Rocket Aerodynamics and Stability By Jan-Erik Rønningen Norwegian Rocket Technology [ contact@rocketconsult.no ] [ www.rocketconsult.no ] Version: 1.40 2008

Rocket Flight Video

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

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] 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 0.9 - 1.1 : Transonic or sonic (M = 1) M > 1 : Supersonic M > 5 : Hypersonic

F-18 at supersonic flight 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) Almost factor 30 better than the flat plate! Cd: 0.37 Cd: 0.31

CD Values for Various Nose Designs Cd for different nose design (subsonic velocity) and zero alpha: Cd: <0.05 >0.01 0.20 0.20 0.34 0.90 1.00 4:1 3:1 1:1

CD vs. Mach Cd Mach

Pressure Distribution Around a Rocket  v v

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

Center of Pressure 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 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=ø70mm0.07m D

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

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”)

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

Axis Definition

Center of Gravity

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

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

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

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

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

Static Margin SM = (XCG - XCP) / dref

Stable Rocket Flight?

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