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Basic Rocketry Aerodynamics

What basic aerodynamic forces affect a rocket's flight?

The basic aerodynamic forces that affect a rocket's flight are drag and lift. Drag negatively
affects a rocket's acceleration, velocity and ultimate altitude. It must be minimized. Lift
causes directional changes in a rocket's flight that can be used to stabilize a rocket's direction
of flight.

What is drag?
Drag is a component of aerodynamic force acting directly against a
rocket’s velocity by virtue of the rocket’s motion through surrounding
air. Drag acts as a brake on a rocket’s motion.
What is lift?
Lift is a component of aerodynamic force acting perpendicular to a
rocket’s velocity with respect to surrounding air. The lift causes a
rocket to pitch (pivot) around its center of gravity.
What is AOA?
AOA stands for Angle Of Attack. The angle of attack is the angle
between a rocket’s velocity vector and its centerline. AOA

What is stability?
Stability is a name given to how a rocket behaves when flying at
various angles of attack (AOA). A rocket can either be stable,
unstable or be neutrally stable:

1. Rocket is stable:
- If when flying at an AOA a pitching movement occurs on the rocket’s airframe that reduces
the AOA. This self corrects errant flight.

2. Rocket is unstable:
- If when flying at an AOA a pitching movement occurs on the rocket’s airframe that increases
the AOA. This makes errant flight worse.

3. Rocket is neutrally stable:

- If flying at an AOA does not create any pitching movement on the rocket’s airframe. This
has no effect on errant flight. The result is total unpredictability.

In other words:
A stable rocket will automatically steer away any unwanted AOA. Its flight path may be
predicted by trajectory calculation.
If the rocket is not stable
however, its flight path will be
unpredictable. Unstable
rockets will "try to fly
backwards", entering a fierce
spinning movement in which
they are prone to break up.

Neutrally stable rockets may

turn and fly in any direction
whatsoever without warning.

Stable Neutrally stable Unstable Important

Mach number
In dealing with rocketry aerodynamics one must apply fluid dynamics (air is a viscous fluid) to
the problem. In fluid dynamics, velocity in absolute terms is virtually unimportant. Instead, the
behavior of fluids depends on a handful of dimensionless velocity measures, one of them
being the Mach number.

The Mach velocity refers to the speed of sound in the fluid, and varies with the temperature.
For dry air we may write:
c  20.055 T
Where: c is the speed of sound in m/s; and T is temperature in Kelvin.

Then Mach number is the velocity normalized to the speed of sound:

M  v c
Reynolds number

As with the Mach number, the Reynolds number is a dimensionless measure of velocity. It is
primarily used for determining whether the flow is laminar (smooth and coherent over a
surface) or turbulent (disrupted and disorganized over a surface) which then allows for an
estimation of skin friction.

For a rocket of length L, flying at velocity v in air of density , the Reynolds number is:
Re 

The quantity is the dynamic viscosity of the air. Some representative values of and  are:
1.8*10-5 kg/(ms)
 = 1.2 kg/m3
Reynolds numbers easily gets quite large - in the range of 105 - 108.

Reynolds numbers easily get quite large - in the range of 105 - 108.
Coefficients of lift and drag
For a rocket traveling at velocity v, in air with density , the aerodynamic forces may be
written as:
Lift  ½ AClv 2
Drag  ½ ACdv 2
The properties Cl and Cd are the coefficients of lift and drag. The property A is a reference
area. A is coupled to Cl and Cd in the following way: A might be chosen at random, but Cl
and Cd scale accordingly. Most commonly, A is chosen to be the largest cross sectional area
of a given rocket body.

Cl For small angles of attack, the lift coefficient (Cl)

is proportional to AOA. For a symmetrical
rocket, Cl is zero at zero AOA. Under such
circumstances, the lift coefficient itself partly
looses its meaning. Instead, the slope of the Cl
versus AOA curve becomes the property of
interest. This is often referred to as the lift curve
AOA slope coefficient.

