## Science, Physics, Math, & Myth

Kingfish   10 GW

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### Science, Physics, Math, & Myth

My Father-in-Law used to tell me:
• “There are two types of people in this world: Those that can count…”
(with anticipation of a conclusion that never arrived)
Moving the sub-conversation here to this thread where we do not disrupt a fruitful conversation on the MXUS thread that has apparently moved on. Here is where we branch.

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
* My 2WD Garden Wall
* Kinaye MotorSports
* Primary ride: 2WD Disc 9C 2806-equiv / Dual Lyen 12FET / 20S7P LiPo.
* Epics: Going to California: 2011
* 50-mph, 101, 10k-Club. 12,527 miles-to-date, 7037 as 2WD.

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It is by the beans of Java that thoughts acquire speed.
The hands acquire shakes, the shakes become a warning.
It is by caffeine alone I set my mind in motion.

zombiess   1 GW

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### Re: Science, Physics, Math, & Myth

...
Last edited by zombiess on Nov 21 2014 11:10pm, edited 1 time in total.
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liveforphysics   100 GW

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### Re: Science, Physics, Math, & Myth

Phew... That was one of the most windy posts I've seen.

Lets say we have some motor, and it's wound with 2 pieces of say 14awg wire in parallel, and it's wound with 4 turns around each tooth. If we take this same motor, and re-wind it to have 8 turns of a single pieces of 14awg (identical copper fill %) or rewind it with 2 turns of 4 pieces of 14awg in parallel (identical copper fill).

So, we have 3 winding options for this motor now, each one yielding a substantial difference in kV, but do any have a performance difference?

We know the 8-turn needs half the amount of current to make a given amount of torque than the 4 turn, yet the 8 turn is 50% of the cross section of wire AND twice as long, giving it a 4x increase in phase resistance. This 4x resistance increase perfectly balances the I^2*R difference, both make precisely the same amount of loss per unit of torque produced, both are capable of exactly the same continuous power, continuous torque, etc. Now let's look at the 2 turn, it needs 2x the phase current to generate the same torque as the 4 turn, yet, it's resistance dropped by 4x, because the wire is now twice the cross section and only half as long. It is also capable of exactly the same continuous torque, continuous power, same loss per unit of torque produced, etc.

Are you following up to this point my friend?
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liveforphysics   100 GW

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### Re: Science, Physics, Math, & Myth

Try thinking of what generates the field in terms of amp-turns.

If the tooth has 10 turns with 1 amp of drive current, or 1 turn with 10 amps of drive current, the field in the tooth is 10 amp-turns either way.
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Each engine start sprays them into a shared atmosphere which includes beings not offered an opportunity to consent accepting these cancer experiences and defective genetics life experiences.

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### Re: Science, Physics, Math, & Myth

no matter what turn count one version of motor has, nominal RPM, nominal TORQUE, nominal POWER and EFFICIENCY stays the same (if copper fill is identical).
what can differ is the efficiency of the complete drive system (including controller losses, influence of inductance, wire losses etc).
as because high current is bad to handle (fat wires, big connectors, high current controllers) many prefer higher volts instead of higher amps. For example the KTM freeride e has only 2400 watt hour battery but 300V. thats insane. Also RC model builder prefer higher battery voltage instead of faster wound motors because of this.
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liveforphysics   100 GW

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### Re: Science, Physics, Math, & Myth

Perhaps try thinking of a motor with many teeth and many repeating patterns in the windings.

Some amount of copper is wound around each tooth in a way that fills each slot to the same percentage, and each tooth has the same number of windings.

If you terminate all of the repeating teeth in parallel, or terminate all the repeating teeth in series, the kV of the motor changes in a big way, easily a factor >10, yet you can see, it makes no difference, each tooth's coil can be driven with X amount of current either way.

Likewise, it's no difference in power from the battery either, as the turns count decreases, the resistance decreases, as well as the BEMF, so the phase voltage varies inversely with the required drive current, making the power identical.

The torque is a result of the magnetic field strength. The field strength is a property of the flux around it, which is directly the number of amp-turns.

The tooth could never know or care if the loops of current around it are terminated in a long series loop or a big parallel connection.

The relationship between amp-turns and the amount of flux generated (and hence torque) does not discriminate on the basis of what arrangement the coils may happen to be configured.
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Chalo   100 GW

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### Re: Science, Physics, Math, & Myth

For what it's worth, a slow wind motor usually gets to spend a whole lot more of the time in a high efficiency, low waste heat regime. It gets closer to its no-load speed sooner and reaches equilibrium conditions at a lower power level. There are a lot of folks out there using winds so fast that their available electric power can't push them to speeds in which the motor operates near its peak efficiency.
This is to express my gratitude to Justin of Grin Technologies for his extraordinary measures to save this forum for the benefit of all.

