New E-Bike Conversion - 26" vs 29"

[Vonkrumm]

Whoops. Ok my physics is a bit rough it's been a while.

Anyway back on topic, I think I'll get the hub motor anyway, MAC, with a good battery in the $300-400 mark.

Thanks guys I'll post photos after.

 

[crea2k]

26" will give you more torque and acceleration , 29" will give you less torque and acceleration but more speed. 29" will make the motor work a lot harder too.

 

[EV_Ron]

Based on physics, the total work done by a motor- whether to move you a distance of 300m at a constant speed or to accelerate you from say 0 to 30 kph- will be the same regardless of size of the wheel- 26 or 29".

The torque from the motor will be the same regardless of being in a 26 or 29" motor. The motor's power will be the same regardless of being in a 26 or 29" wheel. You may perceive a difference based on the motor's optimized RPM (220, 260, 328 RPM...) but the work will be the same, and a motor in its optimal torque-RPM-power band shouldn't 'work' any harder- that'd be power (working harder infers more work over time or more power). Hopefully this helps- I know it helped me as I was testing my bike last week and trying to refresh my college physics!

In fact, a motor operating on a certain torque-RPM curve based on its diameter and number of windings may even work less 'hard' (lower power) with the 29" wheel because its windings & wire diameter might just be optimized for the lower RPM. Also, the RPM difference of a 29'er at any speed is only 3/29's less, or 10%, so instead of 260 RPM on a 26" wheel the motor in a 29" rim would be running at 234 RPM, within the work and power band of say a 260 RPM motor (though likely not a 328).

Why do I say this? The principles are these: F=ma, and Work = Fd, and Power = W/t.

Let's do force F=ma first:
Mass: If I weigh 160 lbs and my bike weighs 60 lbs, then 220 lbs is what? 220lbs x kg/2.2lbs = ... 100kg.
Acceleration: if I want to go from 0 to 30 kmh in 20 seconds, then changing velocity to m/sec first, 30 kmh x 1000 m/km x hr/3600 mins = 8.3 m/sec
Now, acceleration a = delta velocity/time = (0-8.3 m/sec)/20 sec = -0.42 m/sec2 (disregard the negative sign for now, only a convention).
So, the motor must apply the same force to the ground whether it sits in a 26" or 29" wheel. The only difference will be its RPM.
But, the RPM will only be about 10% less for the 29'er. You may perceive it turning slower, but the force translating to the ground is the same.
Force:
The force during that acceleration is ma, or 100kg x 0.42 m/sec2 = 42N, and it's the same force whether the motor is on a 26 or 29" wheel.

Moving on to W=Fd
The work done during the 20 seconds of acceleration is the same, Fxd or 42N x distance. Distance d comes from x=1/2(at2) (2 being "squared").
d= 1/2x 1.5m/sec2 x (20x20 sec2) = 300m.
Work is 42N x 300m = 12,600 N-m, and N-m is a Joule, so the motor expends 12,600J. Again, the motor, moving you to 30 kmh in 20 seconds will do the same work regardless of whether it's laced into a 26" or 29" wheel.

Finally power. Does the motor expend any more power with a 29" vs a 26" wheel? No, depending on where it works along its torque-RPM curve. Assuming it's a 260 RPM motor optimized to work in the, say, 230-260 RPM range.
Power = Work/time. To accelerate from 0 to 30 kmh in 20 seconds over 300 m requires 12,600 J /20 seconds = 630 Watts, something a 300-400W motor can expend at max output, I recently saw my 250W Q100H put out 504 W.

