O Botafumeiro: parametric pumping in the Middle Age

The pendular motion of a giant censer (O Botafumeiro) that hangs in the transept of the cathedral of Santiago de Compostela, and is cyclically pumped by men who pull at the supporting rope, is analyzed. Maximum angular amplitude attainable, and number of cycles and time needed to attain it, are calculated; the results agree with observed values (~ 82°, ~ 17 cycles, ~ 80 seconds) to the few percent accuracy of both the analysis and the observations and parameter measurements. The energy gain in a pumping cycle is obtained for an arbitrary pumping procedure to two orders in the small fractional change of pendular length; the relevance of the ratio (characteristic radial acceleration during pumping)/g to the gain is discussed- Effects due to rope mass, air drag on both Censer and rope, and the fact that the Censer is not a point mass, are considered. If the pumping cycle is inverted once the maximum amplitude has been attained, the Censer could be swiftly brought to rest, avoiding the usual violent stop. Historically recorded accidents, rope shape, and the influence of relevant parameters on the motion are discussed.

Asymptotic Solution for the Two Body Problem with Radial Perturbing Acceleration

In this article, an approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. The results reveal that the physics of the problem evolve in two fundamental scales of the true anomaly. The first one drives the oscillations of the orbital parameters along each orbit. The second one is responsible of the long-term variations in the amplitude and mean values of these oscillations. A good agreement is found with high precision numerical solutions.

Ion acceleration in underdense plasmas by ultra-short laser pulses

We report on the ion acceleration mechanisms that occur during the interaction of an intense and ultrashort laser pulse ( λ > μ I 2 1018 W cm−2 m2) with an underdense helium plasma produced from an ionized gas jet target. In this unexplored regime, where the laser pulse duration is comparable to the inverse of the electron plasma frequency ωpe, reproducible non-thermal ion bunches have been measured in the radial direction. The two He ion charge states present energy distributions with cutoff energies between 150 and 200 keV, and a striking energy gap around 50 keV appearing consistently for all the shots in a given density range. Fully electromagnetic particle-in-cell simulations explain the experimental behaviors. The acceleration results from a combination of target normal sheath acceleration and Coulomb explosion of a filament formed around the laser pulse propagation axis

Determination of the JWL constants for ANFO and emulsion explosives from cylinder test data

The Jones-Wilkins-Lee (JWL) equation of state parameters for ANFO and emulsion-type explosives have been obtained from cylinder test expansion measurements. The calculation method comprises a new radial expansion function, with a non-zero initial velocity at the onset of the expansion in order to comply with a positive Gurney energy at unit relative volume, as the isentropic expansion from the CJ state predicts. The equations reflecting the CJ state conditions and the measured expansion energy were solved for the JWL parameters by a non-linear least squares scheme. The JWL parameters of thirteen ANFO and emulsion type explosives have been determined in this way from their cylinder test expansion data. The results were evaluated through numerical modelling of the tests with the LS-DYNA hydrocode; the expansion histories from the modelling were compared with the measured ones, and excellent agreement was found.