Mathematical Meme Madness Month #4

All done using R, of course (showtext and igraph packages).

Spoilers: A001349.


American Solar Challenge 2018: The run to Burns

I recently got my hands on the GPS tracker data for the American Solar Challenge last July. Above (for the 6 Challengers completing the stage) and below (for the Cruisers) are distance/speed charts for the run from Craters of the Moon to Burns, which seems the stage of the route with the best data (at this time of year I haven’t the time for a more detailed analysis). Click on the charts to zoom. Small coloured circles show end-of-day stops.

Stage times were 15:Western Sydney 8:05:16, 101:ETS Quebec 8:20:13, 2:Michigan 8:25:08, 55:Poly Montréal 8:42:52, 4:MIT 9:07:58, and 6:CalSol 9:30:12 for Challengers, and 828:App State 10:22:37, 559:Bologna 12:13:57, and 24:Waterloo 15:29:12 for Cruisers (note that Bologna was running fully loaded on solar power only, while the other Cruisers recharged from the grid).

The data has been processed by IOSiX. I’m not sure what that involved, but I’ve taken the data as gospel, eliminating any datapoints out of hours, off the route, or with PDOP more than 10. Notice that there are a few tracker “black spots,” and that trackers in some cars work better than in others. The small elevation charts are taken from the GPS tracker data, so they will not be reliable in the “black spots” (in particular, the big hill before Burns has been truncated – compare my timing chart).

Would y’all like to see a map?

The word y’all is used as a second person plural pronoun in the United States (although in my travels I have also heard it used as a polite singular). The map above (click to zoom) shows the average frequency of use by state, according to the 2003 Harvard Dialect Survey. The usage is primarily Southern.

English needs a second person plural pronoun, it seems to me. What do all-y’all think?

Image produced using the maps package of R. Other visualisations of the survey exist.

A Day in the Life of Solar Energy Racers

By special request, here is another day in the life post, this time for Swiss solar car team Solar Energy Racers (SER). The day is 29 September, the last day of the Sasol Solar Challenge. I am relying on information from a blog by SER strategy person Georg Russ, together with GPS data screen-scraped off the race tracker by a friend, and elevation data from the Shuttle Radar Topography Mission. As before, the horizontal axis of the chart represents distance.

The day began at Swellendam, and the team drove to the control stop at Bredasdorp, stopping there for 30 minutes the first time (it can be seen from the chart that SER was not quite so good as Nuon at maintaining a consistent speed). The team drove two loops, the first of them to Cape Agulhas (the southernmost point of the African continent, and the site of a picturesque lighthouse). It can be seen from the chart that they had to stop on the way (to repair a loose left rear wheel fairing – with duct tape, of course).

The team completed one more, shorter, loop, before heading on to the finish at Stellenbosch (Nuon drove that shorter loop three times). Knowing when to quit driving loops was an important strategy decision. The chart highlights the hilly nature of that final leg (going through part of the Cape Fold Belt), as well as some stops to change drivers.

Georg Russ notes an energy output for the day of 5.35 kWh (with 0.64 kWh recovered), and a photovoltaic input of 4.63 kWh, giving a net battery drain of 0.08 kWh. Pretty good!

A Day in the Life of Nuon Solar Team

This blog post is something a little different: it will use the GPS tracker data feed to describe a day in the life of Nuon Solar Team during the Sasol Solar Challenge. Specifically, it will describe Wednesday 26 September, which Nuon’s media team summarised in this 90-second video:

Wednesday 26 September (day 5 of the race) opened in Graaff-Reinet. On the Tuesday, Nuon had fallen 36 km behind Japanese team Tokai, due to electrical problems. The support engineers began work at 4:00 AM to return their car Nuna to tip-top condition. The morning was chilly, but sunny, which allowed some solar recharging of the batteries.

The plan for the day, as outlined in this livestream by media team-member Bianca Koppen, was to drive to the control stop in Jansenville faster than Tokai. At Jansenville there was an optional 65-km “loop” to Klipplaat and back. The plan was to drive this “loop” six times (Tokai was expected to do so only five times) and then continue to the end-of-day stop in Port Elizabeth, arriving there just before 5:00 PM. In line with this plan, Nuna sets off at around 85 km/h, soon overtaking Tokai:

The chart below (click to zoom) shows the progress of the day. The horizontal axis is distance, and the vertical axis of the main chart is the speed of the solar car. Underneath the main chart is an elevation plot. The letter A marks the start for the day.

The letter B marks the control stop at Jansenville, where Nuna initially stops for 30 minutes (as per the regulations; later stops will only be 5 minutes). Nuna then continues to the small town of Klipplaat, where the route simply loops and returns along the same road (see the map). However, the road to Klipplaat is uphill, and from Klipplaat is downhill. As the chart above shows, the shiny new “intelligent cruise control” adjusts the car’s speed to suit, running more slowly while climbing.

Point C on the chart is interesting. A few minutes into the 4th Jansenville–Klipplaat leg (shortly after noon), Nuon’s strategy team decides that the plan isn’t going to work. Either because of the weather, or the state of the car (I don’t know the reason), they decide that they will only drive five loops today, not six. The whole plan for the day is recalculated, so as to still get to Port Elizabeth just before 5:00 PM (but having used less energy). Instead of peaking around 87 km/h, the next two loops only peak around 70 km/h. The strategy team in the mission control (chase) vehicle must have been working furiously on this plan. On the chart, there is a sudden slow-down at 12:05 PM, but the new driving pattern is established just a few minutes after that. A good strategy team is critical to winning a race!

Point D on the chart marks the last stop in Jansenville, around 2:10 PM:

Race regulation 6.1 requires that a driver can operate the car for at most 2 hours. Given the distance to Port Elizabeth, Nuna stops briefly for a driver change at around 3:45 PM, shortly after this photograph was taken (point E on the chart):

And just before 5:00 PM, Nuna indeed reaches Port Elizabeth. After some more repair work, taking advantage of the energy saved during today’s run, and as the result of teamwork and skill, the plan to drive one more loop than Tokai succeeds the next day.

Of course, much more goes on during a typical day than this story suggests. People are feed and housed. Sick team-members are looked after. Media reports are produced. Nuna, go, go, go!

iESC Race Report #1

The iLumen European Solar Challenge (iESC) in Belgium has held the KO Chicane component of the event, under extremely wet conditions (see this!).

This component of iESC counts for 20% of final points. On mean times, Cruisers were 2.1 seconds faster in the Chicane than Challengers. The revised chart below (click to zoom) reflects the scoring (which, it must be said, has Bochum bringing home the bacon so far). Times shown are the best out of qualifying, semi-final, and final times. See also this excellent video.

Tomorrow is the big race. For fans at home interested in the weather, here is a webcam nearby, looking towards the Zolder racetrack. See also my iESC teams list and information page and the live timing board.


I’m off soon to Vanuatu for a holiday. Above (click to zoom) is a map of this island nation (produced using the raster package of R, with my own colour palette). The map outlines are from (which is missing an island, unfortunately). Elevation data is from the Shuttle Radar Topography Mission (with additional void fill using a lower-resolution dataset).

The overlay in red shows light visible at night (from NASA’s Earth at Night). Apart from the two main towns of Luganville and Port Vila, the active volcanoes on Ambrym and Tanna are clearly visible (take a closer look at Ambrym’s lava lake here).

Not highlighted is the active volcano on Ambae, an island which held 4% of the nation’s population until it was recently evacuated – consider helping the evacuees via Anglican Aid.