World Solar Challenge Cruiser scoring

Having participated in some recent discussions about the World Solar Challenge Cruiser Class, I thought I would explore the scoring again. Scoring in the WSC is based on a multiplicative formula (see reg 4.4.7), but as we all learned in high school, multiplying is equivalent to adding logarithms.

By appropriate scaling of logarithms, the chart above breaks down the various components of the multiplicative formula into additive points (black bars are negative numbers).

For example, on this system, in 2019 Eindhoven received a total of 67 points:

  • 100 points for completing all three stages
  • +12 points for an average of 2.6 people in the car
  • −53 points for 71.2 kWH of external energy
  • −0 points for no lateness
  • +8 points for a practicality of 93.1%

Lateness refers to arrival at stage stops after the “soft cutoffs,” which in 2021 will be Sat 15:30 in Tennant Creek, Mon 16:30 in Coober Pedy, and 11:30 Wed in Adelaide (there are also “hard cutoffs” leading to elimination, of 17:00, 17:00, and 14:00 respectively). According to reg 4.4.8, teams are ranked by the number of completed stages, and then by score.

In 2019 Minnesota received a total of 39 points:

  • 86 points for completing only one stage (thus also ranking after all the finishers)
  • +9 points for an average of 2 people in the car
  • −40.5 points for 25.7 kWH of external energy
  • −21 points for 165 minutes of lateness
  • +5.5 points for a practicality of 76.3%

Suppose a larger battery and a longer race had increased Minnesota’s external energy use to 128 kWH (an extra −20 points), but this had removed the lateness factor (an extra +21 points) and allowed achieving all three stages (an extra +14 points). Minnesota would then have been 15 points ahead, for a total of 54. This would have put them neck-and-neck for second place with Sunswift.

This example makes clear how the rules create an incentive for large batteries. It also highlights the difficulty of the second stage from Tennant Creek to Coober Pedy – I wonder if an extension to the “hard cutoff” is possible there?

Technical note: I am multiplying natural logarithms by 12.48 (so that 3020 gives 100), and I have also doubled practicality, and thus the total score (this doesn’t, of course, give practicality any extra weight). Sanity check for Eindhoven: 12.48 × ln(104×2) = 67.

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 36: Road Race Day 6 wrap

The American Solar Challenge have released official stage 3 timings, summarised in the chart above (click to zoom). Michigan and Western Sydney are only minutes apart. ETS Quebec / Eclipse is in third, and gaining, thanks partly to the brilliant tactic of finishing Day 3 just a few metres from the Stage 2 finish line in Lander. Given the battery impound rules, this gave them substantial additional solar recharging.

Although the American Solar Challenge is far from over, I’m already giving my “Most Improved Team Gem” award to ETS Quebec / Eclipse (team 101, formerly 92). ETS came 18th at WSC 2013 (completing only 1530 km), and 8th at ASC 2016 (after Michigan, Dunwoody/SER, Toronto, Missouri S&T, Principia, AppState, and PrISUm). With their car Éclipse X, however, I think they have reached the world top 12 level, along with teams like Toronto and Stanford. I really hope to see them at WSC again soon! And, it must be said, their compatriots in team 55 (Poly Montreal / Esteban) are not far behind them.

In the Cruiser (MOV) class, the “cactus” diagram above tells the story so far. For each car, the first coloured bar shows the number of person-kilometres (distance driven times the average number of people in the car). Penalties have reduced this person-kilometre amount, so my calculation of the average number of people in the car is a little off. The second coloured bar shows the external energy input, which is the number of charges (including the pre-race charge) multiplied by the battery capacity. This bar points downward, because large values are bad. The third coloured bar, which is the final score, is the first bar divided by the second (all bars are scaled so that the highest value is 100%). Minnesota and Onda Solare have been running on the same basis as the Challenger (SOV) cars – no external recharging during the race. This is an incredible achievement!

However, the regulations specify that Cruisers should arrive in less than 53 hours (dashed green line in the top chart), with time penalties if they do not, and with cars deemed to have trailered after 62 hours (dashed pink line). On performance to date, I estimate that Minnesota will arrive in 59.0 hours, and Onda in 59.7, which means that Minnesota’s score will be multiplied by 30%, and Onda’s by 23%. Onda can still win if they recharge from the grid and finish the race at 70 km/h or so. Eindhoven’s Stella Vie could do that, but I’m not sure that the Italian car can. They may have left recharging too late, having allowed Minnesota to dictate what kind of race was going to be run.

Western Sydney wins Stage 3, Michigan recharges (picture credits: 1, 2)

ASC 32: Road Race Day 4 (part 1)

Today the solar cars in the American Solar Challenge travelled to Lander, Wyoming (Michigan and Western Sydney clocked in yesterday already). As the map above shows, Lander is 48% of the way through the race (by distance) or 44% (by days). This is a good opportunity to see how the teams are going.

