The FORCE dyno

A Blank Slate

As has been said before, an electric motor is a little like a blank slate because you can program it to behave in different ways. If you are designing a sport for "human / motor" interaction then you want to zoom in on ways to program the motors to maximize the riding experience.

My first attempt at a definition was 1000 watts of "input side" limiting that focused on the battery as the limiting factor because in the "old days" the batteries could not typically deliver more than 1C of current. These days 10C is realistic with LiFePO4 or LiPo cells.

...my most recent thinking is that "output" should be limited by constant Force and a convenient yardstick is the british measurement of weight called the Stone. (14 lbs)

...I just recently got my bike running with an as yet unprogrammed Kelly 100A controller and my guess is that most of the extra power goes to waste as either copper losses or core saturation. The motor is designed for 40 amps.

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Just some pictures of the ebike.

More...

Part One - Lessons Learned

My ebike controller was programmed to test "One Stone" as a concept. Here are the results.

0 - 20 mph Performance:

In this area Force is much better than Power because you are required to pedal to get yourself up to speed. When you feel the ebike accelerate in a linear manner the "rush" grows and grows. This is in contrast to Power based ebikes where you get the biggest "rush" at the beginning and then it just seems to fall off and you feel a little disappointed. I have 10,000 miles ebike experience using the older Power based system and can say that Force just feels better... it always feels like things are improving rather than getting worse.

20 - 40 mph Performance:

This is both good and bad. Yes, on flat ground and without a headwind the "One Stone" ebike will reach 40 mph as a top speed. However, the acceleration is painfully slow in getting there and if there is a rise in the road you encounter a problem. The problem is you "slow down" and drop to a speed of about 30 mph with a grade of as little as 2% to 3%. The problem is that you aren't supposed to be pedaling above 20 mph and since 2% to 3% grades are commonplace you get stuck with no ability to do anything. There is a "gap" in performance which is unacceptable.

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Part Two - The Solution

Here are the things that seem to bring about the "ideal rider experience":

0 - 20 mph should require pedaling and not have the feeling that the ebike is slowing as you go faster. Force based systems achieve this, so this aspect of the probem is "solved". Force gives a constant pleasurable "rush".

20 - 40 mph needs to be resolved with a higher Force level than "One Stone". At some other time I will go through the math, but in order to correct for different "Rider + Bike" Weights the Force level should be determined by formula. The table shows the Force levels that seem appropriate:

Heavy People Rejoice !

By adjusting for "Rider + Bike" Weight ALL riders would be able to sustain near 40 mph top speeds on slopes of 2% to 3%.

This would end complaining about heavy people not having equality with lighter people.

Also, as a practical matter, it makes the ebike more usable as a Suburban "pleasure toy" which is kind of how I see it evolving.

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Part Three - Rebuttal to Power Argument

It's inevitable that someone will argue to simply crank up the Power in order to get more top speed on a 2% to 3% grade.

However, if you actually look at the data (which can be done later) you realized that with Power based systems you have to really, really, really crank up the amps to make any difference at high speed. The way Power based systems climb hills is they allow the speed to DROP to get more Force... which is exactly what don't want.

What we "want" is that once the ebike goes above 20 mph we NEVER drop our speed. Once out of the "pedal zone" of 0 - 20 mph we don't want to be forced back into it.

So Force at the "sweet spot" level (which might get fiddled with over time) seems the way to go.

There are two ways to adjust Force:

Option One: Program the controller for different current levels.

Option Two: Change gearing.

...either way it's possible to "tune" an ebike to a desired Force level.
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Force, Hills, Wind and the Result

If you were to look at the Force generated from a 100 hp Electric Motorcycle you might get something that looked a little like the above chart. The motor produces positive Force, while the Hill (if there is one) and Wind resistance act as negative Forces.

Assuming a combined weight of 700 lbs for Rider and Bike and a 5% grade uphill you can see that hills don't do much to slow a bike when the power-to-weight ratio is so high.

