Solar Car World Rankings

Nuon at WSC 17 (photo: Anthony Dekker)

Here is my personal world ranking of the top twenty Challenger-class solar cars. It was produced entirely algorithmically by using linear regression on historical data to build mappings between WSC rankings and those of other races, and then applying those mappings to the results of four recent events (SASOL 16, ESC 16, WSC 17, and ASC 18). There is as yet insufficient data to rate Cruiser-class teams (apart from the actual WSC 17 results: 1 Eindhoven, 2 Bochum, 3 Arrow).

Rank Team SASOL16 ESC16 WSC17 ASC18
1 NL  Nuon Solar Team 1 1
2 US  University of Michigan 2 2
3 NL  Solar Team Twente 1 5
4 BE  Punch Powertrain Solar Team 2 3
5 JP  Tokai University 2 4
6 AU  Western Sydney Solar Team 6 1
7 JP  Kogakuin University 7
8 HU  Kecskemét College GAMF (Megalux) 3
9 SE  JU Solar Team 8
10 US  Stanford Solar Car Project 9
11 CL  Antakari Solar Team 10
12 ZA  North West University 4 P
13 CA  University of Toronto (Blue Sky) 11
14 CA  ETS Quebec (Eclipse) 3
15 JP  Nagoya Institute of Technology 12
16 TR  Istanbul Technical University (ITU) 7 P
17 CA  Poly Montreal (Esteban) 4
18 CH  Solar Energy Racers 8
19 US  Massachusetts Institute of Technology 5
20 TR  Dokuz Eylül University (Solaris) 9

Note that, for ESC 16, the 3rd, 4th, and 5th place cars were all Bochum Cruisers and are therefore not listed here, while 6th was Onda Solare, which is now also a Cruiser team. The letter P marks cars that participated in WSC 17, but did not finish, and thus were not ranked. It must also be said that Eclipse, Esteban, and MIT should probably be ranked higher than they are here – the algorithm is not taking into account the dramatic improvement in ASC teams this year.

Michigan at WSC 17 (photo: Anthony Dekker)


ASC 40: Reflections

Well, I have blogged about the results of the American Solar Challenge, and produced this summary chart (click to zoom):

I would like to supplement that with some general reflections (as I did in 2016). First, let me complement the ASC organisers on the choice of route. It was beautiful, sunny, and challenging (but not too challenging). Brilliant planning!

The beautiful ASC route (picture credits: 1, 2, 3, 4, 5, 6, 7, 8)

Second, the FSGP/ASC combination worked well, as it always does. Teams inevitably arrive at the track with unfinished and untested cars (App State had never even turned their car on, I am told). The FSGP allows for testing of cars in a controlled environment, and provides some driver training before teams actually hit the road. The “supplemental solar collectors” worked well too, I thought. I was also pleased at the way that teams (especially the three Canadian teams) had improved since 2016.

Supplemental solar collectors for Poly Montreal (picture credit)

If one looks at my race chart at the top of this post, one can see that the Challenger class race was essentially decided on penalties. This has become true for the WSC as well. It seems that inherent limits are being approached. If experienced world-class teams each race a world-class car, and have no serious bad luck, then they will be very close in timing, and penalties will tip the balance. For that reason, I would like to see more transparency on penalties in all solar racing events.

I was a little disappointed by the GPS tracker for ASC this year. It was apparently known not to work (it was the same system that had failed in Nebraska in 2016), but people were constantly encouraged to follow teams with it anyway. It would almost have been better to have had no tracker at all, instead just encouraging teams to tweet their location regularly.

Cruiser Scoring

I though Cruiser scoring for ASC 2018 was less than ideal. A great strength of the ASC Challenger class is that even weak teams are sensibly ranked. This was not entirely true for the Cruisers. I would suggest the following Cruiser scoring process:

  • Divide person-miles (there’s no point using person-kilometres if everything else is in miles) by external energy input, as in existing scoring
  • Multiply by practicality, as in WSC 2019 scoring (for this purpose, it is a good thing that practicality scores are similar to each other)
  • Have a target time for Cruiser arrival (53 hours was good) but no low-speed time limit – instead, calculate a lateness ΔH (in hours) compared to the target
  • Convert missing distance to additional lateness as if it had been driven at a specified penalty speed, but with no person-mile credit (the ASC seems actually to have done something like this, with a penalty speed around 55 km/h)
  • Multiply the score by the exponential-decay term e−ΔH/F, where F is a time factor, measured in hours (thus giving a derivative at the target time of −1/F)
  • Scale all scores to a maximum of 1

The chart below applies this suggested process to the ASC 2018 Cruisers, for various choices of penalty speed and time factor F, drawing a small bar chart for each choice. Sensible choices (with a grey background) give each car a score of at least 0.001. It is interesting that all sensible choices rank the cars in the sequence Onda Solare, Minnesota, App State, and Waterloo.