So, why do we perceive "more work" from one motor when it's operating in a 29" vs. 26" wheel? I think it occurs when we begin to translate a, f, work, and power into torque.
I think it's because if you have a faster motor- maybe a 328 rpm in a 26" wheel and it works ok for you at most RPM, then if that motor, as Chalo mentioned, doesn't have the power (from its windings and magnet strength) to move a 29" wheel at the same torque at a given acceleration- it's only because it's not operating at its optimal RPM and torque. If you put a 260 or 220 RPM motor in either a 26" or 29" wheel then you won't notice a difference in push/pull force when you turn the throttle the same degree. If you try to accelerate from 0-30 kph in the same time and distance then you won't see a difference in power, work, or force. And though we perceive it "works" harder, the numbers indicate that, as long as the motor is on the effective portion of its designed torque curve, it must put out the same work to move you and the bike from one velocity to another.

Edits: minor grammar mistakes.

 

[EV_Ron]

I was in doubt about my previous post and even deleted it because I re-read Vonkrumm’s posts that a 500W motor would exert less force on the ground (thrust) at 29” vs. 26”and so you’d go slower with the same motor in a 29” wheel. And I said to myself that can’t be correct in and of itself; if the motor puts out 500W then it puts out 500W and it directly translates to the same pulling force regardless of the wheel diameter. There must be something else, the same motor must put out the same pulling force regardless of wheel diameter! (assuming it’s in the optimal range of its RPM-Torque curve).

Then I recalled just using this equation P = 2πT x RPM => T= P/(2π RPM). I love this equation.

Let’s first test it on a vehicle we know well, the car, to verify it works.
Let’s say you have a Mustang or Vette with 500HP. Well P = 2πT x RPM
Let’s say it runs at 6000RPM. Does the equation give a reasonable torque?
First convert RPM to Rev/second because seconds are the units in power & energy (Watt= N-m/sec and energy is Joules = N-m & N=kg-m/sec)
6000 revs/min x min/60sec = 100 rev/sec
And let’s convert 500HP to Watts. 500 HP x 0.735 kW/HP = 367.5 kW or 367,500W.

What is the Vette engine's torque? Well, T = P/(2π RPM).

T= 367,500W/( 2π x100rev/sec) = 584.0 ft-lbs. That’s a healthy motor, well within the norm for a performance car. In fact the 2015 Vette makes 650 lb-ft of torque!
So, the equation works.

We already know torque must be constant at all radii, whether 26” and 143N force or 29” and 129N thrust. So, how can I help to show Vonkrumm’s posts are missing an aspect? How can I say that a 500W motor will propel a 100kg to 30km in 20 seconds (faster even) in 300m regardless of 26” or 29” wheel?

Well, because the motor mounted in the 29'er maintains the same force on the ground as in the 26" wheel, it's just that the motor's RPM changes! More accurately, the motor automatically finds its correct (lower) RPM for the associated torque on its torque curve. How? Why? Because someone designed it that way.

What’s the equation? Ground Speed = RPM x πd. Yes, RPM is a function of diameter. Or, the number of times your wheel goes around in a minute times the circumference of the wheel is your ground speed. But RPM is also dependent on the motor torque-RPM curve.

Try it for a 26” wheel first. Let’s assume power is the same 500W, and T torque is the same at all radii, so from the prior post, laws of physics dictate the 500W motor must cause the same pulling force and get you to the same speed, call it 30 kmh in a set time period. What’s the RPM of the 26” wheel. 26” x 2.54= 66cm sans tire = 0.66m.
30 km/h = 1000m/km x hr/60min = 500 m/ min.
RPM = Ground speed / πd. RPM = 500 m/min / (3.14 * 0.66) = 241.3 RPM for 26"

Again, we already know P is same, torque is same, and pulling force is same. What’s the RPM for the 29” wheel?
29” x 2.54/100= 0.7366m.
RPM = Ground speed / πd = 500 m/min / (3.14 * 0.74) = 216.18 RPM.
Yes, for the same power the larger wheel turns slower- makes sense. And that will become important momentarily, because while torque may be the same at all radii, torque is not the same at all RPM. A 29'er can afford to 11.6% turn slower because each revolution is 11.6% larger=longer.

