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### Calculating the highest, possible speed you can get

Posted: Dec 20 2015 6:19am
I have tried myself on this to figure out the highest real speed I could get with 4kW motor.

P(Motor)=((A/2 x CW x D x v³)+(Cr x m x g x v)) x 1,11

P(Motor) = 4kW = 4000W = 4000
A = Stirnfläche des Objekts = face of the object = around 0,6m²
CW = Luftwiederstandswert = Air resistance = around 0,7
D = Dichte der Luft = Density of air = at 400 meters over the sea at 25 degree Celcius = 1,196 kg/m³
V = Geschwindigkeit = Speed = That´s what we want to calculate
CR = Rollwiederstandwert = Roll resistance = (downhill wheel with bad conditions) = 41 Watts
m = Masse = Weight of Rider and Bike together = (65kg + 44 kg bike) = around 110 kg.
g = Erdanziehung = gravity = 9,81
Verlustfaktor = Dissipation Factor = 1,11 at efficiency 89%.

RED COLORE = not real, surce on example motorcycle, google search motorcycle.
BlUE COLORE = personal value or just real data.
GREEN COLORE = differnt, not consistently data.

-When calculating it with your datas, you have to change the green marked data, and parts of the blue marked data.

4kW = ((0,6/2 x 0,7 x 1,196 x v³)+(41 x 110 x 9,81 x v)) x 1,11
4kW = (0,25116v³)+(44243,1v)) x 1,11
4kW = (0,25116v x 0,25116v x 0,25116v + 44243,1v) x 1,11
4kW = 4510,015938Vv x 1,11___________I /4510,015938
4000 / 4510,015938 = v x 1.11
0,8869148268 = v x 1,11_______________I / 1,11
0,7990223656 = v

=> 79,9 KM/H

Im just not shure if this means 79,9 km/h.
Tell me if you have something to add.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 7:14am
Hi.
Several points:

1. Where did you get the formula from?
2. Assuming the formula uses SI units, than the result is probably in Meter/Second not KM/Hour.
3. You can compare your results to this calculator: http://www.ebikes.ca/tools/simulator.html
4. Keep in mind that the motor produces maximum power at around 50% of it's max RPM therefore, if calculations show a 4KW power consumption at a certain speed and your motor can make only 4KW, you will have to gear the motor to spin at 50% of it's max speed when the bike is at the calculated max speed.

Avner.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:09am
That number is very close to what the Grin simulator gives for 4kw motor output in a mountain bike, right at 80 kph.

4kw in a full recumbent though is 103 kph so aerodynamics plays a big part in speed at a given power level.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:16am
Be aware and differentiate the deviance from battery output watts and motor output watts!
Graph is motor output watts required for various speeds.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:19am
ferret wrote:Hi.
Several points:

1. Where did you get the formula from?
2. Assuming the formula uses SI units, than the result is probably in Meter/Second not KM/Hour.
3. You can compare your results to this calculator: http://www.ebikes.ca/tools/simulator.html
4. Keep in mind that the motor produces maximum power at around 50% of it's max RPM therefore, if calculations show a 4KW power consumption at a certain speed and your motor can make only 4KW, you will have to gear the motor to spin at 50% of it's max speed when the bike is at the calculated max speed.

Avner.
1. From another german question forum.
2. Well if so, then I could go max. 28,80 kilometers per minute. And this can´t be the fact.
4. I think a brushless rear hub motor has maximum rpm when maximum power / maximum speed is used.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:24am
Be aware that maximum motor output must be geared to coincide with maximum speed.
Gearing (or winding) low will give better acceleration but never attain best speed.
Gearing (or winding) high will retard acceleration and never allow attaining best speed ... unless with tailwind, drafting or on downhill grade.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:24am
DrkAngel wrote:Be aware and differentiate the deviance from battery output watts and motor output watts!
Graph is motor output watts required for various speeds.

Your tabel sais that 3,5kW = 5 PS. Thats not right as far as I know. 4000 Watts = 5,4 PS.Otherwise it would be a bit extreme.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:33am
I agree with jonathan that above 30-MPH (48 km/h) aerodynamics plays a major role in the top speed attained. But at 20-MPH and below (32 km/h)...not very much.

