Aerodynamic Forces & Moments

Feb 05 Aero Coeff Definition & PRODAS Entry 1

If you can’t get a bigger target...

Basic Aerodynamics

Definition of Forces & Moments


If you can’t get a bigger target...Aerodynamic Forces

External Projectile Shape Determines:– Drag Force, Normal Force, Magnus/ Side Force Coefficients; – Normal Force and Magnus/Side Force Center of Pressure Locations

As a Function of Mach Number and Angle of Attack

Normal ForceCenter of Pressure


If you can’t get a bigger target...Aerodynamic Moments

Mass Distribution Within the Projectile, Combined With the Force Coefficients / CP Location(s) Determines:

–Pitching Moment, Magnus/Side Moment, Pitch Damping Moment Coefficients

As a Function of Mach Number and Angle of Attack

Normal ForceCenter of Pressure Center of Mass


If you can’t get a bigger target...“Odd” Aerodynamic Moments

Manufacturing Tolerances & Processes, With “First Order”Aerodynamic Forces and Moments Determine:– Projectile Center of Mass Offset (Causing Torque Forces & Moments)– Trim Forces and Moments

PA Tilt

Misaligned Fin & Fuze

Offset Center of Mass WRT Projectile Exterior


If you can’t get a bigger target...Aerodynamic Force Definition

Normal Force

V

αm

Axial Force

Angle of AttackPlane

Magnus Force(acts @ Magnus Force Center of Pressure)

(acts @ Normal Force Center of Pressure)

Center of Mass (Gravity)

Notional diagram to showvector orientation, not location


If you can’t get a bigger target...Aerodynamic Moment Definition

Angle of Attack Plane

V

αm

Pitching & Pitch Damping Moments

Magnus Moment

Spin Decel Moment




Aerodynamic Force &Coefficient Definition

Axial Force = - 1/2 ρ A Cx V2

Cx = Drag Coefficient = Cx0 + Cxα2 (Sin αm)2

V

αm

Axial Force

Angle of Attack PlaneNotional diagram to show

vector orientation, not location




Normal Force = 1/2 ρ A CN V2

CN = Normal Force Coefficient = CNα Sinαm + CNα3 (Sinαm)3

Normal Force

V

αm






Magnus Force = 1/2 ρ A (pd/2V) CYp V2

CYp = Magnus Force Coefficient = CYpα Sinαm + CYpα3 (Sinαm)3

V

αm


Magnus Force




Aerodynamic Moment &Coefficient Definition

Pitching Moment = 1/2 ρ A d Cm V2

Cm = Pitching Moment Coefficient = Cmα Sinαm + Cmα3 (Sinαm)3+Cmα5(Sinαm)5


V

αm

Pitching Moment




Pitching Moment (Static Stability)

Center of Pressure

Velocity Vector

Center of Gravity

Normal Force

Pitching Moment

Center of Pressure

Velocity VectorCenter of Gravity

Normal Force

Pitching Moment

“Finner”(Large - #’s)

“Spinner”(+ #’s)

Pitching Moment, M = 1/2 ρ A d Cm V2

Where: Cmα Sin(α) = CNα Sin(α)(CG-CPN)




Pitch Damping Moment = 1/2 ρ A d Cmq (qd/2V)V2

Cmq = Pitch Damping Moment Coefficient = Cmq0 + Cmq2 (Sinαm)2+Cmq4(Sinαm)4


V

αm

Pitch Damping Moment

- -


α&α&α&




Magnus Moment = 1/2 ρ A d Cnp (pd/2V)V2

Cnp = Magnus Moment Coefficient = Cnpα Sinαm+ Cnpα3 (Sinαm)3+Cnpα5(Sinαm)5

Acts Perpendicular to the plane of the Angle of Attack


V

αm

Magnus Moment





Spin Deceleration Moment = 1/2 ρ A d Clp (pd/2V)V2

Clp = Spin Deceleration Coefficient = Clp0 + Clpα2 (Sinαm)2


V

αm

Spin Decel Moment




Aerodynamic SpinnerInput Reference

Meplat Dia.

Ogive Length

Ogive RadiusBand Length

Band Dia.

BoattailDia.

BoattailLength

BoomLength

BoomDia.


If you can’t get a bigger target...“Spinner” Input

Ogive Input

Band InputBoom Input

Boattail Input

Meplat Dia

• Enter Appropriate Meplat Dia., Ogive Radius, etc.• Check Aero Config. Vs. Geometry on Aero Model Tab



“Spinner” Physical & Aero Model Comparison

Ogive Radius

MeplatDia.

• Are Meplat Dia. & Ogive Radius Appropriate ?• Is Boattail (if used) correct length & aft diameter ?• Band Length & Diameter Correct?• Check Boom & Boattail Info If Used• Adjust if req’d in Geometry Input Tab• Then Push “Calc New Aeros” Button on Geometry Input Tab



Aerodynamic FinnerInput Reference

BoomLength

BoatTail

Length

SpikeLength

Band

SpikeDia.

