Motors ARE Efficient at Low Throttle

Electric Motors and Controllers
Alan B   100 GW

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Motors ARE Efficient at Low Throttle

There seems to be confusion regarding the efficiency of motors at low throttle. Yes, efficiency drops a little, but not as much as you would think from looking at the efficiency graph from the Simulator (at ebikes.ca).

Why is this?

The Simulator is an excellent tool, however we must understand what it is graphing. One popular view is basically a calculation of a full-throttle run-up to maximum speed and beyond. At the single point where acceleration is zero on the graph, the system efficiency is correct. At ALL other points on the graph, the system is either accelerating or decelerating, so the power in is powering not only the motion, but also the acceleration (or the deceleration is adding power to the system). So in those cases a simple calculation of power in versus load does not yield the expected efficiency.

Let's take a simple example. If we bring up the simulator with default values and zero out the human power default, then enable System B and set it's throttle to 50%. We see that at full speed, the system efficiency is 81.5%, and at half throttle the efficiency is 75.9% for an efficiency loss of only 5.6%. This is going from 600 motor watts to 124, which is quite a wide range. There's no big penalty. The range also goes from 47 to 122km. Pretty efficient at half throttle.

Note that this is not the only way to view the simulator data, but the simulator documentation is not clear on how it should be viewed, and I think this view is closer to what most people expect when they look at the graphs. Another view will be discussed below.
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fechter   100 GW

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Re: Motors ARE Efficient at Low Throttle

I think people get confused when they look at the graph for the condition of full throttle and enough load to make the speed drop to half. This is nothing like running at 50% throttle.
"One test is worth a thousand opinions"

teklektik   10 GW

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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:It is basically a calculation of a full-throttle run-up to maximum speed and beyond. At the single point where acceleration is zero on the graph, the system efficiency is correct. At ALL other points on the graph, the system is either accelerating or decelerating, so the power in is powering not only the motion, but also the acceleration (or the deceleration is adding power to the system). So in those cases a simple calculation of power in versus load does not yield the expected efficiency.
Not really.
While it's true that motor efficiency is pretty much independent of rpm, the explanation in terms of the simulator is not exactly accurate - it suggests the efficiency plot is accurate only at one point, the other efficiency points are "unexpected", and that efficiency is not calculated as (Power Out)/(Power In).

The confusion about simulator plots come from a misunderstanding of what the various plots actually show.

The simulator plots show two completely unrelated and different kinds of calculations - one set for the motor and one for the vehicle:
The first plots are the motor/controller plots (red/green/blue) that show how the motor behaves. These have nothing to do with acceleration, aerodynamics, hills, or vehicle weight. They reflect motor operation under different loads. If you switch the x-axis to rpm instead of speed, you are essentially looking at a dyno plot of the motor showing the power and efficencies for different motor torques that derive from increased load. Think of a dyno pull where the motor is running unloaded and you apply the brake until the motor stalls. The simulator gives pretty accurate readings except at very low rpms.

Importantly, efficiency is calculated in exactly the same means as a dyno:
efficiency = (Power Out) / (Power In) = (rmp x torque) / (battery power in)

This is accurate at all rpms (except perhaps very low rpm because of the model).
• Bike Calculator:
The second plot is the black line which is a plain vanilla bike calculator that shows the power required to propel the bike at various speeds. This knows nothing about the battery, controller, or motor. You can use the black line alone to figure out how much power it takes a bike to go any speed regardless of the motor, battery, or controller - this curve is all about aerodynamics, weight, and incline.
The key gimmick of the simulator is that it figures out the terminal speed of the bike by finding where the red and black lines intersect - the point where delivered motor power is exactly equal to the power required to propel the bike. While it's absolutely true that at that exact speed the bike is not accelerating and that it is accelerating at lower speed, that has nothing to do with motor efficiency as shown by the green curve in the 'dyno data'.

So - when we look at the efficiency curve, the first thing we know it that it's part of the 'dyno data' and is not really related to the vehicle or whether it's accelerating or not.

A more accurate way to look at the simulator efficiency plot is that it is showing the efficiency under different loads at the given throttle setting. This load could be from acceleration or it could be from climbing a hill - it makes no difference - load is load. From that perspective the plot shows that the efficiency declines at low rpms when the speed (rpm) reduction results from increased load.