Applied to the WSC 2015 finishers (with a target of 35 hours), penalty speed is obviously irrelevant. A time factor of F = 10 preserves the rankings awarded in that event, while higher time factors would have put Bochum in second place. In that regard, note that regulation 4.4.7 for WSC 2019 is equivalent to a very tough time factor of around 1.66 hours.

Of course, another option would be to return to the additive scoring systems of WSC 2013 and WSC 2015, and this has been suggested.


I have posted about basic Challenger strategy. This race illustrated the fact that Cruiser strategy can be more complex. First, it is inherently multi-objective. Teams must carry passengers, drive fast, and conserve energy. Those three things are not entirely compatible.

Second, even more than in the Challenger class, the Cruiser class involves decision-making under uncertainty. In this event, teams could build up a points buffer early on (by running fully loaded without recharging, planning on speeding up later if needed). Alternatively, and more conservatively, teams could build up a time buffer early on (by running fast and recharging, in case something should go wrong down the track). Both Minnesota and Onda chose to do the former (and, as it happened, something did go wrong for Minnesota). In the Challenger class it is primarily weather uncertainty that requires similar choices (that was not a factor in this wonderfully sunny event).

Third, even more than in the Challenger class, psychological elements come into play. Onda were, I think, under some pressure not to recharge as a result of Minnesota not recharging. In hindsight, under the scoring system used, Onda could have increased their efficiency score by recharging once, as long as that recharge made them faster by at least 3 hours and 36 minutes (not that it mattered in the end, since all teams but Onda were given a zero efficiency score).

Together, factors such of these underscore the need to have a good operations analyst on the team, especially in the Cruiser class.

Media Coverage Summary

ASC 30: A Milestone

One of my eagle-eyed readers has pointed out an interesting milestone – Italian team Onda Solare has competed in solar car races on all six continents not covered in ice. I believe that they are the first team to do so.

  • North America: this event, the 2018 American Solar Challenge
  • South America: the Carrera Solar Atacama (coming 2nd in the Evolución class in 2016)
  • Europe: the European Solar Challenge (coming 6th in 2016) and the Albi Eco Race (winning in 2017)
  • Africa: the Moroccan Solar Race Challenge (wnning in 2016)
  • Asia: the Abu Dhabi Solar Challenge (coming 10th in 2015)
  • Australia: the World Solar Challenge (coming 10th in 2013)

Well done, Onda Solare!

ASC 18: Convoys

A typical convoy (click to zoom, photo of solar car by Jorrit Lousberg)

Solar cars in the American Solar Challenge each form part of a convoy – a typical convoy is shown above. The lead (front) escort vehicle must travel 500 metres or less ahead of the solar car, with headlights on and roof-mounted amber lights flashing.

The chase (rear) escort vehicle follows directly behind the solar car, also with roof-mounted amber lights flashing, and bearing a sign that says “CAUTION: SOLAR CAR CARAVAN AHEAD.” Both escort vehicles must carry safety equipment such as first aid kits and fire extinguishers. The chase (rear) escort vehicle typically also houses the team’s Decision-Making Unit (DMU), who plan the strategy for the race.

Left: Michigan’s lead and chase vehicles for the 2010 American Solar Challenge (credit). Right: interior of Nuon’s chase vehicle for the 2011 World Solar Challenge (credit).

The truck (or car with a trailer) rides further behind (at least 1 km). It carries equipment and provides the ability to transport the solar car in the event of a breakdown.

Left: Michigan’s semi-trailer driving down the Stuart Highway in the 2011 World Solar Challenge (photo: Marcin Szczepanski). Right: Calgary’s road crew truck from the 2005 North American Solar Car Challenge (photo: James Tworow).

