A Coker is a famous and fairly commonly used unicycle with a large wheel. The wheel is nominally 36" in diameter but exactly how large it is, is the very subject of this page. The exact wheel size is of particular interest for riders who use a cycle computer on their Coker. Over the years, in the newsgroup rec.sport.unicycling many rollout values have been given and in 2003 I offered to integrate all available data into a model. For the Coker only one tyre type is available (manufactured by Coker), which simplifies things as far as 'the' wheelsize is concerned. On the other hand, two types of rims are commercially available (standard and Airfoil) but hardly anyone specified which rim they use and I have ignored a possible size difference between the two. 

Before going into 'how I did it', here is the result. Download Rollout_predictor.xls (by rightclicking and then Save As), open it in Excel 4 or higher, and enter your rider weight, tyre pressure and tread wear. See screenshot if you want, use your Back button to return here. You will get three numbers:

• unloaded straight rollout, this is the distance that the wheel rolls during one full revolution on a flat surface if you push it in a straight line, under the weight of the unicycle alone. 
• loaded straight rollout (with rider); this is the distance that the wheel rolls during one full revolution on a flat surface in a straight line, under the weight of the unicycle with a rider on it. 
• dynamic road rollout (incl wobble); this is the distance covered during one wheel revolution under realistic road riding conditions. 

Enter the number of your choice (see below) in your cycle computer, and you're off to go!

Why these different numbers? The unloaded straight rollout is used by many Cokeurs, partly because it is the easiest and most straightforward number to measure. Also, since it is rider-independent, it is the best basis for comparison. However, because the tyre will always compress when the unicycle is ridden, the unloaded straight rollout gives too high speed and distance values, which can be a reason to prefer a loaded rollout value (I phrased that carefully). There are two loaded rollouts because there are (at least) two schools of thought as to what 'speed' and 'distance' mean in relation to unicycling. If one wants to know the speed and distance that the tyre contact patch has travelled along its path, including all the wobbling and turning that one may do, then one should base oneself on the loaded straight rollout. However, if one is interested in road speed, or road distance (i.e. the distance from A to B), one should use the dynamic road rollout. "Dynamic" means to include all deviations from riding a straight line, such as single-cycle and multi-cycle wobbling (both horizontal and vertical), the way one torques up a hill, etc. U-Turn, fanatic Cokeur and builder of the Strongest Coker Wheel in the World, considered these factors in more detail in a post in rec.sport.unicycling. 

Some issues and conclusions worth mentioning:

• For starters: I had to work with a very limited dataset. While the model predicts the input rollout values on average within 10 millimeters, the accuracy would certainly increase with more data. Oh well.
• For every kg increase in rider weight, the (loaded) rollout decreases by about 0.32 millimeter.
• For every bar increase in tyre pressure, the (loaded) rollout increases by almost 15 millimeters.
• For every additional % in tyre wear, the rollout decreases by almost 0.3 mm. From that number, I can derive that the tread height (or more precisely, the difference in radius between a new tyre and a completely worn-down one) on the Coker tyre is 4.5 mm. I've never seen a Coker tyre in person, but it seems realistic. 
• A modeling result is that the effects of dynamic riding (as opposed to riding in a perfectly straight line) decrease the rollout by about 5.5 millimeters. In fact I think this is too low, and more data might give a more realistic value. Ken Fuchs was the only individual who measured both straight rollout loaded with rider and dynamic road rollout under comparable conditions, and assessed a 20 mm difference. That looks more realistic to me. However, dynamic riding effects will be very much rider-dependent anyway.
• Lastly, a word of warning. Some people measure the distance between wheel axle and riding surface and take that as a "loaded wheel radius" to calculate the loaded rollout. This is based on a wrong assumption. The effective rolling radius of a loaded wheel is in fact somewhere between said distance and the unloaded radius. The tyre contact patch does not have a single radius. At the ends of the centre line the 'radius' is the unloaded tyre radius while in the middle the 'radius' is the distance from the wheel axis to the ground. At the sides of the tyre contact patch the situation is even more complicated (3D).

* * * * *

For those who are interested in how I arrived at my model, I will now give some detail. Warning: this is not hard science, but the best I could do based on the sparse and inconsistent data at hand. 

Firstly, I collected all data that I could lay my hands upon. This was all from the newsgroup rec.sport.unicycling over the last couple of years (since the Coker unicycle came into existence). Some of the data were not given in a very 'hard' way, and I have firmed them up before the analysis. The available data are presented in this table:

© Klaas Bil, July 2004