There is a difference between 'loud' for a player and 'loud' for a listener.
This is not so easy to understand and is often the reason why an instrument is chosen with the expectation that it will really be heard in a big church where in practice this is far less than expected.
Professional players know that they therefore cannot only rely on there own impression while playing but have to ask listeners at some distance as well.
I am giving my own reasoning combining here information from  and the phenomenon of the so called missing fundamental (*) e.g. . Let us first describe in simple terms this missing fundamental phenomenon. Let us say we record a piano tone. Then we filter out electronically the fundamental. So all other harmonics are still there. We play it for a piano player with good ears. If we now ask this piano player to strike the key for this note he will strike the key for the (missing!) fundamental. His brain fills in the information.
We are most sensitive for tones between 2000Hz and 4000Hz. So if an instrument has the harmonics in that range prominently present we will fill in the fundamental below that range as loud. Therefore, an instrument with a good fundamental below 1000Hz (e.g.) but soft harmonics between 2000Hz and 4000Hz will be heard as booming by the player but will be heard at some distance as soft by the listener.
On the other hand an instrument with not such a loud fundamental below 1000Hz but very strong harmonics between 2000Hz and 4000Hz will be heard by the listener as loud because he fills in the fundamental. This is the difference between loud and carrying!
What does this mean for the traverso? If a1 is 415 the d1 is 4/5*415=332 Hz, and a3= 3*415=1245Hz. The traverso therefore is between 332Hz and 1245Hz. The harmonics between 2000Hz and 4000Hz therefore are very important for the carrying properties of the instrument. I do not know much about the Boehm flute, but one might imagine that there the same applies. However, playing equal temperament implies that the higher the harmonics, the more out of tune. Therefore the Boehm flute has to rely on an extremely strong fundamental.
Of course, an airplane when flying low will also be heard below 1000Hz, so if we make it loud enough it will be heard.
Maybe loud is aimed at by increasing the mouth hole and further undercutting it then is original. Possibly this makes the flute louder but less carrying.
For the traverso this in my opinion is not the right solution. The player also influences the harmonics in the tone which is one of the reasons why some players project and others cannot be heard!
Also interesting in this context are the following two websites
and on http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/earsens.html.
Specially interesting are the graphs of equal sensitivity for the human ear showing that the lower the sound intensity the more we have a sensitivity for the higher frequency (>1000Hz) and even have a definite problem hearing the fundamental in a flute tone! I quote the following: For very soft sounds, near the threshold of hearing, the ear strongly discriminates against low frequencies. For mid-range sounds around 60 phones, the discrimination is not so pronounced and for very loud sounds in the neighbourhood of 120 phones, the hearing response is nearly flat. This aspect of human hearing implies that the ear will perceive a progressive loss of bass frequencies as a given sound becomes softer and softer.
Practical experiments to check the above theory are missing. I think that they are difficult but hope that somebody will pick it up and do them!
(*) I am grateful for my former colleage Drs J. van Wely for pointing out the connection to me. This was one of his usual fast reactions as I have witnessed often when we were still brainstorming in my former life as a mathematician.
 James Beament, The Violin explained. Oxford University Press, www.oup.com ,ISBN 0-19-816739-3
 Search for 'missing fundamental' and find e.g.