Solar Racing Basics: Chassis

Click to zoom / Image credit: American Solar Challenge

Continuing the analysis of my Solar Racing Basics Poster (see this tag), solar cars have to keep their driver safe and the vehicle in one piece. There are two basic ways of doing this. First, a car can have a carbon-fibre-reinforced polymer body over a metal chassis. For example, Bochum’s thyssenkrupp blue.cruiser (below) is supported by a tubular frame of ultrahigh-strength steel. Second, a car can have a load-bearing “monocoque” body, possibly also of carbon-fibre-reinforced polymer. Carbon-fibre-reinforced polymer is strong for its weight, and this is significant, since a noticeable amount of energy in a solar car (though less than aerodynamic drag) is lost in rolling resistance. The rolling resistance of a car is proportional to its weight (it also depends on the quality of the tires), and so reducing weight makes the car faster. In 2019, the lightest solar car (from Western Sydney) weighed just 116.8 kg without the driver.

Cars may include a “roll bar” or “roll cage” to protect the driver in addition to the monocoque body. This “roll bar” or “roll cage” may be made of metal tubes, or it may also be made of carbon-fibre-reinforced polymer. A close look at unpainted carbon-fibre-reinforced polymer shows the “chequerboard” pattern of carbon-fibre “cloth” embedded inside transparent epoxy polymer (as in the body and roll bar of Durham’s Ortus, also below).

 
Click to zoom / Image credits: Anthony Dekker (Bochum’s thyssenkrupp blue.cruiser and the interior of Durham’s Ortus)

To read more, see see this post about car body and chassis by Nick Elderfield of the University of Calgary Solar Car Team, this Instagram post about composite materials by MIT Solar Electric Vehicle Team, and this UMNSVP wiki on Composite Chassis Design.

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Australia Day Honours, 2021

It’s Australia Day again, which means the annual Australia Day honours. Some recipients of note this year in the field of the sciences include:

• Emeritus Professor Cheryl Elisabeth Praeger, now a Companion of the Order of Australia (top left in photo: credit John Henstridge). Professor Praeger has published extensively in group theory and other areas of mathematics, and was the Inaugural Director of the Centre for the Mathematics of Symmetry and Computation at the University of Western Australia.
• Professor Mark Randolph, now an Officer of the Order of Australia (top right in photo: credit UWA). Professor Randolph is a geotechnical engineer specialising in foundation systems for offshore structures such as oil rigs, and has published extensively in that field, as well as holding important academic and other posts. He is a Fellow of The Royal Society.
• The Honourable Patricia Lynne (Trish) White, now a Member of the Order of Australia (bottom left in photo: credit @trishwhiteeng). Trish White has been an engineer, academic, government scientist, politician, cabinet minister, board member, company director, and National President of Engineers Australia.
• Dr Carden Crea Wallace, now a Member of the Order of Australia (bottom right in photo: credit Carden Wallace). Dr Wallace is an expert on corals, and has published extensively in that field, including her book Staghorn Corals of the World. She is also Emeritus Principal Scientist at the Queensland Museum.

Congratulations to all four of these outstanding Australians, and to the many others on the list.

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For another perspective:

• Top left: the Petersen graph is the smallest vertex-transitive graph which is not a Cayley graph. One of the many publications of Professor Cheryl Praeger AC constructs other such graphs.
• Top right: an oil rig (photo credit Ken Hodge). Professor Mark Randolph AO is an expert in their engineering, and a Fellow of The Royal Society.
• Bottom left: the headquarters of Engineers Australia (photo credit Bidgee). The Honourable Trish White AM is a past National President.
• Bottom right: a staghorn coral (photo credit Albert Kok). Dr Carden Wallace AM has written a definitive book on Staghorn Corals of the World.

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Cistercian numerals

Somebody recently pointed me at Cistercian numerals (above), an interesting base-10 numeral system used by Cistercian monks in the Low Countries and northern France from the 1200s to the 1500s (that is, after the Liber Abaci introduced Hindu-Arabic numerals to Europe, but apparently based on an older English system, not on that).

Most extant uses of the system relate to dates and item numbering, rather than arithmetic. This online conversion tool will let you experiment with the system. It is interesting to note the relationships 5 = 4 + 1, 7 = 6 + 1, 8 = 6 + 2, and 9 = 8 + 1 = 7 + 2 = 6 + 2 + 1.

