Course Syllabus: In Cycling 310, Wormdrive Motors and You, we will be investigating the plausibility of utilizing a 'wormdrive' motor with planetary gear, powered by a small battery, to assist world-class cyclists through a six-hour race. We will use factual and experimental data, review information presented by supposed testers of the system, and apply a little old-fashioned common sense and engineering judgement. This class is in no way intended to provide actual in-lab experimentation and analysis; rather, the material makes basic educated assumptions and extrapolations.
Oh, boy. Here we go. Fabian Cancellara, the reigning Switzerland National Champion, has been accused of using a hidden motor within his bike's seat tube in order to gain the upper hand in his victories at Paris-Roubaix and Tour of Flanders earlier this year.
After watching some of the YouTube videos out there describing how this would have been possible (and supposedly accomplished), and understanding what the sport of Professional Cycling has been enduring the last several years regarding blood doping and other performance "enhancements", I came to the opinion that this step - using an electric motor hidden in the bike - is in the realm of human cloning.
You just don't cross that line. If that line were to be crossed, and someone got caught, competitive cycling would not recover. It would officially hit the validity in sports of the WWE. Not to say it's not an athletic achievement, but not considered sport anymore.
Anyways, I set off over lunch today to really take a look at what would have been possible.
Supposedly, the battery for this system is installed under the bottom bracket, according to the video. First of all, no pictures of the battery, yea or nay. However, given these races are across some of the roughest roads known to man, let's suffice it to say that installing a battery pack on the underside of the bottom bracket wouldn't be the smartest idea, with the possibility of it being banged around and being rendered inoperable.
Installation of the motor seems plausible to me. However, the installation shows the wiring going down the seat tube from the top, not vice versa. Not sure how you hide that cable...seems to me that, with the number of riders staring at Cancellara's rear end for that long, someone would have noticed something.
Now for the power aspect:
Something so small as to not be seen by anyone means it's a pretty small battery. A Shimano DuraAce Di2 battery pack would be way too big. We're talking something in the realm of two to four AA-size batteries, if it were to be installed on the underside of the bottom bracket.
A new Energizer e2 lithium AA battery is capable of producing about 3000 milliamp-hours (mAh) at 1.5 volts. Series-connect four batteries together, that gives us 3000mAh at 6.0v. However, that's at very small amp draws. In order to put this motor to good use, we're going to need to see at least a 200-watt increase in power. Simple electrical engineering equations (P = v i ; v = i r) show us that to provide 200 watts of power, we need to supply 33.3 amps at 6 volts.
Unfortunately, taking a look at the data sheets for the e2 lithium AA battery, the maximum continuous output of the battery is 2 amps (due to internal resistances); 3 amps at 2 second pulses. Two seconds is not enough time to allow for a cyclist to truly pull away from another rider, so we throw that out. Two amps is the most this battery can discharge for us.
In order for the AA-battery bank to provide 200W of power to a motor (let's forget about resistance of the wiring, motor efficiency, and parasitic electronics for the time being), we would need to series-connect four AA cells into a set, and then parallel-connect 17 of these four cell sets. Yes, that's 68 AA batteries.
I don't think Fabian had that hidden anywhere. That's over two pounds of batteries, plus wiring. Not exactly a Walkman, like we were looking for.
However, to this point, we've just explored the raw power available from the battery. Now let's look at power available at the motor...
Assume, for this application, the circuit between the motor and the battery consists of 24AWG copper wire, which may be small enough to use electrical tape to sufficiently "hide" it from view. Resistance of that wire is 0.0302 Ohms/ft. Let's also assume that there is approximately 5 feet of wire in all. That means the wiring exerts 0.151 Ohms, which the battery must overcome. Applying Ohm's Law:
V=IR
V=(33.3A)*(0.151ohms)
V=5.03 volts
As this shows, the voltage to overcome the resistance in the wire, or "voltage drop" across that wire with our 68-cell setup is nearly as large as the voltage that is being applied...i.e. the motor does not see enough power to run. The power available from the battery is spent trying to overcome the resistance in the wire.
Reversing the equation:
0.3v = (33.3A)*R
R = 0.0090 ohms = 0.0018 ohms/ft
In order to see within 10% of the output voltage (operating range), or 2.7 volts, at the motor, the resistance of the wire needs to be reduced to 0.0018 ohms/ft, which puts us at a 10AWG copper wire. This wire is larger than most of the electrical wiring in your home. Not exactly "hideable" on a bike.
Alternatively, the voltage of the battery could also be boosted to operate the motor. Let's say we wanted to use 24AWG wire because it's small, and we still wanted to have a 200W output. Let's make it a 24v motor:
P = V*I
200W = (24v)*(I)
I = 8.33 amps
2.4v = (8.33A)*R
R = 0.288 ohms = 0.0576 ohms/ft
Since our required wire resistance is greater than the actual resistance of a 24AWG wire, looks like it would work. This scenario would put 16xAA-cells in series to create 24V, then 5 sets paralleled to create more than 8.33 amps. Now we're at an 80 cell battery.
And we have not addressed the efficiency of the motor (not 100% mechanically efficient), or the fact that the electronics are probably parasitic to the power input (meaning the button and the "memory" functions also pull power from the battery). Needless to say, this was not the power solution.
The most obvious choice would be to use a Shimano DuraAce Di2 battery. This device is compact, and can be found on a number of bikes in the peloton (but not on Cancellara's bike either of those days). Put the Di2 battery on, still use a standard mechanical transmission, voila. Plausible, at least.
The Di2 battery has a rating of 530mAh at 7.4v.
200W = (7.4v)*I
I = 27.0 amps
At zero internal battery resistance (i.e. perfect battery):
530mAh / 27.0A = 0.196 h = 70.7 s
At the rated capacity and amperage required to operate the motor, with zero internal resistance, the battery *could* power a motor for a little over a minute.
But...
- Wire size would need to be in the realm of 16AWG to get power to the motor.
- Assuming a 5W leech of electronics, and a 90% mechanically efficient motor assembly, the actual power applied by the motor is limited to 175.5W.
- Again, with any battery, power supplied will decrease with the life of the battery. So assume (again) you only get 80% of the useful life of the battery in one application, or 56 seconds.
Taking into account these assumptions, a perfect battery sized the same as the Di2 battery could potentially add 175.5W for nearly four 15 second bursts during a race.
But know that this perfect battery does not exist. Internal resistances will likely limit that output current to just a couple of amps, and we're right back in the same boat as the AA battery. As you will with any scenario. The battery technology just doesn't exist to provide the kind of power these guys would need. The battery needs to be huge to provide the kind of power these guys would notice (especially to justify the risk), and you just can't hide that size of a battery.
Adding 25W to a bike (which is what you would probably get out of an "invisible" battery) across a minute of a six-hour race is not going to change the outcome of the race. And it sure as hell isn't going to gap those guys like he did on several occasions. That is a solid 200-300W difference...also known as "dropping the hammer". And I think I showed that you can't put 200-300W of mechanical assistance without having a battery that would be large enough to be recognized by anyone.
Ask yourself this - if this motor is how Fabian Cancellara "won", how do you explain his ability to time-trial across the last 15-45 MINUTES of the race, still opening the gap on Boonen? Maybe Tom found someone that had a couple of lines scraped out for him...
Look, Cancellara might be all doped up on designer EPO or doing the "Floyd Method". But never underestimate the power of the human motor.
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