Hi! Welcome back to Killa’s Garage!
Today’s post starts with a few definitions shamelessly pulled off the internet:
Stiffness – the rigidity of an object — the extent to which it resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Compliance – a property of a material undergoing elastic deformation or (of a gas) change in volume when subjected to an applied force. It is equal to the reciprocal of stiffness.
Compliance and stiffness are opposites!
A current manufacturer makes the following (very typical) claim:
“[Their new frame] uses a 27.2mm seatpost, which is designed to both shave weight and increase vertical compliance. Of course stiffness and efficiency remain important, as one can see by the large downtube, tapered headtube, bulbous chainstays, and wide PF86 bottom bracket shell. The net effect is a bike that is 24 percent stiffer…”
Wait a minute. Stiffer and more compliant? It’s one or the other isn’t it? Not necessarily. Read it again. Maybe the greater compliance is all in the seatpost. I assume the old design used a larger OD seatpost that was stiffer than the new one. Maybe there is nothing more compliant about the new frame at all. The large downtube, tapered headtube, bulbous chainstays, and wide PF86 bottom bracket shell certainly all scream stiffness, not compliance.
The claims actually may both be true – more compliance while seated, achieved with a more flexible seatpost, and greater stiffness when that’s important (sprinting, climbing off the saddle) due to a stiffer frame.
There is another whole discussion around vertical vs lateral stiffness. But for the rest of today’s post I am going to consider only vertical stiffness and compliance.
BTW, the frame is also claimed to be 20% lighter, but that’s also for another day.
Time for a little physics, but don’t run away. It’s all about springs.
A bicycle and rider can be modeled as a system of weights (where the rider is by far the most significant weight) and springs. The seat is a spring. The seatpost is a spring. The frame, the cranks, the wheels, the tires – all springs.
The stiffness of a spring, also known as the spring rate, is defined as the force required to deflect the spring a given amount.
For instance, consider a tire as a spring. Suppose we apply a load of 100 pounds on a tire and it deflects 1/4″. The tire’s spring rate is calculated as 100/0.25 = 400 lbs/inch.
A spring’s compliance is the inverse of the spring rate. So the tire in the example above has a compliance of 1/400 = .0025 inches per lb.
This sounds like a very small number, but it is huge compared to the compliance of other parts of a modern bicycle system.
The neat thing about using compliance instead of spring rate for a series of springs is you can add up the compliances of all the elements to arrive at the compliance of the whole load path. Because the tire has the largest compliance, it dominates the compliance of the system. But still, the compliance of each component contributes to the total compliance.
A rider can be viewed (simplistically) as resting on two stacks, or series, of springs. One series leads down from his/her butt through the rear wheel to the ground. The other leads down from his/her hands through the front wheel to the ground.
What about the series of springs that lead from the rider’s feet through the pedals/cranks/bottom bracket/frame, etc. For now, discussing compliance, let’s ignore that one. When you judge a bicycle’s comfort (compliance), do you think of your feet? I think of my butt and my hands. Later when we consider stiffness and efficiency, that one becomes critical.
I hope this introduction has gotten you interested. In coming posts I will wax esoteric on each load-bearing element of the bicycle system from the rider to the ground. I think I’ll start with wheels.
Until next time,