A
question often heard is, "What is the effect of wind on performance?" The wind blows on a rider on a road course. The wind can come from any direction and be of any speed.
Notes 
Ironman Hawaii Course
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Wind speed is not always constant. Road courses change direction and go up and down hills. This Model accepts wind and course descriptions, writes the equations of motion for the rider, solves the equations, and presents performance data in the form of plots and tables.
Two Input Forms are provided. One has menus of choices for courses and wheels. The other lets you enter raw data.
Response times depend on the complexity of the fundamental integration. Complex courses with lots of turns (Sydney) or long courses with lots of turns or lots of apparent wind changes (Ironman Hawaii) require long compute times. The Est Min Ave Speed parameter controls how long the computation runs (try 8 m/s for the default data on the Ironman Hawaii Course). This parameter should be set as close as possible but not greater than the speed you expect from the slowest rider. Responses for the default data take about 5 to 10 seconds. A onelap evaluation of the Sydney 2000 TT course takes about 30 to 45 seconds. An evaluation of the Ironman Hawaii Course takes about a minute and a half or more. The topic will timeout before reaching the end of a full three laps of the Sydney course (the full TT distance) and is likely to timeout before reaching the end of the Ironman Hawaii Course if conditions are exceptionally complex. Don't be surprised and do be patient. Contact us privately if you have a special interest in longer calculations.
Since the input form is detailed and takes a lot of screen space, this topic is best viewed on a high resolution monitor.
The Model uses the Estimated Speed parameter to make a guess in seconds (distance divided by estimated speed) as to how long to run. If you are computing a slow, uphill effort, you may get an error, something like "Interpolation function is out of range". If this is the case, set the Estimated Speed to something slower. If you expect your model rider to ride fast, set the Estimated Speed to something faster. For example, an evaluation of the Sydney 2000 TT course takes about 30 seconds with default estimated speed and takes about 20 seconds with an 8 m/s Estimated Speed.
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Questions This Model Can Answer
The wind is fluctuating. What range of times can I expect due to wind variability? Try This—Using the Advanced Input Form, reset it and enter a value for wind variability, say 2, for each course segment in the Course and Wind input table, check the Plot Wind Data box, and evaluate several times. One series of evaluations produced the following list of time differences (seconds): {7.37, 9.82, 9.11, 9.81} Notice from the plot of wind speed how it changes over the course and with each evaluation.
The wind is coming at an angle. Some wheels perform better with wind at an angle. Which wheels should I use? Try This—Find some drag data on the wheels you want to test. This needs to include drag at various yaw angles. Setup a course of interest and do the evaluations for different wind directions. You can use the data in the Advanced Input Form in an example of the process. The default values for the Test Rider's wheels are for a aero wheel in front and a disk in the rear. Reset the Advanced Input Form and run values for wind direction of {0, 10, 90}. The Test Rider beats the Standard Rider by {3.62, 6.89, 13.40} respectively. Now change the rear wheel on the Test Rider to have the same drag values as the front wheel on the Test Rider. Evaluate again for {0, 10, 90} wind directions. This gives values of {3.36, 5.14, 9.40} respectively. The Test Rider still beats the Standard Rider but not by as much. This demonstrates that speed depends on drag characteristics of the wheel at various yaw angles.
It's reported by the manufacturer that I can reduce drag by 0.1 pounds if I use the aero bars. Given that the course is mostly up hill, is there an advantage to using them? Try This—Reset the Advanced Input Form, click on the PointtoPoint radio button, change the slope in the second line of the Course and Wind input table from 3 to 6 and change the direction from 180 to 0. This creates an uphill, pointtopoint course. Check the Plot Course Data box. Change the estimated speed in the Rider Data Table to 3. This gives the model more time since the riders are riding up hill. Evaluate. Notice that the test rider is ahead by 15 seconds even with heavier aero wheels. Now check the Reduce Drag on Test Rider box. This reduces drag on the Test Rider by an amount equivalent 0.1 lbf at 30 mph and proportionately less at slower speeds as when going uphill. Evaluate. The reduced drag due to the aero bars gives an additional 2 seconds advantage to our Test Rider even in an uphill time trial.
I need to handicap riders for a time trial. How much time should I allow, given the wind and hills? Try This—In the last time trial, a flat, 40k, outandback course with wind at 5 m/s, the Standard Rider rode the 40k course in 61 minutes corresponding to a 300 watt effort. The Test rider who is slower and heavier at 85 kg, rode it in 65 minuets, a 250 watt effort. There was a 3:42 difference between them. There is a lot of wind today and the course is uphill on the out leg and downhill back. What differences in times can we expect? Using the Advanced Input Form, set the new course up for 20000 meters out and 20000 meters back. Change the wind speed to 10 m/s and the slope to 3 on the out leg and 3 on the return. Set the power for the Standard Rider to 300. Set the weight of the Test Rider to 85 kg. Evaluate. Note that the Test Rider takes 12:11 minutes longer this time than the Standard Rider. Give the Standard Rider a 12:11 handicap.