What this means is that for a stable rocket flying

straight and true, the AOA is zero and the Cl is zero. The rocket should then continue in its
straight and true path. If, for whatever reason, the AOA should change to an angle other
than zero then the Cl will also increase and thereby tend to force the rocket back to the
intended flight path.

Center of Pressure - CP.

The center of pressure is the position where the resulting aerodynamic lift acts on a rocket’s
airframe. The position of CP depends on the distribution of lift on the rocket. Normally the fins
generate the major part of lift, thus for rockets with only one set of fins; the CP is generally
located in the vicinity of the fins.

Subsonic and supersonic velocities

When a rocket travels through the air, the flow around it depends on the rockets velocity with
respect to the velocity of pressure distortions in the air. Pressure distortions are percieved as
"sound", hence the the flow field depends on the rockets velocity with respect to the speed of
sound (ie. its Mach number).

The movement of the rocket through the air, creates sound waves. As the sound travels at
the same speed in every direction, the emitted sound will generate a spherical wavefront,
analogous to the circular wave created by interrupting a calm water surface in a single point.
If the rocket travels at a speed less than the speed of sound, the sound waves are able to
escape the rocket, and it emits sound like any other object we are used to. However, if the
rocket travels faster than the speed of sound, the sound waves does not escape from the
rocket in the usual maner. Instead, they add up to form a wavefront of conical shape with the
rocket in its vertex. This conical wavefront is often reffered to as the Mach cone. Note, that
this is analogous to the "V" shaped wavefront generated by a ship, that travels across a water
surface. The faster the rocket travels, the sharper Mach cone.
The Mach cone explanes why a supersonic object generates a sonic boom: all the acoustic
energy is compressed into one single wavefront. Anyone who are hit by the Mach cone will
percieve a short spike of noise - the sonic boom. The Mach cone also explains, that those
who stays in the viscinity of the launch tower when a supersonic rocket is launched will not
hear any sonic boom - they are at the inside of the Mach cone, and are never hit by the
Mach Cone
Sound Waves
Sound Waves

Rocket Rocket

sinθ = 1/M

Rocket at subsonic speed Rocket at supersonic speed

Speeds lower than the speed of sound (M < 1) are said to be subsonic - speeds higher than
the speed of sound (M > 1) are said to be supersonic. The flowpatterns of subsonic and
supersonic speeds are fundamentally different, however also within the subsonic or
supersonic regions there are subregions of different flow behavior.

At low subsonic speeds, the air has plenty of time to adapt to the rocket and generates a nice
flow around the rocket without any pressure build-up. This is the case for speeds roughly up
to half the speed of sound, and the flow is said to be incompressible. When the speed of the
rocket gets higher than roughly half the speed of sound, the air has no longer time for
creating ideal flow patterns. Instead the air in front of the rocket starts to compress, and the
coefficients of lift and drag increases (basically with a factor of 1 / 1  M 2 ) from their
incompressible values. This is the region of subsonic compressible flow.

As the air cannot move straight through the rocket, it has to move around it instead. Basically
it does that by slowing down and changing direction to get by the nosecone, accelerate to get
past the rocket body, and then again slowing down and changing direction for getting by the
base of the rocket. This means, that the speed of the air around the rocket is somewhere
higher and somewhere lower than the speed of the rocket with respect to the undisturbed air.
For this reason, the airflow can be partially subsonic and partially supersonic if the rocket flies
at high subsonic speeds (roughly 0.8M or higher) or at low supersonic speeds (roughly 1.2M
or lower). This is known as the transonic speed region. The actual limits of the transonic
region depends on the shape of the rocket. For most rockets, the coefficients of lift and drag
reaches their maximum in the transonic speed range.

In the supersonic speed region, the coefficients of lift and drag decreases (basically with a
factor of 1 / M 2  1 ) from their maximum, but at high supersonic speeds they approach
some constant nonzero values. At high supersonic speeds, the air simply has no time to
move away from the rocket, and it starts to act more like a bunch of independent air
molecules. High supersonic speeds are said to be hypersonic. Again the actual limit for
hypersonic flow depends on the shape of the rocket, but as a rule of thumb, hypersonic
conditions begin at five times the speed of sound.

