Dunsfold Solar Car Takeover

The Ardingly, Durham, and Cambridge cars, with the retired 747s on display at Dunsfold in the background (credit: Ardingly)

On 26^th September, the 4 active UK solar car teams (see this illustrated list) got together at Dunsfold Aerodrome, site for the BBC television series Top Gear. The teams are:

• Durham University Electric Motorsport 
• Cambridge University Eco Racing 
• University of Nottingham Solar Racing Team 
• Ardingly Ifield Solar 

The University of Nottingham team have previous experience with their sister project in the Formula Student competition. Their solar car is still being completed, but they showed off their racing car, Frankie (credit: UoN team)

During the day, the three solar cars ran slaloms and figure eights, and exchanged experiences in a spirit of friendly competition.

DUEM’s Ortus from the chase car (credit: DUEM)

At a time when Covid prevented the UK teams from participating in International competitions, this event did much to keep the solar car spirit alive, so I am glad that DUEM organised it.

Three solar cars and four teams (credit: DUEM)

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European Solar Challenge laps

Supplementary to my charts of iLumen European Solar Challenge results, the chart above shows lap timing during the race. Solid lines are Challenger class, while dashed lines are Cruiser class (Onda Solare won the Cruiser class on points). As in the 2020 event, key to Agoria’s success was stopping to recharge only once during the night. Also notice that Lodz covered 235 laps (943 km) in their Cruiser without stopping to recharge at all.

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European Solar Challenge results

The iLumen European Solar Challenge is over. Challenger Class results are shown above, and Cruiser Class results below. The heights of the bars show points allocated in the various categories. Twente was third overall on points in the Challenger Class, although a very close second in terms of laps (344).

A number of teams had some unfortunate problems, and the Cruisers from Eindhoven and PUT Solar Dynamics were not able to hit the track at all. For pictures, see team social media (see my list of teams) or iESC social media at        (click on the icons).

Update: see also this lap chart.

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European Solar Challenge begins

The iLumen European Solar Challenge is on again at Circuit Zolder (located roughly in the centre of the triangle formed by the nearby cities of Leuven, Eindhoven, and Aachen). The 24-hour track race starts at 13:00 on the 18^th, with sunset at 19:45 that evening and sunrise at 07:20 the next morning, and with the race continuing until 13:00 on the 19^th (see chart above). The race begins with a Le Mans-style start. The track is 4.011 km long.

For fans at home interested in the weather, check the forecast. Also, at the top of this page is a webcam nearby, looking west, towards the Zolder racetrack. This webcam is at the track itself (with a view of the “Kleine Chicane,” looking roughly north from just about the centre of the track). I have already posted a list of teams.

Follow the official race news feed and also social media at        (click on the icons). There is also a live timing board and tracker and a provisional results page.

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Solar cars in the UK

Here is a list of 4 active UK solar car teams. On 26^th September, Durham has invited all the UK teams to a friendly track race at Dunsfold Aerodrome, site for the BBC television series Top Gear. A sort of “Top Solar Gear,” I guess.

A retired 747-200, registration G-BDXJ, parked at Dunsfold Aerodrome – so it will be true to say that the solar cars will be faster than the 747.

20    Durham University Electric Motorsport 

Asymmetric challenger (Ortus) – Durham are the UK’s premier team. They have been upgrading their car after racing in Australia in 2019. They are one of the few teams to report a CdA value (0.107 for Ortus). They displayed great initiative by running their own Ouston Solar Challenge when Covid-19 prevented their travel to iESC 2020. They are currently engaged in a Solar Tour of the UK as an outreach activity, concluding with the Dunsfold event.

Previously, Durham came 27^th at WSC 15; participated at WSC 17; and came 14^th at WSC 19.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

12    Cambridge University Eco Racing 

Four-seat cruiser (Helia) – they will be staying in the UK this year, and attending the British Motor Show.

Previously, Cambridge came 22^nd at WSC 15; participated in the WSC 19 Cruiser class; and came 10^th at iESC 16.

