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Rocket Aerodynamics
The word aerodynamic contains the two words "aero" and "dynamic". The word "aero" is from Greek and means "air". "Dynamic" means movement. Combined the two word says "air movement". When we use the word "aerodynamic", we mean the study of fluid movement around an object. In this respect a fluid is a gas, not a liquid.
 
The field of aerodynamic is large and complex, and requires years of training in order to fully understand.
In this article we will discuss some very basic rocket aerodynamics and learn what aerodynamic forces that acts on a free flying rocket.
 
Aerodynamic Forces
Aerodynamic forces are generated and act on a rocket as it flies through the air. The magnitude of the aerodynamic forces depends on the shape, size and velocity of the rocket, and the properties of the air (or atmosphere) through which it flies.
Aerodynamic force is broken into two components: the drag force which is opposite to the direction of motion, and the lift force which acts perpendicular to the direction of motion. The lift and drag act through the centre of pressure which is the average location of the aerodynamic forces on an object, see the figure below. Click the figure to get a larger version.
 
 
Aerodynamic forces are mechanical forces. They are generated by the interaction and contact of a solid body with a fluid, a liquid or a gas. For lift and drag to be generated, the rocket must be in contact with the air. Aerodynamic forces are generated by the difference in velocity between the rocket and the air. There must be motion between the rocket and the air. If there are no relative motions, there is no lift and no drag.
We can think of drag as aerodynamic friction, and one of the sources of drag is the skin friction between the molecules of the air and the solid surface of the moving rocket. Because the skin friction is an interaction between a solid and a gas, the magnitude of the skin friction depends on properties of both solid and gas. For the solid, a smooth, waxed surface produces less skin friction than a roughened surface. For the gas, the magnitude depends on the viscosity of the air and the relative magnitude of the viscous forces to the motion of the flow, expressed as the Reynolds number. Along the surface, a boundary layer of low energy flow is generated and the magnitude of the skin friction depends on the state of this flow.
We can also think of drag as aerodynamic resistance to the motion of the object through the fluid. This source of drag depends on the shape of the rocket. As air flows around a body, the local velocity and pressure are changed. Since pressure is a measure of the momentum of the gas molecules and a change in momentum produces a force, a varying pressure distribution will produce a force on the body. We can determine the magnitude of the force by integrating or adding up the local pressure times the surface area around the entire body.
The equation for air drag is:
 
 

where:

p  : air density [kg/m3]

A   : frontal area [m2]

CD  : drag coefficient [-]

v     : rocket speed [m/s]

The negative sign is indicating the drag is opposite to that of velocity. The equation above shows us that the drag includes a drag coefficient. The drag coefficient containts all properties that are hard to measure or quantizie like viscus effects, flow effects due to varying Mach-number and angle-of-attack. In other words the drag coefficient can be said to be a coefficient that say something of how good the object is to penetrade the air.

Typically, the CD for a model rocket is around 0.35 to 0.70 as long as the flight speed is subsonic (less than the speed of sound). For professional rockets the CD may vary more since they are flying over wider speed regime. At Mach=1 the CD often has its gratest value, and it will usually decrease with increasing Mach-number.

To sum up what drag is:
1) Drag is a mecanical force due to air friction
2) Drag is measured in Newton (SI units)
3) Drag increases with the square of the speed
4) Drag increases with the square of the rocket diameter
5) Drag depends on air density (or the density of the atmosphere which the object are flying in)
6) Drag depends on the shape of the object, flying attitude, laminar or turbulent flow and more. These effects are summed up in the unitless drag coefficient, CD

 
Rocket Stability
What do we really mean with stability? Consider the following situations as shown in the figure below.
In the first figure a ball is placed inside a curved tray. As long as the ball is stationary we can say that the ball is stable since all the forces acting on the ball are zero. If we hit the ball with a certain force, it will roll up one side of the tray until the speed is zero and then roll back again to the other side. After a short while we intuitively know that the ball will end up in the same position as were we first hit the ball.

What has happened? Well, the ball has with the help of the curvature of the tray and gravity damped out the energy of that initial kick force and thus returned to the essential same position. So, every system that has this ability can isolated be said to be stable, since they react to the disturbing force and dampen that force out and reach the same condition as before the disturbance hit the system.

A system may be said to be labile, if it cannot return to the same position or attitude after a disturbing force have acted on that system. This can be visualized by turning the tray upside down and placing the ball on top. We know for sure that the ball never will return to the top of the tray after a disturbing force has acted on the ball.

These simple analogies are true for a free flying rocket stabilized by fins.

