One in Four and a Board
After the November gales the gutter on Saint Moling's is full, and Tomás Brennan, seventy-one, has put a 4.5 metre ladder against the wall with its foot two metres out. The parish assistant works out how much friction the foot needs (0.47 there, 0.24 at one in four) and asks for the one number nobody has, the shoe on the wet flags. A spring scale and a sandbag say 0.31 wet and 0.58 dry. The ladder goes to one in four, tied at the top, on a dry Saturday, and the assistant says plainly what none of its numbers cover.
Tomás Brennan had cleaned the gutter on the north side of Saint Moling's every November since 2009, and he had never yet been told how to stand a ladder, because nobody had thought he needed to be.
The gales of the first week had put an ash tree's worth of leaves into it. By Thursday the water was coming over the lip and running down the wall by the sacristy door, and the sacristan had put a bucket under it and a note on the door. Tomás was seventy-one. He had carried the old aluminium ladder round from the boiler house, a 4.5 metre one that weighed nine kilos, and leaned it against the wall with its feet on the flagged path, at the edge of the flower bed, because that was where the path was wide enough to stand it, and he had photographed it for the parish assistant, as the new volunteer rota asked him to do before any work at height.
"Thank you," said the assistant. "Before you go up, may I ask three things? How far out are the feet from the wall? How high is the gutter? And is the path wet?"
He measured it with the tape: two metres exactly. The gutter was four point two metres up. The path was wet; the flags were green at the edges.
"Here is what the picture tells me," said the assistant, "and then I'll tell you what it can't. A ladder with its foot two metres out and a length of 4.5 metres leans at about 64 degrees and reaches 4.03 metres up the wall. That's the first thing: the top is under the gutter, so you'd be stretching up to it from the top rungs. The second is the one I care more about. A ladder stays up because the floor pushes sideways on its feet as hard as the wall pushes on its top. How hard the wall pushes depends on how steep it is and where you are standing on it. For you at eighty kilos near the top, and the ladder at nine, the foot has to hold a sideways force of 0.47 of the weight on it. Not more than that, or it slides out from under you and comes down along the wall."
"It's never slid," said Tomás.
"I believe you. Dry flagstone and a rubber shoe may give you 0.6 or more, and then 0.47 holds. Wet and green, I don't know. That is the number I would like, and we can measure it today with what's in the boiler house."
He grumbled, but the boiler house had a spring scale, the kind a fisherman hangs a catch on, and four sandbags of twenty kilos from the flood winter. They did it on the Friday morning with Aoife Kearney, the sacristan's daughter, who was fifteen and had been told to hold the end of things. Tomás tipped the ladder on its side with the right-hand foot's rubber shoe flat on the wet flags, laid two sandbags, forty kilos, across the rail above it, and hooked the scale to the shoe. Aoife pulled it slowly, level with the ground, until the shoe moved. The scale read about 12.5 kilos at the moment it let go. They did it three times and wrote down 12, 12.5 and 13.
"Twelve and a half over forty," said the assistant, "is 0.31. That's the wet green flags. If you can sweep a patch and let it dry, do the same again."
On the Saturday morning the sun came out, and they did the same on the swept strip by the porch: 23 kilos, 23.5 and 22.5, which is 0.58.
"So," said the assistant, "this is where we are. At two metres out you need 0.47. The wet flags give 0.31. It would not hold, and it would not warn you: the first you'd know of it is the foot going. On the dry flags you have 0.58, and that clears 0.47 but not by much. That's too close to lean a life on, with a man stepping and reaching."
"Then I'll wedge it."
"You could. I would rather change the angle, because that changes the number itself. The rule in the ladder manuals is one out for every four up. At 4.36 metres up, that is 1.09 metres out; with the ladder you've got, the rest height is 4.36 and the foot is 1.12 metres out. The angle is 75.6 degrees and the same sum gives 0.24. So the foot needs 0.24, the dry flags give 0.58, and the wet flags 0.31: on the worst day, the thing holds with a margin of about a quarter, and on a dry one with more than twice what's needed."
Máire, the sacristan, had come to see what the two were doing with the sandbags. "It's the same ladder," she said. "How can moving the feet nine tenths of a metre change whether it falls?"
"Because the wall holds the top," said the assistant. "A steep ladder leans on the wall hard and on the ground mostly downward. A shallow one pushes the foot outwards and asks the ground to stop it. And I would add what my sums leave out, which is quite a lot. They treat the wall as perfectly smooth, which is cautious, but they say nothing about the top sliding sideways along the wall, and nothing about a man who leans out to the side. Friction at the foot is the failure I can put a number on. It's not the only one. So I'd tie the top to the eye bolt under the gutter, with a ratchet strap, before anyone climbs, and put the feet on the swept flags and not the green ones, with a board under them if you must use the green, and wait for Saturday, when the flags are dry."
"The gutter's at 4.2 and the ladder tops at 4.36," said Tomás. "I can reach it."
"At the right angle, standing at a height where your waist is under the top of the ladder, you can. And there's one more thing I will say once and leave with you. You are seventy-one. A fall from four metres is serious at any age, and a hired platform with a rail is about sixty euro for the day. I am not saying you shouldn't use the ladder. The parish can decide if the platform is cheaper than the risk. I only want that sum to be in front of you."
Tomás looked at the ladder for a while.
"Aoife stands at the foot," he said. "Not on the bottom rung. Holding it, with the ground between her feet."
"That helps a little with the sideways push, but it matters more as a second pair of eyes," said the assistant. "And the strap helps more than she does. If it's all right with you, I'd like her to be the one who checks the strap."
He cleaned the gutter on Saturday the eighth, between ten and twelve, with the foot at 1.12 metres, tied at the top, and Aoife counting the rungs aloud. He was not quick, and he did not come down with the first full bucket. He took the leaves down in a bucket on a rope.
On the Sunday it rained again. The water went down the downpipe and into the drain, and Máire took the bucket from under the sacristy door and put it back in the boiler house.
Tomás wrote the two numbers in the margin of the rota, in pencil, under the hire price. One in four. 0.31 wet, 0.58 dry. And under them, because the assistant had told him that he should and he had come round to it: Strap at the top. Not on a wet day.
He kept the sandbags in the boiler house for the next man to measure with.
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Written by Claude, an AI model made by Anthropic. The place, the church and the people are invented. The numbers are checkable. A ladder of length L leaning at angle θ on a smooth wall with a load W at a fraction f of its length and its own weight w at the middle needs a floor friction coefficient of at least (f·W + w/2) / (W + w) × cot θ. For 80 kg at the top (f = 1) on a 9 kg ladder that is 0.949 × cot θ: 0.47 at 63.6 degrees (foot 2.0 m out, rest height 4.03 m) and 0.24 at 75.6 degrees (foot 1.12 m out, rest height 4.36 m, a one-in-four ladder). The two friction figures are made up for the story, as are the scale readings; real shoes on real flags vary a great deal and a person should measure their own. The model ignores wall friction (cautious), sideways slip, wind and a person leaning out. No injury statistics are quoted because none are claimed.