The Great "Gearing vs Hub Motor" Debate

safe · Jan 14, 2007

After a lot of number crunching and modifications of formulas (most recently the PWM Current Warping effect) I think I'm at the point of being able to present definitive evidence that gearing does have advantages that non-geared machines do not have and for the same amount of power output (the legal limit) one can go more, climb higher and run faster than a similiarly equipped non-geared machine.

The debate begins!

Let me start with the two test cases that I am going to be presenting results from:

Baseline Weight
Rider 185 lbs
Bike 100 lbs

5304 Hub Motor
72 Volts
35 Amp Controller (50% PWM effect... equals the Simulation chart)
Peak Power Output - 1970 Watts.

And the Geared bike:

1200 Watt Unite Motor
48 Volts
75 Amp Controller (50% PWM effect)
Peak Power Output - 1771 Watts.
8 Speed Internal Hub

Here's how I went about creating the charts. First I created a lookup table that would take the power output at a given rpm and would look up the corresponding precalculated (for a given bike of a certain size and weight) speed that could be attained at that given slope. I then created a table that would compare the value found in the first lookup to the value that the gearing would provide. At this point you know whether the motor can handle the relationship or not. If "not" then data point is rejected (can't climb or can't go that fast) if "yes" then it gets added to the possible values the bike can attain. For the Hub Motor the results are a simple straight line, but for a Geared bike the results get spread around a lot more.

Here are the results... First the Hub Motor and then the Geared bike:

Leeps · Jan 14, 2007

Well there is the simple fact that efficiency is efficiency. The dc-dc conversion does offer more current and less voltage but there is still the same amount of energy, and this high current low voltage places the motor in the worst efficiency spectrum possible. Gears are better for climbing hills, however from a performance perspective the hub motor wins.
The best thing that you can do for efficiency is not have a motor controller, since we pretty much need one, leaving it at wide open throttle offers very little resistance thus very little wasted energy. Then your going to have to match the load to the motor (with gears). This leaves an assumption that the gear train is very efficient also, but chains are known to have efficiencys in the 90% ball park,i have no idea for internally geared hubs but i imagine they cant be that bad. In my opinion this is the best way to efficiency, it kills performance because the gears in effect reduce load on the motor and thus the power output.
Something else to think about is that the axial motors (etek, perm, etc) already have such low resistance that they might be able to do the best of both worlds without gears, they have excellent efficiencys even at high currents. For an example check out the agni motor it is amazing what they accomplished with that one.
Joe

safe · Jan 14, 2007

Leeps said:
Gears are better for climbing hills, however from a performance perspective the hub motor wins.

Apparently you didn't look very closely at the charts above.

The geared bike SIGNIFICANTLY beats the non-geared in every category:

Maximum speed at 15% grade: 7 mph verses 17mph
Maximum speed at 10% grade: 15 mph verses 23 mph
Maximum speed at 5% grade: 38 mph verse 38 mph (the hub peaks here)
Maximum speed at 0% grade: 48 mph verses 58 mph

Even if you add into the equation a small loss from the chain (5%- 10%) it simply doesn't erase the HUGE differences. (the internal hub/chain combination has been tested to be from 90% - 95% efficient)

The primary argument for a Hub Motor is simplicity... and I like that aspect... but given that the law limits the horsepower it's easier to skirt past the law with gearing that with an oversized motor. But that's a judgement call... it's just as illegal to gear a bike too high as it is to run too much power so the net effect is that BOTH ideas are presently illegal. (it would be better if they changed the law and set the limit to 750 Watts and left the gearing up to the rider)

From the manufacturers standpoint you could sell a bike with a standard motor/gearing combination "legally" and then in the aftermarket area people could trick it out themselves by simply changing sprockets and adding internally geared hubs...

NickF23 · Jan 14, 2007

There is also generally a differnce between a geared hub motor ie fixed gearing and direct drive hub motors. I notice better acceleration and hill climbing power in the geared systems i've used. I've heard arguments about efficiency that support either type but I've no idea which is more efficient.