Practical considerations
How do I check my rocket’s aerodynamic stability?
You need to determine the position of CP for the rocket and its center of gravity (CG) at any
condition throughout the rocket’s flight. CP is the resulting point on the rocket, where the lift
forces act. CG is the weight balancing point of the rocket. If CG is located forward of CP, then
the rocket is stable.

Note that CG and CP are not fixed in their locations but generally move with varying
conditions. CG moves as propellant is consumed whereas CP moves with the velocity of the
rocket and its AOA.

How do I determine the location of CP?

For rockets flying at low speeds - less than approximately 180m/s (600fps), two methods are
applicable: The method of Barrowman and the cardboard cutout method. The method of
Barrowman estimates the lift and center of pressure for every major part of the rocket and
combines them to values applicable for the complete rocket. In the cardboard cutout method,
a silhouette of the rocket is cut in cardboard, and its weight balancing point is determined.
The cardboard cutout method gives a rough estimate for the CP at 90 deg. AOA. The method
of Barrowman estimates CP at 0 deg. AOA. As rockets normally fly at AOA of less than 10
deg., the method of Barrowman is normally more consistent with reality. One or both methods
are commonly implemented in rocketry software packages, such as:

· RocketCAD
· RockSim
· Aerolab
· Rogers Aeroscience Software (not shareware)

For rockets flying at speed higher than 180m/s (600fps) calculation of CP gets rather
complicated, and high speed CP calculation is not yet commonly included in rocketry
software. In general, rockets that are stable at low speeds will be stable until velocity gets in
the range of Mach 2 - however, rockets with fins with high thickness ratios might exhibit
stability problems in the transonic speed range (0.8-1.2 Mach).

The position of CP is also affected by angle of attack, commonly CP moves forward with
increasing AOA. If the rocket leaves its ramp at low speed in high winds, the resulting AOA
might be considerable and cause the rocket to be unstable.

Rocket movement further affects the position of CP. Pitching and rolling movements induce
additional velocity components around the different parts of the rocket. The induced velocities
vary with distance from CG and cause the different parts of the rocket to fly at different AOA,
thus affecting the position of CP.
In brief - the method of Barrowman
The most common method for determination of CP among model, High Power and amateur
rocketeers is the method of Barrowman. The method is based on scientific works, but is
greatly simplified in a way that makes it suitable for amateurs. It requires no more than a
pocket calculator, and college level mathematical skills.

In order to keep the method simple; Barrowmann makes some basic assumptions:

1. The angle of attack is small - less than app. 10O

2. The velocity of the rocket is less than 180 m/s (600 fps).
3. The airflow around the rocket is smooth with no abrupt directional changes.
4. The length of the rocket is significantly larger than its diameter.
5. The rocket body is pointed.
6. The rocket body is symmetrical around its centerline.
7. The rocket body is stiff, so that all parts of the rocket flies at the same AOA.
8. The fins are made from thin plates..

Barrowman divides a rocket into standard components - nosecones - fins - conical transitions -
and indirectly: cylindrical body tubes. For each component, he has established simple
expressions for the lift curve slope coefficient and the center of pressure for that particular type
of component. By combining theese, the resulting position of CP is easily calculated. According
to the assumptions, the AOA is unimportant, as it is the same for all components of the rocket.

How do I determine the location of CG?

The best way of finding the center of gravity is simply by keeping track of the weight and
center of gravity for every single component of the rocket. The resulting CG is then
determined by a moment analysis - Actually, some rocketry software like:
· RockSim
· Aerolab
will do the CG calculation for You.

Finally, the location shoul be verified by finding the weight balancing point of the actual rocket
- both with a fully loaded motor and with an empty motor.

Is there an optimum relationship between Cp and Cg?

