Writ

what the picture can say about itself

A skywriter writes in a flat plane three kilometres up, and the letters lie face down over the people who read them. Seen from above they are backwards. A retired skywriter put the rule as “Write upside down and backward, so the people on the ground can read it.” The page does the same: each word is laid out mirrored at 3,048 metres, where skywriters flew, and it reads from the beach.

The letters are Allen Hershey's, drawn in 1967 for machines that write with a single pen. The aircraft is a pen that cannot turn. At 50 metres a second and no more than 73 degrees of bank, its tightest turn has a radius of 76 metres, an eighth of a 600 metre letter, so every curve is flown as tight as the aircraft allows and no tighter. With the smoke on, it follows each stroke by steering at a point a little ahead of it on the line. With the smoke off, it flies from the end of one stroke to the start of the next by the shortest path a vehicle with that turning circle has, which Lester Dubins described in 1957: a turn, a straight line and a turn. Those are the loops you can see it make. A letter takes a little over a minute; the sources say sixty to ninety seconds, or two minutes.

I expected the pilot to have to break a third of the corners, where rounding them would spoil the letter. It broke none. Hershey had already lifted the pen at every sharp corner: his A is three strokes and his M is four. A plotter and an aircraft want the same thing from a letter.

The turn was the one number here chosen without a source, and the pilots said it was too gentle. Sixty degrees of bank is two g; skywriters who have said what they pull name three or four (Mark Sorenson) and four and a half to six (Nathan Hammond). Since 2 October the pilot pulls three and a half g, a bank of 73 degrees: it turns in 76 metres instead of 147, a letter takes about 67 seconds instead of 84, and the smoke keeps within 8 metres of Hershey's line where at two g it strayed by as much as 56. Three and a half is the middle of what they said, not anyone's own number; a working skywriter has been asked for his. The film and the card for this page were made with the two g pilot and are kept as its record. Both pilots also let the wind do the spacing: they stay in one spot and the wind carries each letter away, the way a typewriter's carriage moves the page. This pilot still travels with the air.

Then the air. The smoke is a line of puffs, each a small cloud with a size. The air around them is turbulence built the way Fung, Hunt, Malik and Perkins did it in 1992, from 132 random waves with the energy of Kolmogorov's spectrum. A puff is carried by the air averaged over itself, which removes the eddies smaller than the puff, and it grows by the law Lewis Fry Richardson wrote down in 1926 for the atmosphere between a metre and ten kilometres: the square of its size grows as the cube of time. Those small eddies are the ones the growth law stands for, so each is counted once.

The two ways a word dies are different. Turbulence bends a stroke before it widens it. In the air called fair here, two points a hundred metres apart drift about as far again in five minutes (measured: 109 metres; 57 in calm air, 197 in rough), so a letter goes crooked long before it goes soft. Measured on the first stroke of an H, the width that closes the letter up comes after 25 minutes in calm air, 11 in fair and 5 in rough. People who fly skywriting say a message lasts “about 10 minutes”, and anything from a few moments to twenty. The page opens on a calm day, which is the day skywriters wait for.

What this is not. The smoke's density, the lumps it leaves the exhaust in and its width as it leaves the aircraft's wake are chosen. The air is treated as the same in every direction; at this height it is stably layered, and eddies larger than some tens of metres are flattened, which is not modelled. The waves that make the turbulence do not carry the small eddies along with the large ones, and for that reason neighbouring puffs part at about a quarter of the rate real air would give them (measured here: 0.15 against the 0.5 to 0.57 found in real turbulence); the puffs' own growth carries the measured rate. The sea, the sand, the grain and the aircraft's shape are drawn. The sky's light is Preetham, Shirley and Smits's model of a clear afternoon, and the red filter is taken as the red of its colour.

Seven checks and five guesses were written down before any of the code existed. The one that failed as written was a check on the turbulence: I asked for Kolmogorov's constant as it is in endless turbulence, and this air has an edge at 400 metres. Against its own spectrum it is right to 1.2 per cent. The others held: the bank limit is never broken, no smoke is lost, the words read the right way round, a line of puffs spreads within a third of how one cloud would, and a fair-air word lasts inside the range skywriters give. Three guesses held and two were wrong: the corners, and how far the wind carries a word while it is written, which is two and a half letters (two, since the pilot pulls harder), not less than one.

When the pilot has no word from you, it writes the first ones. In 1922 Cyril Turner wrote “Daily Mail” over the Derby at Epsom in smoke from Jack Savage's apparatus, and later that year “Hello USA” over New York. An oil company's name was probably written days before. The title is from the stone in Rome where Keats asked to be remembered as one whose name was writ in water.

Keeping the frame saves the sky at 2,400 pixels, with a line beneath it naming the word, the air and the hour. With reduced motion the sky holds still, and a word you write is shown already written.

3,048 m · 50 m/s · bank 73° (3.5 g, since 2 October; 60° before) · turning radius 76 m · letters 600 m · Richardson g 0.55 · Kolmogorov C 1.58 · calm 1e-5, fair 1e-4, rough 1e-3 m²/s³ · a 24 mm lens · 17:00 on 18 July, 40.6° N