## Tesla 3 Calculator v.0.91

Once completed, you'll be able to use this calculator to study how various parameters can effect the energy use and range of a Tesla 3. The internal calculating engine is based on "first principles" - no assumptions. It solves the cubic expression for the resistance of a rolling object moving through air. However, there are many parameters involved - some we know well, some we have to guess about.

At this stage of development, the model is in reasonable conformance to observations.

Have special knowledge or insight? Let me know. ADK46 on Model 3 Owners Club.

### Background

In theory, you just need a few parameters to predict closely the resistance that must be overcome to move a rolling object through air. The aerodynamic shape factor Cd (0.23), the frontal area (2.18 m^2), weight, the rolling resistance of the tires (about 0.008 times weight), headwind, grade, elevation and temperature. That can give you the required power to the wheels for a given speed. More parameters are needed to get you to the power being taken from the battery.

The inaccuracies in a model stem from the difficulty in establishing or measuring the correct values for the parameters. Here, for example, Tesla says the Cd for the car is 0.23 - that's great to know, if that's what it really is. Energy loss between the battery and the wheels is unpublished information, so we can only guess while trying to get the model to fit real-world data.

### Discussion of parameters

Version 0.91 adds the medium range model to the ... model. Some interpolation from range numbers was required to deduce the battery size.

Cd: Tesla stated in a press release that the Cd of the car is 0.23. Presumably, that is in its best configuration, meaning with the standard 18" wheels with their aerodynamic wheel covers.

Frontal area: 2.18 m^2, as determined by Photoshop version of the classic photo cut-out method. Traditionally, this involved weighing a print of a photo, before and after trimming it to only contain the car, and doing some scaling.

Effect of wheel options: Cd was altered from the base 0.23 for wheel/tire options to fit published EPA range data. It was done at a speed of 66 mph, somewhat arbitrarily. Rolling resistances of different tires will play a role, but I don't have that data. It also gets complicated it's affected by inflation pressure. Assuming it is mostly an aero effect is not unreasonable - low profile tires expose more of the spokes of a wheel. Of course, the effect of the aero covers is pretty big, entirely aerodynamic.

Motor and drivetrain efficiency: Motor efficiency is at best 95%, ranging down below 90 at low load. Ditto for DC to AC conversion. There's some loss in the gear reduction, too. I've left this adjustable, but 86% can't be far off. It is unknown outside of Tesla, so it is left to you to guess.

AWD efficiency penalty: For dual motor cars, the second motor is less efficient. the EPA range data in Troy's chart shows a loss of 7.1%. This doesn't seem to be an independent measurement, however, since the exact ratios are seen in both the LR and SR figures. There's also difficulty in knowing if this a "raw" result of the dyno testing at 48 mph, or manipulated to reflect real world conditions.

System power: The power consumed when the car is powered on, but not moving. For example, the computers, display, idling convertors and pumps. This is not known outside of Tesla, so you may apply your own guess.

Battery conditioning power: Apparently, the Model 3 battery is heated only by waste heat from the drive unit coolant. Cooling will engage the AC compressor. This parameter is a candidate for elimination from the model.

Range data: The aforementioned range data is from Tesla's testing for the EPA, as contained in a post by Troy (Tesla 3 Owners Club).

Tesla Model 3 Performance: Data is scarce, so it's currently excluded from the model.

Weights: from Wikipedia. An oddity: the extra weight of the second motor is considerably greater for the long range model than the short range model. New: I found the weight for the MR RWD model, but guessed about the AWD model.

Battery usable capacity (for range predictions): 78.3 asserted by Troy for long range battery (need original source); short range assumed to be proportional to cell count (2976/4416 * 78.3 = 52.8). Tesla has been coy about actual capacities. Capacity degrades over cycles and time. New: I had to deduce the the size of the medium-range battery from range info, 62.4.

Temperature: This is only to compute air density for its aerodynamic effect - not battery performance.

Elevation: Also for computing air density. Cyclists are constantly asking me why I think they should be able to go faster in thin air. Thinner air means lower air resistance , so you can go faster until your lungs say otherwise.

Grade: Distance traveled divided by elevation gain, expressed as a percentage. Note this does not mean "average" grade - just a constant slope up or down. The problem is non-linear, so averages don't work well. An "effective" grade can be fudged for a known course to make predictions match actuals, then used to estimate relative effects of, say, temperature.

Headwind: This parameter hides a serious complexity to any aerodynamic model. The predictions are valid only for a straight-on headwind (or tailwind - enter a negative number). Crosswinds change Cd and frontal area in complex ways. Actual winds are capricious, too.

Results: Aside from the obvious, you'll find the power needed to overcome each the three forces involved in this problem: aerodynamic, rolling resistance and gravity. Here's a exercise for the student: at what grade and speed are these three forces equal to one another?

What's the deal with those wheels in the header graphic? They're Porsche 928 "manhole" wheels from the 1980's. Photoshopped. I have an extra set ...

Power at wheels:
kilowatts

Velocity:
mph / kph

Units:

Recalculation:

Model:

Wheels:

System Power:

HVAC Power:

Battery Conditioning Power:

Other Power:

Conversion Efficiency, battery to wheels (RWD):

lbs / kg

%

mph / kph

Temperature (for air density only):

F / C

Elevation:

ft / m

Distance:

mi / km

Predictions:

Power req'd from battery:

kW

Energy usage rate:

Wh per mile/km

Range:

miles / km

Energy for distance:

kWh

Aero resistance:

kW

Tire resistance:

kW

Gravity resistance:

kW