 
Left: Nigel / Right: credit (click images to zoom)

23    University of Nottingham Solar Racing Team 

Cruiser (new team) – their rather radical approach is to modify a Renault Twizy to have solar panels, improved electrics, and second life Nissan Leaf batteries. They aim to participate at iESC 2022 with their first car.

photo: UoN team (click image to zoom)

43    Ardingly Ifield Solar 

Two-seat cruiser (Ardingly Solar Car) – this high-school team came 6^th in the 2018 iESC Cruiser class, and have upgraded the car since then. They also did a UK solar tour, and also attended the British Motor Show.

Previously, Ardingly participated in the WSC 15 Cruiser class; participated in the WSC 19 Adventure class; came 6^th in the iESC 18 Cruiser class; and participated at Albi Eco 19.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

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Solar cars: Belgium and Morocco

Here is a list of 17 European teams from 11 countries (including Turkey and Morocco) – 11 Challengers and 6 Cruisers – intending to race in two major upcoming solar car events in the region this year. These events are:

•   iLumen European Solar Challenge        (16–19 September): Aachen, Agoria, Onda, Bochum, Twente, SER, ITU, Eindhoven, Lodz, Chalmers, PUT, Solaris, and Cluj
•   Solar Challenge Morocco (23–29 October): Solaride, Delft, Top Dutch, Aachen, Agoria, Twente, Chalmers, and Mines Rabat

In other recent news, several new cars have been revealed, and there was a small solar car event in Sweden.

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1      Solaride  

Two-seat cruiser (new team) – this new team from Estonia has built a good-looking Cruiser. They are based in the city of Tartu.

picture credit (click image to zoom)

3      Vattenfall Solar Team (Delft) 

Three-wheel (outrigger) challenger (new car: Nuna11) – this year will be the last year that Delft partners with Vattenfall. Starting in 2022, Brunel will be their main sponsor. They have been recruiting for the 2022 Sasol Solar Challenge, and will also race in Morocco. Their new car features an asymmetrical top surface (to create more downforce on the left wheel), a new motor controller (suitable for hills), and a LiFePO₄ battery.

Previously, Delft won WSC 13; won WSC 15; won WSC 17; came 12^th at WSC 19; won SASOL 14; won SASOL 16; and won SASOL 18. Their team number (3) is a long-standing tradition.

 
Left: credit / Right: credit (click images to zoom)

6      Top Dutch Solar Racing 

Challenger (new car: Green Spirit) – they are hoping to race their new car in Morocco.

Previously, Top Dutch came 4^th at WSC 19 and came 3^rd at iESC 20.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

7      Sonnenwagen Aachen 

Three-wheel (outrigger) challenger (new car: Covestro Photon) – this team did very well in 2019, in spite of being blown off the road. They are excited about racing at Zolder again. They will race 2 cars at Zolder: the new car (7) and the previous car (70). In Morocco they will race as number 7.

Previously, Aachen participated at WSC 17; came 6^th at WSC 19; came 3^rd at iESC 18; came 5^th and 8^th at iESC 20; and came 2^nd and 6^th at iESC 21. Their usual team number (70) is the number they raced with in 2017.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

8      Agoria Solar Team / KU Leuven 

Three-wheel (tadpole) challenger (new car: BluePoint Atlas) – they have built a new car to defend their title. It is named after the Atlas Mountains. They are racing their previous car (BluePoint) at Zolder.

Previously, Agoria came 6^th at WSC 13; came 5^th at WSC 15; came 3^rd at WSC 17; won WSC 19; came 3^rd at Abu Dhabi 15; came 2^nd at iESC 16; came 6^th at iESC 18; came 1^st and 6^th at iESC 20; won iESC 21; and won Carrera Solar Atacama 18. Their team number (8) is a long-standing tradition.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

9    Onda Solare 

Four-seat cruiser (Emilia 4 LT) – they won the American Solar Challenge (Cruiser class) in 2018, and they have written up their design process here, but they have since made substantial improvements to the vehicle, including to the aerodynamics, suspension, battery, and solar panels. There is also an unusual open tail.

Previously, Onda came 10^th at WSC 13; participated in the WSC 19 Cruiser class; won the ASC 18 Cruiser class; came 10^th at Abu Dhabi 15; came 6^th at iESC 16; and won the iESC 21 Cruiser class. Their team number (9) is taken from the SS 9, the highway through Bologna, which was once the Roman Via Aemilia (hence also the name of their vehicle).

