Editor's note 09/01/2010: for an updated ranking of current wheels using some of the criteria outlined below, check this BTR page out...and now back to your regularly scheduled reading!
Sir Isaac Newton proposed his second law of motion nearly 350 years ago. This law elegantly describes the behavior of many systems, bicycles included. It is difficult to argue with the analytical results of this equation. It is my goal to use Newton’s law to demonstrate what variables determine wheel performance and their order of significance. Furthermore, I will show how wheels rank in the big picture of overall cycling performance.
Newton declared that the sum of all the forces on a system (F) are equal to its mass (m) times its acceleration (a), or:
Several companies offer power-measuring devices to help you quantify cycling performance. Power is defined as how much work is done during a given period of time, and it is a more convenient variable for illustrating wheel performance effects quantitatively. We can easily manipulate Newton’s law to incorporate this rider power variable. Our once simple equation now becomes:
- Aerodynamic drag resulting from
- Rider, frame, front wheel, rear wheel
- Inertial forces
- Bike and rider mass
- Front and rear wheel mass and its distribution (wheel inertia)
- Rolling resistance
- Total system mass
- Tire pressure and width
- Gravitational forces
- Bike and rider mass, front and rear wheel mass
- Miscellaneous
- Drive train losses
- Component flex
The details of this equation are beyond the scope here, so I will spare you the agonizing math (see Appendix A if that kind of stuff cranks your chain). The starred variables above are the only ones that matter when determining wheel performance. The question then becomes, which is the most important?
The obvious answer is that it’s the rider pushing the pedals that matters most. This may not be the answer you were looking for, but swapping out your wheels will not make you the next Eddy Merckx. They may, however, help out a bit in your next race.
Based on the model developed in Appendix A, and data I have collected while riding (velocity and elevation profiles), it is possible to quantify the effect your wheels have on the average power required to complete a given ride/race. I will look at the following three course examples:
- 6.5 hour solo training ride with 1200m/3940ft of climbing (31 kph/19 mph average speed from El Cajon, CA to Mexicali, B.C. Mexico)
See Appendix B for more details - Uphill portion only of training ride above (similar to an uphill TT – 27 kph/16.8 mph average speed)
See Appendix C - 11999 Barrio Logan Grand Prix – 50 minute Pro 1,2 criterium with 10 m elevation change per lap (45 kph/28mph average speed – sitting in the pack)
See Appendix D
With my model, I varied the wheel mass, wheel inertia, and wheel aerodynamic variables independently to come up with the data in the following table:
So, what do all these numbers mean? It means that when evaluating wheel performance, wheel aerodynamics are the most important, distantly followed by wheel mass. Wheel inertia effects in all cases are so small that they are arguably insignificant.
How can it be that wheel inertial forces are nearly insignificant, when the advertisements say that inertia is so important? Quite simply, inertial forces are a function of acceleration. In bike racing this peak acceleration is about .1 to .2 g’s and is generally only seen when beginning from an initial velocity of 0 (see criterium race data in Appendix D ). Furthermore, the 0.3kg/0.66lb difference in wheels, even if this mass is out at the rim, is so small compared to your body mass that the differences in wheel inertia will be unperceivable. Any difference in acceleration due to bicycle wheels that is claimed by your riding buddies is primarily due to cognitive dissonance, or the placebo effect (they paid a lot of money for the wheels so there must be some perceivable gain).
The following table illustrates how other variables in the power equation affect overall performance.
It can be seen that rider aerodynamics dominates the power requirements of racing bikes. Frame and combined wheel effects are roughly equivalent, and it is interesting to note how power requirements are affected by rolling resistance changes in the examples.
Roughly, the average rider power requirements on a course with a zero net elevation gain is broken down into 60% rider drag, 8% wheel drag, 8% frame drag, 12% rolling resistance .5% wheel inertia forces and 8% bike/rider inertia. The uphill TT example given is a special case where the rider aerodynamics and the bike/rider weight have nearly equal contributions to power – somewhere around 35% each with wheel mass contributing around 1%. The steeper the hill, the more important mass becomes and the less important aerodynamics becomes. In all cases, however, there is approximately 3% of the average power unaccounted for.
