My final trumpet will be natural trumpet. That is, it will have no valves, much like a bugle. It will be in the key of Bb, which is the same as a normal trumpet or bugle. This will allow me to play bugle calls on the trumpet.
To figure out the length of tubing needed in the trumpet, I used a few different methods. I found out that a trumpet is roughly approximated by a open ended tube in the physics world. If you send a wave through this theoretical open tube, only certain frequencies and their harmonics will resonate, and that is found by the equation f=v/(2*L), where f is the frequency, v is the speed of sound, and L is the length of tubing.
This trumpet is very much based off of existing trumpets. The bell is designed directly from my own trumpet. I literally took a picture of my trumpet’s bell then I brought that into Autodesk Inventor and traced it using the spline tool to create a smooth curve that represents the bell in CAD. Then I rotate extruded it 90 degrees and exported it to mill it.
The leadpipe design is based off of a patent I found that has since expired. The dimensions were literally taken directly off of the patent, so that I know it would work. It also seems like a very novel type of leadpipe that contributes to the sounds greatly. Here is that patent: https://docs.google.com/viewer?url=patentimages.storage.googleapis.com/pdfs/US4559859.pdf
I looked on the Wikipedia page for trumpets and it says that the most common length of tubing in a trumpet is about 148cm. I wanted to confirm this, so I plugged it into the equation for open tubes and found that a length of 148cm produces a tone of frequency 114hz. I then looked up this frequency in a table showing frequencies vs musical notes, and found that 116hz is a Bb. This is well within the range that the trumpet can be tuned to, so 148cm is a good length to shoot for.
I also measured the length of tubing on my trumpet fairly approximately and came up with a length of 140cm, which produces a tone closer to B rather than Bb. This trumpet of course produces Bb when played, though, so that discrepancy must come from measuring error. As long as I leave room for tuning, I should be fine with aiming for 148cm.
Here is an image of the natural trumpet I designed that I will be building:
Here is an screenshot of the 3d bell over-layed on the image of the bell it was taken from: