Theoretical distances calculated from the speed of sound
I've calculated the length of tubing corresponding to wavelengths of different pitches to determine the theoretical distance a trombonist must move the slide for the various positions.
The calculation for this page is available at this spreadsheet.
First the speed of sound is calculated using the "more accurate" equation from this Wikipedia page. At 72 F (22.2 C) the speed of sound is 344.5 m/s. The speed of sound is essentially independent of pressure, so this calculation should work up in Denver as well as in the low lands.
Then wavelength is determined for a particular frequency by dividing the speed of sound by the frequency. For A at 440 Hz the wavelength at 72 F is 78.3 cm.
To go from A to Bb (a half-step) on a well-tempered scale, the wavelength is divided by two raised to the 1/12th power. This wavelength is multiplied by 4 since a pedal Bb on a trombone is three octaves below the Bb just above A at 440 Hz, and a pedal Bb is produced by a half-wavelength.
At 72 F, this calculation says the length of a tubing of a Bb trombone is 295.6 cm, or 116.4 inches, or 9.7 ft. I have seen websites that say a trombone is 9 ft long, but this length corresponds to a temperature of 0 F. Slide positions are usually irrelevant much below 30 F because the slide tends to freeze.
Here is a graph showing the slide distances in cm at 72 F for a Bb trombone, as well as for trombones in F, E, Eb and D. These are all calculated using a well-tempered scale, as above. The distances are given for the 7 positions going from left to right. Most slides are about 62 cm long, so anything greater than that is off the horn. Click on the graph for a larger view.
Thanks to Benny Leonard for a correction on the explanation for the wavelength of a pedal Bb.