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### Re: Science, Physics, Math, & Myth

Chalo wrote:For what it's worth, a slow wind motor usually gets to spend a whole lot more of the time in a high efficiency, low waste heat regime. It gets closer to its no-load speed sooner and reaches equilibrium conditions at a lower power level. There are a lot of folks out there using winds so fast that their available electric power can't push them to speeds in which the motor operates near its peak efficiency.
thats because many only swap the motor and stay with the same controller (settings) and battery voltage.
in this case the slower motor will reach topspeed faster and maybe will climb a hill more efficient, but thats a different story and apples vs oranges..
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dogman dan   100 GW

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### Re: Science, Physics, Math, & Myth

I agree with Chalo. The reason a slow wind works good for some, is less time is spent in the wrong rpm for efficiency, on each start up. Or, the rpm you get climbing a hill is closer to the efficient rpm, if wattage is insufficient to go any faster than 12 mph. This is true ONLY in the case where the bike will be low wattage, at or close to the legal limits in much of the USA.

But if you power up the fast wind correctly, it spends little time in the wrong rpm and is quite efficient. 1000w at 22 amps is not powering up the fastest winds correctly if you have a 26" wheel, IMO. It needs more like 1500w or more.

The combination of a fast wind, big wheel, and low power is not a great idea. Give it some more watts and it works fine. Give it 36v at 22 amps, and it leaves a stop sign like a slug, and you see on the CA that it's pulling 750w for the longest damn time before the rpm gets up to cruise speed of 20 mph, and draws 400w. Running 750w, I've seen a 20% difference in wh/mi, between a medium fast winding and a one turn faster one when riding downtown through stop signs. Since I rode the same speed, where did the 20% go? Heat?

Unless you give it some watts to get going, it ( fast wind underpowered) just spends a lot of time getting going. This sluggish start is the problem. This is very bad for overall efficiency if you have a stop sign every block. Take the same thing and give it 1500-2000w, and you get very efficient. Almost no time spent getting going.

Or if you don't have to stop, it's still very efficient. If you don't stop, you can cruise at exactly the same speed, at close to exactly the same efficiency with the faster wind, even if it's underpowered. But if you cruise faster because you can, then you will get a lower wh/mi because you ride faster.

This is why I advise those who will run less than 1000w, to choose a slower wind for urban riding. If they have a stop only every 5 miles, the winding speed won't matter near as much. But if you have no choice but to stop every block, a slower wind dd motor will get there on less wh/mi than a fast wind dd motor.

Fortunately for urban riders, there are good choices of 1000w capable planetary gear motors. With a Mac 10t or something similar, you still get a medium fast winding, AND decent efficiency getting from 0-15mph. Its a no brainer for most urban riders to just choose a geared motor.

Why else did I type " go to EM3ev" so many times?

miuan   10 kW

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### Re: Science, Physics, Math, & Myth

Chalo wrote:For what it's worth, a slow wind motor usually gets to spend a whole lot more of the time in a high efficiency, low waste heat regime. It gets closer to its no-load speed sooner and reaches equilibrium conditions at a lower power level.
It does reach equilibrium conditions sooner and at lower power level because it is unable to reach the speed of a faster wind. Of course efficiency, heat management and power consumption are all better at low speed. However if you DO match the battery, wiring and controller to compensate for the lower turn count, the fast motor will do the same.
Chalo wrote:There are a lot of folks out there using winds so fast that their available electric power can't push them to speeds in which the motor operates near its peak efficiency.
Yes and no. It's true many have too low a current limit to avoid riding in PWM mode at top speed. If they set the controller for more amps and reconfigure their lipo bricks for less V and more Ah, they could easily reduce the heat produced by motor as a result of dirty switched power signal. Of course the controller fet voltage limit need to be appropriate for the voltage used. My 4110 6fet controller got nearly toasted driving an 8-turn BPM, now it gets barely warm driving a 9-turn 9C at similar speeds, because the phase current of 9C is less than half that of Bafang.

Now a side note. In my understanding, there are 3 reasons the slow motors CAN contribute to a more efficient propulsion system.
1. ebike controllers are not optimized for high currents. They have long skinny PCB traces and the mosfets have thin legs. As a result the controllers heat more when driving fast motors.
2. phase wires are usually also thin, bearings have small ID, and modifying motor axle to allow thick wires is a pita. As a result the phase wires of fast motors heat more.
3. low number of turns usually means more interconnections between teeth and more end turn copper losses. As a result the fast motors heat more.

