Here are some examples of cavalry trumpets , and some explanation, which I hope will be generally helpful .
Trumpets were originally rather long instruments, about 30” overall, like the ones still used for ceremonial by the Lifeguards in State Dress. They are formed in one loop, which makes them nice to look at but somewhat fragile and inconvenient to handle on horseback.The total length of tubing of seven feet allows a lot of notes, and gives the characteristic rasping tone used for calls, which were sounded on the lower notes .
From about 1750, all European cavalry started to use twice-wound “ short model “ trumpets when on campaign , which are much more robust and markedly shorter, at around 18” overall , though of course the length of tubing is the same.
Here’s one from 1815, an ornamental one carried by the 12th Light Dragoons:
And a typical British issue pattern from a little later, by Potter’s of Aldershot. Both these have the bell extending to the front bow, the usual British style.
Another pattern has the bell extending beyond the front bow, like this one of mine ( Boosey & Hawkes, modern ), shown here with a Bb Duty Bugle ( sorry, it needs cleaning ! ). In both the Bugle and the Trumpet the tube goes around twice, which is the point I was making in the first place.
And here’s a 19c French one, which seems to be identical to the Napoleonic period pattern which you are portraying :
Just as an afterthought , Trumpets should not be confused with Bugles, though in fact the two have done rather a lot of interbreeding , particularly in the US.
Historically , the Trumpet was for cavalry , and goes back to the Ctrusades. The Bugle was a much later arrival, around 1780 ,used originaly by Jaeger and Light Infantry.
The Trumpet is LONG, the Bugle is SHORT, which affects the number of notes they can play , and thus the calls they can sound .
Enough...