Tuesday morning, Day 4 (picture credits: 1, 2 3 4)

For the Cruiser (MOV) class, the “cactus” diagram below tells the story for Stage 1 (first two days). For each car, the first coloured bar shows the number of person-kilometres (distance driven times the average number of people in the car). All cars ran full. The second coloured bar shows the external energy input, which is the number of charges (including the pre-race charge) multiplied by the battery capacity. This bar points downward, because large values are bad. The third coloured bar, which is the final score, is the first bar divided by the second (all bars are scaled so that the highest value is 100%). Congratulations again, Minnesota!

For the race as a whole, Cruiser (MOV) scoring also includes speed and practicality components.

ASC 24: Track Race Wrap

CalSol, Waterloo, MIT, and SIUE on the track (picture credit)

Well, the Formula Sun Grand Prix or FSGP (the 3-day track race component of ASC) is over. I have updated my race information page and teams list with news and some pictures. To summarise the event, the chart below (in the colours of a Nebraska sunset) shows the total laps (after penalties) for each car (as with all images on this page, click to zoom). Teams which qualified for the road race are marked (with “P” indicating provisional qualification). The Russian team (89) had a rather slow car (not to mention that the motor eventually died), but they also received a large penalty (possibly for battery replacement?).

Some teams treated FSGP purely as a qualifier, while others went out hard to win it. Congratulations to Poly Montreal / Esteban (55) for being the winner, to Berkeley / CalSol (6) for coming second, and to Western Sydney University (15) for coming third! These will all be strong contenders in the road race (along with Michigan, who seem to have taken things fairly easy on the track). For the Cruiser (MOV) class, things are a little more complex, and are discussed later in this post.

FSGP 1st, 2nd, and 3rd (picture credit)

This chart shows the fastest lap speeds for each team. Western Sydney University (15) ran the fastest lap, at 80.5 km/h (50.0 mph):

And here is a revised (and, I think, final) teams poster, with the teams qualified for the road race marked in green:

For the Cruiser (MOV) class, the “cactus” diagram below tells the story. For each car, the first coloured bar shows the number of person-kilometres (basically the number of laps times the average number of people in the car). Cars mostly ran full (although PrISUm ran with only 2 people). Onda Solare (559) had less than 4 people in the car for a few laps (they also had technical problems, which is why they scored no laps on Day 3). As the first chart showed, Minnesota clocked up almost as many laps as the top 3 Challengers, which is why it has the tallest bar here.

For each car, the second coloured bar shows the external energy input, which is the number of charges (including the pre-race charge) multiplied by the battery capacity. This bar points downward, because large values are bad. And in the brilliant sunshine of Hastings, the Minnesota car refused recharge opportunities, drinking in the sun like the Challenger (SOV) cars. The third coloured bar, which is the final score, is the first bar divided by the second (all bars are scaled so that the highest value is 100%). The high lap count and low external energy input put Minnesota way ahead in the final scoring. Ultimately, this was due to the beautiful and efficient aerodynamics of their car. Third place was decided on AppState’s battery (11.025 kWh, compared to 15.876 for Waterloo).

Minnesota drinking in the sun (picture credit)

The road race for the Cruiser (MOV) class will be interesting. We will, I think, see more strategic refusal to recharge from the grid (which we have not seen at WSC), and we might see Minnesota, with its small (6.75 kWh) battery, struggle a little in the mountains. Anything can still happen!

Meanwhile, one more picture to say farewell to Hastings, Nebraska:

Illini, Western Michigan, and Esteban on the track (picture 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.

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)

ASC 8: About Cruiser Practicality

The American Solar Challenge Cruiser class is a contest for multi-person solar vehicles, each 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 on time, carrying as many people as possible, and drawing as little power from the grid as possible.

Cars are also scored partly on practicality. This can mean different things. Eindhoven’s 2015 car (Stella Lux), for example, was designed as a four-person family car, and the team took photos of it doing family things like shopping, going on holiday, and picking children up from school. A big feature was that, for an average family in the Netherlands, the car would produce more electricity than it used. The car scored 84.5 for practicality at the 2015 World Solar Challenge.

Eindhoven’s Stella Lux (photos: TU Eindhoven, Bart van Overbeeke 1, 2, 3, 4 – click to zoom)

Bochum’s 2015 car (ThyssenKrupp SunRiser), on the other hand, was a luxury two-person sports car, with leather seats and an incredibly beautiful interior. It was an almost perfect example of the car it was trying to be, and scored 80.5 for practicality (far higher than the next car, which scored 63.5).

Bochum’s ThyssenKrupp SunRiser (photo: Anthony Dekker)

One of the highest WSC 2017 Cruiser practicality scores went to PrISUm for their four-seat Penumbra, which was intended as the kind of practical SUV that you might take on a fishing trip. The car has plenty of room for carrying your esky, tackle box, etc. PrISUm deliberately made some aerodynamic compromises in order to achieve their practicality goal, and the car scored 79.8 for practicality at WSC 2017.

PrISUm’s Penumbra (composite image)

This year at ASC, PrISUm’s Penumbra is again a strong contender. Minnesota (UMNSVP), Appalachian State (Sunergy), and Waterloo (Midnight Sun) are entering two-person solar sports cars, while Onda Solare from Italy seems to be inspired by Eindhoven (see my annotated teams list). It promises to be an interesting field.