Reference Dia.

Boat Tail Dia.

BoomDia.

Flare Dia.

Flare Length Grooves

Ogive Length

Meplat Dia.


If you can’t get a bigger target...“Finner” Body Input

• Body Inputs Identical to “Spinner”


If you can’t get a bigger target...“Finner” Fin Input

Finner 2000 Allows Up To 3 Fin Sets(No Fins on: Ogive, Spike, or Boattail)

1st Fin Set2nd Fin Set

3rd Fin Set



Fin Geometry Definition

(Taken Perpendicularto Fin Leading Edge)



Fin Geometry Definition (Con’t)Distance From Fin Leading Edge to Nose


If you can’t get a bigger target...“Finner” Groove Input

Finner 2000 Allows Up To 3 Different Groove Sets1st Groove Set

2nd Groove Set

3rd Groove Set


If you can’t get a bigger target...“Finner” Groove Definitions


If you can’t get a bigger target...“Finner” Flare Input


If you can’t get a bigger target...“Finner” Flare Input Definitions


If you can’t get a bigger target...“Spinner” Tabular Output


If you can’t get a bigger target...“Spinner” Plot Output

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 1 2 3 4 5 6 7 8

Mach Arrow Tech Assoc-PRODAS2000 30heaj.pr2 30MM PGU13 HEI AEROJET 08/26/1999

Cx0 Zero Yaw Drag



“Finner” Physical & Aero Model Comparison

Root Chord

Tip

Boom Length(2 Elements on 2 Components)

Boattail Length(5 Elements on 2 Components)

Groove

“Wetted” Ogive Length(4 Elements on 3 Components)

Ogive Radius

• Physical Geometry Above, Aero Description Below• Allows User to Visually “Verify” Correct Aero Description• Improves Accuracy & Confidence in Predicted Aero’s


If you can’t get a bigger target...“Finner” Tabular Output


If you can’t get a bigger target...“Finner” Plot Output

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2

Mach Arrow Tech Assoc-PRODAS2000 #120m934.pr2 120mm M934 Mortar, Aug 97 Mass & Aeros 08/26/1999

Cx0 Zero Yaw Drag



““Higher OrderHigher Order””Aerodynamic Aerodynamic CoefficientsCoefficients



PC-PRODAS Aerodynamic Forces & Moments

Aerodynamic TrimsAerodynamic Trims




Aerodynamic Trim

• Caused by mis-aligned projectile components• Trim angle rotates with projectile body• No dynamics stability problem for spinners (dispersion?)• Trouble for finners• W/O spin, trims force projectile to fly at an angle of attack• When roll rate = yaw rate,

angle of attack = Trim Angle x Amplification Factor!• Can lead to Angle of Attack Induced Side Force,

Side Moment & Roll Moment = Roll-Yaw Lock-In

Angle of Attack

Velocity



Finner Assembly Trim


CPNFinCPNBody

CG

23.47cal from nose 13.19

cal from nose 2.59

CNαFin = 11.58CNαBody = 3.36

Assume: 0.1 Deg Fin Mis-alignment: (difficult to measure) Fin Trim Moment About CG = Separation x Normal Force Coeff x Angle

= (23.47-13.19) x 11.58 x 0.1 = 11.9 cal-deg. Which is reacted by body

11.9 cal-deg = (Forebody CP-CG Separation) x CNαBody x Angle= (13.19-2.59) x 3.36 x αbody= 35.62 αbody

αbody = 0.33 deg. (Body Angle of Attack) αTotal = (0.33x3.36)+(0.1x11.58)/(CNα

Total) = 0.15 deg.




Finner Automatically Predicts Trim Force & Moment Coefficients




Angle of Attack Induced Angle of Attack Induced Forces & MomentsForces & Moments




Angle of Attack Induced Side Force, Side Moment, & Roll Moment

VelocityAngle of Attack Plane

Angle of Attack

Flow Symmetry, No Induced Side Force, Side Moment, or Roll Moment Vs.

Airflow

Fin “shadowed” from air flow

Asymmetric Flow Across Fins Due to:• Angle of Attack (> ~ 10 Deg.)• Roll Orientation

Induces Forces & Moments on Projectile

45 Deg.





Fin “shadowed” from air flow

VelocityAngle of Attack

InducedSide

Moment InducedRoll

Moment

ClγαCnγα

InducedSide Force

CYγα Cmγα

InducedPitching Moment




Induced Side Force Coefficient vs. Angle of Attack & Roll Orientation

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 10 20 30 40 50 60 70 80

Roll Orientation, Deg

Indu

ced

Side

For

ce

Coe

ffici

ent

12.2 Deg16.2 Deg20.2 Deg




Induced Side Moment Coefficient vs. Angle of Attack & Roll Orientation

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 10 20 30 40 50 60 70 80

Roll Orientation, Deg.