Yes, it is the Static Stability Margin. The Static Stability Margin is defined as the ratio of the
distance between CP and CG to the maximum body diameter of the rocket. As a rule of
thumb, the static stability margin should be between 1 and 2. If the static stability margin is
too small, the stability of the rocket could be in danger, especially at low velocities. If static
stability is too large, the rocket will be more sensitive to the wind. Also the forces acting on
the rocket in terms of lift and drag will be greater, increasing drag and mechanical stress on
the fins.
Nosecone lift
lift lift
1-2 diameters


Stability design considerations

Fins on rockets primarily generate lift. The nosecone, shoulders and boattails on rockets also
generate lift. While fins, nosecone and forward facing shoulders generate lift in one direction,
boattails generate lift in the opposite direction - in stability considerations, one might say that
boattails generate negative lift.

If there are more than one set of fins, the most forward set of fins interrupt the airflow around
the fins behind them. This reduces their lift, thus reducing the stability of the rocket. Warning,
this effect is NOT covered by the Barrowman or cardboard cutout methods of determining

Practical rules
When designing an airframe:

1) Place the fins as far away from nosecone as possible.

2) Use only one set of fins if possible. Otherwise, make the most aft set of fins larger than
indicated by Barrowman analysis.

3) Do not use a boattail without increasing fin size accordingly.

4) On multistage rockets, make sure that the rocket is stable in any of its configurations
during flight.

It's worth noting that we can do any "worst combo" of breaking the rules if the design
equations say that it will fly correctly. The math is king of this hill, and the practical rules can
be violated and the rocket will be stable - if it is so designed.

Aerodynamic drag
The drag of a rocket depends on velocity (in terms of Mach and Reynolds numbers) and of
the angle of attack.

The drag of a rocket is basically generated by 3 different mechanisms:

· skin friction
· pressure drag
· base drag.

Skin friction is not really friction between the rocket and the surrounding air, but rather friction
between air molecules moving at different speeds in the boundary layer that surrounds the
rocket. This effect is coupled to the overall surface area of the rocket. At subsonic speeds,
skin friction is normally the largest contributor to overall drag, and even at supersonic speeds,
it is a main contributor.

Pressure drag is the drag caused by a rocket "pushing the air in front of it aside". At subsonic
speeds, pressure drag normally contributes only slightly to the overall drag. At supersonic
speeds, pressure drag (then commonly named wave drag) can be significant, especially if the
forward facing parts of a rocket are blunt.

Base drag is created by the wake trailing behind a rocket. During powered flight, base drag is
significantly reduced as the wake tends to get filled by the exhaust from the motor. One
common way to reduce base drag is the use of a boattail that makes the rearmost cross
sectional area smaller than the cross sectional area of the main rocket body. The drawbacks
of boattails are that they tend to increase wave drag at high velocity and reduce stability of a
rocket due to their "negative" lift.

The coefficient of drag is affected by the angle

of attack. At small values of AOA, the drag Cd

coefficient may be written as:

Cd  Cd 0  const .( AOA) 2

Drag design considerations

Optimal design in terms of minimum drag
depends heavily on the velocity in question. No
design is generally optimal for all velocities AOA


For rockets spending most of their flight at subsonic speeds, the nosecones should be
rounded and they should have boattails. Similarly, the leading edges of the fins should be
rounded and have sharp trailing edges. Maximum fin thickness should be closer to the
leading edge, than to the trailing edge.

For rockets spending most of their flight at supersonic velocities it is essential that all forward
facing surfaces, i.e. nosecone and leading edges, are sharp. Boattailing and sharp trailing
edges are also desirable. The fins should be thin with maximum thickness midway between
leading and trailing edges.

Rockets that reaches transonic speeds might benefit from what is called the area rule: For
slender bodies - like most rockets - it turns out, that the transonic pressure drag does not
really depend on the actual shape of the body (ie. diameter versus length), but rather on its
distribution of cross sectional area (ie. cross sectional area versus length). The practical
consequence of this is, that when adding a set of fins to a rocket body, increase of the
rockets pressure drag can be avoided by reducing the rocket body diameter where the fins
are attached, so that the cross sectional area is unchanged.
In general, the total surface area of any rocket should be kept as small as possible. Also, the
cross-sectional area should be kept at its minimal practical value. Making a rocket very fat or
very long is undesireable.

When drag considerations contradict stability considerations, then stability conditions are of
greater importance.

