At The Wheel Torque Graphs

[Purplemeanie]

Hi All,

  As part of my EV conversion project I wanted to get a better grip on how an electric motor would perform against an ICE powered car. Lots of people have commented on how any Seven with an electric motor will probably be a crazy accelerating beast. But while that could be the case, the amount of space in a Seven chassis (even an SV) may be prohibitive.

And what matters is torque at the wheels. As we all know "power" is just torque multiplied by RPM. So its torque that determines the performance of your vehicle.

Then you have to take into account any gearing between the motor and wheels. Any gear reduction will "amplify" the torque created at the output (and gearing up will decrease output torque of course).

But in general a Seven has a gearbox going one stage of gear reduction followed by a differential doing a second stage. And then the differential also splits the torque in two to each wheel.

Therefore, the torque to each rear driven wheel at any given motor speed is: wheel_torque = motor_torque * gearbox_ratio * differential_ratio / 2.

So it should be simple to come up with a Wheel Torque vs Speed graph, showing the torque produced by the motor.

I tried to come up with a way of doing this in a spreadsheet but found it was a bit of a blunt instrument. So, I wrote a script.

I made the script so it can be reasonably easily modified to provide different "motors" and "gearboxes". The script runs through each motor configuration and plots each gear it finds in the gearbox on a chart. 

THIS CODE IS NOT PRODUCTION GRADE: I threw this together for my own benefit. If I'd have wanted to get paid for the code then it would have looked quite different. It also evolved and could probably do with a refactor and prune.

Anyway, here's a plot form the code as it stands at posting date. I created a benchmark set of in-gear plots for a Caterham Seven 420 (I found the data at the link repeated in the code). I then created two motor variants based around a motor I'm thinking of using in my conversion project. The two variants vary by the current that can be supplied to the motor and by a gear reduction I'll need to include in the design.

You can see from the graph that for the variants I've configured, the 420 beats the EV configurations in 1st gear but the EVs then take the lead from 2nd gear onwards.

If you have any comments or suggestions then please let me know below.

The link to the code is here:

https://github.com/Purplemeanie/TorqueAndPowerComparisons

John

[aerobod - near CYYC]

I think it is a good comparison, John. Just looking at your code, you have taken a 2.0m wheel diameter, I think 1.7m (85%) is much closer to the typical rolling circumference of a rear tyre on a 420R (typically 195/45-15 in the original size).

With a 0.85 multiplier on the speed shown in the graph, it would seem the 550A motor would be turning about 14,400RPM when peak power is reached at 85mph, or 150kW (201bhp) at 100Nm motor torque. The power would then drop off to 113kW (152bhp) at about 21,600RPM at the max speed of 128mph, likely also being the drag limited speed at that power level.

This behaviour seems to be as expected from a BEV, strong mid range and a drop off in power at the top end.

[Jonathan Kay]

Neat.

Initial thoughts.

1 How can you fill in what happens below 10 mph for the clutched ICEV?

2 What are the useful on-the-road outcome measures? I was brought up on 0 to 60 mph figures and the repeated simultaneous insistence that they weren't very relevant (see also GDP). Motor or Autocar advocated 30 to 50 mph times and distances as being much more informative, possibly in non-overdrive top. 

3 When you've decided on those measures how much effect does the need to change gear have on them? There were always allegations of gear ratios specifically chosen to make it just possible  to reach the final speed without another shift. The Lotus Elan Sprint might have been mentioned. 

Jonathan

[Jonathan Kay]

Why do electric Porsches have a two-speed transmission?

Jonathan

[Purplemeanie]

16 hours ago, aerobod - near CYYC said:

I think it is a good comparison, John. Just looking at your code, you have taken a 2.0m wheel diameter, I think 1.7m (85%) is much closer to the typical rolling circumference of a rear tyre on a 420R (typically 195/45-15 in the original size).

