As an engineer, I appreciate that for acoustic waves turning corners, making curves 'gentle' is mostly a result of relying on intuition rather than understanding physics. Is this common knowledge among those who apply modern technology to instrument design? You are the first respectable horn designer I have ever heard mention this fact.
For those less informed, the problem of bends in an instrument has two aspects. One is simply air flow, which will respond to straightening curves the same way unkinking a hose will. The other aspect is bending the actual acoustic wave. The optimization of this tends toward using straight tubing, as much as possible, and designing couplers between the straight sections to make the bends. The couplers geometry is optimized by reflection angles directing the acoustic wave around the corners. Knowing the nature of the acoustic wave will identify places where you absolutely don't want to locate a bend. The optimum shape of the coupler will undoubtedly deviate from a simple bent tube. Interestingly, I have one instrument in my collection whose design would indicate some understanding of the physics. It is my oldest brasswind, an antebellum contrabass Saxhorn made by E.G. Wright in the 1850's. Wright's designs are characterized by lengths of straight tubing connected by short couplers turning very sharp 180 degree bends. The couplers will couple two 3/4" tubes running within 1/8" of each other. I'm not sure what the engineering reasoning was behind Wright using these uniform 180 degree couplers wherever possible. I have split coupler that I showed to Robb Stuart because it far exceeds my ability to bend large diameter tubing. Robb thinks he can bend one, but will require several annealing stages. Wright horns are among the best players from the era. This horn rivals the best horns being made today. Just about the time I was congratulating Mr. Wright on his forward thinking design, I further studied the cracked crook from the perspective of my manufacturing engineering experience. I discovered that rather than being a labor of love to bend the tubing, each coupler was made of two stamped shells silver soldered together. I surmise each shell was stamped from sheet stock, then the mating flanges sanded to produce a sharp inside corner. After soldering, the remaining flange was trimmed back flush to the outside wall. It looks just like a piece of tubing with an incredibly difficult bend, except it has two seams right where the flanges were. So was it a cost saving step or an application of physics way before its time?
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