this is a real problem i am currently facing. i am building a bridge out of stone, a footbridge crossing a creek. my problem is that not only is the bridge a natural arch, but to make things difficult on myself, i have decided to make the bridge curve, so it is in the shape of an 'S' if you like.

i have made a nice flowing curve by using hose, and pinning it to tall steel pins coming out of the ground. so i have one side marked out, and looking great. problem is, i need to replicate this curve, 2 metres away, running parallel to this first curve. keeping in mind that the first curve not only starts low, raises in a nice arch and finishes low on the other side of the creek, but it sways like an 's' whilst doing so.

i tried finding the middle point of the first curve, then marking increments of 1200mm either side until each end of the bridge. then setting out the second curve, getting the 's' roughly right by eye, and doing the same, by marking a mid point, and the 1200 increments. then between the 2 curves i have measured 2 metres every 1200 increment making the second one symetrical to the first. but. and its a big but. using a laser level, getting the second curve to be the same arch as the first has proved to be most difficult. i transfer the levels from one curves increment, to the other curves opposing increment, and both curves do not seem to match.

so what i am really asking, is there a formula, or method of duplicating curves, that not only bend in a slight 's' shape (if you were looking from birds eye view the bridge would appear as a slight 's'), but also bend like an arch aswell (looking at the side of the bridge, it arches over the creek) because not only do i need to copy my first 's' but i need to transfer all its level points onto the second curve, making both sides of the bridge flow.

hopefully someone can not only understand what im saying, but come up with an answer???