The first 2 factors can be almost eliminated by proper choice of controller and wiring. To what extent the 3rd factor influences efficiency is beyond my knowledge.
Last edited by miuan on Nov 23 2014 5:28pm, edited 1 time in total.

John in CR   100 GW

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### Re: Science, Physics, Math, & Myth

Chalo wrote:For what it's worth, a slow wind motor usually gets to spend a whole lot more of the time in a high efficiency, low waste heat regime. It gets closer to its no-load speed sooner and reaches equilibrium conditions at a lower power level. There are a lot of folks out there using winds so fast that their available electric power can't push them to speeds in which the motor operates near its peak efficiency.

The part you're still missing Chalo, is that they're the same motors regardless of the wind. They just need different voltages and current settings to achieve the same power, speed, torque, and efficiency. I believe that you're capable of stepping back from the trees and seeing the forest. If nothing else, trust what Luke is saying, just like he trusted you about using thinner 14ga spokes on his crazy power wheel.

Before 2010 people were getting the effect you mention with X5303 and X5302 motors, but it was primarily due to a lack of controllers up to the task of driving them properly, and short comings in how much torque the X53xx could deliver, so they couldn't push through the wind at high speed especially with the high gearing of a big wheel.

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### Re: Science, Physics, Math, & Myth

miuan wrote:My 4110 6fet controller got nearly toasted driving an 8-turn BPM, now it gets barely warm driving a 9-turn 9C at similar speeds, because the phase current of 9C is less than half that of Bafang.
have you changed battery voltage? otherwise it cannot be true. if topspeed was similar, than also phase amps must have been similar at this speed (if the set battery amps are not the limiting factor anymore)
this means the controller is in block commutation or 100% PWM and the motor sees the full battery voltage.
imo the reason was the 9C does have higher inductance than the 8-turn BPM and was easier to drive for the controller and / or higher phase amps during acceleration (before the controller was working in block commutation). it also could be higher ERPM on the BPM caused higher switching losses in the controller.
3. low number of turns usually means more interconnections between teeth and more end turn copper losses. As a result the fast motors heat more.
why there should be more interconnections / end turn losse with lower turn counts?
Last edited by madin88 on Nov 22 2014 10:31am, edited 2 times in total.
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John in CR   100 GW

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### Re: Science, Physics, Math, & Myth

miuan wrote:3. low number of turns usually means more interconnections between teeth and more end turn copper losses. As a result the fast motors heat more.

The first 2 factors can be almost eliminated by proper choice of controller and wiring. To what extent the 3rd factor influences efficiency is beyond my knowledge.
If by interconnections between teeth you mean the portion of the magnet wire that isn't productive, then yes that is the single thing that actually makes the different windings have different results within the motor itself. Those segments don't change in length like wrapping around the teeth a different number of times, so in Liveforphysics' example the resistance of the copper in the 1/2 Kv motor is slightly less than 4X. The difference is relatively insignificant though, especially compared to what can be achieved with proper controller tuning or the effects of even a small change in wheel size. Even just a tiny change in how you ride can have a far greater effect on efficiency.

I agree with you that 1 and 2 are easily overcome. Regarding number your #1, the controllers, that's were big gains are possible for most rigs, because the number of members who take the time to experiment with settings to gain efficiency is a tiny minority. Also, the stock settings for the battery/phase current relationship coming in controllers out of China are only appropriate for running power below 1kw. Add that the 2.5:1 rule of thumb passed around the forum is grossly erroneous for running high power, and it's no wonder guys have such heat problems in hilly terrain, even those pushing relatively light loads.

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### Re: Science, Physics, Math, & Myth

is it because in relation to total length of the winding, less copper is wasted in the high turn motor than in the one with lower turns?
but isn't than the low turn motor only a bit heavier? I do not catch it completely..

what i know is only the copper in the tooth does create a magnetic field and the copper on the left and right side does nothing..
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miuan   10 kW

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### Re: Science, Physics, Math, & Myth

madin88 wrote:what i know is only the copper in the tooth does create a magnetic field and the copper on the left and right side does nothing..
what it DOES is make heat since it still has to conduct current.

amberwolf   100 GW

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### Re: Science, Physics, Math, & Myth

madin88 wrote:what i know is only the copper in the tooth does create a magnetic field and the copper on the left and right side does nothing..
Oh, it does indeed create a magnetic field, but since (most of?) the part of the field it creates isn't directly interacting with the magnets (at least in a direction useful to desired work), it's not useful to making torque and motion in the motor.

