## Efficacité et autonomie du Roadster

With more than 100 Roadsters delivered to customers so far and more on the road each week, it’s natural for some customers to run “experiments” on them. Because we have such an entrepreneurial and highly technical customer base, many of these experiments are quite detailed and attempt to answer questions that we have in some cases never discussed publicly.

One of the most common and tricky experiments is testing how far the Roadster will go on a single charge in various driving conditions. For the latest powertrain configuration (powertrain 1.5), we have demonstrated dynamometer test results of 244 miles range in a complicated combination of highway and city drive cycles defined by the EPA.

However, this is just one data point; real-world range can vary substantially depending on driving style, environmental conditions, and usage of accessories such as the electric cabin air conditioning system and the electric cabin heating system. The cycles defined by the EPA attempt to make a representative average of these different factors and combine it into one number. Many customers, potential customers and curious observers want the details behind this average and how results may change depending on conditions.

We need a designed set of experiments to understand how efficiently or how far a Roadster could drive under different conditions. This can quickly become a huge amount of testing as there are so many variables and conditions, but fortunately we have spent quite a bit of time internally building a very accurate computer model of how the Roadster will behave under different driving scenarios. We’ve validated the model by testing at a reduced number of points -- enough to give us good confidence in the results. The details of this model are quite interesting and could be a whole separate blog, but for now let’s just use it as a tool to help us understand Roadster efficiency and range.

The simplest experiment to consider, and one that gives great insight into the whole vehicle performance, is how efficiency and range vary as a function of driving speed. This is assuming that speed is held constant (i.e. cruise control) at each point. For any test or model run, there are many inputs that need to be specifically stated to make the results meaningful. So here are some of the critical inputs that we have assumed:

• Single driver ~180lbs

• Soft top or Hard top on vehicle (with windows up)

• No air conditioning usage

• No heat usage

• No headlights or cabin air blower (large 12V loads)

• Tires inflated to recommended efficiency setting 30/40 front/rear psi

The outputs of this model run are in battery energy usage per mile. In the case of an EV this is typically expressed in terms of Wh/mile. A 100W light blub running for 1 hour will use 100 Wh of electricity. Since 1 Watt is also just 1 Joule/second you can easily convert Wh into Joules by multiplying by (60 [seconds])*(60 [minutes]). It is also important to note that we are discussing DC Wh/mile or energy coming OUT of the battery pack inside the vehicle. This is very relevant to range but does not consider the losses associated with the onboard battery charger or some of the slight round-trip energy losses in the battery itself.

Here is the DC Wh/mile predicted result for a Tesla Roadster with the above assumptions over the entire operating speed range.

The shape of this curve might not be immediately intuitive, but it makes sense once you consider the different types of drag and energy loss at work. (We will look at those soon.) Remember that this is not a power curve but instead a plot of energy per mile. You can directly determine power from this data by multiplying the Wh/mile by the mph at a given data point. The expected DC power required to drive the Roadster at a steady speed is shown below.

This probably looks more intuitive since it is always increasing as speed increases. The shape of this curve is obviously not linear. To cruise at 60 mph takes about 15kW. However, if you double that to 30kW you will only accelerate to about 80mph -- far less than twice as fast. And if you double it again to 60kW you will accelerate to about 107 mph using 4 times as much power as you did at 60mph, yet you’d only travel about 1.8 times as fast.

Energy Loss Distribution:

To understand why these curves have the shapes that they do it is helpful to examine where the energy actually goes. For simplicity we will group the energy usage into four “buckets”:

1. Aerodynamic Losses (drag from the air over the body of the car and through the front radiator)

2. Tire Losses (aerodynamic and rolling drag from the tires)

3. Drivetrain Losses (Inverter, motor, gearbox, bearings)

4. Ancillary Losses (12V loads, cooling fans and pumps, lights, etc.)

Each of these loss components has very different characteristics and is affected in different ways by making real world changes to the vehicle.