With a 0.85 multiplier on the speed shown in the graph, it would seem the 550A motor would be turning about 14,400RPM when peak power is reached at 85mph, or 150kW (201bhp) at 100Nm motor torque. The power would then drop off to 113kW (152bhp) at about 21,600RPM at the max speed of 128mph, likely also being the drag limited speed at that power level.

This behaviour seems to be as expected from a BEV, strong mid range and a drop off in power at the top end.

Thanks for the comment. As it happens I knew the wheel/tyre circum. was just a guess. If you look at the code now you’ll see it calculated out correctly - and I even went to the garage and wrapped a tape measure around to verify I was making things better! 🤣

[Purplemeanie]

6 hours ago, Jonathan Kay said:

Neat.

Initial thoughts.

1 How can you fill in what happens below 10 mph for the clutched ICEV?

2 What are the useful on-the-road outcome measures? I was brought up on 0 to 60 mph figures and the repeated simultaneous insistence that they weren't very relevant (see also GDP). Motor or Autocar advocated 30 to 50 mph times and distances as being much more informative, possibly in non-overdrive top. 

3 When you've decided on those measures how much effect does the need to change gear have on them? There were always allegations of gear ratios specifically chosen to make it just possible  to reach the final speed without another shift. The Lotus Elan Sprint might have been mentioned. 

Jonathan

Hi Jonathan,

To answer in turn…

1. I had this conversation with someone on WhatsApp last night about this. I started off writing the code to work out a 0-100 (or other arbitrary similar stat) but decided it made more sense for an overall picture to start with wheel-torque vs speed. I may come back to acceleration graphs (including gear change estimates and starting clutch slip).

2. Hmm. I think all performance measures only capture some of the driving experience. I’m also a fan of Autocars more realistic in gear acc.n metrics. The graph I’ve created here first was a stab at putting a nail in the ground on what sort of performance I might expect. I think it shows an EV based on this configuration would be really punchy from 20 to 80 but might not be quite as quick up to 20 as say this 420. I should probably try and create an acceleration graph, that might give a better sense of how it would feel to drive 🤷‍♂️

3. Hmmm, yes. People often don’t appreciate the careful planning that goes into gear ratios. There’s the basic misunderstanding that with more power you can pull a bigger gear, but fail to appreciate the cube law of power needed to overcome wind resistance. Thee are many many more twists to the gearing conundrum.

EDIT: And of course when you get this "increased gearing" really wrong you find that while you might have enough max-power to achieve a higher top speed, you now find that at slightly lower speeds you now sit off the peak power and so don't have enough power to make you go faster and therefore can achieve this new theoretical top speed. Gearing needs careful planning.

4. Electric Porsches. Well it goes back to point 3. Even though EV motors can spin fast, the torque multiplication through the gear sets, power and top motor RPM didn’t give Porsche both the 0-60/100, top speed and range they wanted without needing two gears. Gearboxes in EVs are especially tricky as there’s not the same inertia as in an ICE car (which is a twin edged sword) so the gear change timing has to be made in association with probably a partial powering of the drivetrain to match revs as the gears change. Downshifts also need to be thought of in this context. 

[Jonathan Kay]

Thanks, John.

Looking forward to the next version.   : - )

Jonathan

[Purplemeanie]

Following some tinkering last night and more pondering today, I've updated the code and created a new plot. The plot in the first post was a statically pasted image to this site. The image below is a link to the file on GitHub, which should therefore change as the code and image changes on GitHub...

[Purplemeanie]

17 hours ago, aerobod - near CYYC said:

I think it is a good comparison, John. Just looking at your code, you have taken a 2.0m wheel diameter, I think 1.7m (85%) is much closer to the typical rolling circumference of a rear tyre on a 420R (typically 195/45-15 in the original size).

With a 0.85 multiplier on the speed shown in the graph, it would seem the 550A motor would be turning about 14,400RPM when peak power is reached at 85mph, or 150kW (201bhp) at 100Nm motor torque. The power would then drop off to 113kW (152bhp) at about 21,600RPM at the max speed of 128mph, likely also being the drag limited speed at that power level.

This behaviour seems to be as expected from a BEV, strong mid range and a drop off in power at the top end.

