Writeup updated slightly on June 3, 2010
So dear readers, quick recap : there's this idea floating around of Swiss rider Fabian Cancellara using an electric motor at the classics. It seems to have originated at the rumor mills of il Italia and a couple of journalists, an ex-pro cyclist and a little known e-bike maker are in the thick of it. Meanwhile, Fabian tossed out a statement today in the press calling hogwash to these claims. Hey, the truth is out there...
Last evening, I spent some time re-watching 2010 Paris Roubaix clips. My focus was upon the attack from Cancellara with 48k to go. To me, there were three segments to this attack :
"..can we dissect this attack and see its parts to get a perspective of what's happening?"
1) At 55K remaining, there were a lead group of 40 favorites at the front. They included Tom Boonen (Quick Step), Fabian Cancellara (Saxo Bank), Filippo Pozzato (Katusha), Adam Hansen (HTC-Columbia), George Hincapie (BMC Racing Team), Leif Hoste (Omega Pharma-Lotto) etc.
2) In the next 2 or 3K, the group splintered. Leif Hoste, Björn Leukemans, Frederic Guesdon and Sébastien Hinault pushed to the front.
3) At 49 K to go, Fabian Cancellara surged ahead from the bunch to join the four leaders. In a few seconds, he took one sideways look behind him, saw that the title defender Boonen had decided not to mark him down. Riis, the team manager, radioed to him. "Go". Yup, it was a bad move from the Belgian champion. Fabian was then gone and the rest is history.
The jump Fabian put forth was strong and decisive. To most of us, watching the surge (see video below) may seem almost like, well, like he had a motor somewhere on the bike. How on earth can he pull away so quick, right? Well the Italians asked that hard question and came up with the answer - 'Oh mio dio, he has a motor on his bike!'
But regardless of whether he used a motor or not, can we dissect this attack and see its parts to get a perspective of what's happening? I think we could.
So I used a physics analysis software and some basic physics to get an idea of the speed and acceleration involved in this attack. This may seem pretty ghetto to some of you but perspective is what ultimately matters.
1) First, I downloaded the above video of the action from Youtube. I cut the video segment only to the points of interest, from 2:07 to 2:22 or so. I eventually a few hundred frames at 25 frames/second. I decided a timestep of about 0.03-0.04 seconds would be more than adequate to the capture the stages of the action.
2) I scaled the segment with a known dimension of some entity. That entity was going to be Cancellara's 58cm Specialized bike. I looked up its specs and found out that the wheelbase of the frame is pretty close to 100 cm or 1m. Good enough.
3) I imagined myself seated inside the TV helicopter, shining a path co-ordinate axis down at the action below, somewhere in the middle of the screen. I reckoned that the zoom and pan from the helicopter camera would create complexities, but luckily for me, there was not much. The cameraman in the helicopter had kept his focus remarkably steady on the racers, without much shaking and distraction. There was a bit, but I knew exactly where it was. Then I positioned the axis angle to be somewhat parallel to the direction of motion on the road.
4) I then stuck point mass trackers on Fabian, spectators and motorcycles. These trackers would give me position vs time information of the object as the cross-hairs of the camera sped past them.
I finally had distance vs time plots from objects to plug into MS Excel. Since velocity depends on the observer, and since the observer is in a moving state in a helicopter, any relative motion between the observer and the cyclists is either a surge or a deceleration.
Let's explore the stages of the attack :
A) At what speed was the peloton with favorites moving initially?
Here, helicopter camera was very focused on the action with little shaking. Hence, a spectator appearing and flying out of view may give an indication of the speed of the riders. The position time graph was a straight line. The data was exported in Excel and a "linest" operation on the data yielded a slope, as shown below.
25 mph is not hard to believe.
B) What was the speed of the lead group that surged away?
C) The attack : How fast can Fabian put a 5 second gap on others?
Fabian was to the right of camera's origin (purple axis) before he attacked. The camera was focused on the lead group and did not follow Cancellara when he attacked due to the "lag" in reaction time from the cameraman. The downward slope on this graph indicates Cancellara moving towards the negative left side of the origin with his surge. In a little over 4 seconds, the brunt of the attack came, when the slope of the graph dips further, indicating acceleration. The area of interest is limited to 12 seconds because the cameraman suddenly finds out what's happening and shifts his focus to Fabian. This is why the red line begins to curve back up again.
So I exported that graph into Excel, inverted the graph so I would get nice positive numbers. Then I cut the graph to the area of interest.
Presto! This shows us that Fabian puts in a 5" gap very quickly. But how quick is "quickly"?
...this gives us an idea of Fabian's relative speed from the camera focus. So what happens in this 5" gap that Fabian puts relative to peloton? In the first 2 seconds, he manages +1.6 mph. In the next half second or so, he increases that to +3.3 mph, which then bumps up to +6.5 mph until at the second before the camera catches up with Fabian, he's riding at an impressive +7.4mph.
I stuck a tracker on a passing motorcycle as it sped past Cancellara to "get out of the way". Perhaps it was Graham Watson in the back seat as the flashes of a camera went off. Nevertheless, I found it had a relative speed of +25mph from similar analysis. Adding this to Cancellara's speed of 29mph gives a roundabout motorcycle speed of 60mph (96kph). Its believable.
Also, if I were to plug in the speed I obtained and Cancellara's weight and cadence into Analytic Cycling's "Forces on Rider" calculator (with generic parameters), it gives me about 680 Watts of power. Still believable by STATIC riding standards.
But since I said that he's accelerating with 0.9m/s, given a weight total weight of 87kg (80 kg Fabian and 7 kg bike) and a final speed of 16m/s, we should really calculate his power output and crank torque in a dynamic situation. For the crucial 5 seconds of attack time, I calculate all those below.
I assume Fabian was on his 53-11 gear, which I'm sure he could easily pedal.
Onto the propulsive force required.
Work done then becomes :
So what is his power output to accelerate for those first 5 seconds?
Though not very relevant, also notice that this power output equates to a rough 5 sec power to weight ratio of 1200W /80kg = 15 which is nothing out of the ordinary based on a power to weight ratio chart for male cyclists (See Power to Weight Ratio).
Using a stopwatch, I figured Cancellara increased his RPM from his previous 100 to 110 RPM for his attack. The average torque required for this acceleration at the crank is then :
That value is within the realm of competitive cycling. Since I said this is an average, it would be the average of the "sine-curve" of torque on the y-axis and crank angle on the x axis. The crank torque is scaled down at the rear wheel by a factor of the gear ratio, calculated earlier, since it rotates faster.
For readers on both side of the Atlantic Ocean, I put this all together in one table with units :
My sanity check is over. The numbers are believable by DYNAMIC riding standards. Any doubt? Note that some data from the recent Tour of Flanders indicates that he put in 1450 Watts during the attack on the Muur. That number came after a very long day of riding. If he can manage that, he can surely manage 1200 Watts in the initial moments of his breakaway.
This is my two cents.
It is the first 5-10 seconds of an attack that is most crucial and most tricky. Attackers must be able to speed off from an already high pace, and the objective is to dig in to hell, gather the firepower and deliver the maximum blow without suicide.
It is the rapid rate at which Fabian Cancellara increases his speed that is mind boggling to see in the video, even though such speeds are pretty normal for him.
Don't get hung up on the numbers presented here, which is all approximate. But we know from historical data that Fabian is someone who can out-sprint the best by simply staying seated on his saddle, even after 230K of racing. The following is one of those spectacular moments of Tour de France history that will not erode away with time. Watch :
Some Probability and Statistics of the Individual Time Trial
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