Is Time-Trial Equipment Choice “Significant”:
An in depth analysis of Chris Horner’s 2002 Redlands Prologue TT victory

5/20/2002

words and images by Kraig Willett

(4/10/2005: A note from the author:  The mathematical modeling methods in this article have been dramatically improved in the days since this article first appeared in 2002.  With the better models, the absolute numbers may have changed for this analysis, but the overall message remains the same...)

One of the favorite questions that I like to ask any bicycle company representative I meet is: “Are the performance benefits of the widget you sell, significant?”  It is a great question because the answer one receives tells a lot about the person you are talking to.  If a one sided answer proclaiming that the widget in question is the best thing since sliced bread is received, it can be assumed that the “dark side” of the force (marketing/sales hype) has overtaken this particular person.  However, if a well-balanced answer stating that significance is a difficult subject open to many interpretations and perceptions, it can be assured that the person is firmly grounded in reality.  I would much rather chat with the person who holds the latter opinion of “significance”.

The discussion of significance may also eventually lead to the psychology of bike racers, a subject I am fascinated by.  I truly believe in the power of the mind - in fact, just a few days prior to the Mount Rubidoux Redlands Prologue, the team director of Prime Alliance (OK, but, “my brother” doesn’t sound nearly as impressive) called me and the topic of equipment selection came up.  Since the race was so near in the future, I had a hunch that the best answer to the equipment question would come in the form of another question – “What does Horner think is the fastest?”

I did not want to put any doubt in the mind of Chris on the start line.  The last thing Horner needed to have was some number crunching geek second-guessing his bike choice.  I had a feeling that the fastest thing Chris could ride that day was exactly what he thought would be fast – a standard road bike (Pinarello) with deep-dish carbon wheels (Bontrager) and some old-school bar extensions (Profile Jammers).  At the time, I didn’t need to do an in-depth analysis; I knew enough to respect the psychology of the rider.  For me to pipe up at the time and say that I thought he was wrong would not have been the best decision on my part.  I am just glad that things worked out the way they did and Chris won the prologue handily.

Clearly, people who ride bikes as a matter of transportation or recreation will judge performance based on a different set of criteria than those who race competitively.  The tourist/commuter values reliability and serviceability, whereas the racer values pure speed.  The Mount Rubidoux prologue at the Redlands Bicycle Classic is a venue in which there is little room for error – the winner in 2001 was Roland Green with a time of 8:53 over 5.15 kilometers.  This was fast enough to win by a scant 5 seconds over the Tour of Spain revelation, Levi Leipheimer.  In this case, 5 seconds would clearly be significant.

In 2001, Roland Green rode a standard road bike with a rear disk.  In 2002, he rode to sixth place with a 9:06 (17 seconds slower than winner Chris Horner’s blistering 8:49) on a standard road bike and the new Bontrager Carbon wheels.  Why did Roland change his mind with respect to his wheels?  Only Roland knows the answer to this question, but after an extensive analysis, I believe it was an approximate 2.6-second mistake to swap out the rear disk in favor of the lighter rear Bontrager Carbons.  Furthermore, the decision not to ride with “heavy” bar extensions cost Roland an additional 15.4 seconds.  These two equipment selection mistakes may have been the difference between a sixth place finish and the top spot on the podium.  In the context of “significance”, eighteen seconds might not mean a whole lot when one commutes to work; however, in the world of competition, eighteen seconds can mean the difference between winning and losing.

The Mount Rubidoux Time Trial is an interesting event.  The point-to-point route covers 5.15 kilometers (3.2 miles) and gains a total of 122 meters (400 feet).  It is an uphill time trial where most riders and teams believe that lightweight equipment will be faster than aerodynamic TT equipment.  Less than 10% of the field of 203 opted to ride full TT setups, which would include full aero bars and rear disks.  It is true that the TT is uphill, however, it is a fast uphill with the winner usually averaging over 34 kph (21 mph).  This fast average speed is enough for aerodynamic equipment to be the superior choice.

The Analysis

For an in-depth derivation of the power model that I used for this analysis, check out this article.  The crux of this analysis was in the digitization of the racecourse.  Using the scanned drawings from the Redlands Race Bible as shown below, I was able to numerically represent the course heading and elevation at 304 discrete points.

Below are 2-d and 3-d plots of the Mount Rubidoux prologue TT course.