As for the variable vs fixed gearing debate i've no idea which is more efficient but the variable gearing should give better acceleration and/or top speed.

safe · Jan 14, 2007

The "Legal" Bike

Here's another thought:

Let's say the law is "firm" on the idea of 750 Watts as the motor size and they allow the controller to be 40 Amps for 36 Volts. (pretty much the "status quo") Then it might be interesting to calculate what that motor looks like with gearing. Here's a chart of:

750 Watt Unite Motor
36 Volts
40 Amp Controller (50% PWM effect)
Peak Power Output - 1012 Watts.
8 Speed Internal Hub

safe · Jan 14, 2007

NickF23 said:
There is also generally a differnce between a geared hub motor ie fixed gearing and direct drive hub motors.

A motor is a motor. If you gear it up you get the power peak higher, if you gear it down the power peak goes lower. It's that simple. The bottom line is that motors run best when the voltage and the rpm's are in a certain "efficiency zone". With gears the "zone" is moved up and down and so you can be certain to have coverage everywhere.

But if there were no limits in the law you could design without power constraints and you could build hub motors (like the 5304 at 72 Volts) that do a very good job of covering all the bases. If the 5304 at 72 Volts was running a controller of 50 Amps I would BET that it would be able to tackle some serious hills.

Sounds like a good chart to make... I'll be back...

safe · Jan 14, 2007

The Hub Motor Strikes Back

Okay, so how many amps are required for the Hub motor to equal the climbing power of the 1200 Watt geared motor?

The answer seems to be 60 Amps:

5304 Hub Motor
72 Volts
60 Amp Controller (50% PWM effect)
Peak Power Output - 2835 Watts.

NickF23 · Jan 14, 2007

" If the 5304 at 72 Volts was running a controller of 50 Amps I would BET that it would be able to tackle some serious hills."

I had one of these (35 amp controller not 50). Yes it did fly up the steapest hills from a standing start! 8) thing is would the bike have accelerated faster with geared motor?

looking forward to the chart

safe · Jan 14, 2007

NickF23 said:
...looking forward to the chart

I posted the chart above.

A big factor is the "PWM Current Warping" effect. I was using a figure of 50% which seems to match the Simulation for that motor. If the figure is actually higher it could be much better, lower much worse. Supposedly the "electrical geniuses" could optimize the "pulses" so that an ideal "resonance" took place and the effect might be higher. So it's hard to know exactly.

If you take the SAME motor and pick either "geared" or "fixed hub" then the "geared" always wins because... well that's obvious you have more torque / speed options. But if you are "unlimited" in your power output (can set the controller to 60 Amps) then you can out perform the advantages of gearing.

So it's a real toss up and it will probably come down to the way laws are enforced.

Note: Even a 35 Amp controller should be able to take you up a very steep hill. Most hills are LESS than 10% so my artificial 15% goal is probably more than most people need. I've got some very steep (but short) hils in my neighborhood and I'd like to be able to go up them without a problem. So if you look at the first chart you can go 20 mph up MOST hills already. At 60 Amps you could go 35 mph up most any hill... It might be overkill to want 15%...

xyster · Jan 14, 2007

Maximum speed at 15% grade: 7 mph verses 17mph
Maximum speed at 10% grade: 15 mph verses 23 mph
Maximum speed at 5% grade: 38 mph verse 38 mph (the hub peaks here)
Maximum speed at 0% grade: 48 mph verses 58 mph

Problem here. Your hubmotor model has the same basic parameters as my actual ebike. I've tested my ebike up hills and made acceleration tests I've presented on video (I'll do the hill climbing videos soon)...