1. Aerodynamic losses are almost entirely determined by driving speed. The other issue to keep in mind is that these losses are determined by relative wind speed over the vehicle -- not necessarily the speed over the ground. So if you are driving into a 10 mph headwind, it is nearly the same as driving 10 mph faster from an aerodynamic loss point of view. As you can see from the graph, this can have a huge impact on overall Wh/mile with even very small changes in wind. It is also important to note that, because the loss is not linear with air speed over the car, you cannot “zero out” the effect of wind by driving in a closed loop course the way you can with elevation changes. Driving into the wind for 1 mile and then turning around to drive downwind for the same 1 mile (all at the same speed) will use more energy than driving the same speed with no wind over 2 miles. Even a direct crosswind will slightly increase forward moving aerodynamic losses due to its interaction with the body shape.

2. Tire losses are mainly determined by the weight of the vehicle and the rolling drag of the tires themselves. For the Roadster we have chosen tires that offer a great combination of low rolling resistance and traction or grip. The air pressure in the tires has a large effect on this rolling resistance, grip and the overall tire loss. Higher pressure gives lower rolling resistance but a harsher ride and degraded handling. The above modeling is done at 30/40 psi front/rear. You can expect about a +/- 10Wh/mile variation with a +/- 20% variation in tire pressure. Similarly, by reducing vehicle mass you see a proportional reduction in rolling loss. So if you reduce total mass by 1% then you would reduce rolling loss by about 1%. In the configuration above, 1% equals about 30 lbs. So it is good to make sure that you are not “accidentally” carrying extra weight in the trunk or elsewhere if you are trying to get the best range possible.

3. Drivetrain losses include those that the user doesn’t typically control: the efficiency of the motor controller, the motor itself, the gearbox and generally all losses in converting the DC electricity from the battery pack into useful torque at the wheels of the car. This is proportional to speed due to spinning losses in the gearbox and motor and also proportional to power output due to conversion losses in the various subsystems.

4. Ancillary losses are caused by all “other” electrical loads in the vehicle, particularly the 12V cooling blowers and pumps, the 12V radio, internal and external lighting, etc. For the modeling above, we assumed that there was not heating or air conditioning load, but if there were it would show up here. These losses are somewhat different than the others because they represent a roughly constant power draw on the vehicle regardless of speed, winds or elevation changes. Because of this, they cause the energy usage per mile to start becoming high again at very low speeds. This effect would be even more pronounced if the heater or A/C system were operating. Likewise, the impact of ancillary losses is extremely small at high speeds because the primary propulsion power is very high and these small power draws make a relatively tiny contribution.

Range:

Now that we have a better understanding of how much energy the Roadster uses per mile, the next question is how far can it go? The typical full capacity of a new battery pack when charged to 100% in maximum range mode and discharged steadily over 3 hours is about 55kWh. Using that number you can calculate an interesting driving range curve for various speeds.

While this graph shows that driving range greater than 300 miles should be possible, the conditions to do this are quite rare: steady-state driving at 30 mph (no stops or starts) for more than 10 hours! What is most relevant for real world driving and trip planning is how the range varies between perhaps 45 mph and 80 mph.

One clear driving “tip” to take away from this is if you are ever nervous about making it to a given destination: you will do much better to slow down instead of speeding up. I’ve talked with many people who intuitively think that minimizing time to the destination will also minimize the energy usage, but just the opposite it true!

As you have probably seen from the discussion in this blog, many factors and assumptions affect range. The real world has wind, variations in road surface, hills, occasional stops and starts and other conditions. Given the complexity involved, I would be happy if a real-world test fell within about 10% of the modeled result for energy usage and range.

If you would like to “play” with these numbers yourself, below is a link to an Excel file with the table of data used to generate these graphs.

To our customers, happy driving. And we are always interested to hear back from you about other experiences with your Roadsters!

Best regards,

-- JB

Download the excel data files here