As I've been contemplating adding gambrel attic trusses to the truss plugin I've had to give some thought to what constitutes a good gambrel design. I've looked into this before but my conclusion is that no matter the lower and upper pitch of the roof a good looking design seems to be always achievable if the lower and upper legs of the roof are more or less equal in the length. To that end I've devised a simple spreadsheet calculator that will quickly throw out the numbers and display a graphic of the gambrel profile:
I'm not saying this is a hard and fast rule but it seems to give decent results. Minor variations (ie. L1 not equal to L2) are generally okay but if one leg is significantly longer than the other the gambrel profile becomes distorted.
The math to come up with this equality and generate the coordinates of the overall roof height and the pitch break is rather interesting and for those mathematically inclined is given below. Note that the equation ends up being a quadratic equation with the positive root extraneous:
I'm not saying this is a hard and fast rule but it seems to give decent results. Minor variations (ie. L1 not equal to L2) are generally okay but if one leg is significantly longer than the other the gambrel profile becomes distorted.
The math to come up with this equality and generate the coordinates of the overall roof height and the pitch break is rather interesting and for those mathematically inclined is given below. Note that the equation ends up being a quadratic equation with the positive root extraneous: