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)


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MODSIM Conference, Day 1

I am attending the MODSIM International Congress on Modelling and Simulation in Hobart, Tasmania. It promises to be another great event.

I spoke today on “Sampling bias and implicit knowledge in ecological niche modelling.” Out of the many interesting talks I listened to, one that stands out is “The Waroona fire: extreme fire behaviour and simulations with a coupled fire-atmosphere model” by Mika Peace. It introduced me to “pyrocumulonimbus clouds,” and some of the complex weather–fire interactions in severe bushfires. This is certainly a phenomenon that needs to be better understood.


Angélique du Coudray, pioneer midwife


Angélique du Coudray

Angélique du Coudray (c. 1714–1794) was a pioneering French midwife. In 1759 she published a midwifery textbook, Abrégé de l’art des accouchements. Her introduction notes the fact that incompetence or lack of care can lead to the death of both mother and child, and continues with a politico-religious imperative: “Ignorons-nous que ces deux viâimes étoient chères aux yeux de Dieu, utiles à leur famille, & nécessaires à l’État? C’étoit un dépôt qui nous avoit été confié. Pouvons-nous, en les sacrifiant à un vil intérêt, ne pas trembler sur le compte exact que nous en rendrons un jour à celui qui leur avoit donné l’être?” (“Do we not know that these two lives were dear to the eyes of God, useful to their families, and necessary to the State? They were a deposit which was entrusted to us. Can we, if we sacrifice them to a vile interest, not tremble at the exact account that we shall one day render to Him who gave them to be?”).

To avoid such deaths, du Coudray explains proper prenatal care, and provides instruction on both normal deliveries and a range of common obstetric problems.


Illustration of a normal delivery, from the 1777 edition of Abrégé de l’art des accouchements

Also in 1759, Angélique du Coudray was commissioned by King Louis XV to tour the country training midwives, in the hope of reducing perinatal mortality. She personally trained thousands of midwives, many of whom went on to train others. Her training course was assisted not only by her book, but also by her Machine, a pioneering lifesize obstetric simulator. The Machine included realistic internal structure, such as bones and ligaments, and could be used to practice delivery of a baby in a range of different positions, while giving the trainee midwife a feel for the forces involved.


Angélique du Coudray’s Machine (photo: Ji-Elle)


MODSIM Day 1: Honeybee Colony Collapse

The MODSIM 2015 International Congress on Modelling and Simulation opened today with a plenary talk by Mary Myerscough on honeybee colony collapse disorder. The talk was based on work published in PLOS ONE and in PNAS.

Mathematical modelling strongly suggests that the problem is caused by the death of foraging bees. The colony reacts by drafting younger hive bees into the foraging role. This strategy works well as a response to short-term problems but, since younger bees are less effective foragers, it sets up a positive feedback loop which can cause colony collapse. What is worse, the signs of impending collapse are subtle, being reflected only in the number of adult bees.

This interesting talk also provided a wonderful answer to the perennial question “how is mathematics useful?” The mathematics was accessible to anyone who could understand differential equations, and the problem was accessible to anyone at all. And, because of their role as pollinators, bees are very, very important.


World Solar Challenge: Team 23

23  Kecskemét College Faculty of GAMF (MegaLux)

The team from the Faculty of Mechanical Engineering and Automation at Kecskemét College are first-time participants in the WSC this year. Their car (above) has a really cool steering wheel (below). Hopefully, it is very fast as well!

The team have also developed this fantastic simulation model of the car in action. Good luck, team 23!

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