Here's a speed = RPM + tire diameter chart to help make calcs faster and easier:

https://endless-sphere.com/forums/viewt ... 28&t=16114

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:38am
DasDouble wrote:
1. From another german question forum.
2. Well if so, then I could go max. 28,80 kilometers per minute. And this can´t be the fact.
4. I think a brushless rear hub motor has maximum rpm when maximum power / maximum speed is used.
1+2 You need to check what units does the formula use, if it's in German I can't be much help.

4. That is wrong. Electric motors give maximum power at approximately half maximum RPM.

Avner.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:48am
ferret wrote:
DasDouble wrote:
1. From another german question forum.
2. Well if so, then I could go max. 28,80 kilometers per minute. And this can´t be the fact.
4. I think a brushless rear hub motor has maximum rpm when maximum power / maximum speed is used.
1+2 You need to check what units does the formula use, if it's in German I can't be much help.

4. That is wrong. Electric motors give maximum power at approximately half maximum RPM.

Avner.
4. Oh ok, I see. I just thougth that you have to use as much power as you have to go to higher speed. Like at 299 km/h you have to use more powern than at 150 kp/h because of air resistance.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 8:49am
ferret wrote:
DasDouble wrote:
1. From another german question forum.
2. Well if so, then I could go max. 28,80 kilometers per minute. And this can´t be the fact.
4. I think a brushless rear hub motor has maximum rpm when maximum power / maximum speed is used.
1+2 You need to check what units does the formula use, if it's in German I can't be much help.

4. That is wrong. Electric motors give maximum power at approximately half maximum RPM.

Avner.
#4 Motors are capable of maximum output at ~40-50% of no load speed ... only if supplied sufficient amps!
Many motors use lighter windings and lower amps to push (reduced) maximum power to near peak efficiency and speed - 75-80%+ of no load speed

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 9:01am
Anyone here who has some datas how long it takes with a 10 kW motor from 0-100 kph / 0-60 mph?
Also I could need the weight of this rider. If so I could calculate how long you will need from 0-100 / etc. with 4 kW..

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 9:18am
DasDouble wrote:Anyone here who has some datas how long it takes with a 10 kW motor from 0-100 kph / 0-60 mph?
Also I could need the weight of this rider. If so I could calculate how long you will need from 0-100 / etc. with 4 kW..
Too many unknown factors!
Operational weight of entire bike w/rider?
kW rating is motor output or input?
Output curve of combined controller-motor?
Gear ratio (torque x rpm / gear ratio etc)?
Wind resistance factor?
etc.
etc.
etc.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 9:25am
DasDouble wrote:
4. Oh ok, I see. I just thougth that you have to use as much power as you have to go to higher speed. Like at 299 km/h you have to use more powern than at 150 kp/h because of air resistance.
That is correct, the higher the speed the more power is needed. Theoretically, to reach twice the speed would require 4 times the power. But that does not mean the the motor is capable of supplying enough power to maintain that speed.

A motor (electric or combustion) usually delivers it peak power at a specific RPM. In order to reach the maximum speed possible, you have to gear the motor so that it is at it's peak power RPM when the vehicle is at the maximum speed.

That is why many cars can't reach their top speed in top gear. The reason is that at the theoretical top speed, in top gear the motor RPM is below the peak power RPM and the motor can't produce the power needed for that speed. At one gear lower then top, the motor RPM is higher (and closer to the peak power RPM), therefore the motor is making more power and is able to maintain a higher speed.

As has been mentioned in this thread and many others, unless it is artificially restricted, an electric motors peak power RPM is approximately half its no load RPM.

Avner.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 10:27am
DasDouble wrote:Anyone here who has some datas how long it takes with a 10 kW motor from 0-100 kph / 0-60 mph?
Also I could need the weight of this rider. If so I could calculate how long you will need from 0-100 / etc. with 4 kW..
The velocity at any moment of time during acceleration from zero will be given by v=((2*P*t)/m)^.5 You can rearrange the equation to solve for t with v as a given, this equation neglects friction from all sources which would make the entire calculation considerably more complex.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 11:25am
The problem with this formula is that P is not constant, it constantly changes as a function of motor RPM.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 11:36am
I was answering the theoretical question, as I indicated the practical real world results will differ substantially from theoretical calculations, you add another term that would be necessary to introduce to the equation to more closely model reality.

