![]() ![]() ![]() G_grav = 9.80665* m/s/s # standard gravity The code would run much faster without the Unum units in every computation. I added the explicit units to check to see if we had any conversion errors (there were none). The code written by the students did not include explicit units, but did everything in standard SI units. Here is the latest draft of the simulation code, which uses the VPython library for graphing and the Unum library for handling units. I’d like help from the physics (or rocketry) experts, both on the simulation the students wrote (with help from me) and on how to do the empirical measurements to test the fit of the simulation. If the simulation predicts super-sonic air flow, then we need to change the model, since the lack of any expansion nozzle means that there is definitely a limitation to Mach 1 for the air jet. For example, we have not simulated any friction for the water or air leaving the bottle, nor checked to see whether the air flow is subsonic (I think it is). Look for phenomena we haven’t properly included in the simulation.For height, we are probably limited to a trigonometric measurement, but I have my doubts about the accuracy of measurement with a protractor and plumb-bob. Lots of people do water and compressed-air rocket labs of various sorts-what do they measure and how? I considered measuring time of flight (which is simpler to measure than height), but the variation in time of flight is fairly small. My main concern here is coming up with an accurate measurement. Do a lot of launches with various amounts of water and measure the flights.One thing that the model does get right is that it predicts a much higher flight for a 14g paper and masking tape “rocket” fired with compressed air off a 30cm long launching tube than for a 42g bottle off the triggered launcher. ![]() We consistently get that the amount of water for max height is around 1/9th the volume of the bottle, but I seem to remember getting the best results in the past with amounts around 1/3rd. We now have a simulation that has roughly the right values at the extremes (empty bottle and full bottle), and that peaks at an intermediate value, but I’m still not convinced that the model works properly. We didn’t measure barometric pressure, temperature, and humidity ourselves, but relied on reports on the web from a local weather station a couple blocks away. The model with both the water jet and the air jet predicted too high a max height, so one more term was added: a drag force proportional to the velocity squared.Īll the parameters except the drag coefficient (and frontal area, if the bottle tumbles) are directly measured, except for the local gravitational field for which we used a Wolfram Alpha widget. By this point I was heavily involved in the modeling, because I wanted a model that we could use. The model was then improved by adding an air jet after the water was expelled, using essentially the same equations as for the water jet, but with lower density and a slightly different update for the pressure on each time step. The first simulation, which was done almost entirely by the students, predicted much too low a max height, because it only included two sources for thrust: the initial slide off the launcher (using a simple energy model and constant pressure), and conservation of momentum as the water was expelled. Then they did some preliminary tests to see whether the simulation was anywhere near correct (with 0g of water and with 400g of water). The bottle here has no pressure in it, so did not leave the launcher, even though the lever is pulled back to release position.įirst, I insisted on them coming up with equations to model the rocket and writing a simulation, so that they could optimize the amount of water to put in the rocket. Note that we had to add a paperclip to the launch lever as a jump ring, since the hook provided for the cord would not reach the hole in the lever intended for it. The stake can be seen just to the right of the bottle.
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