James, also picking up on your point about drag. It's probably also something I should try and graph... motor power output vs power required to overcome drag. As you are well aware, but I'll state for others reading, it's important get a balance of peak motor power and drag. Though TBH... in my first incarnation of this project I'm almost certainly going to be current limited (current determines torque -> T ~ BI). I'm going to struggle to get enough current to the motors AND enough voltage to also get past the knee of the torque curve (which equates to needing increased voltage due to field weakening). Though I do have a cunning plan (cue Baldrick voice) to cheat a statically set current and voltage tradeoff that you normally get with BEV battery packs.

John

[aerobod - near CYYC]

From a drag perspective John, I have previously estimated a 7 with roof off having a drag coefficient around 0.65 to 0.70. The frontal area is about 1.5m^2 for an SV or about 1.4m^2 for an S3, leading to an estimated CdA of 1.05m^2 for an SV. Power required is of course is closely related to the cube of velocity at high speed due to the predominance of aerodynamic drag.

[Purplemeanie]

1 hour ago, aerobod - near CYYC said:

From a drag perspective John, I have previously estimated a 7 with roof off having a drag coefficient around 0.65 to 0.70. The frontal area is about 1.5m^2 for an SV or about 1.4m^2 for an S3, leading to an estimated CdA of 1.05m^2 for an SV. Power required is of course is closely related to the cube of velocity at high speed due to the predominance of aerodynamic drag.

I agree with your calculations James. I think I posted speed vs drag (and power??) in a Low Flying article last year. It’s surprising how closely my graphs correlated with max speed at max power. with my drag calculations showing drag power equal engine max power. 🤔😉

[Purplemeanie]

Here's a quick screen grab of my spreadsheet...

[aerobod - near CYYC]

3 minutes ago, Purplemeanie said:

I agree with your calculations James. I think I posted speed vs drag (and power??) in a Low Flying article last year. It’s surprising how closely my graphs correlated with max speed at max power. with my drag calculations showing drag power equal engine max power. 🤔😉

I'm assuming if you take 20% linear driveline and tyre rolling resistance losses (i.e. add 25% to the power required at the wheels at a given speed to determine motor power), then as drag is 0.5 x ρ x CdA v^2 in Newtons, then work done (in Joules) per second is power in Watts, i.e. P = 0.5 x ρ x CdA x v^3, with torque (in Nm) at the wheels being P / (2π x RPS). RPS is v / (π x d).

So wheel torque required to overcome drag is 0.25 x d x ρ x CdA x v^2, (or torque at the motor is about 0.0267 x d x ρ x CdA x v^2 with 20% loss). This seems to correlate with a top speed of 128mph (57.2m/s) at a wheel torque of 606Nm (ρ=1.225kg/m^3, d=0.576m, Cd=0.7, A=1.5m^2).

[Purplemeanie]

1 minute ago, aerobod - near CYYC said:

I'm assuming if you take 20% linear driveline and tyre rolling resistance losses (i.e. add 25% to the power required at the wheels at a given speed to determine motor power), then as drag is 0.5 x ρ x CdA v^2 in Newtons, then work done (in Joules) per second is power in Watts, i.e. P = 0.5 x ρ x CdA x v^3, with torque (in Nm) at the wheels being P / (2π x RPS). RPS is v / (π x d).

So wheel torque required to overcome drag is 0.25 x d x ρ x CdA x v^2, (or torque at the motor is about 0.0267 x d x ρ x CdA x v^2 with 20% loss). This seems to correlate with a top speed of 128mph (57.2m/s) at a wheel torque of 606Nm (ρ=1.225kg/m^3, d=0.576m, Cd=0.7, A=1.5m^2).

Hmm. I had some of those assumptions in my spreadsheet but not all. For me, being within two significant figures was all I was aiming at. 🤣
 

When I get some time I’ll update my spreadsheet with your factors included.

 

This is why it’s so good to share thoughts, somebody (often you James! 😉) has something to teach me! 🙏
 

Thanks!