I want to try and summarize a point or two. For a given mass, acceleration abides by a fixed proportionality with the ratio of power to velocity. For a given mass, the greater the ratio of power to velocity, the greater the acceleration. Within any given gear, this ratio takes on its greatest value at the same point where torque has its greatest value.

The thing about this stuff that many people seem not to understand is that, at that point where torque is as great as it is going to get (and ditto for the ratio of power to velocity), if you have the ability to alter the gearing ratio so that the motor will spin faster, such that power is increased to the detriment of motor torque, then wheel torque and acceleration will increase notwithstanding that engine torque or motor torque will decrease. This fact is the essence of the correct understanding of this torque vs. power business, and this fact is obfuscated as soon as anyone starts talking about what happens “in a given gear”.

Whether you design for a single gearing ratio or a set of discrete ratios, the goal is to cause power, not motor torque, to be as great as possible for as broad a range of vehicle speeds as possible. The original question misunderstood this.

Consider the simple case of a single, fixed ratio. If you were to choose a ratio that keeps motor speed low in order to maximize motor torque, then wheel torque would suffer as a consequence. There is more than one way to understand why this happens. One such way is to realize that when the ratio of motor speed to wheel speed is low, the ratio of wheel torque to engine torque is also low, because these two ratios are the same ratio. Another way to look it is to realize that wheel torque is equal to power divided by wheel speed, and that power depends as much on motor speed as on motor torque.

Thus, rather that choose a ratio that would keep the motor speed low, you would do much the opposite, except to avoid the situation where you would run out of torque too early and be left with little or no passing power at highway speeds. You could probably go about selecting an appropriate ratio by thinking only in terms of wheel torque, but to my way of thinking, the power perspective is more direct notwithstanding the fact that you have to keep in mind that you need more power at high vehicle speed than at low vehicle speed to achieve the same acceleration at both low and high vehicle speed. Keeping that in mind, I would select a ratio whereby power is maximized for a typical highway speed. Subjectively, I would desire to improve the passing ability as much as I can for a vehicle speed in the vicinity of 60 mph, which would mean that I would choose that single ratio such that the motor’s no-load speed will coincide with vehicle speed twice that great, i.e., 120 mph, taking into account the wheel radius.

Now, at this point the question becomes whether it would make much sense to add a second gear. Doing so would not improve matters at 60 mph, because I have selected the ratio such that at this vehicle speed, I get the best performance from the motor that I can possibly get from it. But in doing so, I have chosen a ratio that causes performance at low vehicle speed to be less than what it might otherwise be. Acceleration at low vehicle speed will still be stronger than at 60 mph, because motor torque declines steadily from low vehicle speed to high vehicle speed, but the fact remains that performance at low vehicle speed is made less than I could otherwise have made it, by virtue of my having selected the ratio so that performance at 60 mph will be as great as it can be made, at that vehicle speed.

Thus, the question of whether I want to add a second gear ratio reduces to the question of how badly I want acceleration at 10 mph to be even greater than it is. When considering that question, the first fact that occurs to me is that acceleration at 10 mph is already six times greater than acceleration at 60 mph. The key underlying fact is the fact that motor torque decreases in a steady, linear manner from low rotational speed to high rotational speed. Because of this fact, it is invariably true, even when a single gear ratio is used, that acceleration will be better at low vehicle speed than at high vehicle speed. When you consider this fact alongside the fact that using more than one ratio will not permit you to make power at 60 mph (or any other vehicle speed that you select) any greater than you can make it when using only one ratio, the justification for using more than one ratio seems very weak. If the acceleration at 10 mph, which already is six times greater than the acceleration at 60 mph, is not as good as you want at that vehicle speed, then it is more than likely the case that acceleration at 60 mph is a far greater problem than acceleration at 10 mph, in which case you need a bigger motor and bigger batteries.

The question that was posed was oblivious to the fact that as you alter the ratio of wheel speed to motor speed in order to keep the motor torque high, that in doing so, you cause wheel torque to decrease relative to motor torque. Time and time again I encounter comments, in various motorcycle and automotive forums, that imply that the person making those comments does not understand that as you change the gear ratio so as to keep engine speed adequately low, that you necessarily and consequentially cause wheel torque to decline in relation to engine torque. I would wager that fewer than half of motoring enthusiasts understand this. Anyone who does not understand this can take comfort in knowing that they are in good strong company.

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I think some people that use comments like you referred are the ones on drugs.

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Got these pics as my desktop and I’m knocking 50 there is still the kid in me some where.

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Your reason for changing your mind is not the right reason. It might be possible to use a DC motor for a bike without regenerative braking, but the context of this little discussion, per Anothersquid’s question, is specifically about the use of regenerative braking, and this changes things fundamentally. The device known as a dynamo, which is a DC generator, is a historical artifact. I can’t say with certainty, but I doubt if any power generation at all is done with DC generators. They required a large commutator, and the brushes wear out and required periodic replacement. There is also the fact that the power grid and powered devices all assume AC, but this would not be a consideration in a contained application. It is nonetheless reasonable to assume that we are talking about an AC generator, and when it is operated as a motor, it would presumably have to operate as an AC motor. Therein, I suspect, is the real difficulty, because ordinary electric motors are synchronized to the frequency of the AC supply voltage. Previously I hazarded a guess that the frequency would be varied as need in the oscillator used to produce AC from the DC battery, but after doing a very brief investigation into this, it is likely the case that nowadays there are types of motors that are driven with AC but that are not synchronized to the AC frequency, but rather behave much the same as DC motors.

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