See-Saw Math
April 12, 2010 9:39 AM   Subscribe

What is the optimal fulcrum height, plank length and maximum angle for a teeter-totter/see-saw?

Google knows of lots of plans and instructions for see-saws but I can't find any specifics. For example, if the fulcrum is 28" high, how long should the plank be?
posted by I'm Doing the Dishes to Sports, Hobbies, & Recreation (9 answers total) 1 user marked this as a favorite
I can't give you specific ratios but having been an enthusiastic teeter-totterer in the not so distant past I can say that longer is better. Sixteen foot plank at least. The fulcrums on the best ones I remember seemed to be less than two feet high. One caveat is that longer=higher on the upside so falling off becomes more serious.
posted by stubborn at 9:48 AM on April 12, 2010

Your fulcrum should be high enough that, when somebody's sitting on each end of the teeter-totter, their feet are on the ground and the seat is against their butt (they should be able to straddle the fulcrum and be on their tip-toes). If the fulcrum is too tall, one person would be on one end of the totter but the other person wouldn't be able to get on the other end because it would be tipped up into the air. Too short a fulcrum, and the rider would still be touching the ground when the other end is close to the bottom.

As for length: It depends on how far you want somebody to fall if they're up in the air. Use your high-school geometry and figure out , based on how high the fulcrum is, how high one end would be if the other is touching the ground. Also consider the height of other kids on the playground - you don't want somebody unwittingly wandering beneath a raised teeter-totter with a kid on it. When I was in school the playground had two lengths of teeter-totters; the short teeter-totters still gave you a pretty good bump if your teeter-totter partner dropped you, but we young'uns were terrified of the long totters -- because we had to be, like, five feet up in the air when at the high-point. There's also a question of material strength of the plank itself; if it's too long it could break at the fulcrum.
posted by AzraelBrown at 9:49 AM on April 12, 2010

I suspect the target weight of the riders is an input into this equation.
posted by jeffamaphone at 9:51 AM on April 12, 2010

When one side of the see saw is on the ground, the opposite side will be twice as high as the mid point (fulcrum) no matter the length. Unless of course the plank is off center.
posted by K5 at 10:27 AM on April 12, 2010 [2 favorites]

The height of the fulcrum largely depends on how tall the expected users are. You want it to be about the same height as the person's butt while sitting (with their feet touching the ground). If it is too tall the users won't be able to climb on and you risk the case where the second person climbing on launches the other person up and off the plank. Too short and the end of the plank will hit the ground too early.

The length of the plank depends on two variables. First, it's limited by how strong the material is. Too long of a plank with too weak of a material will result in bending at the fulcrum, or worse twisting which will tip the users off to the sides. The second factor is how high you want the users to go. The longer plank and taller the fulcrum, the higher the users will go.
posted by arcolz at 10:33 AM on April 12, 2010

What K5 said. The length of the plank doesn't come into the height at the highest point at all, so you can make it whatever length you want.

(You can see that the triangle made by the angle of the plank touching the ground and the fulcrum is congruent with the triangle made by the angle of the plank touching the ground and the invisible line from highest point to the ground... You can see this is a half/double ratio by considering the length of the hypotenuse, for the first triangle it is half the length of the plank, for the second triangle it is the full length of the plank. Or you can just do the trig.)

That being said, I recall the see-saws from elementary school being approximately 3-child-heights long, with the handles about 1/2-child-height from either end. Both kids being able to stand flat footed or slightly on toes when the plank is level also seems right.
posted by anaelith at 10:57 AM on April 12, 2010

But the length of the plank does effect how hard it is to lift the person on the other side, right? The longer the plank, the easier it is to lift? I'm trying to remember highschool physics...
posted by jeffamaphone at 2:22 PM on April 12, 2010

Since the fulcrum is dead center*, it shouldn't make a difference for lifting. The see-saw is similar to a set of balance scales, if you can picture that. (Similarly, even if the plank itself is quite heavy, the weight of the plank on the other side is balanced by the weight of the plank on your side.)

For a traditional lever, like, say, a crowbar, you push the long end a further distance to easily lift something heavy on the short end a shorter distance.

*I'm going to assume this is professional looking DIY see-saw building, not alcohol-inspired see-saw building.
posted by anaelith at 8:40 PM on April 12, 2010

Very good see-saws also include a bracket at center, to adjust the plank to be off center in either direction, to compensate for weight differences. Some modern commercial models are made with a pipe, with attached seats, instead of a plank. This kills the fun of walking on the plank and standing in the middle, which is a great balance exercise.
posted by Goofyy at 9:31 PM on April 13, 2010

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