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:

**Simulated Dyno Results**:

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 1066 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 1066 times