When I'm building a building from scratch, it seems that one of the hardest pieces for me to cut is the roofing pieces for a hip roof. Flat roofs are easy since they are only in one plane. Traditional peaked roofs are easy too in that you only have two equal-sized rectangles to work with. But a hip roof... that one is a toughie. What makes it so tough is that you are working with a piece of two dimensional material, the roofing material, to build a three dimensional shape, the roof itself.
This has been a struggle of mine and I wanted to try to figure out how to do it with a minimal amount of trial & error; cutting & taping pieces of paper together to get the right angle before cutting the roofing material.
It will be hard for me to explain this process because my drawings are two dimensional but I'll give it a shot. Take a look at the image below; think in terms of looking directly at the end of the building where the hip roof is located.
There are two considerations: the slope of the roof or pitch, and the angle of the cut at the corner of the roofing material to create that particular slope. You must keep in mind that in the above illustration, the roof section that you see is NOT straight up & down but is sloping away from you at the same angle as the sides. In this case, the drawing is about 30°. But that is the slope, not the corner marked as the Roofing Angle.
The Roofing Angle value changes with every degree of slope so I have various slopes here in increments of five degrees up to a 60°. The calculator I was using to get these values wouldn't calculate the angle beyond a slope of 55°
So, from the table below, you can see that to get a roof with a slope of 30° such as the one pictured here, you must cut your roofing material at an angle of approximately 49°. Here are all of the calculated values from 5 - 55 degrees:
This may help you the next time you have to struggle with those nasty hip roof cuts to build that station or even house roof for your prized model. One word of caution... these values work only when both adjacent sides of the roof slope at the same angle. If they are different, then these values are meaningless.
Until next time.