Back to the discussion about hiding an electric motor in a pro racing cycle. Before, I looked at a video of Fabian Cancellara to see how his speed and acceleration compare to other bikers. The claim on the internet is that he pulls away so fast that he must have a motor hidden in his bike.
Just to be completely clear, I don’t think he is cheating. Then why bother? If you ask that then this must be the first time you reading this blog. I welcome you. No, but really, this is what scientists do. How hard would it be to cheat?
From my analysis, it seems that a person could ride like he does without a motor. But, the question is: how much power for how long could he get if he DID hide a motor? I am going to assume that you could put some batteries in just two parts of the bike. Here is a typical bike with some estimated measurements.
The other post is where the motor would go – so no batteries there. Now, how big is the inner diameter of these tubes? I am going to estimate the outer diameter at about 4 cm. I guess a 3.5 cm inner diameter is not unreasonable. Right? So, what volume of space for batteries are we dealing with here?
Next question – what kind of battery would I put in there? Here is Wikipedia’s page on energy density. In the chart, there is a Lithium ion nanowire battery with an energy density of 2.54 MJ/kg. I don’t know anything about this kind of battery. I would use this, but I don’t even know the mass density (or the volume energy density). The next highest on the list is a Flouride ion battery with an energy density of 1.7 MJ/kg or 2.8 MJ/L. Just for comparison, Wikipedia lists the lithium ion battery with an energy density of 0.7 MJ/kg and 0.9 MJ/L.
If I used the fluoride ion battery, how much energy would I have stored?
That seems like a lot of energy. But now, what if I want to run a 500 watt motor? How long would that last?
Well, what about the mass of this battery? Using the mass energy density and a total energy of 2.8 MJ:
1.6 kg seems really too low for the mass. That is a weight of just 3.5 pounds. I guess you would also have the weight of the motor, but that shouldn’t be too much. So, maybe if you are James Bond and have access to this kind of stuff, this is possible. (I still don’t think he cheated).
What if you do not have access to these Fluoride ion batteries? What if you just use lithium ion? I would only have 0.9 MJ of energy which would last 30 minutes at 500 watts (oh, assuming 100% efficiency – which is obviously not going to happen). Also, this battery would have a mass of 1.2 kg. Not too bad.