Crosshype: How Fast Is Tim Johnson?

Everyone knows that Tim Johnson and the rest of the Elite Men field is ridiculously fast. But how much faster than you is he?

What about Elite Juniors? Or A Masters? Or B Men?

Anyone could look at lap times and answer these questions, but it's a fair amount of number-pushing to get to the points where you can say "Tim Johnson rides X% faster than me." Lucky for you, I like numbers, so I did the heavy lifting, and now I want to talk about it. If you're anti-math or anti-cross, read on at your own peril.

Ok, so we're going to use the results from Caster's Grand Prix last December. Not because I have a particular affinity for that race, but it had long laps so it's pretty easy to figure out how many laps each field did. And the results have times for almost everyone, which is great.

Here's the initial breakdown:
CategoryWinnerTimeLapsLap Time% of TJ
Elite MenTim Johnson57:3587:11 100
A MastersMichael Yozell46:2367:43 93
U19 JuniorsNick Keough38:5357:46 92.5
B MenGary Douville39:1957:5291.5
Elite WomenLyne Bessette41:3358:1986.5
C MenMatt Knight33:4548:2685.3
B MastersMike Triosi34:0948:32 84.3
Masters 55+Phillip Bannister35:3648:54 80.8
B WomenErin Duggan47:2459:2972

Sweet. A chart. The last two columns are where it's at -- lap time, and speed as a percentage of Tim Johnson's speed. So, for example, C men ride at 85% of Tim Johnson for half as many laps.

Math warning: Division is hard. If C Men are 85% of Tim Johnson, what % faster than C Men is Tim Johnson? (Not 15% -- 17.6%)

But, if Tim Johnson is going 17% faster than C Men, how much more power is he putting out? An excellent question, my friend! Unfortunately we can't measure the rolling resistance of a cross race. If we treat cross as frictionless (haha) we can get some numbers from air resistance and use them as an upper bound.

Riding 17.6% faster, if you are only being slowed down by air, requires 38.3% more power. (Resistance proportionate to velocity squared, 1.176/100 * 1.176/1 = 1.383)

So Tim Johnson is putting out somewhere between 17.6% more power (ignoring air resistance) and 38.3% more power (ignoring rolling resistance). The true number is somewhere between the two. Anyone want to estimate average rolling resistance for a cross race?

Man, I don't know what this proves, except that Tim Johnson is fast. Don't forget that part of going 17% faster is handling your bike at that speed.

As long as we have the numbers here, lets look at how the fields stack up. Note that everything here assumes you could maintain lap times in a longer race, which is unlikely.

  • The winning A Master and Elite Junior would have placed 19th/41 in Elite Men

  • The winning B Man would have placed 21st/41 in Elite Men

  • The winning Elite Woman would have placed 23rd/64 in B Men (although she actually raced B Men and was 12th!)

  • The winning C Man would have been 28th/64 in B Men

  • The winning B Master would have been 38th/64 in B Men and 44th/66 in A Masters

  • The winning B Woman would have been 18th/20 in Elite Women

In summary, anyone near the front of their group can easily move up and be competitive, with the possible exception of B women. If you have any friends who are waffling about what category to ride at Verge races, show them this.