It wouldn't be impossible to set up a controller such that a motor put out constant power over a fairly wide speed range, taper the current and hence the torque with rpm at just the right rate.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 11:48am
Even a simple controller of lower Amp capability can stabilize watt output over a broad range ... at severe reduction of peak motor output rating.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 2:12pm
DrkAngel wrote:...Gearing (or winding) low will give better acceleration...
Gearing (or winding) high will retard acceleration...
This highlights an all too common misconception, because "(or winding)" makes the otherwise correct statements incorrect. Proper gearing is critical to any electric motor application, and hubmotors are no exception, but improper gearing of DD hubmotors is the norm on ES. Winding has absolutely nothing to do with gearing. Different windings of an otherwise identical motor are capable of exactly the same torque, power, speed, acceleration, efficiency, etc. Simply vary voltage and current in the correct proportion for the same power in and power out at the same rpm and load. The only way to change the gearing of a direct drive hubmotor is to change the wheel size, and it turns out that attaining maximum speed and power from any given hubbie requires running wheels with an outside diameter smaller than 20". Due to our practical limitations on voltage, it also turns out that higher Kv DD hubmotors are capable of higher speed and power than their slow wind kiddie sisters simply because they are capable of higher rpm. That's why I typically refer to them as slower lower power motors.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 2:26pm
You seem confused ... ?
You state that gearing and windings are totally different factors ... then you explain how windings can be enhanced-moderated by voltage and amperage >>> exactly the same methods that can be used to enhance-moderate gearing ... with the same results!.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 2:55pm
DrkAngel wrote:You seem confused ... ?
You state that gearing and windings are are totally different factors ... then you explain how windings can be enhanced-moderated by voltage and amperage >>> exactly the same methods that can be used enhance-moderate gearing.
I have the fastest hubmotored ebike on the planet, so no I'm not confused. Voltage and current can't do anything to enhance-moderate gearing. Don't confuse yourself with vague words to try to support a misconception. Gearing is simply the mechanical relationship of the distance traveled in relation to one revolution of the motor, whether it is in the wheel or uses a chain, belt, or gears to drive wheel. If we ignore the maximum and minimum limits of voltage, different windings of the same motor are identical motors in terms of every measure of performance and capability.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 3:27pm
John in CR wrote:
DrkAngel wrote:You seem confused ... ?
You state that gearing and windings are are totally different factors ... then you explain how windings can be enhanced-moderated by voltage and amperage >>> exactly the same methods that can be used enhance-moderate gearing.
I have the fastest hubmotored ebike on the planet, so no I'm not confused. Voltage and current can't do anything to enhance-moderate gearing. Don't confuse yourself with vague words to try to support a misconception. Gearing is simply the mechanical relationship of the distance traveled in relation to one revolution of the motor, whether it is in the wheel or uses a chain, belt, or gears to drive wheel. If we ignore the maximum and minimum limits of voltage, different windings of the same motor are identical motors in terms of every measure of performance and capability.
But ... isn't the exact same thing true of different gearing of the same motor?

### Re: Calculating the highest, possible speed you can get

Posted: Dec 20 2015 6:09pm
DrkAngel wrote:
John in CR wrote:
DrkAngel wrote:You seem confused ... ?
You state that gearing and windings are are totally different factors ... then you explain how windings can be enhanced-moderated by voltage and amperage >>> exactly the same methods that can be used enhance-moderate gearing.
I have the fastest hubmotored ebike on the planet, so no I'm not confused. Voltage and current can't do anything to enhance-moderate gearing. Don't confuse yourself with vague words to try to support a misconception. Gearing is simply the mechanical relationship of the distance traveled in relation to one revolution of the motor, whether it is in the wheel or uses a chain, belt, or gears to drive wheel. If we ignore the maximum and minimum limits of voltage, different windings of the same motor are identical motors in terms of every measure of performance and capability.
But ... isn't the exact same thing true of different gearing of the same motor?
Absolutely not. Gearing multiplies or divides the torque of the motor for thrust at the wheel. Winding doesn't change anything other than the voltage and current required for the same power input and output with exactly the same efficiency and torque at a given rpm and gearing. Increase the torque/amp with more turns on the stator teeth, and the copper gets longer and thinner to exactly offset it. Current handling goes down too, so the motor is only capable of the same torque.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 21 2015 10:14am
The highest possible speed you can get, does rely on how steep the slope and how big your balls.

### Re: Calculating the highest, possible speed you can get

Posted: Dec 25 2015 2:50pm
I found a Mobilphone-App to calculate not the highest, possible speed, but the maxial range you can get. The App is called "E-Wolf". Just test it out.