This makes perfect sense - the torque goes up and the rpm goes down to maintain the same power (power = rpm x torque). The increased torque means increased current which gives increased I^2R losses and so lower efficiency.

This is exactly what we expect.
It is accurate at all points, not just one.
What it is not, is an indication that running a motor at low speed is intrinsically less efficient regardless of load.

Here's a sample simulator plot of the same motor with the same throttle setting but on the flat or climbing a hill.
• The first thing we notice is that the motor plots (dyno data) are identical for both cases (the motor characteristics don't change on a hill).
• The next thing we see is that only the black 'bicycle calculator' curves changed - the power required to propel the bike is different on a hill (!)
So - both terminal speed effiencies are drawn from the same efficiency curve which is accurate at all points (all loads) - not just one.

simLoadExample.png (65.22 KiB) Viewed 1151 times

From some years back:
https://endless-sphere.com/forums/viewt ... 1#p1040697

Here's a plot of a variety of motors at different speeds in the (old) simulator where the speed is reduced by reducing the throttle not by increased load as in the simulator plot. There are some inaccuracies in the simulator at low rpms but in general all these motors give pretty flat performance simply by turning down the throttle. We also see that motor efficiency doesn't materially change with different voltages. This is the plot that most folks think they are seeing in the simulator and so draw the wrong conclusions about efficiency and rpm.

MotorEfficiencyByPctSpeed2a.png (78.77 KiB) Viewed 1151 times
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

Nice explanation, though it is too complicated.

Virtually everyone who looks at the simulator graphs interprets it as efficiency vs speed of the ebike, since speed is the X axis. Perhaps it should be labelled more precisely as to what it is or what conditions under which it is valid.

Virtually everyone who looks at the simulator misinterprets this.

teklektik   10 GW

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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:
Mar 21 2018 7:09pm
Nice explanation, though it is too complicated.

Virtually everyone who looks at the simulator graphs interprets it as efficiency vs speed, since speed is the X axis. Perhaps it should be labelled as "efficiency vs torque" instead.
Sorry, but that makes no sense. It actually IS a plot of efficiency vs speed. The confusion is that people leap to the conclusion that there is a simple causal relationship that achieving speed by any means causes the efficiency on the other axis.

The X-axis must be speed (not torque) for the graphical solution of terminal vehicle speed to work when intersecting the two sets of calculations "watts to propel vs speed" and "motor watts vs speed". Without the common X-axis the solution by intersecting curves is impossible.

Hence the "too complicated" explanation - although it was apparently also unclear. Sorry about that.
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

Sorry, but it is not efficiency vs bicycle speed. That assumption is what got us into this problem in the first place.

The only way that graph can be efficiency at that speed is if there is an implied load creating equilibrium at that speed and torque, a load that is not shown, a load that is equal to the acceleration/deceleration that I spoke about in posting #1. That isn't useful and is quite confusing.

If we cannot clearly describe these graphs in a few short sentences, we have failed to graph them properly.

teklektik   10 GW

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Re: Motors ARE Efficient at Low Throttle

Of course it is.
It is more properly efficiency vs rpm, but that has been adjusted to speed by wheel diameter to allow the graphical terminal speed solution.

If you look at a conventional motor dyno plot you see the same information albeit plotted against torque. The simulator is simply plotting the same information but against the rpm data in that data set. The underlying physical principles that relate all that data together do not change because you choose to view the data against a different axis. Simply re-plotting this dyno data against rpm changes the appearance but it doesn't mean that it is not a plot of those other measurements "vs rpm".

dynoPlot2.jpg (212.6 KiB) Viewed 1085 times

In fact, here is a plot of that same dyno data above in 'simulator format'.

Leaf-24-13pct.png (121.4 KiB) Viewed 1092 times
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

I understand all of that.

But telling people effectively that this efficiency graph is the motor's efficiency if you apply your brakes at <selected> throttle until you are going at that speed is not helpful at all. Of what value is that efficiency number to the user of this chart? The efficiency value that people are interested in is efficiency vs the load that is plotted on the load line. They are trying to understand their ebike.