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For a typical ebike with a 1000 watt motor and gearing that is pretty tall we get something like this chart above.

Assuming 250 lbs for Rider and Bike and a 3% hillclimb it's clear that top speed drops significantly.

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Assuming we are using the same "stock" 1000 watt motor but swithing from Power to Force based control we get something like the chart above.

Here we are using the same assumptions as with the "stock" ebike, but we get a better result. The reason for this improved top speed result on a 3% uphill is that we have in effect "moved" the powerband upward so that the bike has less Force at lower speed and more Force at higher speed. If all the factors are considered correctly you can have a cool running motor that can achieve the results you want. This eliminates the need to increase motor size in order to improve performance.

Put simply... it's just a smarter way to get a result.

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Subjective Riding Experience

I'd like to finish this idea with a direct visual comparison of the two styles.

On the left you see the Power based style where it's Force starts high, but fades. The feeling is of disappointment as the "EV Grin" you got at low speed disappears at higher speed.

On the right you see the constant Force style. Here the acceleration is fairly constant, but fades slightly due to aerodynamic losses. You "feel" as though things are getting faster and faster right up to the top speed.

The overall riding experience is "better" with constant Force because you never have the feeling that you are running out of acceleration. By the time you are up to full speed you are thinking about how fast you are going and not what it felt like to get there. The "mental states" of acceleration and speed blend together well.

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Range Anxiety

You can't overlook the Range when talking about force, power and efficiency.

The standard Power based style tends to do very well when it comes to Range because you typically spend most of your riding time at above 20 mph. With Power this means the current is always going DOWN relative to increasing speed.

Constant Force styled systems have slightly better efficiency at low speed, but consume more power above 20 mph because they use more current. The second two data plots show how a difference in aerodynamic drag (0.25 meters squared vs 0.40) can mean a dramatic difference in efficiency and therefore range.

What does this mean?

Subjectively it means that with the right gearing and a Force style bike you will find an "efficiency envelope" at full speed if you are in a tight tuck. But at the same time if you get "lazy" and sit upright you not only lose a couple mph off the top speed, but your efficiency and range go down.

When you sit up you have to drop from 38 mph (at best) down to probably 34 mph.

Range goes from 19 to 12 miles.

So the "feeling" is to want to stay tucked to get the speed... it lures you into doing this because it behaves better.

(the back gets sore in those tight tuck positions... kind of need the incentive to do it)

There's always the ability to let off the throttle... but I'm just thinking in terms of full throttle.
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Summary of "Known" and possible "Upgrades"

First the "Present State" of the ebike:

40 Mph No Load Speed

35 Mph @ Max Power
544 Watts of Wind @ Max Power @ 0.25 m^2 Frontal Area
1274 Watts Max Power Output
1581 Watts Max Power Input
240 Watts Max Heat
13 Miles Range @ Max Power
81% Efficiency @ Max Power

38 Max Speed @ 0.25 m^2 Frontal Area

2889 Max Rpm @ No Load Speed

Gearing 20:100 (will be replacing a 24 tooth front sprocket soon)

Force 18.5 lbs

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The "Crazy" Speed Upgrade

There's room on the ebike for two more battery plates which would take the pack from 12S to 18S:

54 Mph No Load Speed

50 Mph @ Max Power
1615 Watts of Wind @ Max Power @ 0.25 m^2 Frontal Area
2033 Watts Max Power Output
2381 Watts Max Power Input
240 Watts Max Heat
15 Miles Range @ Max Power
85% Efficiency @ Max Power

50 Max Speed @ 0.25 m^2 Frontal Area

4333 Max Rpm @ No Load Speed

Gearing 18:100 (another part to have to fabricate)

Force 20.6 lbs

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Not sure if I want to do this or not... but it points to the "potential" of the ebike and of 20.6 lbs of Force at my weight.

Upgrade costs:

A123 20Ah cells @ $30 each * 6 = $180

Upgrade to 72 Volt controller from 36 Volt = $100

Total Upgrade Price ~ $300 ... at this point I'm tired of shelling out cash.