The (optional) scout vehicle rides well ahead (at least 1 km), checking out road conditions and potential hazards. There may also be additional vehicles, like media cars, or a weather car watching for clouds an hour or so ahead of the solar car. All the cars in the convoy stay in touch using CB radio. It takes a whole team to race a solar car! Here are some team descriptions of their convoys:

This post has been adapted and updated from a previous one.

ASC 16: Tires

Tire on Bochum’s 2017 car (photo: Anthony Dekker)

In response to my Challenger strategy post, someone asked “what about tires?”

Yes, the rolling resistance of tires is a factor with solar cars. As tires rotate, the rubber in them flexes, and some energy gets lost this way. For a top Challenger class car, with good tires, about 85% of the solar energy is lost through aerodynamic drag, and about 15% through tires. That’s why my simple car model considered only aerodynamic drag.

The force required to overcome rolling resistance is g = 9.8 times the weight of the car times a tire-specific coefficient (ranging from 0.002 for an expensive solar car tire to 0.01 for a typical car tire). For a top Challenger class car, car and driver together will weigh around 250 kg. For a four-person Cruiser, it’s more like 800 kg – about triple. Bearing in mind that Cruisers often have tires with a higher coefficient of rolling resistance, this means that rolling resistance becomes quite significant with Cruisers. That is why Cruisers will sometimes turf out passengers to cut their energy use – even when running on a flat road. Climbing the mountains, overcoming gravity will come into play, and that uses up even more energy.

In ASC race news, I have updated my information page and teams list with news about day 1 of scrutineering.

ASC 13: Challenger strategy

This will be a lengthy post on race strategy. I will concentrate on Challenger-class cars, for which the main decision is at what speed to drive (there are also some tactical and psychological issues associated with overtaking, but I won’t get into them here).

The kind of analysis I’m doing assumes that teams have a good predictive model of how their car will perform under various conditions (collecting the data required to build such a model is yet another reason to do lots of testing). I’m using a very simplistic model of a hypothetical car – I only took half a day to build it (in R, of course); a real solar car strategy guy would take months and produce something much more detailed. I’m assuming that aerodynamic drag is the main consumer of energy. Remember that the drag force is:

F = ½ Cd A ρ v2

where Cd is the drag coefficient, A is the frontal area of the car, ρ is the density of air (about 1.2), and v is the speed of the car. The key thing here is that faster speeds burn up more energy.

I’m further assuming a solar model loosely based on the region of the American Solar Challenge, a perfectly flat road (no, that’s not realistic), a race start time of 8:00 AM, and a finish time of 5:00 PM with no rest breaks (no, that’s not realistic either). My hypothetical car has 4 square metres of solar panel with 25% efficiency, and a 5 kWh battery pack which is 80% full at the start of the day. In my first simulation, my car runs at constant speed until 5:00 PM or the battery dies, whichever comes first (solar cars are not intended to run with totally empty batteries). This chart shows what happens:

Initially, the graph is a straight line. The faster you drive, the further you go. But this only lasts up to 73.7 km/h, which takes you a distance of 663 km. Faster than that, and your battery dies before the end of the day, so that you go less far in total. In reality, of course, the driver would slow down before the battery died completely, but I’m not modelling that.

My second chart looks at varying the speed of the car. We start the day at one speed (horizontal axis), gradually speeding up or slowing down to reach a second speed at solar noon (vertical axis), and then slowly shifting back so as to end the day at the start speed:

In the chart, the distance travelled is shown by colour and number. It can be seen that, at least for my hypothetical car, the optimum is fairly forgiving: speeds between about 60 and 85 km/h are OK, as long as they average out to about 73 km/h, which means 653 km travelled. You will also notice that there is no incentive to break the speed limit – the rules have been carefully constructed to ensure that this is true.

In my third chart, I’m assuming a patch of cloud on the road ahead, between 200 km and 400 km from the start. We start the day at one speed (horizontal axis), switch to a second speed once inside the cloud (vertical axis), and then switch to a third speed when leaving the cloud (the third speed is chosen to be whatever works best with the remaining battery charge).