Wind increased later in the day when you rode your time trial. What would your time have been if you had ridden earlier? Try This—Reset the Advanced Input Form. Change the wind speed to 10 m/s on each course segment. Evaluate. You are the Standard Rider. Your time was 9:34.28 late in the day when you rode. The wind was calm earlier. Change the wind speed to 0. Evaluate. Your time would have been 7:04.35 if you had ridden earlier. Tough break.
You are going to ride a time trial on a new course. The course is hilly and windy. Should you use your disk wheel? Try This—Reset the Menu Input Form. Select the 36 Spoke wheel for the front wheel of the Test Rider. The Test Rider's rear wheel defaults to values corresponding to a disk. Evaluate. On this short, hilly time trial course the Test Rider with the rear disk wins by 12 seconds.
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Course and Wind
You can select a course from the menu or use the Advanced Input Form to enter your own data. The course for the model is described by a series of course segments. Each segment has a distance, direction, slope, coefficient of rolling resistance, prevailing wind direction, wind speed, and wind variability. The direction of the segment is the compass direction in which the rider is heading. The wind direction is the compass direction from which the wind is blowing. The wind variability is an amount by which the wind speed increases or decreases randomly over time. If the "Course Closed" box is checked, the course is expected to close both in distance, direction and elevation. In the case of a course selected from the menu, the wind speed, direction, and variability is the same for all course segments and is specified on the Input Form.
The model incorporates wind into the differential equations using the approach explained by Jobst Brandt in his paper, "Headwinds, Crosswinds, and Tailwinds, a Practical Analysis of Aerodynamic Drag", Jobst Brandt, Bike Tech, pp46, Aug 1988.
Course Notes
The Generic TT Course is an out and back course with a 3% slope on the outbound segment and a 3% slope coming back. The course closes so its suitable for multiple laps. (Be aware that you are likely to run out of time before it does more than three laps.)
The Sydney 2000 TT Course data was taken from a map available at Official Site of the Sydney 2000 Olympic Games. Please recognize that the configuration of the course with its many turns makes an exact model difficult to do from an image on a web site. In the image at the right, the black arrows are represent the course directions and distances and the red arrows represent the prevailing wind. A wind speed of 10 m/s and direction of 315 degrees are a bestguess of typical conditions.
The Generic PointToPoint Course is flat. What else is there to say. It computes quickly (relatively so) which makes it useful for quick evaluations of equipment and other ideas.
The Florida 2002 State TT Course is a 40 kilometer, flat time trial course in West Palm Beach, Florida. Wind is typically at 510 miles per hour from the East/South East. Roads are smooth, so use a 0.004 Coefficient of Rolling Resistance. Timothy J. O'Malley of Orlando, Florida, provided the course data.
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Drag on Wheels
Wheel drag is often quoted as force in pounds or force in "grams" at some specified speed, often 30 mph. Greenwell, et al, quote drag coefficients. You can enter drag in various units in the Advanced Input Form and the conversions will be done automatically. Or you Can use the Menu Input From.
Menu Input Form—The default values in the Menu Input Form are drag coefficients taken from Greenwell's paper. The Standard rider uses coefficientofdrag values for conventional 36spoke wheels as default values. The Test Rider uses coefficientofdrag values for a Specialized (Now Hed 3) in front and a disk in the rear as default values.
The following tables list the wheel drag values on which data in the Menu Input Form is based. Conversions to consistent units are automatic.
Cobb Wheel Drag Data (lbf) 
Yaw (degrees)  0  5  10  15 
Rolf Vector  0.318  0.425  0.402  0.358 
Hed3  0.223  0.223  0.117  0.109 
J2  0.259  0.285  0.336  0.320 
Deep/S90  0.216  0.198  0.086  0.081 
ZIPP 404  0.255  0.243  0.142  0.125 
Shimano23 tire  0.261  0.306  0.314  0.373 
Helium  0.399  0.380  0.445  0.414 
Spinergy Spox  0.445  0.494  0.652  0.596 
Lew  0.279  0.284  0.251  0.207 
Std box rim 32*  0.401  0.408  0.402  0.414 
Jet  0.252  0.296  0.254  0.267 
The data for this table were taken from a table published at John Cobb's web site, www.bicyclesports.com. Andrew Coggin, commenting in rec.bicycles.racing on the data in that table, said, "The wheels are tested in the lowspeed A&M wind tunnel ... in a purposedesigned fixture mounted on the tunnel floor (picture the typical roof wheel rack). A recessed roller spins the wheel at 30 mph." He further commented that the values are in lbf at 30 mph at standard air density, 1.226 kg/m^{3}, and that the wheels were tested with Conti Grand Prixs tires.