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Definitely true.

The concept is to develop a "legal variation" of the ebike that has a sportbike mentality. There are people in Los Angeles that race on Go Kart tracks with a blend of gas and electric bikes of varying capabilities. It's mostly flat. So there is an emerging sport associated with this, but it's still too early to say where it might go.

I see this as something fun... so having things like an "efficiency envelope" that you can sometimes get into and sometimes not just adds to the fun.

Brute force power is it's own game. These ebikes accelerate at about 0.1g while the top MotoGP motorcycles accelerate at close to 1.0g so the goal really isn't to compete with that.

It's really about subjective rider experience.

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Getting back to the "subjective rider experience" topic, this chart takes a 1000 watt ebike and compares it to a 20 lbs Force ebike and looks at acceleration from a power perspective. To find "net acceleration" you take the power output and subtract the wind losses.

Basically the "rush" can be seen as the slope of any line segment (first derivative) as well as the curvature (second derivative) of the resulting power. The most intense "rush" is when the curvature goes UP. When the curvature goes DOWN and when the slope goes DOWN it is an unsatisfying feeling.

The Force based ebike can be geared in such a way that it "peaks" right when the acceleration falls off. This will not achieve the highest top speed though, because to get to the top speed you have to slow as you get there as the wind losses creep up to equal the power output.

The maximum "rush" for the 1000 watt ebike occurs at near zero speed. ("EV Grin")

The "rush" for the 20 lbs Force ebike is fairly constant with just a slight letup starting at 25 mph. It's a "longer high", but it's also a "smoother high" that feels more predictable.

More my style anyway.

Many drugs effect the brain in similiar ways. There is always the "rush" followed by it's opposite which is a feeling of withdrawl. The stock 1000 watt motor has an intense "rush", but it's so short lived that it's not a lot of fun. (makes you always crave more like a cocaine high). The 20 lbs Force motor configuration delivers it's effect over a longer period and then SUDDENLY removes it, but at peak speed. You can then "switch mental modes" to notice the speed.

To achieve a "pure acceleration" sensation from zero to top speed would require the Force to INCREASE enough to compensate for the increasing wind losses. By the very design of the stock 1000 watt setup the Force decreases as speed increases. So it's kind of backwards and always a little disappointing.
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Option Three

If the 18S "Crazy" speed upgrade requires an 18 tooth front sprocket (which I have to build from scratch) then it would be easier to build it now and get familiar with 20 lbs of Force at lower speeds. 12S will get me to about 34 mph. (7 mph below the potential at 12S)

This also optimizes the rider experience because the "Rush" caused by the difference in Power Output minus Wind Loss peaks at about 25 mph. So as far as the pleasure goes it's maximized at just 12S (40 volts) when using an 18 tooth front sprocket.

There's always the possibility to own multiple rear sprockets. I own a 100 tooth #219 chain sprocket and they have them in any size I want less than that. (95, 90, 85, etc...). The Go Kart racers typically have a bunch of alternative rear sprockets at the track (quick change half sprockets often) and they fiddle with them on race day.

But if "winning" on the track mattered then the key is $$$ ($300) and more voltage which gives a lot more top end.

It might also be good to "play it safe" at first as I'm testing and learning how to ride the bike fast.

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Newton Simplified

In the never ending quest to simplify the core issues involving ebike racing rules I've put together some super simple charts that show how "any mass" will accelerate.

I take into account:

The total mass. (for our case the Rider + Bike)

The force that accelerates the mass. (which we set as a constant)

The wind resistance. (an upright bike's coefficient is 0.5 and a streamlined bike about 0.3)

The grade of the hill as a percent.

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For this example the two "ebikes" are:

250 lbs Weight, 20 lbs Force, 0.30 wind

350 lbs Weight, 24 lbs Force, 0.30 wind

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Conclusions

When it comes to Top Speed on flat land the heavier bike is ultimately faster assuming they have the same wind resistance. (and rolling resistance, which is doubtful)

It's the 20 mph to 40 mph speed that matters most because that's what you have time for on a tight racetrack. In this area they are pretty closely matched.

