The potential energy of human towers

Roger Cabré

Physicist and researcher in the Department of Engineering, Electronics, Electrical and Automation of the URV.

Physics

The improvement in the quality and the quantity of the rehearsals, the fact that women are now taking part or new features such as passive safety have helped the world of human towers to break new ground in recent years. One of the milestones achieved is the 10-tier human tower: in 1998 the first 10-tier structure was erected and in 2015 the first 4 by 10 with a cover and shackles. The height and the weight of these massive human towers show how difficult they are. Have you ever wondered how much energy is required just to erect a 3 by 10 with a cover and shackles?

All the information and studies published to date indicate that this human tower is up to 11 meters high, with slight variations depending on the team erecting it. It requires at least 600 people to take part in the core, the cover, the shackles and the trunk.

It has been calculated that the structure of this human tower weighs about 7,000 kg, which is supported by the more than 500 people who are needed to make up the core. Of course, the upper tiers bear less weight: the lifter and the crowner bear 0 kg while the builders on the bottom tier have to bear almost 400 kg. This data has been provided by Manel Carbonell ("Què pesa un castell de 10?", Revista Castells, 2019), who gives us information about the load borne by each person in each tier.

By subtracting the weight borne by each tower builder in a tier from the weight borne by each builder in the floor immediately below, the average weight of the builders in a tier can be obtained. It can be calculated that the crowner and the lifter weigh 43 kg between them (21.5 kg borne by each of twos, according to Carbonell). Multiplying this weight by the number of people in each tier, we obtain the weight of the tier as a whole.

Jaume Roset (Manual de supervivència del casteller [A Tower Builder's Survival Handbook]) studied a 3 by 9 with a cover. He used a theodolite to measure the distance between the top of each tier and the ground with the following results: shackles (3.13 m), thirds (4.50 m), quarters (5.79 m), fifths (6.98 m), sixths (8.30 m), lifter (9.05 m) and crowner (9.35 m). Since we are analysing a 3 by 10 with a cover and shackles and not the 3 by 9 with a cover studied by Roset, we have added the shackles tier and assumed that it is the same height as the cover and the core, thus adding a further 1.57 m. From these data, we can obtain the height of each tier.

To calculate the accumulated energy in each floor, we need to take the average between the accumulated height of the heads on one tier and the tier immediately below. In this way, we obtain the height in the middle of each tier or, in other words, the height of the centre of mass of each tier (the stomach), which is what counts when calculating energies.

To finish, we have to calculate the potential energy of each tier. This is the energy that a mass has simply for being at a particular height. It can be found by multiplying the weight (mass) in kilograms by the height at the centre of mass in metres. The result is the energy measured in kilopond metres (kpm). In our case, we have summed the energies of each tier and we have distributed the total among the 25 members of the trunk and all the tower builders in the core, cover and shackles (c+c+s). If we multiply this energy by acceleration (g=9.81 m/s²), we obtain the energy in joules (J). And if we divide the energy in joules by 4.18, we obtain the energy in calories (cal). And if we divide it by 3,600 we obtain the energy in watt hours (Wh).

At this point, we can start to play with the results for a human tower such as the 3 by 10 with a cover and shackles by giving specific examples from daily life of what the energy data summarised in the tables above actually mean.

Firstly, we can see that the core, the cover and the shackles make a much greater contribution than the trunk, which is explained by the fact that there are many more people in these parts of the tower. And secondly, the energy in kilopond metres shows that the total energy of the human tower (38,458 kpm) would be able to propel a rock weighing 1 kilogram to a height of 38.5 km (that is to say, it would reach the stratosphere) or a rock weighing 1,000 kg to a height of 38,5 metres (almost as high as the cathedral in Pamplona).

If we think in terms of calories, the calculations show that the total energy of the structure of this human tower could be used to heat a litre of water to 90.26 degrees, almost boiling point. Finally, in terms of watts, a 3 by 10 with a cover and shackles generates the equivalent of 0.1048 kWh of electricity. At the current cost of a kWh (25 cents including 10% VAT) its energy would cost 2.6 cents.