Drive train losses and flexing of bicycle components can be placed into the miscellaneous term of the power equation. Even though these flexural losses are miniscule when compared to wheel inertial power requirements, lateral stiffness/deflection of wheels has its place in a performance analysis. My requirements are rather simple: road wheels should not rub brake pads during sprints and out of the saddle climbing, provided there is 2mm/0.079in of pad/rim clearance on either side. For reference, 2mm is the clearance when your dual pivot brakes are opened up, yet they still have sufficient braking power available.
In summary, wheels account for almost 10% of the total power required to race your bike and the dominant factor in wheel performance is aerodynamics. Wheel mass is a second order effect (nearly 10 times less significant) and wheel inertia is a third order effect (nearly 100 times less significant). The best wheels in terms of performance are the ones that are lightweight, aerodynamic, don’t rub brake pads and are strong enough to get you to the finish line. The problem with these high performance wheels, though, is that they sacrifice on the other two key variables important in wheel selection: durability and price. High performance wheels are neither durable nor cheap. Nothing is ever easy, is it?
Thanks for visiting BikeTechReview.com!
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written by Tom Lewis, February 26, 2010
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written by kraig, February 27, 2010
Oh, man, sorry things don't seem to be working as I'd like them to be!
What I intended to have happen was for folks to click on the small thumbnail images that should be displayed (can you see anything where the tables should be appearing..or are things just blank/empty?) and then a larger image appears that is legible/readable.
Though, I seem to be having some issues with mac users after I changed the way the BTR website serves pages. If it's not too much to ask, what operating system and browser are you using?
thanks for the feedback, and if anyone else is having a similar issue, please let me know, and I'll do my best to sort things out.
-k
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written by Zach, March 06, 2010
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written by Zach, March 06, 2010
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written by kraig, March 06, 2010
So, I'll bet the watt % values in the paragraph you cite (in a relative/comparative sense) aren't too far off the mark...depending on what you are starting with equipment wise.
I went back and reviewed exactly what I did in 2001...and I'm confused! :lol: I think if you look at frame only, the watt savings should be about the same as wheels. I think that the table should say "50% reduction in bike drag coefficient" (i.e - frame + everything else besides wheels)...then it might be more consistent, eh?
I think it is possible to reduce frame alone axial force by 50% in real life:
http://biketechreview.com/blog...nteraction
and I also think it is possible to reduce wheel axial force by 50%.
Though, these reductions would be relative to non-aerodynamic baseline references. I think my main goal with the article was to help folks get a handle on the sensitivity to, and magnitude of, really large changes in various equipment properties. Stay tuned to the site, and in the next week or so, I should finish up transferring over an article that goes into a little be more detail about how one can spend their dollars wisely when it comes to going fast on a bicycle (although the article was written for a triathlon magazine originally, there are still some eye-opening nuggets for TT/cycling enthusiasts).
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written by Harry, May 19, 2010
Hi guys there are some things I would love you to clear up for me.
I understand the notion of analysing each segment in isolation to gain a picture but I think this is where things get complicated and also pry apart some of your assumptions.
1.I Acknowledge that aerodynamics of wheel, bike and rider are very important because like rolling resistance these forces are at work the entire time the unit is in motion so there is a continued interaction between work and efficiency. But you omit in the case of wheel and frame the effects of leading and trailing edge effects of certain wheels on any given frame. That is to say that a non aero frame might gain a significant level of aero assistance from a deep section aero wheel as it cuts through the air and creates a pressure wake.
2.With regards to your sums for mass and inertia what I think is missing are the repeated inputs of a rider in a given situation, and peak changes in wattage under exertion for different wheel mass. That is to say if a rider during a 100km ride needs to vary speed a repeated number of times, what are the power figures at these peak outputs? They might average out over the entire ride but be much higher at specific moments and have effects on rider fatigue.
I give it some further thought and come back with a few more questions
All the best
Richard
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