Hillclimbing shows a very slight advantage to the lighter bike on a 3% grade, but not much. And if there is a downhill on the other side of equal negative slope the heavier bike will get an advantage.

My opinion:

These bikes would be "evenly matched".

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No Load Current Losses

Kind of interesting...

The way the "simplified model" of iron core saturation and "no load" current works is linear, the higher the motor rpm, the higher the no load losses. This means 1000 watts of Power and 20 lbs of Force produce the SAME losses due to no load current.

This is correct as long as you are below the irons saturation level.

What makes this fascinating is that if you are below saturation in the iron you actually (as a percentage) make better use of the iron at high rpm and load using a constant current 20 lbs worth of Force.

As a percentage the Force based motor runs better.

(another advantage)

...but it all comes down to hitting the "sweet spot" of iron.

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It's fun to feel you "learned something". (it feels good)

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This gives a visual representation of how "watts" enter a motor and as a percentage where they go.

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Hysteresis Modeling

The last couple of days I've been reading up on hysteresis and how difficult it has been to accurately model it's behavior. New models are still popping up and one I read about was as recent as 2010. The entire topic is extremely non-linear and also very dependent on material properties.

The "standard" way to work with hysteresis (iron loss) comes from the Steinmetz equation that goes:

HysteresisLoss = ConstantRelatedToTheMaterial * SwitchingFrequency ^ 1.5 * FluxDensity ^ 2.0

The values of 1.5 and 2.0 are "curve fitting" values and vary along with the constant.

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So when the weather is bad (which there will be plenty of with winter coming on) this is what I'm looking to toy with.

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Interesting point about PWM control methods related to core loss. Apparently lower duty cycles make things WORSE rather than better. This kind of makes sense because when the gaps between pulses are larger the field has time to collapse and that causes a small hysteresis loop (loop within a loop) to take place that causes a loss. The core loss can be 10 times higher than with a steady flux at these low duty cycles.

Force based motor configurations tend to operate at their ideal in the higher duty cycle range which will tend to keep the flux from collapsing. So the idea of driving a motor harder "up high" as opposed to "down low" seems to be showing support in the math as it also does in practice.

More good news. :)

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The Steinmetz Equation

Having done some reading I've found that the "material constant" for laminated electrical steel comes in at:

0.0073 Watts per Kilogram

I then went about creating a "worst case scenario" where I took the "linear" losses expected by the no load current and then added on top of that the "non-linear" losses of the Steinmetz equation. I even went to far as doubling the mass values of the electrical steel to exaggerate the effects of hysteresis.

What I seem to be getting is a result that is not that big a deal.

(it might not be worth a lot of study after all)

There is always the potential that the cited figure is wrong, but I've read several "scholarly works" that seem to point to similiar numbers.

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A Tale of Two Motors

SK3 6374 Aerodrive Motor

Currie Neodymium Motor

Back in 2007 I envisioned an ebike racing concept where people would race on Go Kart tracks. At the time the only baseline anyone could consider for what separated an ebike from an electric scooter or electric motorcycle was that the ebike was limited to about 1000 watts of input and about one horsepower output.

So in the beginning I was seeing motor development in terms of it being an "Efficiency Competition".

This is why I bought the SK3 6374 Aerodrive RC motor because it's efficiency is excellent. Based on the concept of an "Efficiency Competition" you can see that the Aerodrive is vastly superior to the Currie even when you allow for hysteresis losses that are probably exaggerated:

On another forum I came to realize (through discussions) that there are a lot of "heavy set" people who happen to like ebikes. This makes some sense because a lot of times people start off with the goal of losing weight and so they choose an ebike as a way to at least be able to get outdoors and move around.

So most recently I've come to the conclusion that there needs to be some sort of adjustment to account for all the overweight people. America is becoming obese and to ignore that reality (I'm lean and in the top 5% of athletic ability for my age and size) would be a mistake.