 
 
Fin Stabilization
Have you ever questioned why rockets always have the fins located at the rear end? Probably not? But why are they located there? What about placing them at the nose? Well, that you may say should make a design that would look rather odd? Well, I will try to explain why a free flying rocket should have the fins at the rear part of the rocket.

First consider the following analogy. Assume that we have a homogeneous rod supported horizontally at the centre-of-gravity (CG). At the support point the rod is free to rotate in the horizontal plane. We directly should know that the rod length at both sides of the rotation point must be equal since it is homogeneous and supported at the centre-of-gravity.

Assume now that we blow a wind perfectly normal to the longitudinal axis of the rod. What will happen?
Nothing! Why? Well since the air force is equally spread over the entire length of the rod, the rod will not experience any unbalance in the air force pushing the rod.
 
Assume now that we apply a plate on one side of the rod. We adjust so that the centre-of-gravity is still in the rotation point. What will happen this time?
Intuitively you may answer that the rod will rotate up against the wind with the plates (fins) in down-wind position relative to the centre-of-gravity. This is correct. But what has happened? Well, the projected surface area on the plate side has been enlarged compare to the projected area on the opposite side of the centre-of-gravity.

This means that there is now a larger surface area that the wind hits compare to the other side. This simply means that the aerodynamic pressure is grater at the plate area since the area is larger in magnitude. We have now at the same time constructed a weathercock. Refer to the figure below for more details. Click on the figure to get a larger version.
 
 
By looking at the figure above, we may notice that there are a drawn a green point on two of the drawings. This point represents the centre-of-pressure or CP for short. The CP in this case has the same projected area on each side of the point. This means that when we have a plate-less rod the CP will be located within the CG, since the rod is homogeneous. In a real case scenario the CP will be a function of angle-of-attack (angle between velocity vector and longitudinal axis), and rocket speed. It is at the CP we say that the resultant force of the drag acts, thus in opposite direction of the direction of travel. As mentioned in previous chapters, the resultant of the lift force also acts through this location.
Let us now go back to the rod case. In this case the projected area on each side is equal. So it may be said to be a special case, but still true enough.

Let’s go some steps further. We acknowledge that it is in the CP the resultant of the aero force acts. So what will happen if we have a case where the CP is located far from the CG? If we are thinking in rocket terms, you may follow that this situation will make a rocket very wind sensitive. Since all rotations occur around the CG, the CP is simply an force acting at a certain distance from the CG. This makes a over stable rocket that will be safe enough but will tend to ship direction rather easily depending on wind situation. In an opposite case where the CP is located close to the CG, the rocket will be less stable but also less wind sensitive giving it a better directional stability. But what about locating the CP in front of the CG?

That is a dangerous situation! The rocket will for sure tip around and try to fly tail first! And finally, whit the CP inside the CG will make the rocket labile, like placing an egg upside down. It will very easily with zero aero moment rotate around the CG making the rocket flight very dangerous and unpredictable. Such rockets are actually flown in missile systems! They can do so because the missile have a autopilot and guidance system that can sense rapid changes in the rocket attitude during flight and compensate for these forces. In this way the rocket may very fast change attitude compare to a naturally stable rocket configuration.
So, you should never attempt or try to make a model rocket or rocket with CP located in front of the CG, it will for sure not work.
 
So where is the optimal location for the CP relative to the CG? Well, many state that the optimal point is one-body diameter behind the CG. This may be true for a paper rocket, but in real life this is rather a big simplification which may lead to disappointments if followed. Remember that neither CP nor CG is static. CG shifts due to changing mass in the rocket motor and CP shifts location depending on rocket attitude, Mach-number and more. So, how to predict the location of CP?

Well, it is very difficult to do. One may use computer software or perform wind-tunnel testing. Often one don’t have these tools on hand nor the skills to carry such investigations out. But there is a much simpler but still rather limited way of carry of a test. You can simply test out the rocket by placing a cord around the CG and then rotate the rocket around yourself in a big circle. If the rocket flies head (nose) first, the rocket can be said to be aerodynamically stable. But if the rocket flies with the tail first, you should either relocated the CG of your rocket by adding some more weight to the front or enlarge your fins. Remember that testing is performed at very low speed. Your rocket may fly much faster, so this kind of testing has its clear limitations, but it is better than nothing.
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This theme includes:
The dawn of the rocket
The rocket principle
Chemical Rockets
Rocket Trajectories
Different flights and trajectories
Rockets in the Classroom
Water Rocket Exercises
Model Rockets
Building Model Rockets
Preparing Model Rocket for Launch
Launching Model Rockets
Educational Model Rocket Exercises
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in co-operation with the Norwegian Space Centre, www.spacecentre.no.
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