Researchers at the Rubber Caving Institute (RCI) have been busy with mathematical models of plunger function (see SUCKS elsewhere within these pages). Here are a few of our findings, showing the effectiveness and safety of projectile speleoplunging!

Energy stored in the bow: In practice, one can draw an arrow back about 0.6m, and a strong man can pull on the string with a force of 350N. It follows that the available muscular energy must be about 210 Joules (Work = force ´ distance). If we suppose that the bow is initially virtually unstressed, then the archer only works up to his maximum pull when the string nears its maximum extension; therefore the energy stored in the bow is about half the available energy, i.e. 105J. With this information, we can calculate the "muzzle velocity" ( v) of the plunger, as it leaves the bow: mp = mass of the plunger (0.96 kg) Eb = energy stored in the bow (105 J) Eb = ˝ mp v2 105 = ˝ (0.96) v2 210 = (0.96) v2 218 = v2 v = 14.8 m/s	Heights and distances: Knowing how fast the plunger is moving, we can calculate the apogee of its trajectory when launched straight up (for maximum height): vf = final velocity    vi = initial velocity a= acceleration    dh = distance (maximum height) of the flight of the plunger vf2 - vi2 = 2adh 0 - (14.8)2 = 2(-9.8) dh 218 = (-19.6) dh dh = 11.16 metres We can also calculate the range, at 45°: d = maximum distance d = 2 sin(q) dh d = 2 sin(45) 11.16 d = 2 (0.707) 11.16 d = 15.78 metres We leave it to you to solve for the angle of your particular situation. Clearly a lighter plunger is called for. We recommend the more expensive SpeleoPlunger™ Mark IV, which is being developed for the bow application.
Plungersuck: So, now the plunger is stuck to the wall, but can you trust it? Here's the proof! mc = mass of the caver-including gear & beer (79.8 kg) dp = diameter of plunger head (14cm) A = area of the head of the plunger Pa = atmospheric pressure (14.8 psi) Ps = plungersuck A = pr2 A = p(˝d p )2 A = p(7 )2 A = 154 cm2 Ps = PaA Ps = (14.8)(23.9) Ps = 160.4 kg Safety = Ps / mc Safety = 160.4 / 79.8 Safety = 2.01 A safety factor of more than two! Clearly no problem. Note: all calculations and weights are approximate, and assume the use of SpeleoPlunger™ Mark III.

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