# The High School Solar Car Challenge: some physics

This year I am covering the (High School) Solar Car Challenge, as well as the upcoming university competitions. The high school event will take place at the Texas Motor Speedway on July 15–22 (with Covid protocols in place), and will be live-streamed via the event’s YouTube channel. Today I want to say something about high school solar cars in comparison to world-class cars.

Left: Cougar Spirit from Covenant Christian Academy is a high school car in the Advanced Classic Division / Right: Nuna11 is a world-class car from Delft University of Technology in the Netherlands (picture by @lightatwork)

The two main drag forces operating on cars are rolling resistance and aerodynamic drag. The former is indicated in the chart below by red lines. It is a function of the product of the rolling resistance Crr of the tyres times the mass M of the car in kilograms.

The aerodynamic drag is indicated in the chart below by blue lines. It is a function of the product of the drag coefficient Cd of the body shape, the frontal area A of the car in square metres, and the square of the velocity.

The chart at the bottom of the page expresses the same information in terms of the power (in watts) required to overcome drag at various speeds.

At the world-class level, where special low-rolling-resistance tyres are available and cars glide through the air like a hot knife through butter (low values of Crr M and Cd A), the aerodynamic drag is much greater than the rolling resistance at race speeds, and shaving a few percent off the Cd A value becomes critical to winning. At high school level, with cars that students can afford and racing speeds from 15 to 50 km/h (10 to 30 mph), aerodynamic drag and rolling resistance are roughly similar, and reducing the weight of the car becomes especially important. Some of the high school classes do not permit hub motors, and for those cars, reducing drive train losses is also critical.

A few high school cars in the Advanced Division are both under 200 kg and quite aerodynamic this year (e.g. Invictus from the Iron Lions and Lumidos from Oregon Solar Car Team), so it will be very interesting to see how they perform.

# ASC 9: Aerodynamics

For both the Challenger class and the Cruiser class, solar car racing is to a large extent about aerodynamic drag. That’s overwhelmingly what the hard-earned solar energy is being wasted on, and therefore it’s what teams need to concentrate on minimising. The drag force on a car is given by the equation:

F = ½ Cd A ρ v2

Breaking that down, v is the speed of the car, ρ is the density of air (about 1.2), A is the frontal area of the car, and Cd is the drag coefficient, a number which indicates how aerodynamic (and therefore, how energy-efficient) the shape of the car is. For Challengers, minimising Cd allows the speed v to be increased, while for Cruisers (for which the average v is essentially given), minimising Cd allows non-solar energy use to be minimised. Of course, minimising frontal area is important too (and that is the motivation behind asymmetric Challenger cars).

To give a feeling for the all-important Cd, here are some vehicles with values ranging from 0.19 to 0.57:

Drag coefficients for a selection of vehicles. Clockwise from top left: 0.57 – Hummer H2 (photo: Thomas Doerfer); 0.30 – Saab 92 (photo: “Liftarn”); 0.26 – BMW i8 (photo: “youkeys”); 0.19 – General Motors EV1 (photo: Rick Rowen)

Because Cd is so all-important, it is the one thing that solar car teams are really secretive about. Challengers generally have values under 0.1. With no need for practicality, they chase their way towards the impossible goal of Cd = 0, trying to come up with the perfect race car, which will slice through air like a hot knife through butter:

Nuon’s 2005 car, Nuna 3, with Cd = 0.07 (photo: Hans-Peter van Velthoven)

Cruisers, on the other hand, have to balance aerodynamics with practicality. Bochum’s early SolarWorld GT had Cd = 0.137:

Bochum’s 2011 car, SolarWorld GT, with Cd = 0.137 (photo: “SolarLabor”)

Eindhoven’s recent Stella Vie, with its sleek aerodynamic shape, does much better than that (but they won’t say how much better):

Eindhoven’s 2017 car, Stella Vie (photo: TU Eindhoven, Bart van Overbeeke)

I understand that Sunswift’s 2013–2015 car eVe had Cd = 0.16. Appalachian State (Sunergy) have stated that their newly-built ROSE has Cd = 0.17. PrISUm’s Penumbra has a higher value (Cd = 0.2), because of the blunt end which they chose for practicality reasons (although they did do a few clever things to reduce the impact of that blunt end). I’m not aware of the Cd values for other ASC cars.

Appalachian State’s beautiful ROSE, with Cd = 0.17 (image credit)

# World Solar Challenge: The Designs

The World Solar Challenge Challenger class is seeing some nice-looking solar cars this year. The majority of cars (19 so far, or 66% – teams 2, 3, 4, 5, 8, 9, 10, 13, 14, 16, 17, 18, 21, 23, 25, 26, 46, 77, and 82) are some form of the increasingly standard flat wing with asymmetrical cockpit. Solar Team Twente’s Red One (photo above by Jérôme Wassenaar) is a good example. This design has aerodynamic advantages, since the driver sits behind one of the front wheels (often, the asymmetry extends to propulsion as well, with only a single wheel being powered). Such asymmetrical cars were introduced at WSC 2013 by a few teams, including Nuon and Tokai.

However, some teams this year (9 so far, or 31% – teams 7, 15, 22, 27, 30, 32, 36, 47, and 51), have either retained or built some form of symmetrical wing, like Nagoya Institute of Technology’s Horizon Z (below).

Finally, Cambridge University’s Evolution (team 12, below) reflects a quite different, and rather promising, approach.

# World Solar Challenge: Drag Coefficients

The drag coefficient measures how aerodynamic a shape, such as the body of a car, is – and therefore how energy-efficient the car will be when driving at speed. Some example values are shown below, listed from low-drag to high-drag. A solar-powered Hummer is probably not on the cards any time soon.

Entries hoping to win the World Solar Challenge Challenger class should be aiming at drag coefficients around 0.1. In the Cruiser class, values under 0.2 would be appropriate. This year, the wide range of car shapes in the World Solar Challenge demonstrates that there are many ways of achieving these goals.

0.07 – Nuon’s Nuna 3 (photo: Hans-Peter van Velthoven)

0.14 – Bochum’s SolarWorld GT (photo: “SolarLabor”)

0.19 – General Motors EV1 (photo: Rick Rowen)

0.26 – BMW i8 (photo: “youkeys”)

0.30 – Saab 92 (photo: “Liftarn”)

0.48 – Volkswagen Beetle (photo: Robert Couse-Baker)

0.57 – Hummer H2 (photo: Thomas Doerfer)

# World Solar Challenge: Team 8

## 8 Punch Powertrain Solar Team (Punch One)

The Belgian team from the Katholieke Universiteit Leuven came 6th in the World Solar Challenge Challenger class in 2013, in their earlier vehicle Indupol One, and 3rd in the Abu Dhabi Solar Challenge (but 1st among the four-wheeled cars). Their sixth car, Punch One (above), seems to have performed well in wind-tunnel testing (below), and we wish the 16 students on the team all the very best for the World Solar Challenge this year. Good luck, team 8!

For up-to-date lists of all World Solar Challenge 2015 teams, see: