I read this NG in spurts depending on my free time. I constantly see posts about range. Likewise my email and questions sent to me off of the TPIN contain more requests about range than any other topic. I am going to address some of them now.
A very long thread on the TPIN was started by someone who said that to play higher you needed to make your vibrating surface smaller. He stated that the lips were like a string on a violin. It is true that on a "STRING" instrument if you shorten the string by placing a finger on it you get a higher sound. On a "BRASS" instrument this is not how it works. The vibrating surface under the mouthpiece stays the same length from the pedals up. You can stretch a string to play higher but if you stretch too far it breaks. Well if you try stretching your lips then basically they also break. On a violin a thinner string plays higher than a thick one. On a brass instrument we CAN control the lips to make the aperture wider or narrower. This is not the only similarity between the two. To play louder on a violin you pull the bow faster and harder across the strings. To play the trumpet louder you use more air. The original poster also talked about air speed. Well there were and still are so many true artists that believe in air speed we can't argue it's importance. Now how does it work? Well while it is possible to play with slower airspeed the sound seems dull and under pitch. Some people talk about spin on the notes especially in the upper register. The airspeed gives you carrying power. In the leadpipe on a trumpet the speed of the sound wave travels at  331 meters / second. As it gets to the body (which is a larger diameter) it gets to 334 meters / second. In the bell it really speeds up a large wide taper will send the sound wave out at 350 meters / second. A tighter more tapered bell can speed it up to 390 meters /second. This is why some horns carry better than others. Certain metals also help, bronze carries farther than brass for example.

'Pops'
http://www.Bbtrumpet.com/