Two vertical stripes are noticeable on the left and right sides of the chart. At 20 km/h, the race day ends before you reach the cloud, so that the choice of “cloud speed” doesn’t actually matter. And at 100 km/h, your battery dies before you reach the cloud, so that the choice of “cloud speed” doesn’t matter either. The optimum is to run at a constant 70 km/h initially, and then to speed up to 75 km/h inside the cloud (so as to get back into sunshine that little bit sooner). If you run at an optimal 63 km/h after leaving the cloud, this lets you cover 619 km.

The final scenario changes the one above to have a moving cloud. This cloud is circular and once again 200 km in diameter, with a centre 300 km away from the start position. The edge of the cloud is initially 210 km from the road, but moving at a rapid 50 km/h towards and across it:

The optimum here is to outrun the cloud: to run at 85 km/h till the cloud is past, and then to drop back to whatever speed gives you a 73 km/h average. Not surprisingly, this gives essentially the same outcome as my first varying-speed example. A solution that is almost as good is to run at 70 km/h initially, and speed up to 80 km/h once inside the cloud. This gives you about an hour and 20 minutes inside the cloud. Slowing down to an optimal 70 km/h after leaving the cloud then lets you cover 642 km.

In real life, outrunning clouds and speeding up slightly through them can both be feasible options – if you have the right prediction software, and if know exactly what the weather is doing (which is the hard part). This is why the strategy guys in the chase car are always so busy!

Nuon’s WSC 2011 chase car (image credit)

ASC 12: Cruiser Scoring

The American Solar Challenge Cruiser class is a contest for multi-person solar vehicles, powered by 5 square metres of silicon solar cells (or 3.3 m2 of multi-junction cells), with the option of recharging from the grid. The contest is not actually a race – cars must get to the finish line within 53 hours elapsed time (not including the 45 min checkpoint times, which means maintaining an average speed of 33.3 mph or 53.5 kph), carrying as many people as possible, and drawing as little power from the grid as possible. Scoring is roughly as per WSC 2017. It is always difficult to explain race-type events that are not actually about “first over the line,” which is why I developed this “cactus diagram” last year:

For each car, the first coloured bar indicates the number of person-kilometres, which is basically just a weighted average of the number of people in the car. This is expressed as a percentage of the best value. You can see that Eindhoven won here, with an average of a little over 3 people in the car.

The second coloured bar indicates external energy use, which is the size of the battery multiplied by the number of times it was charged from the grid (counting the pre-race charge). External energy use is bad, so this bar is drawn pointing downwards. It is expressed as a percentage of the worst value, and you can see that Eindhoven won here again, because of its small battery.

The overall energy efficiency score (the third coloured bar) is the first bar divided by the second bar, scaled to a maximum of 80%. We then add on the practicality score (grey bar), scaled to a maximum of 20%. This gave Eindhoven an overall score of 100% last year, which was a convincing win.

In a recent rule revision (13.3.A), ASC Cruiser scoring this year will be modified with a time penalty on the energy efficiency score, similar to next year’s WSC rules. Cruisers that do not complete the entire course will receive an energy efficiency score of zero (13.3.B).

The diagram below shows an alternate view of Cruiser scoring (scaled differently, and ignoring practicality):

Here cars are scored based on the assumption that all cars run fully loaded (which doesn’t usually happen) and that they recharge from the grid at every opportunity (which generally does). Coloured triangles show values for the top WSC 2017 Cruisers, and black triangles show values for Cruisers at ASC this year (although the values for PrISUm and Minnesota may be out of date). On these assumptions, the score is just the number of seats in the car divided by the battery capacity, and is shown as coloured numbers.

What generally happens, of course, is that because of clouds, or mountains, or other factors, some Cruisers can’t keep up with the required pace. This means that they have to turf out passengers (rest assured, this does not happen while the vehicle is in motion). That is reflected on the chart by the triangles shifting downwards. The dashed lines show this happening for WSC 2017. Notice that Eindhoven could drop two people and still retain a huge lead in the scores, while Bochum could drop two people and stay just ahead of Team Arrow.

For ASC this year, PrISUm appears to have the advantage, if it can climb those mountains with four people in the car. The Cruiser class is all about people-carrying ability. On the flat, that means aerodynamics. In the mountains, motor power and regenerative braking ability will come into play. It promises to be an exciting contest!

See also my annotated ASC teams list and information page here.