Indu

ced

Side

M

omen

t Coe

ffici

ent

20.2 Deg16.2 Deg12.2 Deg




Induced Roll Moment Coefficient vs. Angle of Attack & Roll Angle

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 10 20 30 40 50 60 70 80

Roll Angle, Deg.

Indu

ced

Rol

l Mom

ent

Coe

ffici

ent

16.8 Deg12.5 Deg4.2 Deg




Catastrophic Yaw





Velocity

Angle of Attack

• Induced Side Force, Side Moment, & Roll Moment are Destabilizing• Results In Catastrophic (Lunar) Yaw For Fin Stabilized Projectiles• Loss of Velocity, Range & Penetration Capability

Side moment acts perpendicular to page, increasing total angle of attack




Side force & moment(at low angle of attack)

can be caused by:

Offset Fins “Wrap Around” Fins




Finner Predicts Side Moment Due to Wrap Around Fins


If you can’t get a bigger target...Wrap Around Fin Indicator


If you can’t get a bigger target...Induced Moment Coefficient


If you can’t get a bigger target...Projectile Parameter Comparisons

Effect of Projectile Design Effect of Projectile Design Parameters onParameters on

Aerodynamic CoefficientsAerodynamic Coefficientsandand

Projectile StabilityProjectile Stability


If you can’t get a bigger target...Subsonic Mach #’s

Length With SQ Base Drag Gyro Stab (Pitch) Dyn Stab (Magnus)> 6 Cal High Poor Poor3.5 to 5 High OK OK (Precession)

With Boattail (.6 cal) Medium Marginal Look Out> 5. Cal (40 % Reduction)

With Boattail (1.0 Cal) Low Poor Bad> 5. Cal (50% Reduction)

Nose LengthShort (2 Cal) Small Increase Better BetterLong (3 Cal) Small Decrease Worse WorseOgiveCone Small changes Small changes Small changes

CG LocationForward NA Better WorseRearward NA Worse Better


If you can’t get a bigger target...Transonic Mach #’s

Projectile Base Config. Drag Gyro Stab Dyn StabWith square base Higher OK OKMedium Boattail Close to low Poor AwfulLong Boattail Low Very Poor Forget it

Nose LengthShort (2 cal) High Best BestLong (3 cal) Low Worst WorstOgive Low Small changes Small changesCone High (Precession)

CG LocationForward NA Better WorseRearward NA Worse Better

Rotating BandCan cause large Magnus effects* Unpredictable


If you can’t get a bigger target...Supersonic Mach #’s

Projectile Base Config. Drag Gyro Stab Dyn StabWith square base OK OK PrecessionMedium Boattail -5% OK May HelpLong Boattail -10% OK ???

Nose LengthShort (2 cal) High Better PrecessionLong (3 cal) -30% ----- May helpTangent Ogive A Bit Higher A Bit Worse PrecessionSecant Ogive A Bit Lower A Bit Better --------Conical Ogive -7% @ M>3.0 A Bit Better --------

CG Location Forward NA ----- BetterRearward NA Worse ------


If you can’t get a bigger target...Estimating Aero Coefficients

• Need to Know:– Drag, Lift, Stabilizing Moment, Damping Characteristics, Spin

Characteristics• The range of aero coefficients is fairly well covered in the table

• The effect of ogive shape in the aerodynamics are shown in the following figures



Alternate Aero Coefficient Sources

ENGINEERING DESIGNHANDBOOK

DESIGN FOR CONTROL OFPROJECTILE FLIGHTCHARACTERISTICS

PAMPHLET AMCP 706-242

HEADQUARTERS, U.S. ARMY MATERIAL COMMAND SEPTEMBER 1966



Effect of Ogive ShapeOn Aeros



Boattail Effect on Aeros


If you can’t get a bigger target...Effect of Nose Radius on CX0

Change in CX per Change of Nose Radius Relative to RT/R = 0.4

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

RT/R

∆C

X0

Mach 0.8

Mach 1.05

Mach 1.5

Mach 2.0

Mach 3.0

Cone Secant Tangent



Effect of Meplat Diameter on CX0

Change in CX Per Change of Meplat Diameter Relative to Dm = 0.12

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Meplat Diameter, Calibers

∆C

X0

Mach 3.0Mach 2.0Mach 1.5 Mach 1.05Mach 0.8


If you can’t get a bigger target...Scale Effects

Effect of Projectile Effect of Projectile ““ScaleScale””onon

Aerodynamic CoefficientsAerodynamic Coefficients


If you can’t get a bigger target...Scale Effect on CX0


If you can’t get a bigger target...Scale Effect on CNα


If you can’t get a bigger target...Scale Effect on CPN


If you can’t get a bigger target...Scale Effect on Cmα

Documents

Aerodynamic Forces & Moments