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Solar Racing Basics: Electrics

Click to zoom / Image credit: Anthony Dekker (first two), mostdece.blogspot.com (battery & motor)

Continuing the analysis of my Solar Racing Basics Poster (see this tag), solar racing cars are powered by the sun (and, in the Cruiser class, also by some external recharging at Tennant Creek and Coober Pedy). The major components of the electrical system include:

• Silicon solar panels, up to 4 square metres in size for the Challenger class and 5 square metres in size for the Cruiser class. These will convert between about 20% and 25% of the sun’s energy into electricity, giving a maximum power level similar to that of a microwave oven.
• A maximum power point tracker or MPPT (like this one) and other high-voltage electronics which will control the voltage and current of the panels (or of sections of panel individually) in order to give the maximum power output possible under different sunshine conditions.
• A battery pack, made up of lithium-ion, lithium polymer, or lithium iron phosphate cells connected together (the first two kinds can catch fire if charged or discharged incorrectly; the third kind is safer, but twice as heavy). These battery packs are quite complex, including electronics to control charging, sensors to detect problems such as overheating, and cooling fans. Typically the total voltage of the battery pack is around 100–150 volts.
• An electric motor. The most efficient solution is usually to mount a motor in one or both of the back wheels (often using a design developed by the CSIRO). This avoids wasting precious energy in gears or a transmission. The motor will also do “regenerative braking,” sending power to the battery as the car slows down.
• A motor controller which controls the speed of the motor. This is in turn controlled by the throttle or accelerator pedal.

 
Click to zoom / Image credits: Anthony Dekker (Twente’s RED Shift showing solar panel, 2017), mostdece.blogspot.com (battery from team SunSpec, 2015)

To read more, see this IEF Solar Car Conference presentation on the same subject or this page on electrical systems in the Solar Car Wiki.

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2 + 2 = 4 and mathematical models

One of the strangest aspects of 2020 was a number of people arguing that 2 + 2 = 4 wasn’t necessarily true, and that it might be the case that 2 + 2 = 5. In fact, 2 + 2 = 4 is not only true throughout the universe, it is true in every possible alternate universe as well. A great many silly arguments were made by people trying to defend 2 + 2 = 5. But there is a deeper response here that relates to how applied mathematics works, and a few people have been trying to express that.

In general, applied mathematics questions have the form A → B, where A is some real-world situation, and B our desired but unknown answer. We abstract our real-world situation A to the mathematical object X, so that X → Y is the mathematical analogue of our real-world A → B. Mathematical questions have clearly-defined answers (although finding them is not always easy). We can then take our mathematical answer Y and reverse-translate it to the real world, giving something that we claim is a good approximation to B.

In the mathematical world of X and Y, everything is crisp and clear (and 2 + 2 = 4). In the real world, things are messy and ill-defined. Furthermore, in going from A to X we introduce simplifications and approximations which may mean that the mathematical answer Y is not “fit for purpose.”

For example, our real-world question might be “what is the distance from Melbourne to Sydney?” There are three ambiguities here: What is “Melbourne”? What is “Sydney”? And what is “distance”?

The conventional location marker for the city of Melbourne, Australia is the Old Melbourne General Post Office (now a shopping centre, at 37°48′49″S, 144°57′48″E). Likewise, the conventional location marker for the city of Sydney is the Sydney General Post Office (at 33°52′4″S, 151°12′27″E). Let’s use those coordinates. But what is “distance”? If “distance” means “as the crow flies,” then a simple answer might be to find the great-circle distance on a sphere approximating the Earth (let’s use the equatorial radius of 6,378.137 km). This distance can be calculated fairly easily as 714.2 km, which might be a close enough answer for many purposes.

A better mathematical model might be distance on the WGS reference ellipsoid model of the Earth. This gives the slightly lower value 713.8 km (according to Google Earth or raster::pointDistance).

Alternatively, “distance” might mean “by road,” in which case we need a computer representation of Australia’s road network. For this question, Google Maps reports a distance of 878 km via the M31. The expected travel time by car (9 hours and 7 minutes when I looked) might be even more useful.

It may therefore be the case that out of various mathematical answers Y, many are not “what you wanted.” But that failure to abstract correctly does not invalidate the mathematical truths involved in X → Y. In particular, it does not invalidate 2 + 2 = 4. It just means that you picked up the beautiful crystal knife of mathematics and cut yourself with it.

As Korzybski liked to say, “the map is not the territory.”

