Exploring the Impact of Non-Stretchy Mat Materials on Trampoline Physics

[Sherwood Botsford]

TL;DR Summary

Thoughts on non-linearity, mat characateristics, damped systems.

Trampolines are in effect coupled springs, with the mat being the much softer spring generally.

E.g. On my Acon, when jumping about 1 meter, there is a max cone of depression about 60 cm deep and 1 meter across (1 meter point has a depression of only about 10 cm) At this same point the 160 or so springs are barely moving.

Now, what would be the effect on using some non-stretchy material for the mat. Now all the rebound is coming from the springs. I suspect much higher rebound efficiency. I suspect that the rebound will be less sensitive to weight distribution on your feet, and whether your center of mass is directly over your centre of support.

Some numbers and observations.

I am by far the largest mass i in the system (84 kg) The mat is about 20 kg. The springs about 60 kg, but they move very little. (About 25 cm long including the hooks)

If I do "bunny hops" That is, jump at a level my feet just barely leave the mat, it takes 54 seconds to do 60 hops. Period of 0.9 seconds

If I go for consistent height -- I think somewhere between .7 and 1 meter. (Hey, I'm a beginner) -- then 60 jumps takes 74 seconds.

That 20 extra seconds is .33 seconds per jump. A round trip of .33 seconds corresponds to a height of .4 m. This suggests that I'm already well into the non-linear portion of the mat.

How would I model the dynamics? What else do I need to know to accurately predict height from jumping period?

 

[jbriggs444]

How would I model the dynamics? What else do I need to know to accurately predict height from jumping period?

When in doubt, simplify. Start with the statics.

You could do this experimentally -- how deep is the depression for a series of test masses (or test people) with varying weights?

Or you could do this analytically -- suppose that the mat material obeys Hooke's law. What is the shape of the depression formed when a point mass lies on the surface and the tension at infinity has a particular fixed value? [Feels pretty nasty to me, and I am not convinced that the fabric obeys Hooke's law over the range of expected tensions]. You might need a fabric swatch to subject to two-dimensional stress versus strain testing. Then you could end up with a computational approach.

Dynamics comes in when you need to account for velocity-dependent effects. Air resistance and possible hysteresis in the material.

 

[rcgldr]

The two main types of high end trampoline beds are string and webbed. Most string beds are "2 string" beds that use pairs of nylon strings, while webbed beds use strips of nylon. Both are very porous with very little aerodynamic drag. There are single string beds, but I don't think they are allowed for competition.



The amount of depression depends on the bed construction. I recall some string beds that didn't depress much, which also shortens the amount of time during compression, requiring more precision. In competitions like the Olympics, the beds are made to some standard, so that the depression distance and time is consistent.

The Acon tramps use a nylon weave bed, intended for outdoor use. I would assume the Acon "air" beds use a more "porous" weave, but from what I can from review videos, they don't look as porous as the higher performance beds.