 
Left: credit / Right: credit (click images to zoom)

11    Hochschule Bochum Solar Car Team 

Two-seat cruiser (thyssenkrupp SunRiser) – for the 2019 World Solar Challenge, Bochum improved their sexy 2-seater SunRiser, which came 3rd in 2015. They also have a solar buggy team. Their current plans involve a hybrid solar-hydrogen vehicle, called SolaH2, based on a 2003 vintage Land Rover Defender 110. They will race two cars at Zolder (the SunRiser and the older SolarWorld GT as 11 and 42 respectively).

Previously, Bochum came 2^nd in the WSC 13 Cruiser class; came 3^rd in the WSC 15 Cruiser class; came 2^nd in the WSC 17 Cruiser class; came 4^th in the WSC 19 Cruiser class; came 3^rd, 4^th, and 5^th at iESC 16; came 2^nd, 3^rd, and 5^th in the iESC 18 Cruiser class; came 3^rd and 4^th in the iESC 21 Cruiser class; came 1^st and 7^th at Albi Eco 18; and came 1^st and 2^nd at Albi Eco 19.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

21      Solar Team Twente 

Three-wheel (tadpole) challenger (new car: Red Horizon) – they have built a three-wheeler this year, and will race both at Zolder and in Morocco. Their Zolder car will be their 2019 RED E.

Previously, Twente came 3^rd at WSC 13; came 2^nd at WSC 15; came 5^th at WSC 17; came 17^th at WSC 19; won iESC 16; came 1^st and 2^nd at iESC 18; came 2^nd and 4^th at iESC 20; and came 3^rd at iESC 21. Their team number (21) is a pun and a wish for success in the race (“Twente-One”).

 
Left: Anthony Dekker / Right: credit (click images to zoom)

31    Solar Energy Racers 

Challenger (new car: SER-4) – they raced their SER-3 in South Africa and Australia. However, they still have their SER-2, and will race that at Zolder again. They are also building a new SER-4.

Previously, SER came 5^th at WSC 13; came 15^th at WSC 19; came 2^nd at ASC 16; came 11^th at Abu Dhabi 15; came 3^rd at SASOL 18; came 8^th at iESC 16; and came 4^th at iESC 21.

 
Left: credit / Right: Anthony Dekker (click images to zoom)

34    Istanbul Technical University (ITU) 

Challenger (new car: Ariba X) – they discuss their plans here. They have built a new car to replace their older B.O.W.

Previously, ITU came 17^th at WSC 13; participated at WSC 17; came 7^th at iESC 16; came 7^th at iESC 20; and came 8^th at iESC 21. Their team number (34) is the vehicle license plate prefix for Istanbul.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

40    Solar Team Eindhoven 

Cruiser (new car: Stella Vita) – after building four “solar family cars,” their focus for 2021 is a Self-sustaining House On Wheels. They also took their Stella Era to Zolder, although they were prevented from racing.

Previously, Eindhoven won the WSC 13 Cruiser class; won the WSC 15 Cruiser class; won the WSC 17 Cruiser class; won the WSC 19 Cruiser class; came 7^th in the iESC 18 Cruiser class; and came 1^st and 2^nd in the iESC 20 Cruiser class. Their team number (40) is the Eindhoven telephone area code.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

45    Lodz Solar Team 

Four-seat cruiser (Eagle Two) – this team has some nice (Polish) news coverage here. They are working on improving their car.

Previously, Lodz participated in the WSC 15 Cruiser class; participated in the WSC 17 Cruiser class; participated in the WSC 19 Cruiser class; came 5^th at SASOL 16; won the iESC 18 Cruiser class; and came 2^nd in the iESC 21 Cruiser class. Their team number (45) is a tradition since 2015.

 
Left: Anthony Dekker / Right: credit (click images to zoom)

51      Chalmers Solar Team 

Three-wheel (tadpole) challenger (new car: Sköll) – they were the first Challenger-class team to reveal a render for their new car.

Previously, Chalmers came 21^st at WSC 19; came 5^th at iESC 21; and participated at Swedish Solar Race 21.

 
Left: credit / Right: credit (click images to zoom)

77    PUT Solar Dynamics (Poznań University of Technology) 

Two-seat cruiser (new team with car: Klara) – they have revealed their car, which weighs 750 kg and has an 18.5 kWh battery. This (Polish) video describes their project. Sadly, they had pre-race electrical problems at the Zolder racetrack.