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No, it is not true that 2 + 2 = 5

The year 2020 was an unusual year. One of the strangest aspects was a number of people arguing that 2 + 2 = 4 wasn’t necessarily true, and that it might be the case that 2 + 2 = 5. This is an idea that had been mentioned by George Orwell in his dystopic novel 1984:

“All rulers in all ages have tried to impose a false view of the world upon their followers, but they could not afford to encourage any illusion that tended to impair military efficiency. So long as defeat meant the loss of independence, or some other result generally held to be undesirable, the precautions against defeat had to be serious. Physical facts could not be ignored. In philosophy, or religion, or ethics, or politics, two and two might make five, but when one was designing a gun or an aeroplane they had to make four. Inefficient nations were always conquered sooner or later, and the struggle for efficiency was inimical to illusions.”

In fact, 2 + 2 = 4 is true regardless of your culture or your skin colour (although you might represent the fact using an alternate set of symbols, like 二 + 二 = 四). If there are aliens out there, it is true for them too. What’s more, 2 + 2 = 4 is true in every possible alternate universe as well as in this one.

Some defenders of 2 + 2 = 5 have appealed to modular arithmetic, and (to take one example) modulo 3 we have 2 = { −1, 2, 5, … } and 1 = { −2, 1, 4, … }, using overbars to distinguish congruence classes from integers (in order to be precise). Consequently, 2 + 2 = 4 = 1. However, we never get 2 + 2 = 5 in such systems, other than in the trivial case where all integers are equivalent (the proof of this is actually quite straightforward). We certainly do not get 2 + 2 = 5.

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Solar Racing Basics: Aerodynamics

Click to zoom / Image credit: Anthony Dekker (top three), Agoria Solar Team (wind tunnel)

Continuing the analysis of my Solar Racing Basics Poster (see this tag), perhaps the most important issue in solar car racing is aerodynamic efficiency. In the Challenger class, average power is limited by the size of the solar panel to about that of a microwave oven. This is about one hundredth of the engine power in a typical small car.

Solar cars must therefore eliminate as much aerodynamic drag as possible. Aerodynamic drag is the most important limiting factor on speed.

The aerodynamic drag force, which is given by the formula F = ½ C_d A ρ v², acts to slow the car down. At maximum speed, the drag force (plus also other factors) exactly balances the force of the motor, which of course acts to speed the car up. In the formula, v is the speed, C_d is the drag coefficient, A is the frontal area of the car, and ρ is the density of air (which we can’t change).

If F_max is the maximum force that the motor can deliver, then the maximum speed is given by rearranging the formula: v_max = sqrt (2 F_max / (C_d A ρ)). One way of speeding up the car is by making the shape more aerodynamic (that is, by reducing C_d). Challenger class teams should be aiming at drag coefficients C_d under 0.1. In the Cruiser class, values under 0.2 would be appropriate (for comparison, C_d in ordinary cars ranges from 0.25 for a modern streamlined sports car to 0.6 for an SUV).

 
Click to zoom / Image credits: Anthony Dekker (Electrum from Michigan, Green Lightning from Top Dutch)

We can also speed up the car by making it narrower (that is, by reducing the frontal area A). In 2019, the 1-metre-wide Electrum from Michigan finished ahead of the 1.2-metre-wide Green Lightning from Top Dutch, in spite of having had problems (79.6 km/h compared to 78.4 km/h). On the other hand, if you make the car too narrow, it will roll over (which means that the car fails pre-race scrutineering). Alternatively, we can reduce the frontal area A by making a “gap” for the air to flow through. If we can make both the drag coefficient C_d and the frontal area A one sixth of the values for a typical small car, then we can travel at 60% of the speed of that car, even though we have only one hundredth of the engine power.

In the past, successful Challenger class designs have included:

• Catamarans: double hulls, one of which holds the driver, held together by a “wing” on which the solar panel is fixed, with a “gap” between the hulls (this design has won every race since 4 wheels were made mandatory in 2013)
• Monohulls or “bullet cars”: long, narrow cars with a tapering rear like Electrum or Green Lightning (this design came second in both 2017 and 2019)
• Outriggers: like monohulls, but with the wheels outside the main body and more widely spaced for stability (this design has not performed quite so well, because of aerodynamic drag from the wheels)

Three wheels are now allowed in 2021. This allows slightly better monohulls (with two wheels inside the front of the body and one wheel just inside the tapering rear of the body). It also allows noticeably better outriggers (only two wheels need to be outside the main body). In addition, there are a number of new designs that teams have been thinking feverishly about for several months.

 
Click to zoom / Image credits: Anthony Dekker (a catamaran and an outrigger car, both Swedish)

During design, aerodynamics is typically assessed using computational fluid dynamics software, but “ground truth” is a wind tunnel or an actual race. In the illustration on the poster, Belgian team Agoria is using a green laser to reveal airflow around their car in a wind tunnel (see also the video here).

