R is for Rocket - Stability
Stability? What do you mean?
All the rocket fuel in the world means nothing if your rocket doesn't fly where you point it. The most common beginner mistake is to make something shaped like a rocket, cram a motor into it, fire it off and wonder why it turns around and nearly hits them or scuttles around on the ground. It is in fact very easy to make an unstable rocket, easier than you might think. Unstable rockets seem to have minds of their own. They don't want to fly straight. They want to fly any way at all but straight. Why isn't it stable? What makes 2 rockets differ even though they appear to be identical? It's all got to do with mass and surface area and the delicate balance between the two.
Making a rocket stable is one of the first steps you must consider before you ever start building one. If you've already built a few kit rockets, you may have already discovered the secret to making them stable or perhaps you've asked yourself why the kit had the design it did and concluded it was just for style. There may be more to it than meets the eye. Some of the most exotic looking rockets may catch your eye but there's also a very good reason it looks the way it does. With rockets ranging from big to small, skinny to fat, sharp, round and everything in between, there are design compromises that have to be made to maintain stability, else your imaginative concept for a rocket will look rather unimpressive setting fire to a nearby shrub.
Two Important Concepts in Rocket Stability
It's time to become familiar with 2 concepts: Center of Mass and Center of Pressure.
Center of mass (often referred to as center of gravity) is fairly intuitive and anyone with a high school education will already be familiar with it. Center of mass is the location within a solid object where a force vector running through that point will not cause it to rotate. This means if you push your finger through a cell phone's center of mass for example, it will move but not rotate. Put another way, any object has mass inside of it. The mass cannot be localized to a single point because the object itself is larger than a point. Therefore if the object is a sphere with a 1m radius, the mass of that sphere is everywhere within that 1m radius. However if you were to average it all out, you could define a "center of mass" in the very middle of the sphere. The sphere will balance perfectly if you put it on a needle that pointed through it's center of mass because all the mass on the left half of the sphere would balance and cancel out all the mass on the right half of the sphere.
Remember that rockets are FREE BODIES in space. They aren't being supported by anything so they will always rotate around their center of mass, as all free bodies do. This is very important for stability as you will soon see because an object will rotate only if an external force is applied to it and only if that force is not directed through the center of mass. It's this tendency for an object to rotate that causes it to deviate from it's course and become unstable. Let's get back to this concept in a moment.
Center of pressure is the second factor contributing to stability and it's a bit harder to conceptualize. It is similar to center of mass in that it is the theoretical center where all of the aerodynamic forces tend to act. Think of it this way. As you drive your car on the highway the fast moving air slams into the grille, hood and windshield and flows around the rest of the car before detaching from the vehicle. The highest areas of pressure are the ones that face broadside to the wind like the grille and windshield. Everything else is just sort of being stroked by the wind. The center of pressure is a means of determining the average force that the air is imparting to the moving object and centralizing it at a single location. In the car example, the center of pressure would definitely be closer to the front of the vehicle and perhaps a bit higher up than center as well, depending on the size of the height of the roof.
If you look straight down on a rocket, you get an idea of what sort of perspective the wind would see as the rocket plows through it. You'd see a circle representing the body of the rocket and thing little rectangles representing the fins. It's these "projections" of the actual 3D features on the rocket that receive the most pressure. Calculating the center of pressure is no easy task, especially if the rocket geometry is complicated but it can be approximated by drawing a cross section of the rocket, to scale, on a piece of paper, cutting it out and balancing it on something. The balance point is a rough estimation of where the center of pressure would be on the real rocket.
