The Swinging Incense Burner of Santiago

Whosoever travels to Santiago de Compostela in North-West Spain, should not miss out on a visit to the cathedral. If you have luck - or have paid a considerable obulus - you will see how their famous incense burner, Botafumeiro, is set in motion and the huge church filled with the characteristic fragrance. The round burner, of height 1.6 m and of mass 80 kg (including incense) is not simply set swinging. Indeed, it usually requires eight men, the Tiraboleiros, using their united force to set it into a powerful pendulum motion.

The burner then careers at up to 70 km/h through the transept of the cathedral, thereby dragging behind it an trail of incense smoke. From one turning point to the other it travels 65m and attains each time a maximum displacement of 82 degrees. At this point, it is not all that far from the vaulting of the over-20m-high side nave.

The Tiraboleiros employ a simple mechanism. Physicists denote it as parametric stimulation, because thereby characteristic parameters of the system are periodically altered, in this case the length of the pendulum. The burner is attached to a long rope, which leads via a pulley fixed in the ceiling vaulting back again to the eight men. One of the participants deflects the burner slightly, displacing it into an oscillation of small amplitude. Subsequently, the Tiraboleiros do nothing more than pulling the connecting rope downwards with united force every time the burner passes through the lowest point of its trajectory. Thereby they lift it by about two meters each time. In order to be able to repeat this procedure periodically, they must afterwards then let it down again subsequently to its former height. The correct point in time is also decisive for this latter operation. The Tiraboleiros always loosen the rope exactly when the burner has reached its highest point.

This is all a bit reminiscent of a trick of Baron von Munchhausen. The main point is that the participants do not ever pull in the direction in which the burner is swinging. And actually they only vary the rope's length. Yet to this spectacular procedure lies at foundation a simple physical principle, which possesses a number of uses in the likes of mechanics or the strengthening of electromagnetic oscillation. If you want to execute it experimentally, you only require a string, on which you hang a ball or another heavy object. You lead the string over a hook in the ceiling - and already the mini botafumeiro is complete. To start off, jolt the thread a little or hit the pendulum body lightly. Subsequently you need only "pump", following the example of the Tiraboleiros - therefore pull at the right moment on the string and let it loose again a little later.

Ideally you need to pull exactly when the pendulum passes through the lowest point. At the turning points, you must loosen the rope again, so that the pendulum regains its original length. At the beginning when the deflection is still small, you might have difficulty coordinating the pumping at exactly the most suitable time and thereby exploiting every offered opportunity - twice per period. But you could lengthen the pendulum rope. As the periodic time increases with the pendulum length, you then have more time to react. The timing will also become easier by virtue of the growing displacement. The Tiraboleiros, on the other hand, need no further advice : they always pump twice per period, and after 17 pulls the pendulum reaches its maximum displacement.

Complete Energy Conversion

Why however do the variations of the rope length affect the energetic content of the pendulum at all? That only appears strange at first glance. Because the burner hanging on the rope is not just moving there and back. A second motion is overlaid on to this : the burner is simultaneously raised from a low point up to its turning point and lowered from there back again - even if it is via a sort of circular path. Therein lies the fundamental principle of the pendulum - when the pendulum body swings upwards, its entire kinetic energy is converted into potential energy, until it finally reaches the turnround. Then the potential energy converts gradually again into kinetic energy, until the pendulum body is maximally fast at its lowest point.

At the moment which the Tiraboleiros shorten the rope, they raise the Botafumeiro a little. So it can climb higher and above all further swing out further. If the men then let it sink again at the turning point, the increased amplitude is extensively retained. During the cycle - shortening of the pendulum at the lowest point and lengthening of the pendulum at the turning point - the amplitude also increases (trying to exceed the maximum displacement of $90^\circ$ will certainly provoke the collapse of the pendulum body).

Yet the Tiraboleiros do not simply set the invested energy free as soon as they let the burner sink back again. Only partly. By raising the burner, the men have not only to overcome the weight. Simultaneously they must raise the centripetal force which is directed to the suspension point, the force which keeps the pendulum body on its particular course. Otherwise, as an inertial body, the burner would move along a straight line - it only executes a circular path thanks to the force, which pulls it towards the suspension point in the church ceiling. This force increases with growing speed, so that by each pull the men must pull with greater exertion.

This they do each time at the most suitable instant, namely when both the speed and the centripetal force are maximum, at the lowest point of the pendulum. They must therefore indeed raise this greatest force, and transfer as much energy as is required for this lifting. During the lowering at the turning point, it is only the potential energy that is lost again (apart from frictional losses) while the energy procured during the overcoming of the centripetal force remains in the system.

What fascinates the visitor to the swinging incense burner so much, is less easy to answer. Possibly is it indeed the discrepancy between the simplicity of action and the power of the effect. Or maybe you sense here especially strongly what Michel de Montaigne already knew. The World is nothing other than an eternal swing.