Greenwell Wheel Drag Data, C_{x} (dimensionless) 
Yaw (degrees)  0.0  7.5  15.0 
22.5  30.0  37.5  45.0  55.0  65.0 
36spoke  0.0491  0.057  0.061  0.059 
0.058  0.070  0.057  0.045  0.029 
Campy Shamal  0.0377  0.047  0.043  0.045  0.036 
0.028  0.018  0.010  0.000 
HED CX  0.0379  0.028  0.034  0.041  0.042 
0.039  0.030  0.019  0.011 
Specialized  0.0379  0.038  0.028  0.031  0.028  0.020  0.009  0.006  .001 
FIR  0.0382  0.026  0.034  0.041  0.037  0.032  0.020  0.011  0.002 
HED disk  0.0361  0.020  .004  .005  0.000  0.001  .003  .005  
ZIPP 950  0.0364  0.023  0.013  0.017  0.018  0.017  0.016  0.016  
Greenwell measured the axial coefficient of drag for various wheels and published plots of his data in his paper, D. I. Greenwell, et. al., "Aerodynamic Characteristics of LowDrag Bicycle Wheels", Aeronautical J., Vol. 99, No. 983, Mar. 1995, pp.109120. Greenwell's plots included many data points and there was significant scatter in the data. Humphries at www.cs.umd.edu/users/humphrie/wheels.html compiled data from Greenwell's plots by taking ". . . the middle of a crayon line drawn through very numerous data points. Typical scatter is +/ 0.002 to 0.005." The data under the column for zero yaw are values taken directly from a table in Greenwell's paper. The Specialized wheel is now Hed 3.

Comments on Wheel Drag Data—If you compare results from Greenwell's data on a Specialized wheel with Cobb's data on a Hed 3 (both wheels are identical, the name is the only change), you will find a difference in performance. Cobb's data covers 15 degrees of yaw angle; Greenwell's, 65 degrees. Both tested wheels in fixtures in wind tunnels. Both are credible sources. The shapes of the drag functions are consistent and the magnitudes are consistent. This gives you some sense of the precision and reproducibility of the data.
Advanced Input Form—You may enter values for drag on wheels in the Advanced Input Form as values of force due to drag or drag coefficients. The model reads the values for the drag for the yaw angles and converts drag in units of force to a coefficient of drag if necessary. It then fits a continuous function through these points. The yaw angle values must range from 0 to 90 and must be strictly increasing. There must be at least four data points (four yaw angles). A whole line of data can be left blank, but if a line has any data, no blank data elements are allowed. You can get drag coefficients or drag forces from the web sites of various wheel manufacturers. However, most that do list data are not complete and seldom offer any basis for the data. An explanation of wheel parameters is given in Wheels Concepts.
Wheel Weight & Inertia—Although discussed a lot in the popular forums, the wheel weight and rotational inertia do not make much difference in the outcome for riders on courses such as these. However, if you want to see the effect, select the Generic PointToPoint course and run some cases with both riders using the same wheels only with different weights and rotational inertias. Check the "Plot Rider Speed Data" box. The last plot, "Speed Difference Between Riders vs Time" shows the difference in speeds of the riders. The large peak during the acceleration at the start is all the difference there is.
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Model
The model uses the standard equations for forces on a rider. The model sums the forces, writes the differential equations for the riders and solves them for distance, velocity, and acceleration. This concept is explained in the Glossary.
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How do you measure these things?
One way to measure distance is by riding a course with a bicycle equipped with an ordinary bicycle computer and noting distances at points where direction changes.
Measure the slope using a machinist's bubble protractor on the top tube of the bike. Note the zero point when the bike is on a known level surface. Turn the bike in several directions to verify the levelness of the surface. Take these measurement while stopped. Taking them at several places on the same hill will give some sense of the precision of the measurement.
Measure the direction of the course by using a compass.
Measure the direction of the wind by using a compass. Measure the wind speed by using a handheld anemometer or use data from the local weather report. Make a guess at the variation in wind speed. Note that valley's and such commonly have wind blowing from different directions than the prevailing wind.
The data for the Sydney 2000 TT course was taken from a map provided by the Organizing Committee. It looks reasonable, but it did require some "tweaking" go get the course to close. As courses go, it has to be one of the more complicated ones to describe.
© 2000 Tom Compton