Now I need to find a torque curve. I will bet a motor designed at about 500W will operate with MORE torque at a slower RPM, enough extra torque to maintain the same pulling force.

And there it is, a motor does not have the SAME torque at lower RPM; rather, all motors on their designed torque-RPM curves have MORE torque at a lower RPM.

As an example – bottom of http://lancet.mit.edu/motors/motors4.html .
Granted, not the same torque range, but in the correct 200-600 RPM range, you can see torque rise as RPM declines.


Bottom line, the same motor installed in either a 26 or 29” rim, operating within its optimal range on its torque-RPM curve, will apply the same motive force and work just as hard in both situations.

The motor in the larger wheel will operate 11% slower in RPM but it will travel at the same ground velocity because the wheel circumference is 11% larger. Though you may perceive the motor is not working as hard possibly because the RPM is lower, rest assured that if you are looking at 500W on your CycleAnalyst, then- whether 26 or 29” wheel- the forward force must be the same.

I'm glad we understand that now.

 

[EV_Ron]

Still figuring things out, hopefully this helps others...

So, I second guessed myself yet again! I thought, someone’s going to say, “As you decrease RPM you necessarily increase torque and that always shows increased power on the chart you show.”

That may appear the way it looks at first, and it may appear the way the overall chart looks, but not specifically in our case of dropping from one RPM to another when using a larger diameter wheel.

I’ve shown two reasonable points on the chart... actually they happen to be the RPMs we just calculated: 241 RPM for 26” and 216 for 29”.

First follow the blue 240 RPM line up to the straight TORQUE line – maybe .49 N-m. Now follow the red line up from 216 RPM for the 29" wheel- torque increases for this motor, great. But now follow the lines up to the inverse parabolic Power curve- as you DECREASE RPM and get INCREASED Torque, for this small motor on this region of its Torque-Power-RPM chart, power DROPS from 4.9 to 4.7W! Yes, I’m amazed, too. I'd hat to be wrong if anyone ever read my prior 2 posts. It's just the way this motor is designed, but other motors have similar curves- you just have to operate on the right section of the curve. If you were operating this motor at 500 RPM you'd get your increased torque at the expense of 100% increase in power.




I know, it won't happen in all instances because all the torque curves are different on all the motors out there, but it matches my best common sense, and it matches the physics. Hopefully that's all correct.

It's kind of difficult to find torque-power-RPM/Speed curves for 250-500W 300 RPM motors. From http://www.edn.com/design/sensors/4406682/2/Brushless-DC-Motors---Part-I--Construction-and-Operating-Principles , this curve at 240 RPM-110W region shows a similar result (lower torque, though) as the same as long as you operate in the efficient part of the motor's Torque-Power-RPM curve. I used the same colors- blue for 241 RPM and red for 216 RPM.

edit= deleted all the white space in the attachment

 

[Chalo]

Torque is force times radius. Therefore, when the radius changes, the force changes in opposite proportion at the same torque value. All your calculations that assume otherwise are wrong.

The bottom line is that with a hub motor, a 26" wheel will outperform a 29" wheel in almost every way. The smaller wheel will accelerate faster, climb steeper grades, and reach a more efficient operating condition at top speed. The 29" wheel might reach a higher top speed, but only if it has enough power at the applicable RPM to reach and maintain that higher speed.

The only reason to use a 29" wheel with a hub motor is because you think the ride quality benefits of the larger wheel outweigh the reduction in performance.

 

[EV_Ron]

Hi Chalo,

Respect your opinion, know you have a lot of experience. The motor in the 29'er runs slower than when it sits in a 26" rim. Lower 29'er RPM on the RPM-torque-power curve causes a higher torque, the higher torque at the large radius causes the same motive force. If you can point out where my calculations are wrong I'd like to know so I can correct it. Simply put, the curve of many motors operating in their optimal regions shows that lower RPM allows higher torque resulting in the same force at the longer radius. Review my posts and you'll begin to see it... or, I could be wrong.