It could also cause eddy currents within the side covers of a hubmotor, if the field is strong enough and teh covers close enough to it, and that could generate additional heat and friction to actively negate some of the motor's motion, though I don't know how much that happens in practice.

Miles   100 GW

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### Re: Science, Physics, Math, & Myth

miuan wrote:3. low number of turns usually means more interconnections between teeth and more end turn copper losses. As a result the fast motors heat more.
The end turn losses are constant for different winds. The only thing that varies is the relative resistance of the section of copper between the coils as this changes in cross-section but not in length...

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### Re: Science, Physics, Math, & Myth

miuan wrote: what it DOES is make heat since it still has to conduct current.
i'm with you, but should't this generated end-turn heat not be the same no matter what turn count?
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### Re: Science, Physics, Math, & Myth

Miles wrote: The end turn losses are constant for different winds. The only thing that varies is the relative resistance of the section of copper between the coils as this changes in cross-section but not in length...
thanks for making it clear
now, does this result in more heat or only in a heavier motor?
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Miles   100 GW

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### Re: Science, Physics, Math, & Myth

madin88 wrote:now, does this result in more heat or only in a heavier motor?
It means lower turn count motors will have a minuscule amount higher copper losses....

kiwifiat   100 W

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### Re: Science, Physics, Math, & Myth

liveforphysics wrote:Try thinking of what generates the field in terms of amp-turns.

If the tooth has 10 turns with 1 amp of drive current, or 1 turn with 10 amps of drive current, the field in the tooth is 10 amp-turns either way.
Niether Kingfish or I are debating the fact that copper losses between equal fill winding options are equal, the proof is trivial.

John in Cr says this:

"Saying that a slow wind motor makes more torque at the same current is irrelevant, because in that comparison the slow wind makes more heat to produce that greater torque. Apples and oranges comparisons simply don't cut it. Your understanding is incomplete, because you can't ignore copper losses."

And that is misinformation, the copper losses are identical.

We all agree that 10 amps into a 1 turn motor will yield the same torque as 1 amp into a 10 turn motor all else being equal. However in the context of speed/torque characteristics it is not correct to say that the motors are the same, if the torque constant is different how can you claim they are the same?

In terms of system efficiency the higher turn lower lower current wind wins every time. I assume we all acknowledge that the batteries have internal resistance. We all acknowledge the switching semiconductors have resistance. Is anyone going to provide a proof that a system consisting of a power source,wiring, controller and motor that requires 10 amps to provide X tractive force at the wheel can do so more efficiently than the system that requires only 1 amp? Particularly in the context of the vast majority of ebikes that are constrained in Voltage and the maximum continuous discharge current. So given those real world constraints a higher wind motor will deliver more torque, more tractive force at the wheel, better acceleration, better hill climbing ability and better overall system efficiency than a lower turn count motor when constrained by the power supply.

There is a very good reason why the engineers who are responsible for designing the tractive systems for the currently available electric cars have not gone with low turn count low voltage high current solutions but rather high voltage high turn count motors and that reason is system efficiency.
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teslanv   100 MW

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### Re: Science, Physics, Math, & Myth

I am a firm believer in the KISS approach.

Determine what voltage best fits with your battery and controller choices. For many, that is in the 48V to 84V range for a variety of reasons, including electrical component specs, regen ability and general electrical safety.

Determine your preferred riding speed. Regardless of motor wind, battery voltage or controller current rating, it will take a fixed amount of mechanical power to propel a bike at a given speed.

Determine your preferred wheel size, with the mindset that smaller diameter wheels will increase torque at the possible expense of ride quality and ground clearance. Availability, cost and quality of tires should be included in this decision.

Then once voltage and optimum speed and wheel size are determined, you can choose a motor wind with the highest efficiency in the appropriate rpm range.

You would then select the controller based on if it can reasonably provide the current (and thus power) needed to reach optimum speed. More capable (more current handling) is always better, since an oversized controller will run cooler and thus more efficiently than an undersized controller.

Finally, make all wiring as large as practical to minimize voltage sag and to increase responsiveness of the power system.

Keep it simple, stupid.
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zombiess   1 GW

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### Re: Science, Physics, Math, & Myth

What about iron tooth saturation? The tooth is only able to handle so much flux before it reaches diminishing returns and eventually full saturation. What about the Perm magnets generated flux? How much does it take to equal the field of the magnet? How much does air gap come into play?

Any easy ways to measure/estimate the saturation point for a motor?
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tearocks   1 µW

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### Re: Science, Physics, Math, & Myth

Kingfish wrote: 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.

7. Torque (τ) = Force (F) * 2 * Radius (r)
This is where I got lost. I'm very new to e-biking, but didn't think classical mechanics had changed that much.