Motor Controller Cooling Calculations

Robin did some heat calculations earlier on the motor controllers Motor Controller Heat Dissipation with some estimates for the max steady state power, and incorporating an aluminum plate into the aerobody of the chassis. To avoid the manufacturing of an aluminum plate inside a carbon fiber layup, we are doing some more calculations with less assumptions (or at least more accurate ones) and using a heatsink with a fan and forced air.

How much heat will we generate in the motor controllers - we don’t want to do a crazy over designed cooling solution because we know we can do better.

The motor datasheet specifies the heat dissipation in terms of current and voltage. The current will be higher when we need more torque from the motors, so we look for hills in the route map (ASC 2018 data) and see how much power we will need to dissipate. We will also look at the case of accelerating from stop to full speed, then maintaining that full speed (which we will likely do at some point during testing).

Aiming for 16.6m/s throughout the race. These calculations of torque requirement are done to maintain this given 16.6m/s speed. 16.6m/s = ~60km/h

Old Data - Torque Requirements

Average torque is 15.7Nm
Average of all the positive torques is 17.2Nm (treating the distance between each 2 points as identical).
^Note that the above torques are for each of the motors. The average calculation was done as “an unweighted average, where i just took the mean of all the torque required values between navigation points” (Slack message from Emma Wai)

This data is the map from ASC 2018 with waypoints along the route. We will look closer at the hills at the 1.3 and 2.5 markers.

At 1.5: climbing 1100 over 120km, 13Nm

At 2.5: climbing 800 over 160km, 9Nm

How long will these hills take?
120km @ 16m/s = 7500s = 125minutes, so we can assume this to be steady-state.

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So why is the torque on the hills at 1.5 and 2.5 lower than the average torque? - From Emma Wai: I think it's just that there are a lot of short portions where a lot of torque was required, which is raising the average.

Because of this, we should look in to getting better map data or using a weighted average for the torque depending on the distance between points.

New Data - Torque Requirements

@Emma Wai (Deactivated) Was able to create a weighted average of the absolute value of all the torque values throughout the race:

Weighted average: 10.99 Nm
Median: 11.03 Nm

And a histogram of all the torque values in the dataset (after removing a few outliers - such as the big hills, notice the graph only goes to 150ish and the max hills were ~200Nm):

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With these weighted average torque values, I am much more confident in the estimates of power dissipation in the motor controllers.

Emergency services testing track hill:

Using a combination of this site for elevation and google maps for distance, assuming the distance google gives is the hypotenuse of the triangle:
https://www.mapcoordinates.net/en
https://www.google.com/maps/dir/43.4365484,-80.5795813/43.434044,-80.576786/@43.4357277,-80.5800187,966m/data=!3m1!1e3!4m2!4m1!3e1!5m1!1e4

369m to 384m over 350m gives a 2.5 degree hill.

Heartland Motorsports Park (FSGP 2020 / 2021?)

Looks pretty flat.

COTA Turn 1 (FSGP 2019)

https://www.formula1.com/en/latest/features/2016/10/highs-and-lows---which-f1-track-has-the-most-elevation-changes-.html

Roughly a 30 metre elevation gain over 210m, assuming the distance google gives is the hypotenuse of the triangle.
https://www.google.com/maps/dir/Circuit+of+the+Americas,+9201+Circuit+of+the+Americas+Blvd,+Austin,+TX+78617,+United+States//@30.131248,-97.6388914,664m/data=!3m1!1e3!4m9!4m8!1m5!1m1!1s0x8644b03ad152eaf9:0x8ae827dd1ff5e0ed!2m2!1d-97.6358511!2d30.1345808!1m0!3e1!5m1!1e4

30m rise over a 210m hill gives a degree of 8.21 degrees

From ASC 2018 Map data

List of the 10 steepest portions between two navigation points and torque requirement per wheel.

Angle 13.125         and torque requirement 213.133         over 59.923 metres
Angle 11.526         and torque requirement 188.117         over 28.771 metres
Angle 11.373         and torque requirement 185.715         over 85.577 metres
Angle 10.542         and torque requirement 172.631         over 88.187 metres
Angle 10.435         and torque requirement 170.955         over 29.996 metres
Angle 10.045         and torque requirement 164.805         over 48.502 metres
Angle 9.878         and torque requirement 162.166         over 89.985 metres
Angle 9.744         and torque requirement 160.053         over 57.792 metres
Angle 9.483         and torque requirement 155.932         over 57.288 metres
Angle 9.47         and torque requirement 155.732         over 42.049 metres

*Note that the data we have is incomplete - some stretches of the map have no data points for over 20km, but this gives us a good estimate.

Data we will use for calculations:

The strategy model is currently using a 26cm radius tire.

For calculating power, we use: (https://www.engineeringtoolbox.com/angular-velocity-acceleration-power-torque-d_1397.html)

Where P (W), T (Nm), nrps = number of rotations per second

For calculating phase current, we will use these calculations: Motor Controller Output Current

This desmos graph was used to calculate based on the bus voltage: https://www.desmos.com/calculator/kwklxrs8g3

Steady State:

Average torque = 10.99Nm (using updated data for weighted average)
Power(W) at that torque: = 10.99Nm * 2 * pi * 10.1478 = 700.7W

Robin’s desmos graph on the pages linked above shows that lower bus voltage leads to higher power output, but that is in fact not true. When we decouple the bus voltage from the output current (as it really is), high bus voltages leads to a high power output, so we will use the max Vbus reasonable for our calculations. 145V since the voltage drops off fairly quickly from full charge at 151.2V, and a complete top-balance of the batteries is unlikely.

Vbus = 145V

We’ll use Kv = 6 for the high speed motor coil.
Phase Current (Io) = 10.99Nm * pi * 6 / 30 = 6.91A

Here’s a desmos graph with the Torque on the x-axis and the power and phase current plotted: https://www.desmos.com/calculator/jpffkscexo
This second graph is a little more complicated but includes some extra parameters: https://www.desmos.com/calculator/chlmv9grii

Plugging this in to the motor controller power dissipation formula, we get:
P = 9.785

Transients (On Hills):

Let’s go with a 10 degree, 200m hill, and we climb it slowly, almost as if from a stop. This is chosen since I do not believe that maintaining a 16.6m/s speed up a hill would always be reasonable. There is definitely going to be sometime that the car is only able to travel at walking speed, say when starting and going up a hill.

Choosing an average walking speed of 1.4m/s (https://www.healthline.com/health/exercise-fitness/average-walking-speed#average-speed-by-age), we can find the hill to take 200 (m) / 1.4(m/s) = 142 seconds = 2minutes, 22 seconds.

From above, the torque requirement for a 10 degree hill is around 165Nm per motor per the hills listed above. We’ll also switch to using Kv = 5.2 for the low speed motor coil, as on hilly days, this is what we would require.

This gives a phase current of:
Io = 89.8A, which does not exceed the motor controller’s phase current limit of 100A
And Power:
P = 136.68W

So for transients, I would be comfortable going with a 130W power dissipation for 2 minutes.

What if we have a 36km/h (10m/s) headwind - aero losses will increase, and thus the torque requirement and will increase. Will the torque requirement increase significantly? Should we take the wind into account for this model?