Turbo Vado 2 4.0 or 5.0 or 6.0?

[mschwett]

A short progress report:

Here's how often a record occurred for a particular cadence. 0-10 have been deleted. (O was far and away the most prevalent cadence - coasting)

View attachment 206241

In my ride analysis I'm going to use data for cadences 50 to 90. Eliminating the tails will make the slope and P saturation levels more clearly visible in the plots of actual Pm mechanical vs Pr.




Here's how I got the function relating efficiency to cadence

View attachment 206244

Note the table,
cadence and mech watts are read off the Spec chart.
Electrical watts are the trend line of Pm max values from my data several posts above. Pmax = -0.62 * cadence + 439.
Actual efficiency is (mech watts/elec watts).

The blue line with data points is actual efficiency.
The red curve is a polynomial trend line. You can see from the difference column that it fits quite well.

In my ride data analysis I will use the f(x) shown on the chart to convert motor electrical power to motor mechanical power.

Does this seem right so far?

cool

my guess is, however, that the system is not 84% efficient at 100rpm. more likely it’s just not outputting quite the full 315/320 watts of mechanical power when the electrical draw is only 377w. i think specialized would be crowing about it a lot more if so

it’s very interesting that you’re able to get 420 watts of electrical draw out of the motor at 30rpm. i see you’ve got about 25 samples
there. have you tried to sustain 30rpm in a steady state with enough force to keep the power that high? of course the motor isn’t designed to work like this but i’m surprised how inefficient it is. what i would have expected based on the peak power curve from specialized is that at lower speeds you also don’t have as much power draw.

 

[Jeremy McCreary]

Here's how I got the function relating efficiency to cadence

View attachment 206244

Note the table,
cadence and mech watts are read off the Spec chart.
Electrical watts are the trend line of Pm max values from my data several posts above. Pmax = -0.62 * cadence + 439.
Actual efficiency is (mech watts/elec watts).

The blue line with data points is actual efficiency.
The red curve is a polynomial trend line. You can see from the difference column that it fits quite well.

In my ride data analysis I will use the f(x) shown on the chart to convert motor electrical power to motor mechanical power.

Does this seem right so far?

Strong work! If you want something reverse-engineered, best get an engineer to do it.

The above plots for the SL 1.1 (not 1.2) motor is from an official Spec document, but I no longer remember where I found it.

My only concern is the substantial difference in efficiency curve shapes. Yours for the SL 1.2 motor has a good bit more curvature. Could well be the right answer for that newer motor.

 

[mcdenny]

cool

my guess is, however, that the system is not 84% efficient at 100rpm. more likely it’s just not outputting quite the full 315/320 watts of mechanical power when the electrical draw is only 377w. i think specialized would be crowing about it a lot more if so

it’s very interesting that you’re able to get 420 watts of electrical draw out of the motor at 30rpm. i see you’ve got about 25 samples
there. have you tried to sustain 30rpm in a steady state with enough force to keep the power that high? of course the motor isn’t designed to work like this but i’m surprised how inefficient it is. what i would have expected based on the peak power curve from specialized is that at lower speeds you also don’t have as much power draw.

I haven't tried that experiment but your statement is correct - It isn't designed to work at that low rpm that means it's less efficient at that low rpm.

It makes sense, The controller applies voltage against the resistance of the windings but the rotating winding themselves generate a current in the opposite direction (back EMF). The faster the motor turns the more back EMF and so the lower net current. Most motor labels show an LRA spec, locked rotor amperage (0 rpm) which is the most current the motor can draw. So the lower the rpm the more current. Running a motor under load at too slow an rpm creates a lot of heat because of the higher current flow (little back EMF)

The current flow (amps * volts = power, volts are a constant 48ish at max "throttle") creates torque and power is torque x rpm. You can see the Spec torque chart fall off a lot as the rpm goes up. It's 50 Nm at 30-40 rpm but drops to 30 Nm at 100 rpm. As the rpm goes up the current, hence torque, drop (back EMF) but since power = torque * rpm the increasing rpm has a stronger influence than the decreasing torque until at higher speeds the back EMF effect overcomes the increasing rpm effect and the power starts to fall off.

Sorry this is so wordy. I'm not an EE but have done a lot of tinkering with electric drive systems for boats and kind of understand this stuff but can't express it elegantly.

 

[mcdenny]

For reference here's the Spec charts for torque and Mechanical power

 

[mcdenny]

Strong work! If you want something reverse-engineered, best get an engineer to do it.

View attachment 206249

The above plots for the SL 1.1 (not 1.2) motor is from an official Spec document, but I no longer remember where I found it.

