# How is the suspension frequency response effected by the wheel diameter?

Imagine riding off a curb, crossing a pothole, or hitting a pebble. Would you prefer to ride that with a toy bike or a penny-farthing? Regardless of preference, the penny-farthing would have a smoother ride, but how much smoother?

I want to know how much smoother a ride (less vertical acceleration) is when using a larger wheel diameter assuming the wheels are perfectly balanced and rigid. If I give a Power Spectral Density function of a road, how would the wheel diameter change its effect on the suspension?

I would expect that a wheel of diameter d bound the Amplitude A at distance frequency f to be

``````A < π^2/(2d*f^2) if A << d.
``````

I would like any insights, and if you have questions, I answer the best I can.

• Probably too theoretical for this audience. Might be better asked on physics.stackexchange.com Commented Aug 8, 2023 at 22:28
• Are we assuming the fork has some sort of spring and damper as the suspension or the pneumatic front tire only (as an undamped spring)? My guess is that to quantify whatever you're after, you need to know the angle of attack and the height of the object. The longer the base of that triangle, the smoother the ride. Commented Aug 9, 2023 at 15:44