The mere fact that we're having this discussion thread indicates that we've failed to make the graph clear enough. I can't count the number of times someone here on ES has said something about their motor having very low efficiency at low speed. It's universal.

teklektik   10 GW

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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:
Mar 21 2018 7:34pm
The only way that graph can be efficiency at that speed is if there is an implied load creating equilibrium at that speed and torque, a load that is not shown, a load that is equal to the acceleration/deceleration that I spoke about in posting #1.
Exactly - just like a dyno plot. The data set together shows the motor characteristics.

You are insisting that there is only one way to view a set of related data and that somehow the dataset is valid only if you put the 'proper' variable on the x-axis.

If you simply remove the vehicle parameters from the simulator by turning off the Load Line plot thus taking the unrelated vehicle calculation off the table, the remaining information is simply a replotted dyno plot that describes the performance of the motor. It is identical to all the motor plots distributed by manufacturers. That data and the device being described doesn't change because you change the way it's plotted.

In point of fact, many folks complain that dyno plots are confusing - largely because they are plotted against the torque variable. Changing the plot to clarify our understanding of data relationships is a basic tool. Here that was done to put the motor performance in terms of vehicle speed (instead of torque) which is easier to grasp and absolutely necessary for the terminal speed solution. We could just as easily but motor power on the x-axis if that served our analytical purpose.

My point above was that misunderstanding the nature of the plots was causing confusion. If you look at these plots for what they are - then this is simple. The confusion comes from trying to tie the motor model to the vehicle performance - and that is the business of the graphical intersecting dataset strategy.
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

One thought is that we present this data in a way that tends to mislead the audience the chart is intended for. The users of this chart are not motor engineers.

The rest of the chart can be explained in simpler terms.

Another thought is that it be better documented so people would not develop this widespread incorrect view.

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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:
Mar 21 2018 8:24pm
Of what value is that efficiency number to the user of this chart? The efficiency value that people are interested in is efficiency vs the load that is plotted on the load line. They are trying to understand their ebike.
I will not say what is or isn't useful to people, since you and I clearly differ on that already. I cannot express this any differently than I have above, but I'll say it one more time - this data is primarily arranged as it is with speed on the x-axis to allow determination of the terminal speed for different vehicle parameters and to show the expected behaviors nearby. If the meaning of the plots is understood, then the motor curves become useful beyond that.

Whether or not there may be other more useful ways to view the data is not the topic here - it is your claims that that the plot of efficiency vs speed is not in fact such a plot at all, that only the single efficiency point at the terminal speed is valid, and that the efficiency curve is not the conventional PowerOut/PowerIn calculation.

If you want agreement that there are other plots that may be more useful to many folks, I certainly will agree. But not to those other points.
I'm thinking we would also just agree to disagree...
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

The point of this thread is that motors are efficient at low throttle. The simulator graph's presentation leads people to think otherwise.

There is more than one way to view the Sim's plots. I can see either of the two views that have been presented thus far in this thread. One is a more static engineering view, the other a more dynamic view, the way a lot of simulators are written (and the way I've written simulators).

My perspective is that these plots are more readily understood by the average person by interpreting them as a dyamic view - a simulation of what happens when the conditions are initialized as stated and the ebike allowed to accelerate. This view fits the graphs from zero to equilibrium at least, and beyond that we are not too interested. In this view, all the plots make direct sense except the efficiency line. This one line seems to show very low efficiency for the motor at speeds below equilibrium. I suspect this is much closer to how the vast majority of people will understand this graph.

In the data blocks below the graph, the acceleration is calculated at any point you select, further supporting this view of the graph.

I don't think the motor datasheet / Dyno interpretation of the graph is good for the consumers of the simulator, based on the widespread mis-statements that are made in ES threads from it.

This thread is an attempt to reduce the confusion, and I hope we have achieved that.

Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

This is what is given to the simulator user as the definition of the efficiency plot:
Green Plot: This is the efficiency curve for the electrical drive system. It is a ratio of the mechanical power coming out of the hub motor to the electrical power going in to the controller. This ratio accounts for losses inside the controller and the hub motor, but it does not include losses due to the internal resistance of the battery. Notice though that efficiency does not necessarily mean better range or less battery usage; a fast and powerful setup running at 80% efficiency may draw more power to cover the same distance as a slower arrangement at 75% efficiency.
The simulator documentation does not state under what conditions the calculations are made. I just reread the whole page, and it does not say anything about the "artificial dyno load" that is required to make the efficiency graph valid. If you take the view that there is a "virtual load" then the efficiency graph makes sense. If you take the view that the simulation is a dynamic acceleration calculation, then the efficiency doesn't make much sense. There is little information there to guide the user into any particular view.

teklektik   10 GW

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Re: Motors ARE Efficient at Low Throttle

Just won't let go...
Ok, one last post
Alan B wrote:
Mar 21 2018 9:09pm
My perspective is that these plots are more readily understood by the average person by interpreting them as a view of what happens when the conditions are initialized as stated and the ebike allowed to accelerate.
Here you are again saying the plots are incorrect because you want a different plot. It doesn't make the data plot invalid and it doesn't make the efficiency plot wrong. This is evaluating the correctness of the plot not by what it is but by what you think it should be.
Alan B wrote:
Mar 21 2018 9:09pm
This view fits from zero to equilibrium at least, and beyond that we are not too interested. In this view, all the plots make direct sense except the efficiency line. This one line seems to show very low efficiency for the motor at speeds below equilibrium.
Interestingly , it is your claim that the plots do not follow the standard PowerOut/PowerIn calculation that is the source of this particular confusion. As mentioned above, the efficiency is exactly:

Efficiency = (Power Out)/(Power In) = (torque x rpm)/(battery power)

Since rpm goes down as we move left on the x-axis, the PowerOut must fall to zero at zero speed. In fact we see this on the red motor power curve. This means the efficiency must also fall to zero as we approach zero. or simply:

Efficiency = (torque x 0)/(battery power) = 0 efficiency

This makes perfect sense. Explanations that claim the efficiency is incorrect or that bring in acceleration, braking, or other vehicle characteristics muddy the waters because they are simply not a part of the calculation in any way.

Again - the simulator plots are primarily set up to answer the Big Question: "How fast will it go?"

This is the thing that gets asked the most and it does an excellent job of answering it. Other (different) questions about "How efficient is it at other speeds?" may need other plots or tools to give the best answer in the most easily grasped form. It is really quite pointless to claim that a screwdriver is a lousy hammer - it just wasn't intended to do the job of a hammer. Similarly, it's equally pointless to expect that one analysis tool or view of the data will be the best to clarify all questions. I'm pretty sure that plots that focus on answering your efficiency questions would not answer the "How fast does it Go?" question very well. Tradeoffs...

Anyhow, I think the goal here should not be to make (IMO incorrect) claims that the simulator is faulty from some perspective, but rather should be to educate what it is and why the plots are the way they are.
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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:
Mar 21 2018 8:24pm
I can't count the number of times someone here on ES has said something about their motor having very low efficiency at low speed.
I might be misremembering, but I thought that most of these are talking about low efficiency at low speed at high throttle inputs (meaning, pouring a lot of power into a motor to try to maintain a speed under some load too high for the system to do that, like climbing a steep hill).

I tried to find some in a search, but too many results come up for the searches I could think of, and almost all the results were irrelevant.

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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:
Mar 21 2018 9:58pm
The simulator documentation does not state under what conditions the calculations are made. I just reread the whole page, and it does not say anything about the "artificial dyno load" that is required to make the efficiency graph valid. If you take the view that there is a "virtual load" then the efficiency graph makes sense. If you take the view that the simulation is a dynamic acceleration calculation, then the efficiency doesn't make much sense. There is little information there to guide the user into any particular view.
I see you edited in some extra remarks after I responded to your post above - so let me address them now.

The dyno comparison is a view I presented above - these are not Justin's words so it is unsurprising that you did not find them. This proves nothing except that Justin and I describe things differently. I used the dyno concept instead of Justin's Engineering terminology of 'modeling' the motors because I felt it would be easier to grasp for the sake of discussion. In both cases we are talking about a system of equations that predict (simulate) motor behavior for given operating situations. A dyno run shows an example of how the motor behaves for a certain set of test parameters. The mathematical model (to use Justin's words) does the same thing.

