Water Rocket Computer Model Problems

Answer to problem 7

 I asked for an explanation for the following . . . 1. to find an explanation for the maxima that occur.

This is a bit like the question "Which can you throw further - A cannon ball; a cricket ball; or, a feather?"
The answer is, of course, the cricket ball. But perhaps the tricky bit is understanding why.

Maximum "A" on the optimisation graph represents the combination of rocket weight with water weight that gives the greatest amount of time in the air. At maximum "A", the rocket travels quite a large distance into the air and therefore takes some time to get back to earth. This is analogous to the cricket ball - not so heavy that it is too hard to throw and not so light that it doesn't have enough inertia to overcome the drag of the atmosphere (how far can you throw a feather?)

Maximum "B" on the optimisation graph is analogous to the feather. One thing to notice about its position on the graph is that there is a lot of water in the rocket to start with. All of this water gives the rocket a reasonable altitude (pushing it through the relatively viscous air - viscous relative to the weight of the rocket that is) and then, because it hardly weighs anything, it takes a long time to float back down to earth.

The cannon ball? Imagine that off to the right of the graph somewhere - too heavy to get much height from the thrust and heavy enough to fall to earth, realitively unimpeded by the drag from the air.

Return to Problem Page 7