S. G. Botsford
Agricultural
In most fields there are reference books/papers that give overviews of the design considerations for a particular class of structures/machines. I have been looking for such a reference for the design of trampolines. -- the jumping thingy, not the software thingy.
I initially posted on the Enginnering Stack Exchange. Got a couple refinements to my quesiton which are incorporated here. (Note: Should this be in Mech E and not Struct E?)
At present cheap backyard trampolines sell for a few hundred dollars and consist of a tightly woven mat made of polypropylene, PET, or other synthetic. Often the weave is augmented with a stretchable material, or the structure of the weave itself is elastic. Frames are thin tubular galvanized steel. Springs are short with 3-4.5" of actual coils. Padding over the springs are 1" foam, covered in vinyl fabric.
At the other end, the prices start at 12 grand, springs are 10" long, usually made from piano wire. Frames are heavier, padding is thicker. A large part of the higher price is smaller market, and more hand work.
Really cheap tramps will cheap out on the galvanizing, frame weight, UV resistance of the plastic parts.
It seems to me that there is a market for a higher performing trampoline that doesn't cost the earth.
Here's what I've found so far:
A: The "Throw" of a trampoline is the range of motion while the jumper is in contact with the mat. Long throw trampolines exhibit lower g forces on the jumper, but require longer springs with a lower spring constant. Longer throw also reduces higher order time varying terms -- surge and jerk, and gives the jumper better control.
B: The average g force on a bounce is the ratio of the height above the mat to the the throw. A 5 meter jump with a 1 meter throw has an average of 5 g's. This is simple physics. The maximum g force is considerably more than this, and gets complicated.
C: The restoring force is, I think, roughly proportional to the square of the displacement. This means that you cannot model the bounce as simple harmonic motion when you get into useful bounces.
D: Typical springs have elastic limits of about 60%. A 10 inch spring can extend to 16" without suffering permanent distortion. This varies somewhat by alloy used, with piano wire being the gold standard. I don't know if this can be improved with spring design.
E: The largest cause of energy loss is air resistance of the mat. Competition grade mats are at least 70% holes, and use a mesh instead of a fabric.
F: The second largest energy loss is residual motion of the mat once the jumper's feet leave it. This is proportional to the mass of the mat. A competition mat comes in at about 10 kg for a 8 x 15 foot mat. Lots of backyard trampers claim that making the mat wet improves the jump. I have found that it slows the mat down, giving a feeling of better control, but there are higher energy losses both for air resistance and mat weight. The net result is that you can get a few jumps that are 10-20% higher, but you tire much faster.
G: On inexpensive trampolines, the mat is made of stretchy material. This reduces interference if you have multiple kids on the trampoline at once,but elastic fabrics have high hysteresis, and are a further energy drain. A stretchy mat responds better over a large range of jumper's weights, meaning your 6 yr old and your 16 year old both can have fun. But they should be on there at the same time. This mat also allows shorter cheaper springs.
H: Some trampoline frames (Acon, Alley Oop) use very heavy tubular steel for the frame. Much heavier than even the olympic tramps. I don't know why.
There are two ASTM standards that apply: ASTM 371 at 11 pages and a price of $U.S. 68 and ASTM 2970, which applies to trampoline parks. I've been unable to find a download site for either of these at a reasonable price.
So on the face of it the following is needed:
For a given size jumping surface:
Larger frame to allow for longer springs. If modifying an existing trampoline this could be done by inserting chunks of frame material around the perimeter. In some designs the legs would also have to be extended.
Possibly a taller frame to allow for a longer throw without hitting the ground. This could also be done by excavating a crater under the tramp.
Longer, better quality of spring. Or chaining together multiple springs.
A flexible mat fabric with the air permeability of window screen, but strong enough to withstand a 200 pound jumper at 10g's. I suspect there is some sort of fabric like this used in industrial processing.
Feasibility test of some of these:
I am trying to locate a pair of cheap round tramps that differ in diameter by two feet. Remove the mat of the larger one. Replace it with the mat and springs of the smaller one. This is a quick test about my understanding of the effect of increased throw.
Downside: With a greater throw, I'm moving more air per jump. Greater air resistance loss.
The second notion is to weave my own mat. My thought for this is to use bailing twine (400 lb knot test) to weave the primary mesh, using a star of david snowshoe weave, in a 1 to 1.5" mesh. Then overlay that with a 1/4" non knotted net that is quilted in place. First experiments with this would be done with a rebounder.
I am very much aware that there are significant legal liability issues with this. Anything that increases the rebound has the potential to produce larger numbers of serious accidents. One windmill at a time, Don.
Answers to comments.
Asked about evaluation:
My goal at present is to get performance between a high quality backyard trampoline. (On these a fit teen gets center of mass elevations of 6-7 feet/ aged chunky old fart (me) gets elevations of 3.5 to 5 feet) and the elevations obtainable by similar people on a competition grade tramp. 16 to 21 feet, roughly double to 2.5 times as great. My evaluation is done by filming with my phone at 240 frames per second to determine bounce and air time. While not perfect, as foot distance from CM is quite variable, it gives a reasonable approximation.
Comment: With feasibility testing in mind, you could also consider making a square or rectangular frame. This allows using standard piping and T- or corner joints, and probably makes the weaving also pretty simple. –
Response: Primary testing on circular trampolines for the following reasons:
I only have one trampoline at present and don't want to take it out of commission to make tests.
One of my goals is to make it possible for owners of common garden trampolines to upgrade to get a better bounce. There are a lot more cheap round ones than expensive rectangular ones.
For making a trampoline from scratch, rectangular is the way to go, although much heavier pipe needs to be used, as the forces are ones that want to bend the pipe, rather than compress it lengthwise.
It would also be possible to make frame out of wood, using techniques of pole barn building, making laminated beams out of dimension lumber for the side rails, and using recycled telephone poles for support.
Specific questions:
What are the tradeoffs in spring design?
Can springs be designed with an extensions to over 200% of base (Can an 8" spring stretch to over 16".
Can springs be designed to have a decreasing spring constant as they extend. (The vector sum of the springs action on the jumper increases as the mat depresses. This results in very high peak accelerations at the bottom. a spring force/extension graph that, if flattened, would decrease this peak, while increasing the throw of the trampoline.
Mesh considerations
How do you calculate the burst limit of a net or mesh? It's not clear at all to me how a load on the middle of a deck is spread out. Meshes are anisotropic. On my current trampoline, there is a lot more extension on springs that are connected to the fibers that run under my feet. At present the only approach is a "build and test" one, putting heavy loads, measuring the spring extensions, and computing the loads on each strand.
Static testing isn't the same as dynamic. Is a gradually applied load (lower a barrel of sand onto the mesh) going to provide different stress than a mass dropped on the mesh but giving the same depression?
Other sources of information
Are there design consideration books for this sort of thing out there? I would expect a multi-billion dollar market to NOT be formed of endless copycat designs. Am I naive?
What journals would consider trampoline design? Where can I find papers about this? Is it all proprietary to individual companies?
Am I asking the right questions?
