The motor isn’t insanely powerful, but it gets you up to full speed quickly enough. I never felt like the bike was underpowered. The motor does make more noise than a lot of other hub motor bikes I’ve ridden though. There’s a definite whirrr to the motor caused by the internal plastic gears. While all geared motors will have some level of gear noise, this one stuck out more to me than others.
The oldest patent for an electric bike I've been able to find at the US Patent and Trademark Office is this one, by Ogden Bolton, Jr. of Canton Ohio, which was filed in September 1895 and granted three months later. You can see from these original diagrams that it bears an amazingly close resemblance to modern electric bikes. In the general picture on the left, you can see there's a hub motor on the rear wheel (blue), a battery suspended from the frame (red), and a simple handlebar control to make the thing stop and go. In the more detailed cutaway of the hub motor on the right, you can see there's a six-pole magnet in the center (orange) bolted to the frame and an armature (made from coiled wire, yellow) that rotates around it when the current is switched on. It's quite a hefty motor even by modern standards; Ogdon mentions "a heavy current at low voltage—for instance, to carry one hundred amperes at ten volts." So that's 1000 watts, which is about twice the power of a typical modern bike hub motor.
Controllers for brushless motors: E-bikes require high initial torque and therefore models that use brushless motors typically have Hall sensor commutation for speed and angle measurement. An electronic controller provides assistance as a function of the sensor inputs, the vehicle speed and the required force. The controllers generally allow input by means of potentiometer or Hall Effect twist grip (or thumb-operated lever throttle), closed-loop speed control for precise speed regulation, protection logic for over-voltage, over-current and thermal protection. Bikes with a pedal assist function typically have a disc on the crank shaft featuring a ring of magnets coupled with a Hall sensor giving rise to a series of pulses, the frequency of which is proportional to pedaling speed. The controller uses pulse width modulation to regulate the power to the motor. Sometimes support is provided for regenerative braking but infrequent braking and the low mass of bicycles limits recovered energy. An implementation is described in an application note for a 200 W, 24 V Brushless DC (BLDC) motor.[43]
In the theoretical electric bike we considered up above, we had the dynamo/motor driving the back wheel directly, simply by pressing on the tire. Most electric bikes work a different way. They have compact electric motors built into the hub of the back or front wheel (or mounted in the center of the bike and connected to the pedal sprocket). Take a look at the hub of an electric bike and probably you'll see it's much fatter and bulkier than on a normal bike. You can read more about how these motors work in our main article about hub motors.

In Opinion No. 2007-00602 of the Attorney General, Jim Hood clarified that a "bicycle with a motor attached" does not satisfy the definition of "motor vehicle" under Section 63-3-103. He stated that it is up to the authority creating the bike lane to determine if a bicycle with a motor attached can be ridden in bike lanes. No specifications about the motor were made.
There are individuals who claim to have lost considerable amounts of weight by using an electric bike.[62] A recent prospective cohort study however found that people using e-bikes have a higher BMI.[63] By making the biking terrain less of an issue, people who wouldn't otherwise consider biking can use the electric assistance when needed and otherwise pedal as they are able.[64] This means people of lower fitness levels or who haven't cycled in many years can start enjoying the many health benefits E-bikes have to offer. [1]
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