There is no forced cadence. The motor is not fixed at a particular RPM; if the motor were unloaded, it would spin a lot faster than it does. It supplies a certain amount of power, and the bike hits a certain ground speed, and through the gear ratio, that determines the motor's speed.
If you only want to go that fast, then you don't have to crank the pedals, and it's awkward. However, you can crank the pedals to go even faster.
That's the point of using the motor. You + motor is faster than you alone or motor alone. Or: you + motor requires a lot less effort on your part to maintain a certain speed than you alone. Suppose that you can go 30 mph, but with great difficulty and not for very long. Suppose that a given motor by itself can go 20 mph. If you use that motor and your own muscles together, you can go 30 mph with a lot less effort, and sustain it a lot longer. The cranking of your pedals and cadence will be natural; you're cranking 50% faster than what the motor can do by itself. It will be like cycling in the slip-stream of a truck, or down a slight downgrade. To the spectators, you will just look like a strong cyclist.
About the 100W, almost any amount of cheat torque can make the difference between placing N-th and N+1st. Every second counts.
Even a 2.5W power boost could be a game changer. If your muscles put out 250W, 2.5W is 1% more, which is significant. It's about 36 seconds shaved off a one hour haul. The game has changed from a neck-and-neck race to the front runner having a 36 second lead.
A tiny, light-weight motor of just a few watts that would be useless in a commuting bike used by someone who is out of shape and cannot climb hills could nevertheless win trophies for a cheater.
One minute you're racing just beyond your lactate threshold. Flip a concealed switch, and a tiny power boost drops you within your threshold.
It's a 250W rated bunch of Chinese-sourced parts on a $50 eBay steel framed budget mountain bike.
It's _so_ hilarious to ride, a friend says "it make you feel like Lance Armstrong!". It just makes everything too easy. I barely ever take it out of top gear - I just lazily pedal up hills, zoom along the flat, and have to brake to stop feeling suicidal down hills. I'm an almost 50 year old overweight and out of shape guy, and I commute to work on it keeping up easily with the lycra-clad mamils on what look like $10K+ carbon-everything bikes - I've been doing it for a few years and it's _still_ so much fun passing them going up hills.
I can _easily_ believe even a fraction of the power I've got there would turn a midfield racer into a winner.
(For the record, I've got a 7 cell LiPo battery powering mine, and off a full charge I see 470W or so coming out of the battery accelerating up a medium incline. It tops out at 25kmh, and pulls barely 100W to do that on the flat, but it's _so_ noticeable accelerating away form stationary or up hills. It's _ really_ fun :-)
Just curious: why not ride a regular bike to work? I've been doing it for a year now (16.5 miles round trip) and it has been great. I never could find the time to exercise before and now I commute and exercise at the same time. Parallelism!
Because lazy! At least mostly. Also we don't have shower facilities at work, so during summer (I'm in Sydney, so summer hasn't quite ended yet) I end up quite sweaty riding to work.
I do have a non-cheater bike as well, I ride it more when it's cooler (but I'm still lazy, so...) More exercise is the plan. Executing on that plan isn't always successful.
I'm looking at getting a similar setup for myself this summer. I hear "that's cheating" or similar from others, in which case my response is: Do you ever use a calculator? Why not work out everything with pencil and paper (or better yet, in your head)?
Of course, several years ago after I decided to get in shape, I tried cycle commuting and really enjoyed it (about 15 miles each way). But I could only pull it off about once a week or so (in order to make good time, it left me mostly worthless at work all day). Coming up, after I move in a month I'll be about 23 miles from work. Adding a hub motor will allow me to not only make the commute in just over an hour, but it will leave me less exhausted (I plan on still putting in some human power, but I won't have to over do it). The good thing though, is by adding electric power to a bicycle, it will get me on it much more often so I'll end up getting even more exercise than without power.
I built an ebike last year to do something similar to OP. I rode my bike (a full suspension mountain bike) a couple times, but found that 20 miles was just too far to cover for a commute. With the ebike, I am still pedaling and getting exercise, but it takes me 50 minutes instead of 90. Still a tad longer than it would take in my car, but I am definitely getting a decent workout (determined by how sweaty I am before I shower). Even if I only burn half the calories, I am getting nearly 2 hours of exercise a day I wouldn't have gotten otherwise, and am not adding much time to my commute.
Maybe someday I will be in good enough shape to make the 20 mile commute in around 1:15 without the assistance, but if it's between pedal assist and driving, pedal assist seems like the far better choice!
