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Rocket Aerodynamics and Stability
By Jan-Erik RønningenNorwegian Rocket Technology[ [email protected] ][ www.rocketconsult.no ]
Version: 1.40 2008
Rocket Flight Video
Contents Aerodynamics
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
Earth Atmosphere (1)
Earth Atmosphere (2)
Launching a sounding rocket at different seasons can give up to 5% variation in performance.
Earth Atmosphere (3)
Mach Definition
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 : SubsonicM 0.9 - 1.1 : Transonic or sonic (M = 1)M > 1 : SupersonicM > 5 : Hypersonic
][_
TR
vMach etlydhastighLokalHastighetSpeed
Speed of Sound
Shock Waves (1)
Shadowfax picture of a supersonic bullet
F-18 at supersonic flight
Shock Waves (2)
What Affects Aerodynamic Drag? The Object
Size Shape
Motion Inclination Speed
Atmosphere Mass Compressibility Viscosity
Air Flow Around Objects
Cylindrical Rod - Lower resistancePlate - Induce large resistance
Symmetrical wing profile (Alpha = 0 °) - Least resistance
Air Flow Around Objects (2)
Almost factor 30 better than the flat plate!
Cd: 0.37
Cd: 0.31
CD Values for Various Nose Designs
Cd: <0.05 >0.01 0.20 0.20 0.34 0.90 1.00
4:1 3:1 1:1
Cd for different nose design (subsonic velocity) and zero alpha:
CD vs. Mach
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4 5 6 7 8
Mach
Cd
Mach
v
v
Pressure Distribution Around a Rocket
Aerodynamic Forces
n
Surface
Aero dAnpAnpF
V
(h)
C.P
C.G
D
L
Faero
+
G
L = Lift, net force normal to air flowD = Drag, net force parallell to air flow
Pressure variation
n
n
Center of Pressure
dxxp
dxxpxCP )(
)(
Taken from ref.: http://exploration.grc.nasa.gov/education/rocket/cp.html
Determine Center of Pressure
Taken from ref.: http://exploration.grc.nasa.gov/education/rocket/rktcp.html
Rocket Drag Equation
][2
),(2
NvAMCD D
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
Dynamic Pressure
Dynamic Load
][)( 221 PavhQ
Student Rocket:
D=ø70mm0.07m
kgNAQF
mDA
0.2165.211700385.0550000
00385.04
maxmax
22
D
Induced Drag
Vortex center
Aft vortex
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
Pu
Po
Lift
Drag due to LiftLift dueto Lift
Airflow
Chord
A symmetrical wing/fin willgenerate lift when | > 0° |
Center ofMass
Drag Reducing Feature
7-9°Mindre undertrykk område Pluft < Pa
Større undertrykk område Pluft < Pa
Rakett med ”boat-tail”
Rakett uten aerodynamisk avslutning
Larger aft surface
Smaller aft surface
Rocket with conical end (”Boat-Tail”)
Rocket with sharp end
QUEST: What Rocket Shape have Highest Drag?
D
A
dD
B
dD
C
Axis Definition
Center of Gravity
The Weathercock Principle
No Rotation
Rotation about C.G since C.P offset of the C.G location
No Rotation
C.G
C.G C.P
C.G
Spin Stabilization (1)
D
L
G
v
Spin Frequency: 2000HzL/D : max. 4
D
L v
G
Spin Frequency: 4HzL/D : > 4
Spin Stabilization (2)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 25 50 75 100 125 150 175 200 225 250Time (sec)
Pitc
h an
d R
oll F
requ
ency
(Hz)
Pitch
Roll Rate = 3.1 Hz
Roll Rate = 2.5 Hz
Roll Rate = 1.9 Hz
Roll Rate Should Have Positive SlopeWhen Crossing Pitch Frequency
NSR Min Roll Rate at Burnout = 2.5 Hz
Active Stability
Naturally dynamic unstable, but maintained stable due to an automatic attitude system. Trajectory and stability canbe 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 ofthe nozzle or by deflecting the plume.
C.G C.P
F
C.G C.P
aFl
Thrust Vector Control System
IRIS-T Air-To-Air Jet Vane TVC System
Static MarginStatic Margin vs. Time
SCA2005 Rocket
5
6
7
8
9
10
11
0 10 20 30 40 50 60 70 80
Time [s]
Stat
ic M
argi
n [-
] SM = (XCG - XCP) / dref
Stable Rocket Flight?
Quest:
C.P
C.G
Aerodynamisk ustabil rakettUnstabel Rocket Configuration B) Finne ant. eller areal økes
C.G
Ny C.P
Alt.2 Increase Fin AreaA) Masse lagt til nesen
Ny C.G
C.P
Ny masse
Alt.1 More mass in front
New Mass