Importantly, the matter of developing a model involves setting up test scenarios, measuring parameters during the test, then coming up with equations that predict the same results as the physical test. Justin's discussion of the simulator not only repeatedly mentions modeling motors, but there is a discussion at the end about the dyno test rig used to create the model. On the face of it then his 'model' of the dyno runs predicts the dyno results. He also provides some basic simulation equations to illustrate the basis for his modelling efforts - these are the power, torque, efficiency terms that we see in the simulator.

simulatorDynoRig.png (98.56 KiB) Viewed 996 times
JLE wrote:The parameter values that are chosen for the motor model are based on directly measured data that we have compiled from tests using a custom built dynamometer made for the task.

Our original 2005 dynamo setup pictured above was limited to a maximum loading of about 5 N-m, but we have since built two newer devices, one of which allows for continuous load testing of the hub motors of over 50 N-m of torque. This has enabled us to verify the mathematical model above to the measured output performance with a high degree of accuracy and over a wide speed and power range.
In short, to claim that his documentation does not relate the model to dyno operation is incorrect.

As far as the efficiency data only making sense if you have a particular view, Justin states the proper view - it's simply PowerOut/PowerIn as you quoted above. This relationship can be seen by example by putting the simulator cursor at any point on the motor curve in any simulation and doing the division on the tabular data. You claim that all the curves make sense except efficiency, but if they do then efficiency must as well since it's a computed (not measured) value based on that other sensible data.

simulatorEfficiency.png (7.49 KiB) Viewed 996 times

Frankly, my intent here is not to dispute the matter of of throttle effects on efficiency, but rather to take exception to statements you made about what the simulator is showing. I would like to see people be able to understand this complicated tool and use it to their advantage, but it can be tough to grasp. It would be unfortunate to have the utility of the tool compromised by folks reading remarks about nonsense data, etc. since that goes directly to the value of the displayed information.

Anyhow - enough of this. This OT discussion has completely derailed your effort to help folks understand the throttle/efficiency issue and for that I do apologize. I hope for some there was something of value in the OT stuff as well...
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Re: Motors ARE Efficient at Low Throttle

Hey guys, I appreciate you trying to shed light on how to use and interpret the simulator. I'd agree that the documentation is not as thorough as it could be, and also that one of the main points of misinterpretation is that hub motors are both inefficient at low speeds, and also have only a small operating band of good efficiency. That is totally not the case, and the idea that you want to keep riding the bike in some narrow "sweet spot" speed range related to the unloaded motor RPM is one of the ongoing myths that gets perpetuated about hub motors.

I tried to address this by providing users with the "auto throttle" checkbox so that when you click to a different speed on the chart, then it automatically recalculates the throttle setting in the simulator so that it has a steady state value at this speed point. That's discussed here
https://endless-sphere.com/forums/viewt ... 1#p1323611

I was initially going to have that be the default mode, but it results in behaviors that can be to first order confusing. For instance, if you click at a low speed, slower than you would get by human power alone, then the cursor automatically jumps forwards to the speed from just human effort. And similarly, if you click faster than the max steady state speed the cursor jumps backwards to the highest speed that the motor can attain. These are correct behaviors, but they lead people to think something is broken or not right.

What Alan clearly wants is that the default plot be changed into a steady state curve as I discussed doing here,
https://endless-sphere.com/forums/viewt ... 8#p1323928

I was hoping that we might have a stab at implementing that while doing the round of updates last year, but it's a more substantial algorithmic change to the way in which the simulator data is calculated and there wasn't time.

However, you can get a very good view of the broader efficiency curve by simply switching from a voltage throttle to a torque throttle, and then running the simulation at lower throttles.

Here's the efficiency and torque curve for the H3540 motor with a 35A controller at 36V full throttle. Efficiency has a peak at 42 kph and drops down sharply below 30 kph. Some people would look at this and conclude that you want to only run in the efficiency hump between 35-45 kph.
Sim_Efficiency_35ACntrlr.jpg (111.25 KiB) Viewed 824 times
However, if you look at the exact same plot but run it with a constant torque motor controller, so that the hub is producing the same torque output at all speeds rather than increasing in torque at lower speeds, then you see a much broader band of very good efficiencies.
Sim_Efficiency_TrqThrot.jpg (95.02 KiB) Viewed 824 times
That's much more reflective of how the motor would be used. You see 70% efficiency at 10 kph, rather than 40% like the first graph. The actual curve that Alan (and me!) want to see at some point is one where the motor torque is not constant like this, but is just matched to equal the required propulsion torque at all speeds. The %throttle value would have to be computed at each step of the graph and would be an output rather than an input to the simulation.
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Re: Motors ARE Efficient at Low Throttle

