Skip to 0 minutes and 9 seconds This is a design study to see what factors affect the performance of an electric vehicle, miniature or full-size. We’ll look at the power required and the range, too, for a spread of conditions. We’ll consider this range of variables– we will need to calculate the tractive force, which we will find from a free-body diagram of the drive wheel.

Skip to 0 minutes and 39 seconds As we saw last week, the motor generates a driving force, a tractive force at the drive wheels. This is the force that overcomes the resistance to motion, but what determines the resistance to motion? We will consider three types of resistance to motion– rolling resistance, aerodynamic resistance, and hill-climbing. Rolling resistance is conventionally represented as weight times a coefficient of rolling friction. We will assume that the coefficient of rolling friction does not depend upon speed. Here’s an example for you to try. Pause the video and give it a go.

Skip to 1 minute and 37 seconds Here’s the answer.

Skip to 1 minute and 41 seconds We’ve got a value of 206 newtons.

Skip to 1 minute and 51 seconds Aerodynamic drag - aerodynamic resistance is conventionally determined from this beautiful equation. We’ve seen it before. Rho is the air density, A is the cross-sectional area, CD is the coefficient of drag, and v is the speed. C is determined from wind tunnel tests. Here’s an example for you to try. Pause the video and find aerodynamic resistance for a vehicle with the following dimensions. Note that 1 metre per second is 3.6 kilometres per hour, and take the area as the box defined by the three dimensions above.

Skip to 2 minutes and 52 seconds Here’s the answer.

Skip to 2 minutes and 56 seconds We got FA– that is, the aerodynamic resistance– equals 198 newtons. Hill-climbing resistance– we can get drag from hill-climbing directly from the free-body diagram. It is the component of the weight that acts down the hill and is calculated as weight time sine of the angle of the incline. Notice that the tractive effort in this case is shown at the front wheels. It is a front-wheel drive car. Small-angle approximation– for small angles, sine is approximately equal to 10, and 10 is the ratio of height gained to distance travelled. Hills are often expressed as height gained to distance travelled– 1 in 10, for instance. Here’s an example for you to try. Pause the video and give it a go.

Skip to 3 minutes and 58 seconds Find the gravity drag for a 2,000-kilogramme car climbing a 1 in 10 hill.

Skip to 4 minutes and 15 seconds The answer is easy. The gravitational drag force is 2,000 times 9.8 divided by 10 newtons, which is 1,960 newtons. This gradient is what you might find on a steep section of motorway. Notice that it is much larger than the rolling drag and the aerodynamic drag we calculated earlier. Now we’ll put it all together. We can show these forces on a free-body diagram of the car. In this case, we’ve shown a point force for the aerodynamic drag, but actually it is distributed all over the car. We’ve shown rolling resistance at the rear wheels for convenience. It actually happens at all the wheels.

Skip to 5 minutes and 11 seconds Again, we have assumed a front-wheel drive car. Assuming no acceleration, we can write some of the forces in the x-direction equals 0. Notice that the x-direction is aligned with the slope. Summing the forces in the x-direction this way gives us FT minus Da minus Dr minus Dg equals 0. So the tractive force is FT equals Da plus Dr plus Dg. To get the power required at the wheels, you need to know that power in watts is tractive force in newtons time speed in metres per second. And to find the power needed from the motor, we need to know how much of the motor power makes it to the wheels. There are losses. We account for losses by using motor efficiency.

Skip to 6 minutes and 16 seconds Motor efficiency equals mechanical power out of the motor divided by the electrical power supplied.

Skip to 6 minutes and 26 seconds We also need to know transmission efficiency. Transmission efficiency equals power at the wheels divided by mechanical power out of the motor. If you know the required power at the wheels, you divide that power by the transmission efficiency to get the power required at the output of the motor. Then you divide that power by the motor efficiency to get the power required from the battery. Now you can find the power needed from the motor at any given speed. Now we can estimate the range. Step 1 - calculate the power required at the wheels for a given speed. Step 2 - divide by transmission efficiency to get the power required at the output of the motor.

Skip to 7 minutes and 21 seconds Step 3 - divide by motor efficiency to get the power required at the output of the battery. Step 4 - find the battery capacity in kilowatt-hours when it’s supplying power at the rate that we determined from step 3. Step 5 - divide the hours found in step 4 by the power found in step 3. Step 6 - multiply those hours by speed to get the range.

Skip to 7 minutes and 56 seconds Now, for your design exploration - 1, download the PDF file of vehicle specifications. There are several vehicles to choose from. 2 - choose operating conditions that interest you. You can vary payload, speed, rolling resistance, drag coefficient, and gradient. Find the required power at the motor. You should compare with the motor power given in the PDF to make sure that your vehicle can actually supply that amount of power. 4 - find the power required from the battery. 5 - find the range. And 6 - report your findings in the discussion. And 7 - have fun.

# Design exploration of an electric car

Where does most of the resistance to motion of an electric car come from? Hill climbing? Rolling resistance? Wind? What performance can we expect with the power that we have? By the time you finish this task you will have answered questions like these.

You have the knowledge you need to work this out. Just in case you can’t quite see how to do it, this video is your guide.

**You will need to download the design specification in the Downloads section below to complete this task.** The specification lists the vehicle characteristics you will need for the analysis. All in all there is plenty of scope in this design task to explore any other vehicles you care to research, from bicycles to B-Double road trains.

If you just watch the video it will take about 9 minutes. If you take the opportunity to do calculations it will take longer. You might get completely hooked on this fascinating exploration and take hours – continuing long after this course ends!

For a worked solution see the solution to Retro Tutorial RT6.3.

### Talking points

- What did you learn about the resistance to motion of a car? For example, did the rolling resistance come out at more than you expected? Did the air resistance at high speeds seem surprisingly large (or small)?
- Perhaps you explored drag coefficients with a web-search. If so, what did you find?
- What vehicles did you apply these methods to?