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I am building a rectangular coffee table and want to build it with two legs The table top will be 120cm x 100cm (approx 47x39inches). The table height will be 40cm (approx. 16 inches) the idea is to use two legs made of 18mm (3/4inch) plywood sheets with widths of 50 cm and 40 cm (20 inches / 16 inches)
The legs will be mounted perpendicular to one another. ( think T)
What is the ideal position of the legs to maximise stability?
Using two legs at a "T" will result in a table that is very prone to tipping. In the diagram below, the sum of the moments (torque) about the R1-R2 axis must be zero for the table to remain in equilibrium. Just before the table tips, all the reaction force from the legs against the floor will be concentrated at R1 and R2.
If the weight of the table at the centroid contributes to a greater moment about the axis than that from a downward force at AB, the reactions from the legs will be distributed more evenly than just the tipping point at R1 and R2.
If you're dead set on a "T" table leg configuration, consider making L1 and L2 the entire length of W and H respectively. That's not enough to achieve stability however, since the far corners of the table are still at a much larger distance from the R1-R2 axis than the centroid of the table is. Therefore, consider trimming the table down to a trapezoid or triangle, with the narrower end corresponding to the bottom of the "T". Otherwise, consider an "H" or "X" configuration for the legs as @Wayfaring Stranger suggests.
you can build the table with two legs on two sides, just like the coffee table in the picture. This can keep the stability.
I believe you cannot make this stable as you may like. Since you will be placing the narrow leg, the one going parallel with the length, there will be 18" of top extending beyond the thickness of the plywood leg. The other end of the table will be ok, it will only have 8 or 9" overhang of the leg if you use the 20" leg there. If you oriented the legs at a 45 degree angle to the top, it will not improve the situation, it will most likely make it worse. It be against your intent of design, but you would need to turn both legs the same direction to make it stable, at least enough to put your feet up on, if you are into that sort of stuff.
