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I was wondering if anyone can help me. I don’t have a homework problem, but a problem I have encountered at work. I am a mechanical engineer working in the railway industry and I am struggling with a problem of reconstructing the vertical geometry of a rail in terms of height and distance along the rail.

The rail is measured using a chord measuring system, with versines taken at two points along the chord:- a point halfway along the chord and a point between the mid-point and the end. The measuring chord is moved along the rail at equally spaced intervals and the versine pairs measured at each point. The chord length is an integer multiple of the measuring interval.

Currently the process used to obtain the original rail position from the versine information uses the centre versine only. However this means that wavelengths equal to half the chord length cannot be reconstructed, hence the requirement to somehow incorporate the information encoded in the second versine measurement. The current method uses a simple geometric relationship to calculate the height of the rail at one end of the chord, given initial starting values of zero (i.e. the other end of the chord is at zero). I don't see how I can use this method and incorporate the second versine though, and i am struggling on how to approach this problem. Can anyone help point me in the right direction?!

I hope that I have defined the problem clearly enough, if not please do ask if there is any more information I can provide.

Many thanks