Tuesday, March 31, 2009

Modulus

What the heck is "modulus", also known as Young's Modulus or the Modulus of Elasticity?  We see it with carbon fiber: "this road bike made by The Coolest Road Bike Company Today is laterally stiff and vertically compliant thanks to the high modulus carbon used in the frame."  


Since I'm back in school and taking tests, exams and quizes, here's one for you.  Which has a higher modulus:
A) Glass
B) Rubber
C) Magnesium

I'll give you the answer at the end.

Before we talk about how modulus can effect the way a bicycle rides, lets get some definitions out of the way. Stress is defined as a force over an area.  The unit is the Pascal (Pa  which is also N/m^2) or in english units, the familiar psi (pounds per square inch).  Strain is defined as the change in length over the initial length.  This is a unitless measurement (inch/inch or meter/meter) and is given as a percent or part per million (ppm).  Now that we've got that out of the way, we can see that the modulus (E) is defined as:

or simply, stress over strain.  Since the strain is unitless, the modulus is reported in Pa or psi (metric and english units respectively).  

"Hey, that's great and all, but what does it tell us?"  

Good question.  It does NOT tell us how strong something is.  Nowhere in the above equation do you see ultimate strength.  What it does tell us is how stiff something is.  

Think back to my quiz above and let me rephrase it.  Which of the materials listed is the stiffest? Disregard strength and you'll likely get the right answer.

So what does this have to do with bicycles?  Modulus is mostly mentioned with carbon fiber and here's why.  As Jon pointed out last week what we call "carbon fiber" is really Carbon Fiber Reinforced Plastic (CFRP)  And that plastic is... well, not something you'd build stuff out of by itself.  What it does do is bind all those thin fibers together, helping to keep them from buckling when a compression load is applied.  The higher the modulus, the stiffer--or more resistive to bending--and individual fiber is.  Since the fibers are all pretty darn strong, using a stiffer fiber allows the builder to use less of them to make that "laterally stiff" bicycle frame.  Less fibers equals a lighter weight frame.  

What about that "vertically compliant" bit?  That is usually achieved by mixing fiber types and laying up the cloth in different ways--by changing the orientation of the fibers.  Shape of the final tube also plays a HUGE part in the overall ride.

What about metal?  Steel and berylium are way up there in stiffness and aluminum is near the bottom of the list for metals.  Now, which bikes tend to ride the harshest?  That's right, aluminum.  Why?  I just said that aluminum has a relatively low modulus so it should have a low stiffness, right?  As anyone who has ridden an OLD Vitus aluminum frame can tell you, aluminum, when built to the same dimensions as steel, can be a very flexy ride.  The reason that modern aluminum bicycles are so stiff is due to the tubing size.  In order to eliminate the flexy-flyer feeling of those early aluminum frames, the tubes grew in diameter while shrinking in wall thickness.  This stiffened up the aluminum tremendously while retaining its lightweight advantage over steel.  If you were to build a steel tube the same dimensions as an aluminum one, the steel would be over the top stiff.  

So, to sum up, modulus is the stiffness of a material--a starting point, if you will.  From there, the builder adjusts the tubing shape and--in the case of carbon fiber, the lay-up schedule as well--to get the ride that they desire, whether that ride is ultra-stiff, more forgiving or somewhere in the middle.  

And the answer is: A) Glass.

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