Here's Classic Unstable Rocket Behavior
Center of Mass, Center of Pressure and Stability
Now that you understand what center of pressure and center of mass are, let's get back to stability. We already established that free bodies will always rotate around their centers of mass when an external force is applied, which doesn't point through that center of mass. Think of your rocket again. As it glides through the air, straight as an arrow, the wind affects it equally on all sides because the rocket is perfectly symmetric. But we're kidding ourselves. Rockets are neither perfectly symmetric nor perfectly balanced. On top of that, the wind isn't perfectly consistent either. So let's assume a more realistic scenario. Your rocket initially flies straight but wobbles ever so slightly because of imperfections in the construction and the air being uneven. The moment the rocket tips, even a little bit, the wind will start to hit it broadside and put more pressure on that one side than the other. This will make the rocket want to tip even more in that direction. However, if the rocket is in fact stable, the large fins in the rear will take most of the air pressure and the rear end of the rocket will be pushed straight again. The reason this happens is because the fins are large, because they create a lot of drag and therefore because they bring the center of pressure towards the rear end of the rocket. Most importantly, the fins bring the center of pressure BEHIND the center of mass. Remember we said that any force not acting through the center of mass will make it rotate? We want to make sure that such a force will act BEHIND the center of mass so that it always keeps the back end of the rocket... in the back, where it belongs and not trying to rotate to the front. We use the center of pressure to choose where that aerodynamic force vector ends up.
An unstable rocket has the center of pressure AHEAD of the center of mass. This could be because the fins are too small or too far forward in the model or the rocket isn't long enough or there's too much weight in the bottom of the rocket. In any case, the wind tips the rocket and starts to hit it broadside at which point the nose and body tube are actually getting hit harder by the wind than the fins are, so the rocket tries to flip around backwards but it can't because the motor is constantly thrusting in the direction the nose is pointed. The result is a chaotic and random tumble which is both dangerous and unpredictable. Now if you go back and think of those tiny models you saw in the hobby store with the long swept back fins that looked like something Marvin the martian would fly in, it was done on purpose to make the rocket stable because such a short rocket doesn't have the length it needs to place its mass forward, so to compensate, the fins had to be swept back, behind the motor and everything that has a lot of mass.
Knowing all too well that a rocket needs to be made stable on purpose, what does this mean for design? Well, always be aware that the motor is often the most rearward thing in a typical rocket. That's a bad start because it's also dense and heavy. To offset this you need a fairly long body tube to make that mass less significant. By putting mass inside the nose or placing your recovery device up near the nose section you can offset some of the motor's weight. A rocket with a 10:1 length to diameter ratio with a parachute near the nose, a motor and nothing else will usually have its center of mass somewhere between 2/3 and 3/4 of the way towards the bottom of the rocket. This is usually fine if you place 4 clipped delta style fins at the rear end, with side length equal to twice the diameter. That's a classic setup. Of course rocketry wouldn't be much fun if you stuck to the same textbook design all the time but it's important to learn the basics before adding all sorts of crazy features to a rocket and then being disappointed when it doesn't fly.
The Bible of rocketry
How to Know if You Did it Right
Here's an easy way to check whether your rocket is stable or not, before you fly it.
1) Find some string and make a slipknot out of it so you can tighten it around whatever you put through it.
2) Make sure your rocket is "flight ready" by installing everything into it that needs to be there when you launch it.
3) Find something to balance your rocket on, like a very thin book or stand a ruler sideways on a table. Place the rocket horizontally across your balancing edge and keep moving it back and forth until you find out where the rocket balances. Mark that location on the body tube with a pencil.
4) Put your rocket through the slipknot at the location of its balance point. What you're doing is anchoring the piece of string to where the rocket's center of mass is. Tighten the knot so the rocket balances when you suspend it from the string and doesn't slide around.
5) Go outside and let the rocket hang from your hand by about 1m or 3 feet.
6) Wait till the rocket is pointing backwards and start to swing it in a circle around your body. The back end of the rocket should be pointed in the direction you swing it.
7) Pick up some speed till the string is almost parallel to the ground.
8) Long before you gain enough speed to whip the rocket around you with the string parallel to the ground, you should notice the rocket flip around so the nose is pointed forward and when that happens you should notice it suddenly become much easier to swing the rocket. The rocket should be pointed nice and straight. If it takes any time for this to occur or the rocket can't decide which way to point and flips back and forth or if it wobbles excessively, you have an unstable rocket.
If your rocket fails the swing test, put some modelling clay inside the nose and try again. If you are adding tons of weight to the nose and the rocket still won't right itself during swing, you have made a major design error and will probably have to start again with a different rocket design favoring more rearward, larger fins or a longer body tube.