Ron

 

[Racer_X]

Alot of physics calculations on this thread. Well i can add real world experience.
I built a 29'er this summer as my new commuter using a 9c 2807 wind hub motor @30amps and 12s LiPo. I can confirm it complains alot accelerating from a dead stop. It also complains alot when going up any kind of incline, this experience i have gained when I compare the 29'er to a 9c 2807 on 26". Must admit it rides and looks bitchin.

If was to do it again I would opt for a higher torque motor and lose top speed in order for a quieter motor 95% of the time.

Another possible options of course would be a MXUS 3000w hub motor. Still don't know which wind of the MXUS 3000 would take me to 45km/h @40-50amps + 12s LiPo.

 

[EV_Ron]

Nice bike!

And yes, lots of calculations, and no, I rarely do physics calculations... maybe 5 times in 30 years ... until I wanted to understand the physics of my bike and motor.

I'm going to guess at the reason your 280 RPM motor complaining on a 29 vs 26" wheel. First a quick story: I was scared to do this at first, but once I calculated that the force at the rubber tire on my wheel with my 250W electric motor was only 67N, which in kg is only 67/9.8= 6.8 kg, and in pounds is only 15 lbs, I realized I could grab and hold my front tire with just one hand if I held REALLY tightly. Sure enough, I pulled, gave partial and full throttle and it pulled like a wild animal, and it growled as the magnet poles slipped underneath each other! It sounded really angry. And it displayed about 480W as I recall. Then I released and hit my hand on the handle bar!

Stall torque on 328, 260 and 220 RPM Q100H's were discussed extensively last year and I don't recall all of it except that the 328's growled at low RPM, especially from a standing start and everyone recommends pedal starts to avoid damaging the motor. You probably bought the 280 because it had a higher overall speed?

So, if you look at the last curve I posted you'll see at 0 RPM on the torque line the motor is at Stall Torque (and I know, the torque numbers for that motor aren't the 50-200N-m range of our e-bike motors, but it's all I've got right now, principles are the same). Still, if you figuratively compare the numbers above i.e. the motor's 216 RPM in the 29'er vs. the 241 in the 26" at about 500W, and walk those numbers all the way down to 0, I think we can say that in the 29'er the motor hits the stall torque much earlier (I guess in RPM) than the same motor in the 26. Makes sense and I'm not going to calculate that, but I would recommend reading the 260 Q100H threads if you get a chance and want to understand the reason.

e.g.

Cute Q100 lightweight builds slow mtb, fast road http://endless-sphere.com/forums/viewtopic.php?f=3&t=49691&hilit=current+control+ESC&start=25#p816033

by chas58 » Mon Oct 28, 2013 9:25 am "The 24v201rpm at 36v is very quiet and starts well from a stop."
And "Q100H ...The 201 rpm is ok for torque but lacks speed, and the 328 rpm one has no torque at all.” And I paraphrase, "The 328 is only good for > 15 mph".

Edit is spelling correction.

 

[EV_Ron]

Before anyone else says it, I have the answer why one perceives the same motor is generally more sluggish in a 29’er than in a 26” bike, and it’s not because a 26” gives more torque (not possible, there's no special torque creator in a 26" bike), nor because the larger wheel generates more speed (larger wheels actually spin slower for the same speed over ground, and from the torque curves we've seen lower motor speed actually results in more torque.)

Instead, half of the answer is what MadRhino said- larger wheels require more energy to accelerate.

In other words, the additional angular momentum of the heavier wheels at a longer radius takes away part of the total torque just to get the wheels moving, and that leaves less torque to be transferred into motive force.

The other half of the answer is that for the same materials and design, the 29’er bike will also have more mass in its larger frame and wheels, thus more linear momentum to overcome.