teklektik wrote:
Mar 22 2018 10:20am
simulatorDynoRig.png
Ugg it embarrasses me that I still have that photo up there. The actual dyno that I use now is a lot beefier than that, with a direct coupled Crystalyte X5 motor direct coupled to the motor under test.
DynoBench.jpg (194.36 KiB) Viewed 823 times
And here on the backside you can see the torque arm going down to the load cell for exact and accurate motor torque measurement, as well as the homemade dyno motor controller, built in 2008 and still going strong
DynoBackSide.jpg (163.49 KiB) Viewed 823 times
Currently recovering from the Suntrip race on a back to back tandem solar powered row/cycle trike. 550 watt solar roof, dual Grin All Axle hub motors, dual Phaserunner controllers, 12 LiGo batteries, and a whole wack of gear.

Now back in Vancouver with my Big Dummy Frame (yes This One, thanks ES!) with Grin all-axle front hub, Phaserunner controller, and 52V 19Ah Cellman triangle pack
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

Thanks for the contributions Justin!

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Re: Motors ARE Efficient at Low Throttle

justin_le wrote:
Mar 31 2018 7:16pm
The actual curve that Alan (and me!) want to see at some point is one where the motor torque ... is just matched to equal the required propulsion torque at all speeds. The %throttle value would have to be computed at each step of the graph and would be an output rather than an input to the simulation.
The plot posted earlier to illustrate this point was produced by this means - multiple simulator runs with throttle adjusted in increments of 10% yielded equilibrium speed and efficiency values that were entered into Excel to produce the plots. The only slight variation is that the speeds were normalized to a relative rather than absolute speed so that, for instance, the efficiency at 50% max speed could be directly compared across motors in spite of the wide variation in actual motor speed.

teklektik wrote:
Mar 21 2018 3:47pm
Here's a plot of a variety of motors at different speeds in the (old) simulator where the speed is reduced by reducing the throttle not by increased load as in the simulator plot.
...
This is the plot that most folks think they are seeing in the simulator and so draw the wrong conclusions about efficiency and rpm.
• MotorEfficiencyByPctSpeed2a.png (78.77 KiB) Viewed 760 times

Here's another plot that was investigating the effect of voltage on efficiency at different throttle settings and loads. As above, the plots were made from simulator data using a manual version of the 'multiple equilibrium speed pt' technique Justin describes. These curves also show a fairly flat efficiency at normal operating speeds. Here we also see from the different curves that although efficiency falls off with higher loads (as we see in the regular simulator plots) there really isn't any change in efficiency from running at different speeds or higher voltages (things that can't be easily seen in the simulator plots).

EfficiencyVsVoltage5.png (68.75 KiB) Viewed 760 times

Anyhow, Justin has suggested some of this could be calculated and displayed with some different simulator plots (which would be very cool!), but a little manual iteration will get pretty much the identical results by pushing the simulator data around into a plot that shows the data the way we want to view it....
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Alan B   100 GW

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Re: Motors ARE Efficient at Low Throttle

We can always do it manually with multiple runs, the value of the computer is to do that for us.

teklektik   10 GW

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Re: Motors ARE Efficient at Low Throttle

Alan B wrote:
Apr 01 2018 1:56pm
We can always do it manually with multiple runs, the value of the computer is to do that for us.
Quite obviously.

These plots were done some time ago to address exactly the speed/efficiency relationships that are the topic of the thread today. It was easy to put them up to illustrate those ideas in the absence of any similar plots in the thread. I merely explained how the plots were derived and how similar results could be duplicated by anyone so inclined.

Additionally, these plots are concrete examples of the method that Justin specifically outlined as a simulator enhancement. I thought it would be interesting to see specific examples of his proposal even though today the enhancement is not realized in the simulator and there are no means for the computer "to do that for us".

I believe the point is really the relationships the plots convey rather than whether the plots were produced automatically.
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