Some rocketry software predicts the coefficient of drag for rockets, such as:

· Rocdrag
· Aerolab
· RockSim (maybe no the demo version)
· Rogers Aeroscience Software (not shareware)

Wind effects on trajectory W in d in d u c e d A O A

The launching of rockets should never be done
under high wind conditions. Basically wind affects a
rocket's flight in two ways: stability and R o c k e t v e lo c it y
"weathercocking". V -W V

When a rocket leaves the ramp, its horizontal

velocity with respect to the surrounding air is the
rocket's horizontal velocity at no wind conditions
minus the wind velocity.

If the rockets vertical velocity is not significantly

larger than the wind velocity, the rocket will be W in d v e lo c it y
exposed to a wind induced angle of attack which
may be substantially larger than the 10 degrees W
covered by common Barrowman stability analysis.
The CP might then moves forward of it's designed
position and thus render an otherwise stable rocket
unstable or neutrally stable. These conditions may
be avoided by awaiting calmer conditions.
If, on the other hand, the rocket stays stable under
windy conditions, it will start to pivot against the
wind to eliminate the wind induced AOA. This effect
is commonly known as weathercocking.
No wind
If the rocket pivot against
the wind while the motor is
burning, the rocket will then
accelerate in the new
Wind With wind direction. The net result is
that the rocket simply turns
in the direction against the
wind, and the trajectory will
be flatter than expected. It
should be noted that
trajectory is affected only
when the rocket
accelerates while under
influence by the wind: When the rocket gains velocity, trajecory gets flatter, and when the
rocket looses velocity trajectory gets steeper. However, the acceleration during powered flight
is dominant, making a flatter trajectory the net result of the wind influence.

After burnout, the trajectory is practically unaffected by the wind. However, stability might still
be in danger. It is sometimes observed that a rocket gets unstable at apogee due to the wind.

Design for stability
Stability is a necessary condition for successful flight. Unstable rockets are failures, and
may even be dangerous. Keep the design simple, with no unnecessary fins or transitions.
Place the fins only at the aft end of the rocket. Make the fins thin - but do not underestimate
the forces that act on them - they should be made from strong materials and thoroughly
attached to the rocket body.

Check the Static Stability Margin

Check the CG for the rocket with and without propellant by a simple balancing procedure.
Easy to do, and it may save You from disappointment. Use some of the suggested programs
to determine the rocket's Cp. Make sure, that CG is between one and two rocket diameters
forward of CP under ANY condition during flight - rather more than less.

Design for performance

If it does not conflict with your stability precautions, design for low drag. Low drag means high
performance. Make the fins thin, and not too large. Make the rocket body slender, but not too
long. As a rule of thumb, the rocket body should be between 10 and 20 times the diameter.
For supersonic flying rockets, a sharp pointed nose and sharp leading and trailing edges on
the fins are preferable. Keep the overall surface down.

Avoid high winds

Never launch a rocket in high winds, and never launch it vertically. Instead, launch it at an 85
deg. elevation directly against the wind. If the rocket weathercocks, then you will know
precisely in what direction it will fly. The trajectory may be longer and flatter than expected,
but if the rocket carries a recovery system, the same wind will make it drift straight back
towards you, thus saving you from a long walk.

Always think safety

Safety first, not only for yourself, but also for the surroundings. Plan everything in detail
before actually setting up a launch.

Note on software:
The suggested software for stability and drag analysis are meant as examples only. There
might exist other excellent software for the same purposes.

Suggested literature in the field of rocketry aerodynamics:

Fluid Dynamic Drag

S. F. Hoerner
Hoerner Fluid Dynamics 1965

Boundary Layer Theory

Dr. H Schlichting

Mechanics of Fluids
W. J. Duncan, A .S Thom, A. D. Young
Edward Arnold

Missile Configuration Design

S. S. Chin
McGraw-Hill 1961

Theory of Wing Sections

Ira h. Abbot, A. E. Von Doenhoff
Dover Publications, Inc 1958

USAF Stability and control DATCOM

Flight Control Division
Air Force Flight Dynamics Laboratory
Wright-Patterson Air Force Base, Ohio