The next thing necessary to increase the accuracy of the analysis was to incorporate the ambient wind conditions.  Having witnessed the TT in person, I estimated the wind at about 2.5 m/s (5.6 mph) coming from the SW (315 degrees with North being 0 degrees).  As a backup, I looked up the average wind conditions on the 10th of March from the Weather service in Riverside (details are shown below).  It appears that my assumed wind speed was OK.

Armed with this information, it was simply a matter of calculating the yaw angle (the angle created by the rider velocity vector and the ambient wind vector) at each of the 304 discrete points along the course.  This small detail drastically increases the accuracy of the analysis, since most objects that are streamlined (wheels, aero tubed frames, aerodynamically positioned cyclists) have drag values that are dependent on the yaw angle.  As a rule of thumb, drag usually decreases as yaw angle increases.  Most back of the envelope calculations neglect the yaw angle dependence – I took the time to incorporate this feature in my analysis.  The following are the instantaneous yaw angles that were calculated for Chris Horner’s prologue (the average yaw angle was 15 degrees):

The Assumptions

Like any theoretical analysis, assumptions must be made.  In this case, it is assumed that the rider completes the course at a constant velocity.  This assumption is not entirely realistic since it implies that brakes are applied to reduce speed on the downhill sections and that inhuman power output levels are possible on some of the uphill sections.  This constant velocity assumption is acceptable when doing a relative comparison of equipment options.  Reality lies somewhere between the extremes of the constant velocity and constant power assumptions.  For our purposes, the constant velocity assumption is satisfactory.  The following plot is what I came up with for Chris Horner’s prologue effort (note the negative power sections – this is where it is assumed brakes are applied to reduce speed).

The average power that Horner put out during this effort was calculated to be 470 watts, or 6.7 watts/kg.  This value is certainly high, but seems to be reasonable for a relatively short 9-minute effort.  As a point of reference, it has been rumored that Lance Armstrong has maintained a 7+ watt/kg output during the extend climbs during the Tour de France.

The Results

With the baseline case of Chris Horner’s prologue dialed in to produce believable results (he used mid depth carbon wheels, a standard road bike and mini aero-bar extensions), it was time to start changing equipment and seeing how it affected the final time.

Rear Disk: -  400 grams heavier:
Would have reduced the power requirement by 2.2 watts and saved 2.6 seconds.
Rear Disk and TT bike (10% lower drag coefficient (Cd) of the frame and 2% lower Cd of the rider): 
6.1 watts less power and 7.0 seconds faster.

Lightweight box section, conventional, wheels - 400 grams lighter:
Would have increased the power requirements by 9.2 watts and increased the overall time by 10.3 seconds.

No aero extensions: (10% greater Cd of rider and 200 grams lighter):
Increases power requirements by 13.8 watts and increases overall time by 15.4 seconds.

How much additional weight could have Horner carried up the hill and still won?
3.4 kilos (7.5 lbs).

If the climb was twice as steep (~5% grade) and Horner averaged 470 watts:
Time would increase by 146 seconds (average speed of 28.4 kph/17.4 mph)
Using a rear disk would be .1 seconds slower
Using lightweight conventional wheels would be 4.7 seconds slower

If the climb was three times as steep (~7% grade) and Horner averaged 470 watts:
Time would increase by 336 seconds (average speed of 21.5 kph/13.3 mph)
Using a rear disk would be 2.7 seconds slower
Using lightweight conventional wheels would be .3 seconds slower
 

These “steeper hill” results lead one to believe that for Horner, the break even point for a disk versus mid section carbon wheels is 17.4 mph or an ~5% grade.  The break even for lightweight conventional wheels versus mid section carbon wheels is an average speed of less than 13.3 mph or greater than a 7% average grade.

It should be clear by now that even though the Rubidoux TT is uphill, aerodynamics should guide the equipment selection.  To go as fast as possible on this course, the equipment used should be the same as for a 40k flat TT.  Chris Horner had a really great ride during the prologue and completely demonstrated his intention to dominate the stage race.  However, I think that he could have gone even faster if he had used a TT bike with full aero bars and a rear disk.

Team Saturn appears to have figured this setup out – nearly all of their team (men’s and women’s) rode full TT setups in 2001 and 2002.  They wound up taking 2 out of the top 5 spots in the men’s race in 2001 and 3 out of the top 5 spots in the 2002 men’s race.  Good form, or good equipment choice?  The truth probably lies somewhere in between.  More importantly, though, Chris Horner proved that the mind and the body are the most “significant” variables when determining cycling performance.