Rocket Aerodynamics and Stability
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Transcript Rocket Aerodynamics and Stability
Rocket Aerodynamics and Stability
By Jan-Erik Rønningen
Norwegian 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
Mach
Speed
Hastighet
Lokal
_ lydhastigh
Speed
of Sound et
v
[]
R T
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 0.9 - 1.1 : Transonic or sonic (M = 1)
M > 1 : Supersonic
M > 5 : Hypersonic
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
Plate - Induce large resistance
Cylindrical Rod - Lower resistance
Symmetrical wing profile (Alpha = 0 °) - Least resistance
Air Flow Around Objects (2)
Cd: 0.37
Almost factor 30 better than the flat plate!
Cd: 0.31
CD Values for Various Nose Designs
Cd for different nose design (subsonic velocity) and zero alpha:
Cd: <0.05
4:1
>0.01
0.20
0.20
0.34
3:1
1:1
0.90
1.00
CD vs. Mach
1.0
0.9
0.8
0.7
Cd
0.6
0.5
0.4
0.3
0
1
2
3
4
Mach
Mach
5
6
7
8
Pressure Distribution Around a
Rocket
v
v
Aerodynamic Forces
V
L = Lift, net force normal to air flow
D = Drag, net force parallell to air flow
(h)
n
n
L
C.G
Faero
n
+
D
C.P
G
F Aero
p n A p n dA
Surface
Pressure variation
Center of Pressure
CP
x p( x ) dx
p( x) dx
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
D CD ( M , ) A
v2
2
[N ]
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
Dynamic Load
Student Rocket:
D=ø70mm0.07m
Q 12 (h) v [Pa]
2
A
D2
0.00385m2
4
Fmax Qmax A 550000 0.00385 2117.5N 216.0kg
D
Induced Drag
Lift due
to Lift
Drag due to Lift
Lift
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.
Center of
Mass
Chord
Po > Pu Positive Lift
Po
Aft vortex
Airflow
A symmetrical wing/fin will
generate lift when | > 0° |
Pu
Vortex center
Drag Reducing Feature
Larger
aft surface
Større
undertrykk
område
Pluft < Pa
Rocket
sharp end
Rakett
utenwith
aerodynamisk
avslutning
7-9°
Smallerundertrykk
aft surface
Mindre
område
Pluft < Pa
Rakett med
Rocket
with”boat-tail”
conical end (”Boat-Tail”)
QUEST: What Rocket Shape have
Highest Drag?
D
A
d
D
B
d
C
D
Axis Definition
Center of Gravity
The Weathercock Principle
C.G
No Rotation
C.G
No Rotation
C.G
C.P
Rotation about C.G since C.P offset of the C.G location
Spin Stabilization (1)
Spin Frequency: 2000Hz
L/D : max. 4
L
D
v
G
Spin Frequency: 4Hz
L/D : > 4
L
D
G
v
Spin Stabilization (2)
Pitch and Roll Frequency (Hz)
3.5
Roll Rate Should Have Positive Slope
When Crossing Pitch Frequency
3.0
NSR Min Roll Rate at Burnout = 2.5 Hz
2.5
Roll Rate = 3.1 Hz
2.0
Roll Rate = 2.5 Hz
1.5
Roll Rate = 1.9 Hz
1.0
Pitch
0.5
0.0
0
25
50
75
100 125 150
Time (sec)
175
200
225
250
Active Stability
C.G C.P
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
Thrust Vector Control System
IRIS-T Air-To-Air Jet Vane TVC System
Static Margin
Static Margin vs. Tim e
SCA2005 Rocket
11
10
Static Margin [-]
9
SM = (XCG - XCP) / dref
8
7
6
5
0
10
20
30
40
Tim e [s]
50
60
70
80
Stable Rocket Flight?
Quest:
New Mass
Unstabel Rocket Configuration
Alt.1 More mass in front
Alt.2 Increase Fin Area