[psychojohn]

Originally Posted by Alan Carruth

Think of it this way: there's not much horsepower in a plucked string. If you want to make a car with a small engine, and you need to have good acceleration and top speed, you need to keep it light. Acceleration in a car corresponds with high frequency output in a guitar, and top speed is like output power.

The most important parameter in the top is the relationship between the density and the Young's modulus along the grain. Young's modulus (designated as E) is a measure of potential stiffness: two things with the same shape and the the same E value will have the same stiffness at a given thickness. There are fairly simple ways to measure the E values of materials to fair accuracy. If you measure a bunch of samples of different kinds of woods you'll find that softwoods and hardwoods tend to have similar long-grain E values, but the hardwoods are normally denser. Sitka spruce often has about the same E value along the grain as Indian rosewood, but the rosewood will be as much as twice as dense. That means that a rosewood top will tend to weigh about twice as much for the same stiffness, assuming it's built in the same way as a spruce top.

What's most interesting is that for most softwood samples you can predict the long-grain E value reasonably well if you know the density: about 60% of the samples I've tested fall within 10% of the same line on the graph if you plot it out. The relationship is very nearly linear in the normal range of densities. Pieces where the latewood lines are narrow relative to the early wood tend to have lower density for a given E value, while heavy latewood lines tend to add weight without adding commensurate stiffness. Run out reduces the E value. As John Arnold points out, the main thing that seems to correlate with cross grain stiffness is the degree of quarter, due to the cell structure. If grain count (lines per inch) does make a difference it's not much of one, IMO.

Since stiffness in a top goes as the Young's modulus and the cube of the thickness, you can usually make a lighter top by using a low density piece of wood and making it a bit thicker. Thus a low density piece of hardwood, such as balsa, which tends to have a lower E value at a given density than softwood, can still make a light weight top simply because the density is so low to begin with. You might have to leave it twice as thick to get the stiffness up, but if the density is 4#/cubic foot, instead of 20#, it's still going to be pretty light. Not many hardwoods are enough lower in density than most softwoods for that to work out very often, but all woods vary, and you might find something that works.

Wow ! Thanks for that info. You know, I've come to think of guitar building as an art. You just gave it a healthy dose of science for me ! Thanks ! John