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Is there a formula for motor wattage and top speed potential for scooters?

I am looking for a formula to predict top speed of a scooter based mainly on motor wattage.  You can assume the rider will be under the limit of the scooter and that the "gearing" (sprockets) are reasonable so as to not lug the motor at nominal voltage but also not so low as to spin the motor higher than normal at its nominal operating (rated) voltage.

Here is an example.  My Mongoose M200 scooter (from 2007 I think) is normally 24V and tops out at 12 MPH (using the standard 15 and 90 tooth sprockets).  I overvolted it to 36V and now it goes 18 MPH (confirmed) using the same sprockets.

Question is, had I not overvolted (either by choice or cuz it would not work), but instead upgraded the existing motor which I think is either 180W or 200W, what wattage motor (at say 24V) would I need to match the increase to 18 MPH?  Would I need a 360 to 400 watt motor?  If so, does that mean my little 180-200 watt motor is now putting out double its rated power (from about 1/4 HP up to maybe 1/2 HP, 1 HP = 746 watts)?  Do you need quadruple power (in watts for example) to double the top speed?  For example, if my original motor was 200 watts and went 12 MPH but I wanted to go 24 MPH, would I then need 800 watts?

All electric motors have a rated RPM, which is the RPM of the motor under full load. If you can find the rated RPM of a motor then you can calculate the top speed using this convient calculator (thanks!): I can't figure out the top speed of an electric scooter with only the wattage of the motor and some other vague details, as each motor has a different RPM. Hope I helped!
Oh, and I forgot to mention that if you double the top speed of an electric scooter with a larger or smaller sprocket, it will half the torque, along with decreasing low-end torque even more plus wearing on the motor a lot, burning it out a lot sooner. Stop riding immediately if you see any smoke coming out of the motor if you do this, and be very careful. Try to keep the motor as cool as possible, as it will overheat fast, which is bad for the motor. On the other hand, you can bring back the torque by installing a motor with twice the rated wattage than the original, it won't be bad for the motor, and you might even get a higher top speed because larger motors tend to have higher rated RPMs. Get the picture?
(last paragraph) an electric scooteer --> a stock low-powered electric scooter (this does not apply to high-powered scooters) One more point: By increasing the top speed with a larger or smaller sprocket, you are not increasing the motor power in any way, rather you are decreasing it through wear (only decreasing power on low-powered scooters, as their motors cannot handle more load).

My question was not answered.  For this particular question, you can further assume that different wattage motors have the same nominal RPMs, so that we are just taking wattage as a yardstick for top speed.  So for example, if my current motor is 200 watts, 2500 RPM, 24 volts, and can propel my scooter up to 12 MPH max speed, how many watts would I need to double my top speed to 24 MPH?  Assume the 24 MPH setup has a motor that is also 2500 RPM and the "gearing" of that scooter is "double" to compensate for the increased power.  That is, the weaker motor will push the scooter 12 MPH at 2500 RPMs and the more powerful motor will push the scooter to 24 MPH also at 2500 RPMs.

Oh I see now! In your case, with a very low-powered electric scooter, you will want to double the wattage of the motor, along with making sure the rest of the electronics can handle it, to safely double the top speed with a bigger or smaller sprocket. You will still get a doubled top speed even if you don't replace the motor and if you change the sprocket, but it would be very bad for the motor. I recommend you double the motor wattage to avoid having to replace the motor all the time. If this still doesn't answer your question then I will just back off and let ESP Support answer your question a whole lot better (I am only fourteen and modding a Razor GFD Fury).

Doubling the wattage will likely not double the top speed.  Until someone else has proof of otherwise, I will assume that to double the top speed, a quadrupling of motor power is needed.  For example, if a 200W motor can propel a scooter up to 12 MPH, then to propel that same scooter up to 24 MPH, an 800W motor would be needed.  This is assuming both motors are sprocketed to put them in their "happy" RPM range (not oversped and not undersped).

I am confused. How come that calculator doesn't account for the most important information like a motor's rated RPM and the sprocket/gear sizes? Was David James correct about everything he said? Was I wrong about anything I said? I want to know because I might have this twisted reality that is wrong about motor power and top speed potential for my mod.

Motor speed and sprocket sizes are not part of the input parameters or result of the motor power calculator so it can focus on estimating the top speed that a motor can be geared for. Once the top speed is determined by the motor power calculator then our top speed and gear ratio calculator can be used to determine which motor and sprocket sizes to use.

Due to so many data parameters being required to determine what speed a motor can propel a scooter to there was not enough data included in any of the above comments to assess if they are correct or incorrect so we suggest using the motor power calculator to estimate what size motor to use for a specific top speed. 

If you're looking for 18mph at least then you will definitely achieve that with a 500w 36v motor with a 44 tooth wheel sprocket and 15 tooth motor sprocket. This is the best way of doing it without having a small over volted system that will ultimately stress the motor.

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