When laying pipes you have to abide with many requirements and constraints. The most complex one is the angle between two pipes.
You would generally assume that if you are not allowed to have an angle greater than, lets say 3 deg, the easiset thing to do would ensure that the vertical and horizontal angles do not extend beyond 3deg. This assumption is in fact incorrect.
Both the vertical and horizontal angles are 2D, and are as most Engineers know, very simple to calculate. 3D angles on the other hand are not. To calculate an angle we have to go back to vectors – something you once learnt at school but never realised there was an actual use for!
By using the dot product we are able to determine the angle between two vectors.
Below are examples of the spreadsheet that calculates the angle from standard coordinated points. The second spreadsheet provides the formulae.
