottom apex point, the decelerating region, the point loading increases the upward angle of the cable to the bottom connection point.

7. May 7, 2017

### Randy Beikmann

Just to add, this curve is interesting. It is essentially kinetic energy lost per unit mass of the person. If you took the y-values on the plot and multiplied by half the person's mass, you would get mv2/2, which would equal the kinetic energy lost by the person to friction, etc.

8. May 7, 2017

### Randy Beikmann

You're right. It probably would have minimal effect on the losses. It would probably increase peak speed due to their dropping further, but at the end of the track (where everyone reaches the same height), it would have no effect.

9. May 8, 2017

### RogueOne

Massive people have more momentum.

The increases in friction that happen due to increases in load are not linear.

10. May 8, 2017

### Baluncore

The unloaded wire hangs in a catenary due to it's mass. When you add a rider as a point load you get a straighter independent catenary curve on either side of the rider. As the weight of the rider increases the wire becomes straighter and the rider hangs lower. Because riders start at the same height at one end, the heavier rider will actually drop further.

Think of the triangle of forces, the rider suspended from the running pulley block is trying to pull the wire straight on either side. So the magnitude of the effect comes down to the rider's mass relative to the mass of the wire.

11. May 9, 2017

### JBA

I agree with the mass relationship; but, since, the from the lowest point onward the angle from the rider to the bottom line connection will become steeper as the travel progresses possibly the deceleration rate would be higher for the heavier rider. On the other hand, the momentum of the heavier rider at his lowest point will be greater as well so I am not sure how that would balance out with regard to the ultimate ride length vs rider weight.
Edited

12. May 9, 2017

### tech99

On the zip wire I went on as a light 16 year old, the person hung from a pulley block which rode down the wire. The bearings of this block, which had not been oiled for months, had a lot of friction, independent of the person's weight. So heavier people overcame the friction easily but light people did not. Hence, I got stuck half way across a lake, and had to swing back and forth for several minutes to get across.