aerodynamic forces & moments
TRANSCRIPT
Feb 05 Aero Coeff Definition & PRODAS Entry 1
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Basic Aerodynamics
Definition of Forces & Moments
Feb 05 Aero Coeff Definition & PRODAS Entry 2
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
Feb 05 Aero Coeff Definition & PRODAS Entry 3
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
Feb 05 Aero Coeff Definition & PRODAS Entry 4
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
Feb 05 Aero Coeff Definition & PRODAS Entry 5
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
Feb 05 Aero Coeff Definition & PRODAS Entry 6
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
Notional diagram to showvector orientation, not location
Feb 05 Aero Coeff Definition & PRODAS Entry 7
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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
Feb 05 Aero Coeff Definition & PRODAS Entry 8
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Aerodynamic Force &Coefficient Definition
Normal Force = 1/2 ρ A CN V2
CN = Normal Force Coefficient = CNα Sinαm + CNα3 (Sinαm)3
Normal Force
V
αm
Angle of Attack Plane
Notional diagram to showvector orientation, not location
Feb 05 Aero Coeff Definition & PRODAS Entry 9
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Aerodynamic Force &Coefficient Definition
Magnus Force = 1/2 ρ A (pd/2V) CYp V2
CYp = Magnus Force Coefficient = CYpα Sinαm + CYpα3 (Sinαm)3
V
αm
Angle of Attack Plane
Magnus Force
Notional diagram to showvector orientation, not location
Feb 05 Aero Coeff Definition & PRODAS Entry 10
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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
Angle of Attack Plane
V
αm
Pitching Moment
Notional diagram to showvector orientation, not location
Feb 05 Aero Coeff Definition & PRODAS Entry 11
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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)
Feb 05 Aero Coeff Definition & PRODAS Entry 12
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Aerodynamic Moment &Coefficient Definition
Pitch Damping Moment = 1/2 ρ A d Cmq (qd/2V)V2
Cmq = Pitch Damping Moment Coefficient = Cmq0 + Cmq2 (Sinαm)2+Cmq4(Sinαm)4
Angle of Attack Plane
V
αm
Pitch Damping Moment
- -
Notional diagram to showvector orientation, not location
α&α&α&
Feb 05 Aero Coeff Definition & PRODAS Entry 13
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Aerodynamic Moment &Coefficient Definition
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
Angle of Attack Plane
V
αm
Magnus Moment
Notional diagram to showvector orientation, not location
Feb 05 Aero Coeff Definition & PRODAS Entry 14
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Aerodynamic Moment &Coefficient Definition
Spin Deceleration Moment = 1/2 ρ A d Clp (pd/2V)V2
Clp = Spin Deceleration Coefficient = Clp0 + Clpα2 (Sinαm)2
Angle of Attack Plane
V
αm
Spin Decel Moment
Notional diagram to showvector orientation, not location
Feb 05 Aero Coeff Definition & PRODAS Entry 15
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Aerodynamic SpinnerInput Reference
Meplat Dia.
Ogive Length
Ogive RadiusBand Length
Band Dia.
BoattailDia.
BoattailLength
BoomLength
BoomDia.
Feb 05 Aero Coeff Definition & PRODAS Entry 16
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
Feb 05 Aero Coeff Definition & PRODAS Entry 17
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“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
Feb 05 Aero Coeff Definition & PRODAS Entry 18
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Aerodynamic FinnerInput Reference
BoomLength
BoatTail
Length
SpikeLength
Band
SpikeDia.
Reference Dia.
Boat Tail Dia.
BoomDia.
Flare Dia.
Flare Length Grooves
Ogive Length
Meplat Dia.
Feb 05 Aero Coeff Definition & PRODAS Entry 19
If you can’t get a bigger target...“Finner” Body Input
• Body Inputs Identical to “Spinner”
Feb 05 Aero Coeff Definition & PRODAS Entry 20
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
Feb 05 Aero Coeff Definition & PRODAS Entry 21
If you can’t get a bigger target...“Finner” Fin Input
Fin Geometry Definition
(Taken Perpendicularto Fin Leading Edge)
Feb 05 Aero Coeff Definition & PRODAS Entry 22
If you can’t get a bigger target...“Finner” Fin Input
Fin Geometry Definition (Con’t)Distance From Fin Leading Edge to Nose
Feb 05 Aero Coeff Definition & PRODAS Entry 23
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
Feb 05 Aero Coeff Definition & PRODAS Entry 24
If you can’t get a bigger target...“Finner” Groove Definitions
Feb 05 Aero Coeff Definition & PRODAS Entry 25
If you can’t get a bigger target...“Finner” Flare Input
Feb 05 Aero Coeff Definition & PRODAS Entry 26
If you can’t get a bigger target...“Finner” Flare Input Definitions
Feb 05 Aero Coeff Definition & PRODAS Entry 27
If you can’t get a bigger target...“Spinner” Tabular Output
Feb 05 Aero Coeff Definition & PRODAS Entry 28
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
Feb 05 Aero Coeff Definition & PRODAS Entry 29
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“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
Feb 05 Aero Coeff Definition & PRODAS Entry 30
If you can’t get a bigger target...“Finner” Tabular Output
Feb 05 Aero Coeff Definition & PRODAS Entry 31
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
Feb 05 Aero Coeff Definition & PRODAS Entry 32
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““Higher OrderHigher Order””Aerodynamic Aerodynamic CoefficientsCoefficients
Feb 05 Aero Coeff Definition & PRODAS Entry 33
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PC-PRODAS Aerodynamic Forces & Moments
Aerodynamic TrimsAerodynamic Trims
Feb 05 Aero Coeff Definition & PRODAS Entry 34
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PC-PRODAS Aerodynamic Forces & Moments
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
Feb 05 Aero Coeff Definition & PRODAS Entry 35
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Finner Assembly Trim
PC-PRODAS Aerodynamic Forces & Moments
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.