To read more about aerodynamics, see this brief post from 2018, this 2015 Solar Car Conference presentation, and this 2021 Solar Car Conference presentation from Durham.

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Vesper Flights: a book review and reflection

Vesper Flights by Helen Macdonald

I have been waiting eagerly for a copy of Vesper Flights by Helen Macdonald. If you have read my review of her H is for Hawk, you will understand why. Early reviews of the new book were also positive – “powerful essays,” said The Guardian; “soul-stirring,” said USA Today; “a beautiful and generous book,” said npr. The Goodreads community gave it 4.2 out of 5.

I was fortunate enough to get a copy of Vesper Flights for Christmas. It is a collection of 41 essays, and Helen Macdonald writes “I hope that this book works a little like a Wunderkammer. It is full of strange things and it is concerned with the quality of wonder.” Many of the essays have an autobiographical component. Several moved me to tears.

A Wunderkammer painted by Domenico Remps around 1695 (click images in this review to zoom)

The essays in the collection are:

1. Nests – a reflection on bird’s nests
2. Nothing Like a Pig – coming face-to-face with a wild boar
3. Inspector Calls – a beautifully written and touching account of an autistic boy meeting a parrot
4. Field Guides – a visit to Australia, and praise for field guides

The hairpin banksia gets a mention in essay #4

5. Tekels Park – reminiscences of a childhood spent among nature in Tekels Park
6. High-Rise – a wonderful account of the surprising amount of life that can be found in the night-time sky
7. The Human Flock – about migration
8. The Student’s Tale – about a refugee
9. Ants – about nuptial flights in ants

A winged queen ant (photo credit)

10. Symptomatic – about migraines and impending doom
11. Sex, Death, Mushrooms – “Many toxic fungi closely resemble edible ones, and differentiating each from each requires careful examination, dogged determination and often the inspection of spores stained and measured under a microscope slide.”
12. Winter Woods – walking through woods in the winter
13. Eclipse – an eclipse is an emotional experience
14. In Her Orbit – with Nathalie Cabrol in the Atacama Desert, site of the now-defunct Carrera Solar Atacama (this chapter is based on a New York Times article)

San Pedro de Atacama, Chile (photo credit)

15. Hares
16. Lost, But Catching Up
17. Swan Upping – swan upping on the Thames as social commentary
18. Nestboxes – are they for the birds, for us, or both?
19. Deer in the Headlights – this essay highlights the problem of deer-vehicle collisions (the UK gets about 1 per thousand people per year); Australia has a kangaroo-vehicle collision problem of similar magnitude, but that issue is perhaps viewed a little differently
20. The Falcon and the Tower – about urban peregrine falcons, specifically in Dublin (see also this short documentary film)

The towers of the decommissioned Poolbeg Generating Station in Dublin, with a magnification of the western (leftmost) tower. These towers, around 207 m high, are home to the peregrine falcons described in essay #20 (photo credit)

21. Vesper Flights – the central and title essay, based on a New York Times article, is about swifts
22. In Spight of Prisons – all about glow-worms, Lampyris noctiluca
23. Sun Birds and Cashmere Spheres – golden orioles and bearded reedlings
24. The Observatory – “a swan had come towards me and offered me strange
    companionship at a time when I thought loneliness was all I could feel.”
25. Wicken – Wicken and other fens, which I imagine inspired the home of Puddleglum in the Narnia stories

A hide at Wicken Fen (photo credit)

26. Storm
27. Murmurations – “Words to accompany Sarah Wood’s 2015 film Murmuration x 10”
28. A Cuckoo in the House – about cuckoos and the man who inspired the character ‘M.’ Yes, that ‘M.’
29. The Arrow-Stork – the arrow-stork and the study of bird & animal migration
30. Ashes – on tree diseases
31. A Handful of Corn – as a famous song says: “Come feed the little birds, show them you care, and you’ll be glad if you do; their young ones are hungry, their nests are so bare, all it takes is tuppence from you.”

32. Berries
33. Cherry Stones
34. Birds, Tabled – a fascinating exploration of the morality of bird-watching versus bird-keeping and the class conflicts involved (a number of reviewers online have taken issue with this chapter, specifically)
35. Hiding
36. Eulogy
37. Rescue – a beautiful account of bird rescue and wildlife rehabilitation
38. Goats
39. Dispatches from the Valleys – a heavily autobiographical chapter, raising all kinds of spiritual questions (but not really answering them)
40. The Numinous Ordinary – “I kept trying to find the right words to describe certain experiences and failing. My secular lexicon didn’t capture what they were like. You’ve probably had such experiences yourself – times in which the world stutters, turns and fills with unexpected meaning.”
41. What Animals Taught Me – “When I was a child I’d assumed animals were just like me. Later I thought I could escape myself by pretending I was an animal. Both were founded on the same mistake. For the deepest lesson animals have taught me is how easily and unconsciously we see other lives as mirrors of our own.”

