Bike Think: Bicycle ride feel and frame materials

Ride Feel

Ride character is primarily affected by three factors: frame stiffness, natural frequency response, and histeretic damping.

Frame Stiffness

The impacts that reach your body are related to the stiffness of the frame in the direction of the applied shock loads. This quality is primarily noticeable with larger dynamic loads such as potholes or larger bumps. The frame stiffness is a combination of frame/tubing geometry and material stiffness. The graph below shows the relative stiffness for seat stays for common seat stay tubing in each material. The results are from my beam FEA frame model. What is interesting is that the aluminum seat is the least stiff and the carbon fiber is the stiffest. Of course the stiffness in each case can be changed by changing the diameter or thickness of the tubing, or by putting a bend in the seat stays. But I think this comparison of common seat stays in each material suggests that frame stiffness is not the primary driver in the ride feel of a frame. The deflections for the loads applied in the FEA model were around 0.5mm for a 220 pound force. A seat stay assemble that flexes 0.34mm is almost twice as stiff as one that flexes 0.65mm. But they are both going to deliver most of a shock load to the rider.

Natural Frequency Response

Natural frequencies can exaggerate rough rode and other vibrations. In general, a higher natural frequency is desirable because is reduces the chance of a vibration in the frame that matches a natural frequency. The natural frequency of the frame is affected by a multitude of factors including frame geometry, rider's position, and how full the water bottle is.

In general, frames with higher stiffness to weight ratio's will have higher natural frequency responses. So materials with higher stiffness to density ratio's will tend to produce frames with higher natural frequencies. But stiffness and mass are also influenced by tubing geometry (diameter, thickness, etc.). The first graph below shows relative stiffness to density ratios. The next graph compares first mode natural frequency response from the same FEA model as above.

The natural frequency graph above implies that aluminum is less harsh than steel or titanium. Obviously there is more to the picture.

Frame Material Histeretic Damping

Smaller vibrations from riding on non-smooth surfaces carry through the frame to your body. These vibrations are diminished or eliminated by the damping, or histeretic, effect of the frame material. This effect would be noticed as the frames smoothness or liveliness. Also, material damping reduces the effect of any natural frequencies.

The illustration below shows a simple model of what is going on in the frame. The red coil is a perfectly elastic spring. Next to it is a damper. If the mass is pulled up and let go it will start to oscillate or vibrate up and down. Without the damper (and in a vacuum), it would continue to move up and down forever. The energy continually cycles between kinetic energy in the mass to strain energy in the spring. But the damper dissipates the some of the energy each cycle, converting it into heat. The "damper" in frame materials is called the histeretic effect. It can be thought of as the material's internal friction. In materials used in bicycle frames this damping effect dissipates about 1% of the strain energy each cycle. The histeretic damping causes vibrations in the frame to decay. Materials such as aluminum with a low damping ratio will resonate longer after an impact. The histeretic damping effect also muffles natural frequency responses.

The response spectrum graph shows how each material would respond to input vibration across a range of frequencies. I excluded titanium due to a lack of reliable damping ratio data. In this plot, carbon fiber exhibits a higher and muffled response. Aluminum shows to be very excitable.

The three clips below are exaggerated audio representations of the first 12 modes of natural frequency superimposed on each other. They give an audible demonstration of what the frame's ride feel is like.