I’m back from the garage with some experimental results on cable routing friction, and they are really cool!
Above: Photo of my custom “Derailleur Cable Friction Tester”, loaded with a 12″ length of housing making a 180 degree turn at a radius of ~2″.
Recall from my previous post, I was wondering how best to accommodate the curve in routing the rear derailleur cable from the chainstay to the derailleur. A short tight hook, or a longer lazy curve? Historically I have preferred a long looping setup to a short tight hook. It turns out I may have been wrong.
With my custom derailleur cable friction tester, I was able to measure the cable force required to overcome the derailleur spring force in a variety of configurations – total direction changes from zero to 540 degrees and turns with radii down to 1.5″ and up to 5″.
It seems this Eytelwein guy’s capstan equation is right. The radius doesn’t matter. The length doesn’t matter. The only relevant parameters are total change in direction and coefficient of friction.
The solid lines are theoretical T/t vs total change in direction for various coefficients of friction. The red dots are my experimental results for 12″ and 24″ length housings in various configurations. To the accuracy of my measurements, which is admittedly not laboratory grade, all my data points lie on a curve corresponding to the capstan equation with a friction coefficient of 0.06.
Above: A couple of the configurations I tested. Left: 24″ housing, 180 degrees, 5″ radius. Right: 12″ housing, 270 degrees, 2″ radius.
For a final test, I arranged my rig to place the cable in a configuration very much like it would be on a bike, from chainstay to derailleur.
Notice how the cable housing tends to curve out before beginning the main turn-around. This results in a total direction change of greater than 180 degrees. (Call it 15 degrees out, 15 degrees back to vertical, then 180 degrees – total direction change of 210 degrees.) And sure enough, the T/t ratio falls on the curve at ~210 degrees.
Constraining the cable so that it does not go through these extra direction changes should lower the required cable force, and it does!
Above: 12″ cable constrained to a simple 180 degree turn at a radius of ~1.5″.
The capstan equation predicts about a 3% drop in T/t and that is almost exactly what I observed.
I repeated my test with an old cable and housing in my rig and the results were almost identical. I was surprised that the friction coefficient was no higher than a new cable and housing (0.06). But what really surprised me was that adding a drop of light oil at each end of the housing increased the required force! Solving the capstan equation for friction coefficient I got a 0.08 for both the constrained and unconstrained configurations with oil.
OK, that’s been a journey. So how can we use this information? Here are my recommendations:
- Route cables to minimize total change in direction.
- Try to pre-form a tight but smooth curve in the cable housing near the derailleur to minimize the bowing effect that results in greater total direction change. My friend Brian suggested that a heat gun might be useful. If I see you riding with a zip-tie on your cable to hold it in to 180 degrees, I’ll laugh at you. Use clear packing tape. 🙂
- Don’t arbitrarily oil derailleur and brake cables. It may actually increase friction.
- Apply this information to derailleur and brake cables all over the bike.
- Appreciate SRAM’s recent mountain bike derailleur designs where the cable enters the derailleur more vertically than to the rear.
- Try not to lose sleep over this, because modern bicycle cable systems work very well. These tweaks will make only a very marginal, probably not discernable, difference.
One day I might do comparative testing on different manufacturers’ cables, or on various oils and greases. I may include some static friction testing. I may do brake cables. But for now I want to move on to other Esoteric Observations on Bicycles and Cycling.
A few closing disclaimers and comments:
- This is all dynamic friction. What I have reported is maximum required force to stroke the derailleur by hand at a dead-slow rate.
- As you might expect, the required force for any given configuration is not constant – or even linear – throughout the derailleur stroke. It starts out low, increases through a maximum at about mid-stroke, then declines.
- My new cables were Shimano stainless steel cable and Shimano OT-SP41 housing. I don’t know the brand of the old cables. They came off of Trekker’s Tarmac the other night.
- And if you just have to know – it takes about 5.8 KG (12-3/4 lbs) cable tension to stroke an old Ultegra 6700 derailleur.