 
Left: credit / Right: credit (click images to zoom)

77      Mines Rabat Solar Team 

Asymmetric challenger (new car: Eleadora 2) – they have worked hard to complete this car (see this video).

Previously, Mines Rabat participated at MSRC 19.

 
Left: credit / Right: credit (click images to zoom)

81    Solar Team Solaris (Dokuz Eylül University) 

Challenger (new car: S11) – they missed the last ESC, but are attending in 2021 with their new car.

Previously, Solaris participated in the WSC 13 Adventure class; came 25^th at WSC 15; came 18^th at WSC 19; came 9^th at iESC 16; came 7^th at iESC 21; came 2^nd at Albi Eco 18; and came 2^nd at MSRC 19.

 
Left: credit / Right: credit (click images to zoom)

99    TU Cluj-Napoca Solar Racing Team

Challenger (new team with car: SolisEV-1) – this is a brand-new team from Cluj-Napoca in Romania. They appear to have no online presence at all (although their institution does have a Formula Student team) but they are present at the track.

Previously, Cluj came 9^th at iESC 21.

public domain photo

This page last updated 18:31 on 29 September 2021 AEST.

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Head to head in Sweden

Right now, at Anderstorp Raceway in Sweden, Chalmers Solar Team ( ) and Halmstad University Solar Team ( ) are participating in the two-day Swedish Solar Race and display event (17–18 August). Here are the two cars (Sköll and Heart 4), each with three wheels. Both teams are building on their experience racing in Australia in 2019. I wish I was there!

 
Left: credit / Right: JU Solar Team (click images to zoom)

Update: Unfortunately, Halmstad University (HUST) had a battery fire. There was therefore no competitive race on the second day, and no live-stream.

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Fast Fibonacci numbers

There was some discussion on reddit recently of the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, 2,584, 4,181, 6,765, 10,946, 17,711, 28,657, 46,368, 75,025, 121,393, 196,418, 317,811, 514,229, 832,040, …) and efficient ways of calculating them.

One way of doing so is using numbers of the form a + b σ where  σ is the square root of 5. Multiplication of such numbers satisfies:

(a + b σ) × (c + d σ) = ac + 5bd + (ad + bc) σ.

We can define the golden ratio φ = (1 + σ) / 2 and also ψ = 1 − φ = (1 − σ) / 2, in which case the n^th Fibonacci number F_n will be exactly (φⁿ − ψⁿ) / σ. This is known as Binet’s formula.

We can use this formula to calculate Fibonacci numbers using only integer arithmetic, without ever evaluating the σ. We will have:

(2 φ)ⁿ − (2 ψ)ⁿ = (1 + σ)ⁿ − (1 − σ)ⁿ = 0 + p σ

for some integer p, and division by a power of two will give F_n = p / 2ⁿ.

I am using the R language, with the gmp package, which provides support for large integer matrices, and this allows us to use the relationship:

If we call this matrix A and calculate Aⁿ⁻¹, the first number in the resultant matrix will be the n^th Fibonacci number F_n. The following R code calculates F₁₀ = 55 using a combination of multiplication and squaring:

n <- 10

A <- matrix.bigz(c(
	1, 1,
	1, 0), 2)

p <- function(n) {
	if (n == 1) A
	else if (n %% 2 == 1) A %*% p(n-1)
	else {
		b <- p(n/2)
		b %*% b
	}
}

p(n-1)[1,1]

This same code will calculate, for example:

The time taken to calculate F_n is approximately proportional to n^1.156, with the case of n = 1,000,000,000 (giving a number with 208,987,640 digits) taking about a minute.

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Rods and cones in the human eye

I already posted these images (click to zoom) on Instagram. They illustrate the sensitivity to colour of the rods (lower right) and the three types of cones in the human eye. Cone sensitivity data is from CVRL.