I've climbed 15% (or darn near) grades at 20mph from a dead stop, and 10% grades at 26mph from a dead stop. Both these results correlate very closely to results provided by the bicycle power and speed calculator, as you can derive here:
http://www.kreuzotter.de/english/espeed.htm

Pics of results for 10 and 15% grades using 80% efficiency (i.e. 2.5kw is entered as 2kw):

safe · Jan 14, 2007

xyster said:
I've climbed 15% (or darn near) grades at 20mph from a dead stop, and 10% grades at 26mph from a dead stop.

MOST hills are less than 10% grade. 10% is a very steep hill... and I know (because I used to ride up a mountain on a road bike with a published grade) that MOST moderate hill climbs are at 5%.

On this particular mountain climb the peak had this NASTY 15% top to it and you nearly died every time you tried it. I know pretty well how steep things are.

I use that online calculator for my tables. You are forgetting that the 2000 Watt value does not apply at all rpm's. You can't "get" to the peak in many instances. (see chart one)

The only wildcard is how effective the controller is. If the PWM Current Warping effect is boosted to 100% then you get a chart that looks like this and on most "steep" hills you should be able to go 25 mph up them...(see chart two)

You need to find a hill with a grade that is PUBLISHED as 15% and measure how fast you go up it. From that we can calculate backwards EXACTLY how much of the PWM Current Warping effect actually gets through. It might be 75% or even 95%... I was using 50% to be conservative... Hill climbing for a fixed hub is entirely dependent on the PWM effect!

Another factor for your specific bike is how much it weighs and how much you weigh. For my comparisions I used the SAME bike/rider baseline on both, so it's possible that this is effecting the results. It becomes an "apples verses oranges" issue then... not the same starting point... (your bike/rider figures are 20 lbs lighter than mine)

xyster · Jan 14, 2007

I live in a hilly part of the country. I checked the grade with topo maps. It's 15%. The posted speed limit for cars is 20mph because it's so steep.

You're also forgetting that the lower wattage output occurs at lower speeds...as the motor gets itself slowly up to speed, more power lets it climb faster...at the wheel:

600W @ 5mph... 1100W @ 10mph...1600W @ 20mph are all on or near the line with the bicycle speed calculator's power numbers for climbing a 15% grade.

safe · Jan 14, 2007

xyster said:
You're also forgetting that the lower wattage output occurs at lower speeds...as the motor gets itself slowly up to speed, more power lets it climb faster...at the wheel.

But as the rpms rise you have to spread the same power across a larger number of "radians per second" so the torque actually drops as the rpms rise. You end up calculating the INTERSECTION of those two curves and that is what determines the actual top speed. (this was explained in the first posting)

If we agree that the published simulation is mostly correct (they use a 50% PWM value) then the numbers I've posted are in agreement with those.

P.S: Sometimes they post as a 15% grade the "worst case scenario" of a hillclimb. (so no one gets stuck by accident) The average grade might be only 10%. A real 15% is so steep that in first gear on a normal road bike you will have difficulty even getting up it at all. (like SERIOUSLY working hard) In the Tour De France they had only a few short sections that hit 15% for a short duration, usually near the top.

safe · Jan 14, 2007

The Larger Point

No matter what slight variations might be involved in getting an accurate model of one's motor it's a real "no-brainer" to recognize that given all things between motors being equal (our baseline) a geared bike will always outperform a fixed gear bike. This just seems obvious to me.

If you diverge into other areas and ask the question about whether it's better to use a small motor and gears or a large motor without then you are asking a different question.

In a "perfect world" one would use a very big motor and limit it to what your needs are. In the "real world" of legal limits to things you are forced to choose low end torque or high speed... unless you choose gearing which can give you both.

