Anyone who attended the Bruce Springsteen concert at Ullevi Stadium in Gothenburg, Sweden, in 1985 will recall more than just good vibrations. During the star’s closing numbers, fans rocked the arena so hard that it needed millions of dollars’ worth of repairs. Now, engineers think they can estimate the impact of crowds in such situations — a method that could make stadiums, bridges, and other civil structures far more secure.

The forces of crowds on civil structures — known as crowd-induced loads — are a serious problem for designers. If loads get too high, a structure can visibly deform. Although the risk of collapse is usually small, people can panic and, in the worst cases, stampede.

Ideally, it would be possible to predict the maximum crowd-induced loads so that designers could introduce adequate safeguards. It’s easy enough to measure the load of a single bopping person —— simply ask them to jump up and down on some weighing scales. The difficulty comes in measuring people’s combined loads. You can’t simply extrapolate the time-varying load of a single person because of the “crowd effect”: People respond to a rhythm more precisely en masse than they do in isolation. Mathematicians know this type of synchronization leads to a big amplification of the maximum load — but quite how big, they can’t say.

Engineers Paolo Mazzoleni and Emanuele Zappa at the Politecnico di Milano in Italy have found a way to tackle the problem. They propose estimating the loads from people’s actual movements using digital video cameras. So long as you know roughly how massive the people are, and how much they are accelerating up and down, you can — via Newton’s equations — calculate their force on a structure beneath them.

Mazzoleni and Zappa tested their idea at the G. Meazza Stadium in Milan. They asked between one and eight volunteers to jump up and down on one of the stands in front of a video camera, following the beat of a metronome. The camera broke down the images into a grid so that the researchers could see frame by frame when each cell was filled or emptied by the volunteers’ movements. Having calculated the acceleration of the volunteers from this process, the team simply had to add up the volunteers’ total mass to estimate their combined jumping force — that is, their load on the stadium.