Bottom line, the reason the same motor in a 29’er feels more sluggish is due to the 10% extra mass it must move and because of the additional angular momentum in the wheels. That said, if you could find a 50 lb 29’er with light wheels (same angular momentum as 26” wheels), then the same motor will accelerate the 50# 29’er to the same speed in the same time and distance as a 50# 26” bike. That, then is one reason to buy a 26"- less energy to accelerate it, probably slightly less energy to maintain speed, and therefore- riding style the same- you would use less battery energy and power and go further on the 26" bike.

 

[Chalo]

Yes, you can find some places along the torque curve for a motor where a 26" and 29" wheel would make the same thrust, because when bogged down to lower speed the motor makes more torque. But that's coincidental to a single portion of the motor's speed range, for one thing. For another, you'll note if you follow not just the torque curve but also the power and efficiency curves back all the way to zero, that all the way down the bigger wheel is making more heat and less power for the electric energy put into it. Right from zero, the smaller wheel is making more thrust and therefore lingering for shorter intervals in the low speed, horribly inefficient part of the curve.

If you follow the curves on up, you'll find that the smaller wheel also runs at higher efficiency when it reaches the equilibrium point that corresponds to top speed. Depending on the motor power and speed and the power demand of the bike, that could be either a lower or a higher speed than you get with the bigger wheel.

 

[d8veh]

The most important thing is that you match the motor winding speed to the speed you want to travel, otherwise you lose efficiency. The same motor in a 29" wheel will always be less efficient than in a 26" one in the bottom half of the speed range, so you'll have less power to accelerate and more wasted battery charge.

 

[scfoster]

Late to the discussion.

EVRon you're correct. What folks are doing is mashing together terms as if they are the same thing. Torque is torque, not bending moment (which folks are describing as torque). They are not the same thing. That's why one needs to use a torque wrench to accurately apply torque to a bolt/nut as the bending moment will change based on the length of the wrench.

For instance, pounds (LBS) which we routinely "convert" to kilograms (kg) is not really accurate. LBS is force and KG is mass. Two different things. I'm bringing this up as this is how people get twisted around when they're saying sort of the same thing.

Below is a nice diagram showing what each part if the bicycle is typically called. What is being discussed is the bending applied to the seat stays (one on each side of the rear wheel assembly) and chain stays. Each seat/chain stay ends at the dropout (left and right). Ignoring a disc brake assembly on the left dropout, the force typically applied by the wheel assembly is essentially vertical, resulting in mostly compression in the seat stays and a bridge beam compression (top)/tension (bottom) on the chain stays. What I'm describing is static loading. Dynamic loading gets a whole lot more complex. Here's a pretty good read from the dark ages (1986) when aviation finite element analysis was making its way into mainstream structural engineering. The second image shows how loads can radically change from frame to frame in ways that are not always obvious.

This image shows dynamic loading. If you look at it long enough, you'll get a sense of how the loads applied to the seat and chain stays are relatively uniform and travel along the tubes, whereas the forces around the bottom bracket and upper seat tube are MUCH more complex and varied. These are the type of loads that a rear hub motor introduces for which the rear drop ins, seat and chain stays were not typically designed.

 

[Chalo]

Torque is torque, not bending moment (which folks are describing as torque). They are not the same thing. That's why one needs to use a torque wrench to accurately apply torque to a bolt/nut as the bending moment will change based on the length of the wrench.

Not clear what you're talking about, but "torque" and "moment of force" are different terms for exactly the same thing.

 

[ewinters]

Is there a reason to not simply go for a mid motor on a 29r?

 

[TheBeastie]

Is there a reason to not simply go for a mid motor on a 29r?

Yes this is probably the best way to go for larger wheels.
So far the discussion has been mostly aimed at direct drive hub motors. I personally have always built my ebikes on gear drive hub motors from Bafang. The DD motors are typically tweaked for smaller wheels while gear drive hubs are fine with larger wheels or most likely like the Bafang CST are deliberately designed with 700c sized wheels in mind.