Cycles

The Tropical Year: 31.6888 nHz

One of the most important cycles we live by is the tropical year, measured from equinox to corresponding equinox (or solstice to corresponding solstice). The tropical year lasts, on average, 365.2422 days (365 days, 5 hours, 48 minutes, 45 seconds), which means that it is an oscillation with a frequency of 31.6888 nanohertz (nHz). This is the cycle of the seasons.

Spring, summer, autumn, and winter are the conventional seasons, but the tropical year may be split up into more than or less than four seasons, and these need not be of equal length. In northern Australia, a frequent division is “the dry” (May to September), “the build up” (September to December), and “the wet” (December to April). Local Aboriginal people, however, may recognise as many as six seasons.

The Sidereal Year: 31.6875 nHz

A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the stars. This is the time that it takes for the sun to move through the “signs of the zodiac.” Because of the precession of the equinoxes, the sidereal year is 365.2564 days, which is about 20.4 minutes longer than the tropical year. As a result, ancient rules assigning dates to the signs of the zodiac are now completely wrong. The sidereal year corresponds to an oscillation of 31.6875 nanohertz.

The Synodic Month: 391.935 nHz

A synodic month is a cycle from new moon to new moon or full moon to full moon. This period actually varies by several hours, but it averages out to 29.530588 days (29 days, 12 hours, 44 minutes, 3 seconds).

In 432 BC, Meton of Athens noted that 235 synodic months (6939.7 days) is almost exactly equal to 19 years (6939.6 days). This period is called the Metonic cycle, and is used for predicting solilunar events such as the date of Easter.

The synodic month is also strangely similar to the average menstrual cycle (28 days), and this is reflected in the word (“menstrual” derives from the Latin mēnsis = month).

The Week: 1.65344 µHz

The week has an origin among the ancient Hebrews. It also has a Babylonian origin (the relationship between the two origins is unclear). The Babylonians related the 7 days of the week to the sun, moon, and 5 visible planets. They also related them to various gods. Our days of the week derive from the Babylonian week, via Greece and Rome: Sunday (Sun), Monday (Moon), Tuesday (Tiw, god of war = Mars), Wednesday (Woden = Mercury), Thursday (Thor = Jupiter), Friday (Frigg = Venus), and Saturday (Saturn).

Early Christians related the two week concepts together, pointing out that the day of the Resurrection (the day after the Jewish Sabbath) corresponded to the day of the Sun in the Roman system. The week corresponds to an oscillation of 1.65344 microherz.

The Sidereal Day: 11.6058 µHz

A sidereal day is the time that it takes the earth to rotate once around its axis. It often surprises people to discover that this time is 23 hours, 56 minutes, 4.1 seconds. It can be measured by the time to go from a star being overhead to the same star being overhead again.

The Solar Day: 11.5741 µHz

A solar day (24 hours, give or take some seconds) is the time from noon to noon. It is longer than a sidereal day because, while the earth is rotating around its axis, it is also moving around the sun. To put it another way, the sun is not a fixed reference point for the earth’s rotation. The difference between the sidereal and solar days mean that the stars seem to rise about 3 minutes and 56 seconds earlier every night.


Solar Challenge Morocco, Last Day

The five-day Solar Challenge Morocco is over. With sandstorms, flooded roads, and mountain passes having gradients of up to 12%, it was without a doubt the toughest solar car race in the world. Six Challenger Class cars competed (for details, see my illustrated teams list with social media links).

Solar Team Twente (NL, team 21) won the event (as well as winning the day, on adjusted timings). They were followed by:

In addition, Solaride, from Estonia, had the only Cruiser Class car, and raced in Adventure Class. The photograph in the graphic is from Solar Team Twente. Official results are here.


Solar Challenge Morocco, Day 4

Four days of the five-day Solar Challenge Morocco are over. Six Challenger Class cars are competing (see my illustrated teams list with social media links for details). Cars climbed to about 1,280 m today, before descending back to about 730 m. The conditions were also challenging, with roads awash with water.

Solar Team Twente (NL, team 21) holds their lead over Agoria Solar Team (KU Leuven, BE, team 8), with Vattenfall Solar Team (Delft, NL, team 3) in third place. The photograph is from Top Dutch. Official results are here.


Solar Challenge Morocco, Day 3

The Solar Challenge Morocco is ongoing, with the race running until 29 October. Six Challenger Class cars are competing (see my illustrated teams list with social media links for details). Cars climbed to about 1,280 m today, before descending back to about 700 m. The weather was also challenging, with clouds and sandstorms.

Solar Team Twente (NL, team 21) has taken the lead from Agoria Solar Team (KU Leuven, BE, team 8), with Vattenfall Solar Team (Delft, NL, team 3) in third place. The photograph is from Hans-Peter van Velthoven / Vattenfall. Official results are here.


Solar Challenge Morocco, Day 2

The Solar Challenge Morocco is ongoing, with the race running until 29 October. Six Challenger Class cars are competing (see my illustrated teams list with social media links for details). Cars climbed to about 1,690 m today, before descending to about 700 m. Some of the mountain roads had inclines of up to 12%.

Agoria Solar Team (KU Leuven, BE, team 8) is still in the lead overall, although Solar Team Twente (NL, team 21) finished first today. The photograph is from Sonnenwagen Aachen (DE, team 7). Official results are here.


Solar Challenge Morocco, Day 1

The Solar Challenge Morocco has begun, with the race running until 29 October. Six Challenger Class cars are competing (see my illustrated teams list with social media links for details). Cars climbed to about 1,850 m today, before descending to about 730 m.

Agoria Solar Team (KU Leuven, BE, team 8) is currently in the lead, followed by Solar Team Twente (NL, team 21), Vattenfall Solar Team (Delft, NL, team 3), and Top Dutch Solar Racing (NL, team 6). The photograph is from Agoria.


Solar Challenge Morocco begins

Scrutineering for the Solar Challenge Morocco has begun, with the race running from 25 to 29 October. Six Challenger Class cars are competing (see my illustrated teams list with social media links for details). The montage above (assembled from team instagram feeds) shows the cars:

That is one 4-wheel bullet car (Top Dutch), three 3-wheel bullet cars, and two 3-wheel asymmetrical catamarans. In addition, Solaride, from Estonia, has the only Cruiser Class car.

Update: qualification lap times were:

  • Top Dutch (NL, team 6): 02:17 (68.69 km/h)
  • Vattenfall (NL, team 3): 02:23 (65.81 km/h)
  • Agoria (BE, team 8): 02:25 (64.90 km/h)
  • Twente (NL, team 21): 02:30 (62.74 km/h)
  • Chalmers (SE, team 51): 02:45 (57.03 km/h)
  • Sonnenwagen Aachen (DE, team 7): car being repaired after an accident
  • Solaride (EE, team 1, Cruiser): –

Update: the route for the event is as follows (the map below shows elevation):

  • Day 1: Agadir to Zagora
  • Day 2: Zagora to Merzouga
  • Day 3: loop from Merzouga
  • Day 4: Merzouga to Zagora
  • Day 5: Zagora to Agadir

Vattenfall is presenting a delayed live feed of the race.


Dunsfold Solar Car Takeover


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

On 26th 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:


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)


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.