A curved windway helps keep a seal on the lead pipe where you breath into the instrument. With a perfect seal, your low notes will sound "brassy," which is most desirable, and you high notes, easily can get three octives, stable and soft. It's got most to do with the embouchure and verly little with the quality of instrument, although, a curved wind way facilitates this seal. When approaching the instrument for address, place the brim of the lover lip where it meets the skin and put your upper lip tucked into the lower so the lower is covering the upper while maintaining your position on the lead pipe of the instrument; the gently pull the cinders of your mouth down and back like when you might pucker after eating a tart lemon, all the while allowing your tucked upper lip to slowly and gently roll out from under the lower lip while gently blowing. Your upper lip should come to rest on the flat surface where the curved bore is. The outer rim of the upper and lower lips should make the shape of the frown like downward turn of the curve on the bore. Never fill your cheeks with air always breath through your nose and never let your upper and lower lips touch; if they do, take them off and try again, fishing is a bad habit, i.e. keeping your lips attached and jockeying for your position. Keep in mine not to drive yourself mad with this; if you keep slipping then go to the next step which is to bring the tip of your tongue up to the roof of your mouth, while keeping a steady breath through the instrument, and make the sound of Tah. Start with long taaahhh (s) on the lowest note and climb the scale with each sharp and natural note (12 steps to the chromatic scale from middle C to high C) untill you get to the High C and now go down the same way making all the flat and naturel notes on the way back down to middle C. Then go middle C repeating it twice and jump to high C (c=low and C= high cc CC cc CC) , this will help you establish your range so when your lips are wide for the low their embouchure will be able to play the high C in the open position of Low C and when narrow (remember never close your lips or otherwise let them touch) in the High C position to effect the brassy quality of the low note. Finally, as your breathing improves through your nose and your seal becomes more and more firm, you may fill the jowls under the tongue, remembering to keep the corners of your mouth pulled down and back, and let it be a type of bag like the bag pipes hold air to keep a contestant flowing note between breaths through the nose. This may be achieved by using the back of the tongue to separate the wind in the mouth that is spending itself to keep the flow forward and note playing while the airway from the nose down the back of the throat fills up the lungs again, then bring the breath back through the mouth to fill up the air pocket under the tongue and keep the note playing. Remember, you won't have to puff your cheeks if you get this right and a way to help facilitate this reciprocation of air, by filling your lungs while the lips are on the instrument and breath out through your nose while at the same time blowing through the lips to make the note. It may seem counter productive like you're wasting your air however it's counter intuitive, for part of the difficulty is getting oxygen deprived with a lung full of air, then you might keep slipping off the lead pipe of the instrument; when therw time come that you lean controll of your breath, it will not be necessary to dump air out of the nostrils, you'll only breath in through them.
I hope this as was helpful. I started playing recorder in 1992 and moved to the trumpet in 1997 and whent to Allen Colin of Charles Colin music on 53rd st New York, New York (at the time of 1997) as well as having taken musical theory at New Jersey City University in 1993, 94 and 95.
Best Regards
Joseph Markenstein
Mountain View Cal.