Not surprisingly, about half the chapters in this book are about birds, in some way or other:

At its best, this book is as good as the superb H is for Hawk, but is not consistently so (indeed, it scarcely could be). While some of the chapters are truly wonderful, others have a moralistic tone that I thought was a little more heavy-handed than it needed to be, and which became a little repetitive after a while. In the last chapter Helen Macdonald offers a corrective: “These days I take emotional solace from knowing that animals are not like me, that their lives are not about us at all.” Or, as C.S. Lewis once put it:

“Come out, look back, and then you will see … this astonishing cataract of bears, babies, and bananas: this immoderate deluge of atoms, orchids, oranges, cancers, canaries, fleas, gases, tornadoes and toads. How could you ever have thought this was the ultimate reality? How could you ever have thought that it was merely a stage-set for the moral drama of men and women? She is herself. Offer her neither worship nor contempt. Meet her and know her. If we are immortal, and if she is doomed (as the scientists tell us) to run down and die, we shall miss this half-shy and half-flamboyant creature, this ogress, this hoyden, this incorrigible fairy, this dumb witch.”

Helen Macdonald has a genuine talent for showing the reader what she saw, and the reader of a book like this will feel appropriate things in that situation. Perhaps the more moralistic tone is the inevitable, and possibly appropriate, nature of an essay written for a newspaper or magazine. The fact that this book is a collection of such essays would then explain why it feels a little repetitive at times.

My recommendation: buy this book, but only read a few chapters each week. And think about them.

Vesper Flights by Helen Macdonald: 4 stars

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That Russian Cyberfarm video

This fantastic Russian video by birchpunk has taken the world by storm. I thought I’d collect up some highlights (see also the screenshots below).

• 0:00, QR code: this goes to the Twitter profile of Dmitry Rogozin, the Director General of Roscosmos.
• 0:28, Izhevsk Dynamics Corporation: a play on Boston Dynamics, but one of the factories in the city of Izhevsk was responsible for the AK-47.
• 0:42, We don’t need them: an apparent Back to the Future 2 or 3 reference.
• 0:44, We suffer from air turbulence: that is what the road sign says.
• 0:50, Two years by Post of Russia: Russian Post has a reputation for delays, although of course they are justified in this case. The dropping parcels may be a reference to incidents like this one.
• 1:06, We took it apart for металлолом (scrap): may be a reference to incidents like this one.
• 1:08, Cyberfolk song: see this subtitled version.
• 1:38, Poster: the poster shows the face of Dmitry Rogozin and says “Let’s Make the Red Planet Green.”
• 2:39, РАССАДА ERROR: something is wrong with Nikolay’s seedlings.
• 2:46, Fractal cucumber: fractals are a real thing, and some strange conjoined cucumbers exist, but this is one of my favourite flights of fancy.
• 2:58, Genetically modified: this is kombucha, which was popular in Russia long before it became a fad in the West.
• 3:31, We have Netflix: notice the two moons, this one and that one.
• 3:45, But network is not so good: I haven’t heard that dial-up modem sound in years.

Oh, and don’t miss the New Year Special sequel.

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Solar Racing Basics: Classes

Click to zoom / Image credit: Anthony Dekker (top), Solar Team Eindhoven (bottom)

Beginning the analysis of my Solar Racing Basics Poster (see this tag), there are two main classes in the World Solar Challenge. The Challenger class is easiest to understand: highly aerodynamic single-occupant cars scored only on the time taken for the race from Darwin to Adelaide (with no external charging allowed, other than an initial full battery). The Challenger class cars show us the limits of what current technology can achieve.

The Cruiser class consists of more realistic multi-occupant cars, with proper doors and interiors. Some teams field two-seater cars, and some four-seater “family” cars. The Cruiser class cars show us options for what commercial solar cars might look like. Cruisers are scored on distance travelled, time taken, passengers carried, external charging along the way (if any), and “practicality” judging. A rather complex formula combines all those factors. To read more about Cruiser class scoring, see my previous posts:

• A simplified view of Cruiser scoring
• 2019 Cruiser scoring

 
Click to zoom / Image credits: Anthony Dekker (Challenger class car from Agoria and Cruiser class car from Eindhoven, both winners in 2019)

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