the maths behind one phase of 415V 3 phase power being 240V and not whatever 415/3 is
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I will take a shot at this… think of the symbol for a Mercedes car, 3 “spikes,” if you will. If the distance from the center of the star to any one point is 240, the distance between the points of the star will be 415. You can draw this to double-check it, 24 cm straight up from the center, 24 down and to the right, 24 cm down and to the left. I should look like the skeleton of a big Mercedes symbol. Then measure the distance between any 2 outside points, should be just over 41 cm. Your numbers times 10 show the relationship you are asking about. The insides of a three phase generator are essentially like this. If you have a generator instead of a Mercedes symbol, the distance (voltage) from one point to the center would be your 240 VAC, and measuring to any of the 2 outside points would be 415 VAC, 120 degrees “out of phase.” Essentially three generators in the space where you might only suppose there is one – a great efficiency. PS Three points on the star is just used for convenience, you could arrange pretty much any low number… getting “polyphase” AC from your generator.
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