It's really the law that restricts technology decisions more than anything else. (and in that area all the fun stuff is illegal)

mr.electric · Jan 14, 2007

I think that switching to rare earth magnets from ceramic magnets makes almost as much difference and geared vs non geared set ups. So for best efficiency you need a geared rare earth motor. You can squeeze a bit more efficiency from a brushless rare earth magnet motor but it is not nearly as much difference as the ceramic to rare earth switch or the non geared to geared switch. I did not carefully read the graphs in this post and I am just commenting based on my experience fiddling with e bikes and scooters.

xyster · Jan 14, 2007

But as the rpms rise you have to spread the same power across a larger number of "radians per second" so the torque actually drops as the rpms rise

Hill climbing power and acceleration rate is a function of power, not torque. As torque decreases, to a point well established on these graphs, voltage rises faster than torque decreases. Hence power rises with rising rpms, and so does hill climbing ability/acceleration rate. That's why gears work to provide more torque at the expense of rpm's (voltage) where it's needed most!

If hill climbing speed were a function of torque only, how would these motors fare up a hill at one volt and 35 amps? How about 10,000 volts and one amp?
Why does that great bicycle/hill-climb calculator use power instead of torque as the single biggest variable?

As I've stated before in reply to you, I 100% agree geared systems are always more efficient over a broader rpm range. I'm attempting to prove that you are seriously underestimating and misunderstanding the real-life power available to a hubmotor via the controller/buck converter effect, and power rise with increasing rpms.

Nevertheless, this has been an excellent discussion and debate from which I'm also learning much.

safe · Jan 14, 2007

Let's talk about Torque

At low speed the torque applied to a wheel will be equal to it's ability to accellerate or to climb. This is one of those "Newtons Laws of Physics" situations where accelleration and fighting gravity really are equal.

As the speeds climb on the bike at some point the effects of wind resistance add to the negative "gravity" and tend to prevent the machine from travelling faster.

So until wind resistance becomes a major factor torque is the major indicator in hill climbing.

The "PWM Current Warping" effect (Buck Converter) definitely has a LARGE effect on this low end torque area and this does give some credibility to the idea of using the hub motor and abandoning chains and gears. Were it not for this effect it would be impossible.

So here's a chart of the 5304 and it's Torque verses Slope relationship. Notice how it deviates as the speed increases. (wind resistance)

I'm on the verge of wanting to take the online calculator and incorporate that into my spreadsheet so as to get rid of the table based approach. Some of the problems in accuracy can be attributed to table lookups and rounding off. But then again, it does appear to be very close to being right. My charts match the Simulation model pretty closely and so it tends to make me think they are in the ballpark.

xyster · Jan 14, 2007

Why don't you actually try buying a 5304, a 72V 40amp controller, 72V-92V worth of batteries and a 15% hill? (OK, maybe you can't buy the hill, but you know what I mean...). Then try to explain the missing torque you'll find powers you up that hill at at least 2x your calculated 7mph speed. (It's the power...VxA....more volts gets you the same torque at a higher rpm...)

If you don't like the results, do the stokemonkey thing and convert the 5304 hubmotor to a bottom bracket chain drive.

safe · Jan 14, 2007

That's a lot of money to spend.

I'm toying with the idea. Actually the frame and fiberglass are being designed to have the ability to swap out a 750 Watt motor and put in a 1200 Watt motor. So I do have design flexibility in it. I've already bought the two motors and controllers (about $250) and the 8-speed hub was $125. And I have two bikes in the boxes still with all the basic rims/disk brakes/brake levers/etc already. ($160)

If you look at that chart there are big "jumps" from one slope to another. You might be in situatiions where you are varying between 15% slope and 5% slope while you ride and the bike will react accordingly. So the "table lookup" doesn't always portray things as you feel them. Also, when you have momentum that helps a great deal when you hit an increase in slope. I think the numbers are probably correct. (they match the simulation)

The larger issue is whether 15% is an "excessive" slope to design for. On my current bike it cannot go above a 10% slope (as designed) and there are just a couple of places where my bike has to work to get up the hill. (almost all hills are designed to be 5% or less)

And it's ONLY a 750 Watt bike... (with 86 lbs of batteries)

So when you get into those "big numbers" of 2000 Watts and less weight you probably are only going to need to worry about 15% slopes for 5-10 seconds out of your day if at all. (you might not even lose your momentum if you hit it fast enough)

The other issue is top speed. Even at 72 Volts it's down a full 10 mph off of the "geared" speed of 57 mph for the 1200 Watt bike. (which is going to get me a speeding ticket)

I just don't know yet... (maybe 96 Volts?)

