The rollout of a Coker wheel 
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:
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 riderindependent, 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 singlecycle and multicycle wobbling (both horizontal and vertical), the way one torques up a hill, etc. UTurn, 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 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: 
name 
rider weight lbs 
tyre press psi 
tread wear % 
unloaded rollout mm 
loaded rollout mm 
dynamic rollout mm 
undefined rollout mm 
cycle comp value*) mm 
remarks 
John Childs 






2775 

Not used as the type of measurement wasn't specified 
UTurn 

60 


2800 



UTurn contributed few numbers but made some very useful comments 
Ken Fuchs 

32 
15 
2839 
2789 
2769 


Deluxe Coker 
Nathan Hoover 
165 
45 
50 


2776 


preDeluxe 
Tom Blackwood 




2756 




Mark (cokerhead) 
237.5 
47.5 





2810 
Not used. Based on road markings, bicyclists and car odometers, erring on the long/fast side 
duaner 
150 
32 
50 


2782 



Chuck Webb 





2800 


Based on making small adjustments based on road markings etc. 
Mikefule 



2873 




Not used, was based on (measured? nominal?) diameter of 36" 
David Stone 
192.5 
52.5 

2852.7 

2789.2 

2810 

Michael Grant 



2819 





Danny Colyer 



2830 




Number allegedly based on past Coker threads (which I (Klaas Bil) wasn't able to find) 
Ken Fuchs (again) 

35 
75 
2858 




Not used, was measured with a tape around the wheel which will yield a too large value 
Kevin Gilbertson (Gilby) 






2820 

Not used; seemed unreliable. Quote: "I've heard measurements range from 277 cm to 285 cm for the circumference of the Coker wheel. I've had mine set to 282 cm before." 
Joe Marshall 



2870 




Not used, seems based on the nominal diameter of 36" 
*) A value for the cycle computer setting is only included in the table if it is remarkable or if there are no other rollouts given by this individual.
The italic lines in above table have not been used in the analysis, for the reasons specified in the "remarks" column. As you can see, noone reported a 'full' dataset. To increase the number of data points available for the analysis:
I have built a numerical model of tyre compression, from which I have concluded that there is a nearlinear relationship between compression on the one hand, and both load and tyre pressure on the other hand. (If anyone is interested in the details let me know.) Therefore I have assumed linear relationships between the three input parameters rider weight, tyre pressure and tread wear on the one hand, and the three 'output' parameters (i.e., predicted values for the three types of rollouts) on the other hand. Furthermore I assumed that the unloaded rollout was not affected by rider weight (duh), and that the effect of tyre pressure on unloaded rollout was only 10% of the tyre pressure effect on loaded rollout (because a Cokeur is typically 9 times as heavy as a Coker unicycle). Then I performed a multivariate leastsquares linear regression for the whole dataset at once, i.e. solving for the minimum sum of the squares of the differences between the given and the predicted rollout values. This processing was done iteratively, using the Solver AddIn of Excel with the default settings. The parameters that were varied in doing the minimisation of the sum of squares were:
The optimised values for these parameters are included in rows 3 and 6 of Rollout_predictor.xls (just increase row height to view them). You will note that, contrary to my usual scientific religion, I did the actual calculations in the imperial unit system. 
© Klaas Bil, July 2004 
Back to Unicycling statistics. 