Fat people need a break. :)

Force based rules can be adjusted for weight in very precise ways to compensate:

At this point the "Efficiency Competition" is gone. Now it's more about reliability and it was for that reason that I bought a second motor that I can actually use. The SK3 6374 Aerodrive is fine for a lightweight RC airplane, but the bearings inside it are comically small. It's simply beyond reason to imagine it could have been reliable at my weight (~175 lbs) and for a fat guy (~250 lbs) it only gets worse.

The Currie Neodymium Motor is not the most efficient motor that's for sure, but the bearings are large and the heat carrying capacity is pretty good and the Kv is half of the SK3:

These two motors (above) can easily deliver the 20 - 25 lbs of Force to the rear wheel.

The Currie motor has 4 magnets and two pole pairs giving it a very low "electrical RPM".

The SK3 motor has 14 magnets and seven pole pairs as well as double the Kv so it's switching rate is SEVEN times faster than the Currie motor.

Force is Force is Force though... one of the great things about it as a metric is you essentially wipe away all the internal logic associated with the motors (things like efficiency) and focus instead on making the racing experience the same for people of different weights.

It might all be "too different" for the masses unfortunately.

(sometimes good ideas sit unused for decades before being realized)

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Today was a little warmer than other days recently and I got a chance to do a couple more test rides.

The bike is geared too tall right now, "One Stone" level verses the 20 lbs of Force that I'm planning on changing to. Even at "One Stone" I'm able to get around pretty good, but long uphills are a real problem because the bike is not designed for continuous standup pedaling. At 20 lbs Force I should be able to sustain 30 mph uphill.

What was interesting is that the heating in the motor was minimal... just as expected. Copper losses were small (240 watts seems correct) and it just doesn't look like hysteresis (core loss) is even a factor.

It's funny... I noticed this "constant current" capability years ago (2007 or so) and did get a brief test of the idea in about 2009 or so, but this is the first time I've built an entire bike around it.

Over the years so many (online) critics would say:

"Oh, you don't know what you are talking about. You can't get power like that up in the higher rpms because iron loss would be catastrophic."

...but it turns out you can. Well at least with a slow moving motor like the Currie.

Sometimes it's like noticing the emperor has no clothes. ;)
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Computerized Control

Let me stress:

To my knowledge no one is doing this yet.

Since we know that for low frequency switching in motors like the Currie Neodymium motor there is not much in the way of iron core loss compared to very high switching rate motors so we should be able to push them harder at higher rpm. Functionally they work like a tractor motor that spins slowly, but can handle a lot of torque and a decent amount of heat which makes them suitable for this sort of thing.

So I was thinking in a "perfect world" you could set up computerized "powerband profiles" that would be customized for each rider based on certain known criteria. You could then equalize racers based on weight.

It would look something like this:

For this powerband I am adjusting for aerodynamic losses so that you get a constant acceleration of 0.08g (20 lbs of Force for a 250 lb Rider and Bike):

When you attempt a 3% grade (hillclimb) the acceleration remains flat, but it just slows relative to the hill:

The Range becomes interesting. At lower speeds the range is good, but as you go faster the Range goes down:

And in the end the iron loss is still a small percentage compared to copper loss:

It's possible some of the more leading edge controllers might be into this already... but I just don't know.

(there are control parameters like "Ramp Rates" that I know of, but nothing this elaborate)

It might be neccessary to use a tachometer to make this work, but it also might be possible to "sense" backEMF like the sensorless RC motor ESC's do. This is NOT an easy thing to accomplish, but if it was done it would open up a new world of possibilities.

We do live in a computerized world these days... but controllers are still mostly "pre-computerization".

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This approach is the opposite of the "simplified" Force only method. Since people these days are "in love" with computers it's possible that this other extreme might gain some interest. The way things are now people seem to prefer that their motors are a mystery.

This could be a smart phone app !!!!!

Install a "slave" power controller and use the smart phone to control it. ;)
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