TubeNet

An old tubenet source gives the actual tube lengths as approximately
BBb Tuba 18 ft. open pipe
CC Tuba 16 ft. open pipe
F Tuba 12 ft. open pipe
Eb Tuba 13.5 ft. open pipe
Bb Euph/Tenor Trombone - 9 ft. open pipe
These vary somewhat because of the end effect of the bell, and are with no valves pressed down. Is this is what you wanted to know?

Here's a list of notes and their approximate wavelength; the actual length on a tuba is a bit shorter because of the bell effect, but this will get you started.

At 20C and A4=440 Hz:
Now, if you were supposing that the length of the first valve slide plus the length of the second valve slide precisely equals the length of the third valve slide, you'll find that it doesn't. SImilarly, 1+3 is short of 4.

For example, consider a BBb tuba. In order to drop the pitch to Ab, the first valve slide has a length of 661.3-589.2 = 72.1 cm.

The third slide has to be 111.4 cm long to drop you to a G (using the same method).

The fourth slide has to be 197.2 cm to drop to a low F.

You'll note that valves 1 and 3 together have a length of 111.4+72.1 = 183.5 cm, which is 13.7 cm too short to result in an accurately tuned F.

You can recalculate for CC, F and Eb tubas the same way.

Given that the BBb length is 18 ft, and that pressing down all four valves, in theory lowers the instrument 12/13 of an octave, then the total length with all 4 valves pressed down is theoretically 34.6 feet!

I once read on the tubenet that a BBb with all 4 valves pressed down is approx 3.5" short of the theoretical length needed to play EEEE. That says that the actual total length of all tubing in a typical 4v BBb is 31 ft. Anyone know if that's accurate?

Whoops - my last post referred to EEEE as the theoretical low note on a 4v BBb with all 4 valves pushed down. I meant BBBB.

Testing.

Yes, the fatness and taper can have a substantial effect on length. How short are you falling? It's not easy to measure the centerline length of a bugle from the outside, especially when all the outer branches are continuously curved.

The bell effect is just an empirical correction. What's happening is that the speed of sound is not constant in the bugle because of the taper, at least at any given frequency of vibration, so the connection between theoretical length and actual length is fuzzy. What we call the "bell effect" is just the equivalence that is arrived at by experimentation. Instrument makers do a lot of testing as they go to check length.

My own measurements were 40-60 cm short of the theoretical lengths Chuck calculated in the historical section of those thread. Of course, those lengths were based on the assumption of constant speed of sound in the bugle.

Rick "https://www.rickdenney.com/york_vs_miraphone.htm" Denney