Feb 05 Aero Coeff Definition & PRODAS Entry 36
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PC-PRODAS Aerodynamic Forces & Moments
Finner Automatically Predicts Trim Force & Moment Coefficients
Feb 05 Aero Coeff Definition & PRODAS Entry 37
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PC-PRODAS Aerodynamic Forces & Moments
Angle of Attack Induced Angle of Attack Induced Forces & MomentsForces & Moments
Feb 05 Aero Coeff Definition & PRODAS Entry 38
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PC-PRODAS Aerodynamic Forces & 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.
Feb 05 Aero Coeff Definition & PRODAS Entry 39
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PC-PRODAS Aerodynamic Forces & Moments
Angle of Attack Induced Side Force, Side Moment, & Roll Moment
Fin “shadowed” from air flow
VelocityAngle of Attack
InducedSide
Moment InducedRoll
Moment
ClγαCnγα
InducedSide Force
CYγα Cmγα
InducedPitching Moment
Feb 05 Aero Coeff Definition & PRODAS Entry 40
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PC-PRODAS Aerodynamic Forces & Moments
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
Feb 05 Aero Coeff Definition & PRODAS Entry 41
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PC-PRODAS Aerodynamic Forces & Moments
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
Feb 05 Aero Coeff Definition & PRODAS Entry 42
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PC-PRODAS Aerodynamic Forces & Moments
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
Feb 05 Aero Coeff Definition & PRODAS Entry 43
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PC-PRODAS Aerodynamic Forces & Moments
Catastrophic Yaw
Feb 05 Aero Coeff Definition & PRODAS Entry 44
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PC-PRODAS Aerodynamic Forces & Moments
Angle of Attack Induced Side Force, Side Moment, & Roll Moment
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
Feb 05 Aero Coeff Definition & PRODAS Entry 45
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PC-PRODAS Aerodynamic Forces & Moments
Side force & moment(at low angle of attack)
can be caused by:
Offset Fins “Wrap Around” Fins
Feb 05 Aero Coeff Definition & PRODAS Entry 46
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PC-PRODAS Aerodynamic Forces & Moments
Finner Predicts Side Moment Due to Wrap Around Fins
Feb 05 Aero Coeff Definition & PRODAS Entry 47
If you can’t get a bigger target...Wrap Around Fin Indicator
Feb 05 Aero Coeff Definition & PRODAS Entry 48
If you can’t get a bigger target...Induced Moment Coefficient
Feb 05 Aero Coeff Definition & PRODAS Entry 49
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
Feb 05 Aero Coeff Definition & PRODAS Entry 50
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
Feb 05 Aero Coeff Definition & PRODAS Entry 51
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
Feb 05 Aero Coeff Definition & PRODAS Entry 52
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 ------
Feb 05 Aero Coeff Definition & PRODAS Entry 53
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
Feb 05 Aero Coeff Definition & PRODAS Entry 54
If you can’t get a bigger target...
Alternate Aero Coefficient Sources
ENGINEERING DESIGNHANDBOOK
DESIGN FOR CONTROL OFPROJECTILE FLIGHTCHARACTERISTICS
PAMPHLET AMCP 706-242
HEADQUARTERS, U.S. ARMY MATERIAL COMMAND SEPTEMBER 1966
Feb 05 Aero Coeff Definition & PRODAS Entry 55
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Effect of Ogive ShapeOn Aeros
Feb 05 Aero Coeff Definition & PRODAS Entry 56
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Boattail Effect on Aeros
Feb 05 Aero Coeff Definition & PRODAS Entry 57
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
Feb 05 Aero Coeff Definition & PRODAS Entry 58
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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
Feb 05 Aero Coeff Definition & PRODAS Entry 59
If you can’t get a bigger target...Scale Effects
Effect of Projectile Effect of Projectile ““ScaleScale””onon
Aerodynamic CoefficientsAerodynamic Coefficients
Feb 05 Aero Coeff Definition & PRODAS Entry 60
If you can’t get a bigger target...Scale Effect on CX0
Feb 05 Aero Coeff Definition & PRODAS Entry 61
If you can’t get a bigger target...Scale Effect on CNα
Feb 05 Aero Coeff Definition & PRODAS Entry 62
If you can’t get a bigger target...Scale Effect on CPN
Feb 05 Aero Coeff Definition & PRODAS Entry 63
If you can’t get a bigger target...Scale Effect on Cmα