Posted by Rick Denney on April 02, 2001 at 10:43:39:
In Reply to: Re: Carbon fiber in tubas posted by Chuck Jackson on March 30, 2001 at 20:17:26:
I've been silently listening to the discussion about carbon-composite tuba bells, and now I'm seeing some of the same mythology creeping in that I have been battling amongst bicycle racers.
So, allow me to describe some engineering principles about carbon-composites, and then the discussion can proceed from there.
A carbon composite is almost identical to fiberglass, except for the fibers. In fiberglass, the fibers are made of glass, which has higher tensile strength than most plastics and is elastic, which most plastics are not. By "elastic," I mean that it stores energy efficiently, and returns it without absorbing it. So, you can make a spring out of an elastic material--you flex it, and it springs back efficiently. A non-elastic material absorbs energy when flexed, and therefore returns to shape inefficiently. In fact, the proper term for a non-elastic material is--plastic.
Note that elastic and flexible are utterly different properties, though they are often confused by non-engineers. A butyl-rubber strap (aka "rubber band") is highly flexible, but also plastic. Stretch it back and forth and it gets hot. A steel car spring is not flexible (try flexing it with your hands if you think I'm wrong), but it is highly elastic.
So, what is a carbon composite? It comprises strands of carbon fiber molded or imbedded in an epoxy plastic, just like fiberglass, only with carbon strands. Carbon strands are much stronger than glass fibers, and carbon composites will therefore be much stronger than fiberglass assuming the same number and size of fibers are used.
But the plastic material in which the carbon is molded is not elastic at frequencies above the pedal range of a tuba. This is also true for fiberglass. Carbon-composite bicycles are remowned for their comfort, though most cyclists incorrectly attribute this to flexibility. It is not more flexible than other materials when designed correctly. But it is plastic at higher frequencies, and a carbon-composite bike is quiet. Tap a carbon bike with a fingernail, and you get a thud. Tap a steel, aluminum, or titanium bike and you get a ring.
It's the same with tubas. Tap a carbon-fiber bell with a fingernail and you get a dull thud. On most brass tubas, you get either a ring or a clang (which is a ring at multiple frequencies, some of which cancel out and therefore attenuate others). Some folks think that a ring is a good thing, and they call it "resonance." Others think it robs the air inside the horn of vibrational energy, and seek ways to reduce or eliminate it (using bell deadeners). Some folks change the way the brass vibrates from something less desirable to something more desireable by adding additional elastic mass, either by using thicker brass or by adding brass stiffeners (e.g. Jay Bertolet's big Cerveny).
Carbon fibers themselves are quite elastic, but they have no strength against buckling and must therefore be held in place using a plastic filler. When you compress the material, it is the plastic bearing the load. When you stretch it, it is the carbon bearing the load. So, it tends to stretch elastically and compress plastically, especially at audible frequencies. Brass and other metals are linearly elastic through the range of loads that don't cause permanent deformation.
The only way to make a carbon composite elastic when loaded in compression is to stretch it before it is encased in plastic, so that it has enough residual tension to absorb all likely compressive loads. Then it behaves somewhat more linearly, though the plastic filler will creep with time and the residual tension will eventually relax out of the material. This would not be a good thing for tubas. Even then, however, the filler will damp vibrations in the audible range, much like a wide leather belt around the bell as favored by some.
So, we get to a question: What effect does the elasticity of the tuba material have on the sound? I've posed this question before, because of the myths that I see spoken. For example, the notion that annealed brass is more dead than worked brass is wrong--annealed brass has the same stiffness as worked brass, it just isn't as strong. And strength is only an issue for dent resistance, not for audible effects (because the material is linearly elastic before deformation).
If we assume that the elasticity is important, then a carbon-composite bell will be different than a brass bell--no ifs, ands, or buts. It may be different in a pleasing way, but different it will be. Its advantage over fiberglass may be its greater strength--it can be made much thinner and still be durable. Barring that, however, I cannot imagine that it would be significantly different than fiberglass.
Rick "who would like to hear an A-B comparison" Denney