An English pig farmer at Low Moor Farm sued a hot air balloon company after a low-flying balloon caused 250 of his pigs to stampede into a ditch. The consequences were disastrous, and costly.

In April 2012, one of Go Ballooning’s sightseeing balloons flew low over the farm. The noise of the fire burners terrified the pigs, and the farm’s cattle broke through a fence and fled 200 yards into a nearby ditch. It was a carnage: three pigs died of heart attack, and 140 sows miscarried an estimated number of 800 piglets. The next days, a boar died due to related injuries.

Other than the actual bloodbath, this accident also had dire economic consequences for Low Moor Farm, whose business is based on pigs.

In the lawsuit that ensued, the central issue was to determine the actual height of the balloon when it flew over the farm, as it is against the law for a flying object to float at a height below 1,500 feet.

The first piece of evidence in the case was a photograph that the wife of a nearby’s farmer coincidentally took that day, depicting the balloon flying over the field. The second piece was a laser rangefinder owned by Low Moor farmer Mick Gilbank, which he used to determine the exact height of the trees.

Those pieces of evidence, however, did not reveal much—that is, until a mathematician tied everything together, using nothing but trigonometry. Professor Chris Fewster, who works in the Department of Mathematics at the University of York, demonstrated that the balloon had indeed floated as close as 300 mt. (less than 1,000 feet) from the pigs. Using a trigonometric formula which included information such as the length of the balloon, the focal length of the of the camera, and the height of the trees, he first calculated the tilt of the camera and then the distance of the balloon.

Trigonometry proved the farmer right, and GoBalloon had to pay  £40,000 in settlement.

“It’s the first time in 20-odd years of practice that I’ve had to use a maths expert,” the prosecuting lawyer told The Daily Mail.

Thank god trig finally came in handy. Here’s the formula that was used to calculate the tilt and angle that the camera was held to show how far the hot air balloon was from the ground:

form

[via Modern Farmer, The Daily Mail]