Rocket Aerodynamics and Stability By Jan-Erik Rønningen Norwegian Rocket Technology [ contact@rocketconsult.no ]contact@rocketconsult.no [ .

Rocket Aerodynamics and Stability

By Jan-Erik RønningenNorwegian Rocket Technology[ contact@rocketconsult.no ][ 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 etlydhastighLokal

HastighetSpeed

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

Nv

AMCD 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

mD

A

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)

Pit

ch a

nd

Rol

l Fre

qu

ency

(H

z)

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

a

Fl

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]

Sta

tic

Mar

gin

[-] 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