Compromise is Delicious

Brent Cullimore

First, let’s be clear: I’m not addressing political dysfunction. If that was your first reaction upon seeing this title, then compromising itself has come to have a negative connotation.

I know it sounds better in engineering to call a compromise a trade-off. That way it sounds like you’re getting something in exchange. Whereas compromise sounds like you’re settling … like you haven’t stuck to your principles or haven’t tried hard enough.

But whatever you call it, I’ve come to love the fact that there are no easy answers in engineering: that you can’t get something for nothing. Because they have too much complexity to fit in one cranium, design problems with no obvious solution are just ... well ... delicious. The fact that it takes years of education and experience and cooperation and communication to pull off truly audacious projects like a skyscraper or a Mars lander is just … inspiring.

Here’s a simple one that you still can’t solve in your head.

Take a pre-recycled 2-liter plastic soda bottle. Empty, it weighs about 50 grams. (By the way, that’s an improvement over how much these omnipresent bottles weighed when they were first introduced. But that’s not the compromise story I’m telling here.)

Now fill it with air and water. You can’t go above the failure pressure, which is about 10 atmospheres. Next, replace the cap with a nozzle so that you get a nicely collimated jet of water when the bottle is upside down.

How well would this bottle serve as a rocket, ignoring the need for fins or rifling or guidance control systems (because those realities have to wait for some other blogger).

You get to pick the nozzle aperture and the amount of water to start with at “launch.” How high could you make it go? Enough to be a hazard to aircraft, or just to yourself?

So simple, but … the greater the mass of “fuel” you start with, the harder it is to accelerate and the less air is available for pressurization. Also, the smaller the nozzle diameter, the greater the specific impulse but the thrust will suffer.

Other than a drag coefficient, I’m not going to solve for external flows. So why did I build a CAD model like this in TD Direct®, and then use a FloCAD® Compartment?

Because this way I can make cool videos of the liquid draining out in the first few seconds.

I didn’t bother to add heat transfer, so there is no plastic wall in this video. All that’s left is the shape of the fluid container: a coarsely meshed volume. I guess I could justify this extra geometric precision by saying that someone could optimize the profile of this volume someday: an optimized bottle shape for rocketry instead of for use as a soda delivery system. (Who am I kidding? We both know “someone” probably means “me.”)

I added a second order differential equation for the equation of motion, taking into account drag, fluid and plastic masses, and gravity. I also included the variable hydrostatic head (vehicle acceleration plus gravity) applied to the nozzle at the bottom of the bottle.

If you’d like to know more, you’ll find this sample problem on our Tips and Samples page.

My initial guess was “half full and a 4mm diameter nozzle.” That rocket went up about 63 meters. Using the built-in optimization module, I found that the rocket could reach 69 meters high if it started about 1/3rd full and if it used a smaller nozzle (just under 3mm).

In both the initial and optimized design, the bottle empties at about 2.6 seconds after “launch.” (I’m going to ignore the inconvenient truth that an empty bottle would tumble instantly.) The optimization basically said “use less initial mass, let the pressure be higher when you run out of liquid, and exploit a tiny bit of air thrust when you have all you have is a tiny mass of plastic remaining.”

That’s the thing I like about optimization. It doesn’t care a thing for ideology and uneducated guesses. All it cares about are the facts.

And compromise is its middle name. Well, it would be if it had a last name.