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Calculating how big a base to attach to a chair to prevent it toppling

Engineering Asked by Steve Ives on March 15, 2021

I have a pair of cinema seats that are designed to be bolted to the floor.

Seats without feet

I don’t want to do this so instead I have made wooden feet and bolted the seat to them and they are quite stable.

Seats with feet

I know that an object won’t topple if its centre of mass lies within its base, so I simply made the feet extend to the rear of the seat back and the front edge of the seat base when folded down. Now they look quite large, so I’d like make the feet as short as possible. The seats do not recline.

I’m pretty sure the centre wooden foot has no effect on front/back stability so can be reduced to be just a few CM longer than the metal plate it is bolted too (for aesthetic reasons).

For the 2 outer feet, can I experiment with the tipping point by standing the chairs (with feet attached) on other wooden blocks with I can move forwards and backwards?

I also have another pair with no feet attached yet, and they will tip backwards if stood up, but with someone sitting in them they will freestand, and are quite difficult to tip backwards but relatively easy to tip forwards, which tells me that they only need to extend perhaps 10-15cm backwards.

Question: How do I calculate how short the feet can be without sacrificing stability?

Assume 2 normal sized adults.

One Answer

This kind of thing is best worked out experimentally rather than calculated, due to the dynamic forces involved. The theoretical limit for "sitting still" won't be stable enough for real use.

Shuffle the blocks forwards gradually, and keep sitting down hard into the chair - throw your weight backwards as you might in real life. Mark the point where it feels scary. Now shuffle them backwards and put all your weight on the front edge, try standing on the front edge as if you wanted to reach the ceiling. Again, keep going until it scares you and mark it.

Now knowing the front and back limits, add an inch or so for safety, cut to length, and Install.

Answered by Jonathan R Swift on March 15, 2021

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