FWIW, I used to bike-commute to school when it was 8-10 miles, and that was great. But 20mi each way is just too much time for me when I need to get home to get kids to practice, or help with homework, etc.
This is a great description of why motors can make a big difference in racing. Even small differences in power output can make a big difference in an elite race where so little can mean the difference between winning and not. It's easy to imagine using a tiny motor (much smaller than the one mentioned in the article) could make the difference between winning and being an also ran.
However I have to nitpick on one point:
"Even a 2.5W power boost could be a game changer. If your muscles put out 250W, 2.5W is 1% more, which is significant. It's about 36 seconds shaved off a one hour haul."
Air resistance is one the most significant factor affecting riders at race speeds, and its force increases at a much greater than linear rate. You'd need about 3% more power in your example to save 36 seconds. In a flat time trial over one hour, 1% extra power would actually save you closer to 12 seconds. That said, the Tour de France has been won by less.
Also, a boost gives you a tactical advantage: an advantage of psychology.
Firstly, in a race, it is psychologically challenging to be the leader of the pack. Are you really faster than those behind you? Or are there opportunists nipping at your heels, wearing you down, who will surge by you when the goal is in sight? With a secret boost, you can overcome some of this uncertainty.
Likewise, you can use the boost to surge by opponents after tailing them for extended distances without the boost. When you surge by someone, it has a mentally devastating effect on them. You show that you have untapped reserves that they don't, which creates the belief that you cannot be beaten. In the absence of cheating, that belief is just a belief. The playing field is level: by trying to create the belief that you are stronger and faster, you're taking a risk (because it's not a given that you actually are; you're faking that out with a little surge that you could well pay for later.)
I believe that with a hidden motor, you can not only reduce your own race time, but make someone else's race time worse. You wear them down with an unrealistic pace, either as a leader or follower (pressure from the back) which you can then maintain yourself thanks to the motor, while they blow their race.
And then, here is the thing. If you win by tactics, that doesn't have to involve coming anywhere near the best time for that course or a world record etc. You get everyone to screw up, and then cross the finish first, but in some credible time that doesn't draw attention to your performance, seconds or minutes behind the best time that was ever observed on that course. That reduces the suspicion of any cheating, unless your splits over the course are scrutinized.
Yes, the math says so. Have a look at the video I posted above though. While E-assist bikes can do this, these hidden motor versions just don't in the real world, for racers. I do believe it will, at some point, I just don't think it's there yet. There's just no money in developing it right now.
The benefit provided by the output of the motor won't be linear, at least not for road races (cyclocross I'll grant is an entirely different beast).
The ratio of power output to speed follows a square law, so if you're going 20 mph and flip on a motor that doubles your power output, you won't even hit 30 mph, let alone 40mph (4x power = 2x speed). But this is an endurance sport and a huge part of your strategy involves dealing with wind resistance (by drafting) so even a little boost means that you might be able to pull off or prevent a breakaway at a critical moment of a race. For much of the race your goal isn't to go faster than the other guys, but merely to match speed without wearing yourself out.
If you only want to go that fast, then you don't have to crank the pedals, and it's awkward. However, you can crank the pedals to go even faster.
That's the point of using the motor. You + motor is faster than you alone or motor alone. Or: you + motor requires a lot less effort on your part to maintain a certain speed than you alone. Suppose that you can go 30 mph, but with great difficulty and not for very long. Suppose that a given motor by itself can go 20 mph. If you use that motor and your own muscles together, you can go 30 mph with a lot less effort, and sustain it a lot longer. The cranking of your pedals and cadence will be natural; you're cranking 50% faster than what the motor can do by itself. It will be like cycling in the slip-stream of a truck, or down a slight downgrade. To the spectators, you will just look like a strong cyclist.
About the 100W, almost any amount of cheat torque can make the difference between placing N-th and N+1st. Every second counts.
Even a 2.5W power boost could be a game changer. If your muscles put out 250W, 2.5W is 1% more, which is significant. It's about 36 seconds shaved off a one hour haul. The game has changed from a neck-and-neck race to the front runner having a 36 second lead.
A tiny, light-weight motor of just a few watts that would be useless in a commuting bike used by someone who is out of shape and cannot climb hills could nevertheless win trophies for a cheater.
One minute you're racing just beyond your lactate threshold. Flip a concealed switch, and a tiny power boost drops you within your threshold.