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Back to Basics - Model Rocket Stability Print
Written by Joe Pfeiffer   
Sunday, 11 July 2010 11:22

 

Where is the middle of a weathervane?

Well, looking at the picture. I can think of several answers. I might say it's at the pivot; I might say it's somewhere in the middle of the flag at the back; or I might say it's at the point where it would balance if I set it on my finger.

 

Illustration of Balance

 

 

Which of these answers is correct? Well, it depends on how you look at it. So far as the pivot is concerned, it defines the center of the weathervane, after all, it is the point the vane rotates around. The wind, on the other hand, would probably argue that it's in the middle of the flag. That's where it resists the flow of the wind the most. And if I were building the weathervane, I'd probably say it was the balance point - and that's where I'd put the pivot.

 

Now, what does any of this have to do with model rockets? It turns out that a model rocket in flight acts just like the weathervane! The point it pivots on when in flight is the balance point - this is called its "center of mass.” The center seen by the wind is called the "center of pressure." And the rocket in flight will always try to keep the center of pressure behind the center of mass. If this is the case when the rocket is flying forward, the rocket is stable. If not. the rocket will continually try to rotate until it does achieve this condition - and if the motor is trying to make it go forward while it's trying to turn around, it will look a lot more like a pinwheel than like a rocket. The possible danger here is that as the rocket burns its fuel, its center of mass moves forward, sometimes they suddenly become stable, while pointing in a random direction. This is not a good thing!

 

How Can I Tell if a Rocket is Stable?

 

The first, shortest answer is that all of the rocket kits sold by all of the manufacturers are very conservative designs. You just don't have to worry about them - they are stable.

 

If the rocket isn't a kit, there are several ways to get a good idea of whether or not the rocket is stable. The quickest, and least reliable, way is to copy a kit. If you build a rocket with the same size (both diameter and length) body tube and the same nose cone as a kit, then if your fins are at least as big as the fins on the kit, the rocket will be stable. But I'd recommend using one of the other methods I'll talk about to make sure after the rocket is built!

 

The next way to determine stability is the "swing test.' Put a slip knot in a string and put it around the rocket at the balance point (if the nose hangs down, you're behind the balance point - move the string forward. If the nose points up, you're ahead of the balance point - move the string back. If it hangs level, you've got it.). Make sure you perform this test with the motor installed! Use some masking tape to hold the string in place. OW, let out some string and swing the rocket around you in a circle. If it swings with the nose pointed forward, it's stable. This is a pretty foolproof test. If the rocket passes this test, you can be pretty confident that it is stable.

 

The third test is the "silhouette" test. Cut out a cardboard silhouette the same shape as the rocket. Find the rocket's balance point just as you did for the swing test (not the silhouette, the rocket). Now, put the silhouette on a pivot at the rocket's balance point. If the silhouette's balance point is behind the rocket's balance point, the silhouette will lay nose up - and the rocket is stable. If it lays nose down, the rocket is not stable. Like the swing test, this is pretty conservative. You're not likely to fly an unstable rocket if it's passed this test.

 

Why Aren't Scale Models Right?

 

Why does the Estes Saturn IB have clear plastic fins? Why does their Enterprise have a weight on a stick hanging out the front of the rocket? Why aren't these scale models really built to scale?

 

There are a couple of factors at work here. First, while our body tubes are essentially empty except for the recovery system, "real" rockets are full of huge fuel tanks. This means that their centers of gravity are substantially farther forward than ours, so their fins can be smaller and the rocket can still be stable. Also, large rockets typically have engines that can be redirected, or fins that can be moved under computer control. Consequently, if they start to veer off course, they can correct for it and fly anyway; this is called using active controls. On our rockets, the aerodynamic surfaces and the motors are fixed in place. So they have to be designed so they are stable. Trying to adjust either the center of gravity or the center of pressure as unobtrusively as possible is one of the challenges in scale modeling!

 

Of course, when we talk about the Enterprise, the designers had it even easier. A fantasy or science fiction rocket, doesn't have to fly at all. So their designers just don't have to worry about it. When we want to make a Klingon Bird of Prey or an X-Wing fighter actually fly, we have to think about all the messy details that the movie people didn't. This is done by introducing non-scale elements like oversize fins to move the center of pressure back (as in the Saturn IB), or weights to move the center of mass forward (as in the Enterprise).

 

In More Detail: the Barrowman Equations

 

In the late 1960s, Jim Barrowman wrote his Master's Thesis on the subject of rocket stability. In the course of the thesis, he derived a set of equations that accurately predict the center of pressure of a rocket when flying nearly straight. These equations, known as the Barrowman Equations for obvious reasons, give the most accurate prediction of the stability of a model rocket - much better than any of the three methods I described above.

 

In brief, t he equations consider each of the major components of the rocket (nose cone. fins. and transitions between body tubes of differing diameters - when flying nearly straight, the body tube's contribution is negligible), and estimate their centers of pressure. By averaging them together, the center of pressure of the rocket as a whole is calculated.

 

There really isn't room for a more complete description of the equations here. You can find them in G. Harry Stine's "Handbook of Model Rocketry," but be warned, the computer program he includes to calculate them has bugs!

 

 

 

 

Last Updated on Friday, 23 July 2010 16:39
 

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