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:
|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
We can also calculate the range, at 45°:
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.
So, now the plunger is stuck to the wall, but can you trust it? Here's the proof!
Note: all calculations and weights are approximate, and assume the use of SpeleoPlunger™ Mark III.
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