My only concern is the substantial difference in efficiency curve shapes. Yours for the SL 1.2 motor has a good bit more curvature. Could well be the right answer for that newer motor.

You can see the spec chart has a good bit more curvature. I did my best to match the spec chart in my spreadsheet to figure out an efficiency vs cadence function to use to adjust all my Pm electrical to Pm mechanical..

 

[mschwett]

You can see the spec chart has a good bit more curvature. I did my best to match the spec chart in my spreadsheet to figure out an efficiency vs cadence function to use to adjust all my Pm electrical to Pm mechanical..

the older specialized chart does confirm very high efficiency at high rpm. it also suggests that the efficiency should be higher at lower rpm, but maybe the new motor sacrificed that a bit, or maybe a longer steady state test would show lower electrical draw?

 

[Jeremy McCreary]

Sorry this is so wordy. I'm not an EE but have done a lot of tinkering with electric drive systems for boats and kind of understand this stuff but can't express it elegantly.

A hobby once forced me into a fairly deep dive into brushed permanent magnet motors. Our ebikes use brushless permanent magnet motors, but these 2 variants still have a lot in common.

I think you did a great job on a topic that turns out to be a lot more complicated than it looks.

 

[Jeremy McCreary]

You can see the spec chart has a good bit more curvature.

Could you elaborate on that?

 

[Jeremy McCreary]

going back to the data, if you consider support factor as the inverse - rider power / motor power, it's actually linear. a very simple first degree equation can go from ease and rider power to motor power - motorPower = (riderPower/(-0.0814*ease)+2.11)

Below is a blue plot of Pm ramp slope S = Pms / Prs based Spec's Prs data for M = 100. The green plot (see below) makes the blue one hard to see.

Symbols
E and M = assist settings E/M
Prs = saturation rider power, here from Spec data
Pms = saturation mechanical motor power
Px = 300W = Pms at M = 100 and 80 rpm.

Approximating S(E)
Also plotted are 3 different ways to approximate the empirical blue plot for calculation purposes. Showed the exponential (red) and quartic (yellow) models previously. What's new here is your hyperbolic model (green). Calling it that cuz the reciprocal of a linear function is a hyperbola.

As you showed, the hyperbolic fit is excellent. And here we see that it's far better than the other two. To improve the fit at higher E values, I added a fudge term H to your formula like so:

S(E) = 1 / (-0.0184 E + 2.111 + H)

Your linear regression gave H = 0, but I plotted H = 0.012.

Before putting the hyperbolic model to work, we'll have to see if the revised field data from @mcdenny supports my hope that the M = 100 ramp slopes also apply to every other M. The Spec data supports this hope, but the original field data stands against it.

Again, well done on finding the hyperbolic formula.

 

[mcdenny]

Could you elaborate on that?

The Spec mechanical power vs cadence is significantly curved. If you accept that the electrical power input is constant across the same cadence range then the efficiency curve is going to have the same shape.

PS, I’m taking my bike in to get the new 2” more rise handle bar this afternoon and afterward I’ll try a very low cadence ride at 100/100 to get verification of the electrical power draw at these low cadences. I may have a problem generating the necessary Pr to get Pm electric max at low cadence. We will see.

 

[mschwett]

The Spec mechanical power vs cadence is significantly curved. If you accept that the electrical power input is constant across the same cadence range then the efficiency curve is going to have the same shape.

PS, I’m taking my bike in to get the new 2” more rise handle bar this afternoon and afterward I’ll try a very low cadence ride at 100/100 to get verification of the electrical power draw at these low cadences. I may have a problem generating the necessary Pr to get Pm electric max at low cadence. We will see.

yeah, that's going to take seriously GRINDING up a hill at 100/100 in a very low gear. be careful, that's the kind of riding that causes people to hurt themselves or have a body <-> pavement interaction.

 

[mcdenny]

yeah, that's going to take seriously GRINDING up a hill at 100/100 in a very low gear. be careful, that's the kind of riding that causes people to hurt themselves or have a body <-> pavement interaction.

Not at all, just ride the brakes.

 

[mcdenny]

New info regarding efficiency. Thanks @mschwett for suggesting getting a lot more low cadence 100/100 data. Big surprise to me anyway, at 100/100 and Pr above 85 watts the controller does NOT just dump in full voltage regardless of cadence. Just as with Pr vs Pm, there is a linear ramp up to a max then a flat line at higher X values.

Behold

Because the electrical input power is reduced at cadences < 55 my formula for converting Pm electrical to Pm mechanical is wrong. One step back is all though.

The transition point appears to be 55 rpm. The efficiency plot presented above will be revised to have higher efficiencies for cadences < 55. It will be less curvy and more like the one Jeremy posted for the 1.1 motor.