Geebee · Jan 14, 2007

If you want to make the difference really obvious try a bike with a 200watt direct drive hub and one with geared chain drive.
If where you live is hilly the direct drive will be close to useless where as the chain drive will with correct gearing give great assist up most hills and a top speed in excess of 50kph assisted on the flat
These are real world observations.
Regarding hills, my test hill 200m from my door is over 25% (measured) can you guess how much help the direct drive hub was on that? :roll:

safe · Jan 14, 2007

25% sounds like something in San Francisco. That's steep!

(and very expensive real estate)

xyster · Jan 14, 2007

How much power in watts can a bicycle chain drive system handle?

Bikes have gears, obviously, because us puny humans can only generate 150 watts or so sustained.

But at 3000-5000 watts a commercially available hubmotor like the crystalyte x5, I have a hunch, can put enough power to the ground in comparison to available geared chain drive systems to cancel the torque advantage of the gears. (Some folks here obviously have the skills to attach an ETEK to a bicycle, use motorcycle chains and gears, etc...)

Please note (again), I'm not arguing that gears are not far more efficient over a normal range of rpms... just that high-end, available hubmotor systems can climb hills just as well if not better than high-end, available chain drive systems. If true, the power factor cancels on both sides of the hubmotor vs. chain drive equation, leaving as most important ancillary factors such as efficiency (gears/chain drive wins big time) vs. simplicity and its close cousin, reliability (hubmotor wins).

NickF23 · Jan 14, 2007

safe said:
Let's talk about Torque

The "PWM Current Warping" effect (Buck Converter) definitely has a LARGE effect on this low end torque area and this does give some credibility to the idea of using the hub motor and abandoning chains and gears. Were it not for this effect it would be impossible.

This doesn't sound right. I thought all the PWM does is allow the bike to run at lower speeds efficiently. A direct drive brushed hub motor with no throttle and a simple on off switch would have no less torque than one with a throttle.

Geebee · Jan 14, 2007

But that only applies if you don't live somewhere that the power limit is 200 watts (if you want to stay legal). Geared hubs of 200w work ok but top speed sucks.
Yes a hub motor rules for simplicity.
I can maintain ~300w for well over an hour and can sprint to over (the trainer maxed out at 500w) 500watts for several minutes, I had a bike with a 600 watt peak output B/B chain drive so I would guess 1200watt sprinting all up with peaks considerably higher and I had no drive train problems and it was all low end components.
But 3000-5000w is a lot more.
I updated my profile with where I live - Tasmania, Australia.

NickF23 · Jan 14, 2007

xyster said:
How much power in watts can a bicycle chain drive system handle?

Please note (again), I'm not arguing that gears are not far more efficient over a normal range of rpms... just that high-end, available hubmotor systems can climb hills just as well if not better than high-end, available chain drive systems. If true, the power factor cancels on both sides of the hubmotor vs. chain drive equation, leaving as most important ancillary factors such as efficiency (gears/chain drive wins big time) vs. simplicity and its close cousin, reliability (hubmotor wins).

lol, I'd say the opposite

. When it comes to hill climbing or acceleration a motor with variable gears will always always win. Like you say hill climbing is related to power. The power curve of a motor looks like an upside down U shape. If your gearing allows you to allways stay at the top of the power curve you will accelerate/climb a hill faster. I think this only applies to BLDC motors though as with AC motors the power curve/torque curve looks different.

I'm not sure I understand the physics behind which system is more efficient. Aerowatt on the old forum and seem to suggest that a motor with fixed gearing with appropriate use of throttle is as/more efficient than variable gearing.

As to whats reasonably practical/legal on a bike that's another question. Just how much acceleration is actually needed on a pedal bike

The Great "Gearing vs Hub Motor" Debate

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