*“There are two types of people in this world: Those that can count…”*

(with anticipation of a conclusion that never arrived)

Reference: Re: MXUS 3000 Hub Motor

John in CR wrote:Bravo KF, not a single substantive argument, though you did manage to demonstrate your lack of understanding of what generates heat in our motors. I challenge you to find the one slightly incorrect statement in my previous post, though the difference it makes is insignificant. Don't bother trying to twist things around to make apples and oranges comparisons, because those will get shot down too. The bottom line is that making more torque per amp is only part of the story, because it can't make more torque without making more heat. The 2 motors can only make the same torque for the same amount of heat, and the maximum torque both are capable is also equal. The relationships of different windings of the same motor are quite simple, and certainly don't require a degree to understand. Having more knowledge than understanding is getting in the way for both you and Kiwifiat.

**John in CR:**

Let me begin by saying that your education level and mine is substantially different.

I am an Engineer having multiple disciplines being Electromechanical, Software Development, Multimedia, Manufacturing, and Operations with over 30 years of experience. You can find me on LinkedIn and view my website through the signature link below. I speak with brevity because it’s faster to get to the point so that we can move to the next. Mathematical formulas speak volumes just as a picture is worth a thousand words.

Let’s begin with your problem. Stop me at the line number when you get lost or think I’m wrong.

You say POWER is the same for the same sized WHEEL, spinning at the same SPEED with the same LOAD, for ALL WINDS: YES or NO?

**Proof that all winds are not the same.**

Unless otherwise specified, units are defined below.

1. Power (P) can be measured in Horsepower (hp) or Kilowatts (kW)

2. Load is measured in Newton-Meters (Nm)

3. Size of the Wheel is given to us as Radius (r) and measured in meters

4. Speed, rotational, is given Radians/Second

5. Winds are given in either # of turns about a tooth, a portion of which belongs to the total length of the conductor, measured in meters.

6. Mechanical Power (P) = Torque (τ) * Angular Velocity (ω)

7. Torque (τ) = Force (F) * 2 * Radius (r)

8. F = Current (I) * Length of Conductor (L) * Magnetic Flux Density (B)

9. If we use the same manufacturer and motor series but only change the windings, then the Length of the conductor must change

10. If the conductor length changes, then FORCE must change, unless we also change Current (I) and/or Magnetic Flux Density (B).

11. For the sake of conversation, do we let Magnetic Flux Density (B) remain the same

12. If we let Current (I) change so as to keep Force (F) the same, then we need another equation…

13. Mechanical Power (P) = Electrical Power (P)

14. Electrical Power (P) = Current (I) * Voltage (V)

15. If Current (I) changes and Power (P) is constant, then VOLTAGE must change

16. Allowing Voltage to change keeps the equation in balance, ideally.

17. The reality is different due to losses with the system, which up to this point have been ignored so as to keep the conversation simple.

18. In reality, Mechanical Power (P) + Mechanical losses = Electrical Power (P) + Electrical losses.

19. Mechanical losses = Bearings, aerodynamics. We expect these would change only if Speed changed, however Speed is stated to be constant.

20. Electrical losses = Winding Resistance, total eddy currents, total hysteresis

21. If Power (P) is the same, we can demonstrate that higher current is less beneficial than higher voltage by using the formula P = I * V = I^2*R = V^2 / R,

22. Therefore higher Current (I) produces more Heat (Q) as loss than can be recovered by other mechanisms within the System, leading to a total loss in efficiency.

23. Therefore motors with faster winds (and having fewer turns) are inherently less efficient than slower winds (and having more turns)…

24. Which affects either Power (P), or Torque (τ), or Wheel (r) or Speed (ω).

25. Motor Constant K = τ/ω

26. Kv = RPM (rads/s)/Volt (V)

27. Kt = Torque (t)/Amps (I)

28. Whenever we change Current (I) or Voltage (V), we affect the Motor Constants – and thus affect the Speed or Torque.

29. In conclusion, the statement “POWER is the same for the same sized WHEEL, spinning at the same SPEED with the same LOAD, for ALL WINDS” is inaccurate and can never exist.

There are a plethora of books and articles available at every common public Library and on the Internet which reference this math. I have made them simple as I can; they can however go way far more into detailed calculus to achieve refined accuracy. Simulators work well as visual tools, and I prefer using FEMM 4.2 when modeling various designs. It is tedious work.

Another example of simulation that is useful can be found right here at

**Grin Tech**:

http://www.ebikes.ca/tools/simulator.html

Different winds are provided so as to map to the correct application.

In the test, I used the 9C 2805 and compared it to the 9C 2808 using the default battery and hardware. The Simulator says the Loads are equal at 306 W. OK, loads are the same. However Speed and power are not the same and can never be. For instance, the 2805 looks like it will top out at 37 mph. Can the 2808 reach that speed? Try setting the dashed-line to 23 mph, a speed we know both motors can reach. Again the loads are the same 478 W, and we’ve set the Speed to be the same, however the Power required is quite different, and using the same battery we see that the range of the 2805 is pretty short when compared to the 2808. Try this test again with any manufacturer and models of the same series and the results are going to be the same: If you set the loads and the speed to be the same, the Power has to change for different winds because the effectiveness of the conductor length varies along with motor losses. Therefore the statement “POWER is the same for the same sized WHEEL, spinning at the same SPEED with the same LOAD, for ALL WINDS” is inaccurate and can never exist.

Are we saying that the Simulators are inaccurate?

Yes, they are. It’s very difficult to create a precise model without spending a lot of time and money. However, the inaccuracy is small enough to set aside when the far larger dataset is closely correct and very useful when comparing motor species.

*You can lead a horse to water but you can’t make it drink.*

My hope is that you give up on this myth business and drink the plain bright water of common knowledge and enjoin with the rest of us in rational thoughtful conversation.

~

*KF*