Teaching and learning

Simulation of trajectories of volcanic bombs:
Andreas Schweizer, Kantonsschule Zürcher Unterland

Andreas «Schweizer Jugend forscht»
(Swiss National Science Competition)

Newspaper articles about this project (german)

«My Geography teacher, Mr. J.Alean, gave me the idea to write a program which simulates trajectories of volcanic bombs. During 1996 I developed this, including a graphical interface, for Apple Macintosh computers».

The program calculates trajectories taking into account air resistance FA (FA=0.5*c*d*v^2*A; c=resistance parameter, depending on the object shape), d=air density, v=velocity, A=cross section area of the bomb). The calculation is performed step by step: The bomb continues to fly over a given landscape profile until it hits the «ground».

The program is based on the simplifying assumption that the bomb travels through stationary air as soon as it leaves the crater.

The programm was later rewritten in Java and can be used interactively directly in the webbrowser.

The following parameters can be predetermined:

  • launch velocity of the bomb,
  • launch angle when bomb leaves the crater,
  • resistance parameter (c),
  • terrain below the trajectory,
  • air density,
  • cross section, density and mass of the bomb.

The output of the program is:

  • horizontal distance of the impact point from the crater, and
  • a graphic representation of the terrain and the trajectory.

Example 1: Determination of possible launch velocities

The following simulations are based on an actual bomb which was thrown out by Stromboli (map on the right). It was found after the unusual eruption of 16. October 1993 in the upper part of Rina Grande. It must have flown almost exactly over Pizzo. The following parameters were held constant:
  • mass: 21 kg
  • resistance parameter 0.5 (sphere)
  • cross section area of bomb: 0.0707 m2
The following launch angles were chosen: 46°, 50°, 55° and 60° . The launch velocities were varied until the bomb hit the ground at a distance of 560m (+/- 1m) from the crater. The parameters for the bomb correspond to a sphere of 0.3m in diameter with a density of 1500kg/m3.

Result: Given these parameters the bomb must have left the crater with a velocity of at least 88.7m/s and the launch angle must have been greater or equal 46° in order to reach the observed point of impact. Any smaller velocity or launch angle would have lead to an impact on the crater side of the summit of Stromboli.

Example 2: Effect of air resistance


Left: no air resistance; right: with realistic air density. Parameters which were held constant:
  • mass: 21 kg
  • launch angle 60°
  • resistance parameter 0.5 (sphere)
  • cross section area of bomb: 0.0707 m2
Result: Given a launch angle of 60° an initial velocity of 78.9m/s would be enough to throw the bomb to the observed distance of roughly 660m in a vacuum. Using a realistic air density of 1kg/m3 (750 to 950m.a.s.l.!) an the same launch angle a speed of 90.5m/s is needed to carry the throw the bomb over the same distance.
Further examples of simulations