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

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

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

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

Magnus Force = 1/2 ρ A (pd/2V) CYp V2

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

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

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

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

Magnus Moment

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

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

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

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 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

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 0.2 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

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 10 20 30 40 50 60 70 80

Roll Orientation, Deg

12.2 Deg16.2 Deg20.2 Deg

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

0 10 20 30 40 50 60 70 80

Roll Orientation, Deg.

20.2 Deg16.2 Deg12.2 Deg

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

-0.015

-0.005

0 10 20 30 40 50 60 70 80

Roll Angle, Deg.

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 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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 0.05 0.1 0.15 0.2 0.25 0.3 0.35Meplat Diameter, Calibers

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

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