### Ich benutzete die Mathematik!

Mar. 9th, 2017 03:58 pmWe turned the shafts upside down and because we had the marathon tips it worked fine, however I doubt it would really fly in a show so I needed a different solution. Shelley suggested turning them horizontal, but I didn't think it would work because we have chunky horses. Sure enough the 21" it left between the shafts was not enough space for Kitt so back upside down they went. The 24" space we set was good so I figured if I could get Magma to engineer me a set that would leave me 24" between the shafts I would be set!

Today I went out and measured the shafts. The tricky part is figuring out the angle the bend needs to be. With my handy plastic protractor I found the current angle is 150* which was my starting point.

The front of the shafts essentially make a trapezoid so I had the distance between the shafts at the base, the distance from the bend to the tip, which made up the sides and the distance between the shafts at the tips, which made the short base. I had two trapezoids, the one that the shafts currently made and the one I wanted to make. I needed the measurement of the angle made by the big base and the side which would tell me how much the bend angle would need to change.

My brain said "Math can tell me!" So I chopped the trapezoids into two triangles by connecting the opposite corners. I used the pythagorean theorem to discover the long sides of the triangles and then looked up the formula to find the angle I needed. It involved a cos^-1, which required me to find a real calculator rather than using the one on my phone.

And lo! I had my answer. The first angle was 47.12 and the second was 50.91, which is just shy of a four degree difference. I had eyeballed it at 5* and it is nice to have the math back that up. I will probably round up to 5* as 25" between the shafts wouln't be a bad thing. There is a little part of me that is worried about sounding too anal when i take the shaft in and say "I want you to make this, but make it x long and I need the bend angle 3.79* larger ... 5* just sounds more reasonable than 4.

You know, you sit in math wondering when the heck you are going to use this stuff and 15 years later you are looking up calculations so you can figure out how much bend you need in a new set of shafts for your horse drawn cart so it fits your pony who is technically 1 1/2" too short for it.

Such is life!