May 2002

# A Soft Frame is Good to Find

Even though stiffer frames are clearly more efficient, they seem to have a major downside - they're terribly uncomfortable, and it seems that the stiffer they are, the more uncomfortable they are. In particular, people have always complained about the infamous Cannondales (in particular, the very early ones), which have very stiff frames, as having a very harsh ride.

However armchair physicists again step in. They mount the bike in a test fixture, apply a load and measure the frame deflection. Then they say, no, no, the deflections of the frame are very tiny, and the differences between frames are even tinier, so no one could ever tell the difference. They even say that this lack of significant deflection means there isn't any significant shock absorption happening. (These same arguments are applied to cross-laced versus radial-laced wheels.)

Again, armchair physicists look at things too narrowly. Deflection has little to do with shock absorption. Shock absorption is a measure of frequency response and damping.

If you've played softball or baseball, you've probably had the experience of hitting a ball just right so that it "rings" the bat and really stings your hands. "Rings" is a perfect word to describe this, because the bat starts vibrating at a high frequency. Bats normally vibrate on the order of a few hundred Hz, however when you get a bat to "ring" like this, it also has a much higher frequency vibration component. The following was stolen from the University of Washington, Physics 208, lecture 22:

This is illustrated to the left. The two oscilloscope traces are outputs from an accelerometer attached to the handle of a baseball bat. When the bat is struck at the node (top trace) only low frequency oscillations occur. But when the bat is struck near the tip (bottom trace) high frequency vibrations can be seen superimposed upon the diving board mode. It is these high frequency vibrations which cause the sharp stinging sensation when a ball is struck improperly.

If you've ever had this happen with an aluminum bat, then you know that the minor sting of a wooden bat can't compare to the hand-numbing experience of the aluminum bat. This is sort of because the aluminum bat is stiffer, but it's more because the aluminum doesn't damp out vibration as quickly as wood does. This damping is related to stiffness, but it isn't the same. It is possible for material X to be both stiffer and more damping than material Y (carbon fiber is very stiff, but it can be a good damper too), but most of the time this is not the case.

Shape matters too. The biggest reason aluminum bats can give you such a painful sting is that they are hollow -- hollow materials have two different types of vibration, bending modes, and shell modes. The shell modes are (generally) much higher in frequency than the bending modes, with frequencies of a few thousand Hz. And while bending modes distort the shape of a bar much like a simple deflection might, shell modes do not.

It's interesting to me that early Cannondales had thinner walls and bigger hollow areas than other frames, and hence their shell-mode vibrations are probably more intense than other frames. Solid shapes on the other hand don't have shell modes, only bending modes.

The frame materials, shape, design, and joining methods, the handle bars and wheels, the tires can all effect damping. In order to really test you have to have the right set up, and simply testing deflection certainly won't do it. Fortunately, testing frequency response in objects is well understood, but unfortunately, you can't do it with stuff that most of us have lying around the house. On the other hand, high frequency accelerometers, A/D converters and portable digital high frequency data loggers are easy to come by and will only set you back a few hundred dollars. If you send me the money, I'll do the test. :-)

Other sports (like baseball and tennis) have spent lots of money on this sort of analysis. As far as I can tell, this is sadly lacking in the world of cycling. It seems likely that studying this could result in design improvements that would increase the comfort of metal frames without giving up significant frame stiffness.

But after all this, you're probably still wondering which of aluminum, steel, and titanium naturally has the least harsh (best damped) ride? I haven't been able to find the damping coefficients or loss factors for these materials in a generalized way. This is probably because the damping can vary widely depending on how they are formed and used. All other things being equal, I would expect all metals to have very small damping coefficients. I have read that cast iron has better damping qualities than other metals. This means you could get a nice soft ride from a solid cast iron bike :-)

So if you want a comfortable ride (and you accept my belief that frequency response affects comfort), then in broadest terms you want frames that are less stiff. Howevery you can probably optimize both stiffness and comfort to some degree, just do lots of test-riding. And if money is no object, then the answer is easy: buy a carbon fiber frame. (Unless of course you want something with graceful failure characteristics.)

But if speed is what you want, then forget comfort and get the stiffest frame you can find.