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2-stage Water rocket hits 800 feet


CaptainSlug
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Water rockets are fun, and a great way to teach the kids some basic physics. When I take my nephew to the park we take some rockets we\'ve been building and a foot pump. After the very first launch, invaribaly we get swamped by all the kids in the park wanting a turn / to be tolld how to make one. Good times.

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  • 2 weeks later...

Pretty sure a homemade parachute could safely return an arduino and a few servo\'s to the ground. Reckon a servo could easily hold 2 bottles together and release them. At the same time it could probably release the pressure from a bottle. True staging. End stage could just parachute to the ground with the servo\'s hanging by their leads no problem.

I\'d be tempted to give a static run a try if I had an arduino and servo.

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  • 2 weeks later...

800 feet? PFFFT. Welcome to ten years ago.

http://web.archive.org/web/20080117120905/http://www.geocities.com/wrgarage/millen.htm

cam3.jpg

On a side note, I\'m thinking of trying to build the world\'s first supersonic water rocket. I still need to run some numbers to see if fiberglass has the material properties I need or not.

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It\'s not an issue at all. You don\'t NEED your exhaust jet to be greater than your final velocity if your mass fraction is greater than 2.72. Of course, mine will be even greater - around 10 or so...

*edit*

Alright, I did a little research and crunched a few numbers as sort of a reality check. I decided that, based on available materials and the scale of other investments I\'d need to get my rocket off the ground, something a little better than fiberglass would be ideal. So, with a new fiber in mind, I found the material properties, and calculated a baseline pressure figure by assuming 1000 feet of 80-lb fiber wound around a 2-liter bottle (realistically, I\'d probably use a shorter length of heavier fiber, still achieving similar figures). Based on these figures I determined I could wind a 2000-PSI body weighing about 100g 50g/liter, for about $60/liter. By comparison to the current world altitude record holder, the carbon-wrapped X-10, this is VERY favorable (then again, it includes ONLY body weight and ignores the weight of the camera, altimeter, and recovery system the X-10 carried).

Yet still, pushing these numbers further, it appears reaching the sound barrier is going to be more challenging than I initially thought. I took this pressure value and cut it in half to roughly account for pressure loss during expansion (realistically the average would probably be less than that, but this is only a reality-check), and then used the Bernoulli equation to estimate a conservative average water jet velocity. This came out to about 117.4 m/s.

I then plugged it into Tsiolkovsky\'s trusty rocket equation to determine what kind of mass fraction I\'d need to get a minimum amount of delta-V (Realistically, I think I\'ll need AT LEAST 400 m/s to account for drag, but that remains to-be-determined). Using 500 m/s I got an impossible 70:1 mass fraction, so I of course jumped to the absolute (unrealistic) minimum - 343 m/s, or exactly mach 1. Here I found that 18.5:1 would be necessary. Given that water rockets are typically filled less than half full for optimal balance between compressed air and mass fraction, this is much higher than the ~8:1 ratio the current concept would realistically achieve. With said ratio and the previous water jet figure, my rocket would theoretically achieve 244 m/s of delta-V - impressive, but not nearly fast enough. Re-figuring the exhaust velocity for the full 2000 PSI and the (again, unrealistic) low-ball delta-V figure of 343 m/s, I finally achieved an ~8:1 ratio, but unless I use liquid methane to pressurize my rocket, I\'m not going to be able to maintain that kind of constant pressure throughout my boost phase.

Furthermore, I ran some numbers for drag and determined that, using a Cd of ~2 at mach 1 (note to self - reference this value against spitzer bullet ballistic coefficients as a reality check) and a sea-level air density, I determined approximately 250 lbs of thrust would be required to penetrate the sound barrier (ideally, you\'d want at least double that to minimize losses) with a 4-inch-wide rocket (i.e. 2-liter bottles). At 1000 PSI, this shouldn\'t be terribly difficult to achieve with larger nozzles, though using a taller, thinner rocket would still be prudent (a rocket with half the diameter, for instance, would suffer only about 1/4 the drag).

I\'m in no way about to write off the idea as impossible at this point; I don\'t really have any stronger materials to turn to, but there\'s still lots of optimization to be done - finding the ideal compromise between empty weight (mass fraction) and pressure (specific impulse), performing a more realistic estimate of gas expansion... and of course, considering the option of using multiple stages.

*edit2*

I found a simple error in my initial container-weight calculations (I forgot to divide the weight of my two-liter wound bottle by two to find grams-per-liter), which puts my mass fraction at a much more promising ~16:1. I\'m still not QUITE there, but it\'s darned close, and I\'m now very confident that a bit of optimization will tip the scales.

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