Notice that red light is pretty much invisible to the rods. This is why red light does not interfere with night vision, and is used in e.g. this aircraft cockpit:

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Greenhouse emissions in Australia

I thought I would take the opportunity today to talk about energy production and greenhouse gas emissions in Australia. The chart below shows the populations (blue bars) and population densities of the six Australian states plus the Northern Territory. Note that New South Wales, Victoria, and Queensland have the highest populations (8.2, 6.7, and 5.2 million respectively), while the Northern Territory has the lowest. However, given its smaller area, Victoria has the highest population density (29.4 people per sq km), while Western Australia and the Northern Territory have the lowest population densities (1.1 and 0.2 people per sq km respectively).

The next chart shows the per capita electricity production of the six Australian states and the Northern Territory, by type. These figures are adjusted for net electricity transfer between states. For example, Tasmania imports some mainland coal-fired power.

Notice that the totals are high in the less densely populated regions (Western Australia and the Northern Territory). The total is also high in Tasmania, because of the widespread use of hydro-electrically produced electricity for heating there.

Total per capita electricity production is lowest in Victoria, in part because of the widespread use of natural gas for heating and cooking (total gas use in Australia generally is about 4 times its use in electricity production). Victorian electricity is the dirtiest, however, with heavy use of brown-coal-fired production. Brown coal is by far the dirtiest fuel; it produces about 47% more greenhouse gases per MWh than black coal, and triple the greenhouse gases per MWh of natural gas.

South Australia has achieved 50% renewable energy, but this is not without its problems:

• Wind and solar power are more expensive, so that South Australians pay about $360 per MWh for their electricity: 44% more than the two large states
• The sun does not always shine and the wind does not always blow: this means that, in the absence of massive-scale energy storage, South Australia has to “borrow” coal-fired power from the East, although this is eventually repaid with interest
• Solar and wind power cause substantial grid stability and grid synchronisation issues, which become very apparent at the 50% renewable level – good solutions are needed for this; South Australia currently copes by turning solar power off

To avoid “borrowing” electricity, massive-scale energy storage is required. South Australia would need several days worth of demand, at 40 GWh per day. Their famous Tesla battery has been expanded to a capacity of just 0.2 GWh, which is about a thousandth of what is needed. Batteries appear inadequate for energy storage at the required scale, and hydrogen storage is probably what we want.

Tasmania operates at a 92% renewable electricity level, thanks to multiple hydroelectric dams, which do not suffer from the problems of wind and solar (and availability is only an issue during lengthy droughts). In addition, hydroelectric dams can also provide energy storage for solar and wind power, simply by pumping water uphill. It is unfortunate that environmental groups in Tasmania have campaigned heavily against hydroelectric power.

The last chart shows the per capita CO₂-equivalent emissions for state electricity generation, plus other emissions (including agriculture, other energy use, industrial processes, waste, forestry, and land use change). Agricultural emissions are highlighted in green. A note of caution, however: the electricity generation data is for 2019, but the total greenhouse emissions are for 2018 (the latest I could find). These numbers cannot be compared to those of other countries, unless the numbers for other countries are equally recent and also include the full range of emissions, per UNFCCC standards (some comparable national averages are shown on the left).

Note that net greenhouse emissions for Tasmania are negative, largely due to tree-planting. Per capita emissions for the large, less densely populated areas are higher than those for New South Wales and Victoria; in part due to transportation requirements (shifting commuters and freight from road to rail would help here). Agricultural emissions per capita are particularly high in the Northern Territory, because the impact of cattle farming is being divided among a tiny population of just 0.2 million people. The overall Australian average of 21.2 tonnes per capita is quite significantly affected by the inevitably high emissions for the large, less densely populated areas. There is also the question of whether emissions due to mining and agriculture should be attributed to the producing country, or to the country of final consumption.

Economically and geographically, Australia is in many ways more like a Central Asian country than a European one, given its large size and its heavy reliance on mining and agriculture (Australia’s greenhouse emissions are comparable to those of Kazakhstan, which produces 21.7 tonnes per capita). However, progress could be made in Australia with more energy-efficient housing and transportation.

It should also be emphasised that, given its small population, Australia’s greenhouse emissions make a neglible contribution to the global and regional climate. If increasing atmospheric CO₂ has an effect in Australia’s region, that is due primarily to emissions by the large countries of the world, particularly China (which produces about a third of the world’s CO₂). Australia should, no doubt, reduce its greenhouse emissions, but whether Australia does so or not will make no measurable difference to the global or regional climate.

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