1. Rocket Aerodynamics and Stability
By Jan-Erik Rønningen
Norwegian Rocket Technology
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Version:

2. Rocket Flight Video

3. Contents Aerodynamics Stability Mach Definition Atmosphere (2)
Shock Waves (2)
Air Flow around Objects (2)
CD Values for Various Nose Designs
CD vs. Mach
Aerodynamic Forces
Pressure Distribution Around a Rocket
Center of Pressure
Determine Center of Pressure
Rocket Drag Equation
Dynamic Load
Induced Drag
Drag Reducing Feature
QUEST: What Rocket Shape have Highest Drag?
Stability
Axis Definition
Center-of-Gravity
The Weathercock Principle
Weather Cocking of a Rocket
Fin Stabilization
Spin Stabilization (2)
Static Margin
Active Stability

4. Earth Atmosphere (1)

5. Earth Atmosphere (2)
Launching a sounding rocket at different seasons can give up to 5% variation in performance.

6. Earth Atmosphere (3)

7. Mach Definition R = Gas constant unique for the gas) [J / Kg-K]
Speed
Speed of Sound
R = Gas constant unique for the gas) [J / Kg-K]
286 J/kg-K for Air
T = Temperature [K]
 = specific heat capacity ratio [-] ( 1.44 for air)
M < 1 : Subsonic
M : Transonic or sonic (M = 1)
M > 1 : Supersonic
M > 5 : Hypersonic

8. F-18 at supersonic flight
Shock Waves (1)
                                                                 
Shadowfax picture of a
supersonic bullet
F-18 at supersonic flight

9. Shock Waves (2)

10. What Affects Aerodynamic Drag?
The Object
Size
Shape
Motion
Inclination
Speed
Atmosphere
Mass
Compressibility
Viscosity

11. Air Flow Around Objects
Plate - Induce large resistance
Cylindrical Rod - Lower resistance
Symmetrical wing profile (Alpha = 0 °) - Least resistance

12. Air Flow Around Objects (2)
Almost factor 30 better than the flat plate!
Cd: 0.37
Cd: 0.31

13. CD Values for Various Nose Designs
Cd for different nose design (subsonic velocity) and zero alpha:
Cd: < >
4:1
3:1
1:1

14. CD vs. Mach Cd
Mach

15. Pressure Distribution Around a Rocket v v

16. Aerodynamic Forces L = Lift, net force normal to air flow
D = Drag, net force parallell to air flow V
(h)  L
C.G
Faero +
C.P D  G
Pressure variation

17. Center of Pressure
Taken from ref.:

18. Determine Center of Pressure
Taken from ref.:

19. Rocket Drag Equation Dynamic Pressure
CD : Drag coefficient. Contains all complex dependencies like air compressibility, viscosity
body shape and angle-of-attack.
A : Reference area, typically the base diameter of the nose. Different A, affect the value of CD.
: Density of the atmosphere of consideration (typically 1.23kg/m3 for air at sea-level).
v : Rocket speed

20. Dynamic Load
Student Rocket:
D=ø70mm0.07m D

21. Induced Drag
A unsymmetrical fin / wing in an airflow will have excess pressure on
the face with least surface (often on the side facing down) and low
pressure on the opposite face with largest surface. The pressure
difference is the lift.
Po > Pu  Positive Lift
Drag due to Lift
Lift due
to Lift
Lift 
Center of
Mass Po
Chord 
Aft vortex
Airflow
A symmetrical wing/fin will
generate lift when |  > 0° | Pu
Vortex center

22. Rocket with conical end (”Boat-Tail”)
Drag Reducing Feature
Larger aft surface
Rocket with sharp end
Smaller aft surface
Rocket with conical end (”Boat-Tail”)

23. QUEST: What Rocket Shape have Highest Drag?B d D C

24. Axis Definition

25. Center of Gravity

26. The Weathercock Principle
C.G
C.G
No Rotation
C.G C.P
No Rotation
Rotation about C.G since C.P offset of the C.G location

27. Spin Stabilization (1) Spin Frequency: 2000Hz L/D : max. 4 L  D v G

28. Spin Stabilization (2) Roll Rate Should Have Positive Slope
Pitch
Roll Rate = 3.1 Hz
Roll Rate = 2.5 Hz
Roll Rate = 1.9 Hz
Roll Rate Should Have Positive Slope
When Crossing Pitch Frequency
NSR Min Roll Rate at Burnout = 2.5 Hz

29. Active Stability C.G C.P C.G C.P  Fl F a
Naturally dynamic unstable, but maintained stable due to an automatic attitude system. Trajectory and stability can
be maintained by moving servo controlled fins or by use of side thrusters. A thrust vectoring system (TVC) can
also be used. A TVC system is a device that can change the thrust vector by changing the orientation of
the nozzle or by deflecting the plume.
C.G C.P  Fl F a

30. Thrust Vector Control System
IRIS-T Air-To-Air Jet Vane TVC System

31. Static Margin
SM = (XCG - XCP) / dref

32. Stable Rocket Flight?

33. Unstabel Rocket Configuration
Quest:
Unstabel Rocket Configuration
Alt.1 More mass in front
New Mass
Alt.2 Increase Fin Area