TM 
AeroFinSim 4.5
NEW Fin Flutter and Loads Analysis Software Includes Spin Stabilization & Unsteady TorsionFlexure Flutter Copyright © 19992017 John Cipolla/AeroRocket & WarpMetrics The United States Air Force uses FinSim 4.0 FinSim used to model the CYA100 True Angle of Attack Display System Flutter velocity for the 2nd stage fins of the Quantum Leap Flutter velocity comparison with MSC/NASTRAN FEA solution Flutter velocity of a wing for a large modern airplane Defining composite material properties Designing spin stabilized Rockets Drag coefficient of spin stabilized Rockets Fin flutter and divergence velocity for supersonic flight (or Fin flutter analysis for the Don't Debate This rocket, the correct way) FinSim flutter velocity compared to NACA TN 4197, FEA and wind tunnel data Defining the thickness of an equivalent rectangular fin Latest Modifications  MAIN PAGE  SOFTWARE LIST  AEROTESTING  MISSION  RESUME  Please note this web page requires your browser to have Symbol fonts to properly display Greek letters (a, m, p, ∂ and w) 
By AeroRocket/John Cipolla 

2 Degree of Freedom Flutter Model featuring bending (h) and torsion (a) springs vibrating around the fin elastic axis (ea) 
Are Your Fins Strong Enough To Survive A
Wild Flight?
If you don't know how
strong your fins are, you'll either be launching an unsafe rocket,
or one which is overbuilt or that won't travel as high as
you'd like. Can you tell simply by looking? FinSim will predict how strong
your fins are. More importantly, it tells you if they will stay attached to the rocket under
the extreme loads
of a wild flight. FinSim can also tell you if the fins are too sturdy,
meaning they are heavier and thicker than they actually need to be. If so,
rocket performance will suffer.
PLEASE NOTE: FinSim s a sophisticated aeroelastic computer program when
using the optional Theodorsen and Ug
methods to predict flutter velocity and divergence velocity. Because FinSim uses a springmassdamper
model in its implementation of the Theodorsen and Ug
methods, fins and wings of almost any shape including winglets can be
analyzed. However, FinSim is easy to use for the untrained rocketeer because the
simple default Pines approximation equation displayed on this web page
provides a first order approximation for flutter velocity while the complex Theodorsen
and Ug
methods provide more accurate flutter and divergence velocity results for
high subsonic and supersonic flights.
What is FinSim?
First, FinSim is a structural analysis program. This portion of the program determines how strong the fins are by determining the
aerodynamic fin loads. You can't know if your fins are strong enough
unless you know the aerodynamic forces acting on them during launch. In its structural analysis mode, FinSim looks at the material of the fins, how long
the fins are, their span, how
thick they are, the size of the fillets, how they are attached to the rocket
(throughthewall or buttjoint), and what type of glue is used. Using this
information FinSim computes the
maximum allowable bending force the fin can handle without causing fin
separation. Then, using the maximum angleofattack the rocket will attain,
FinSim quickly computes aerodynamic loading based on the geometry of the
fins in terms of lift and drag. Then, the program displays the highest speed that can be
tolerated before the fins
will shred or separate from the rocket.
Second, FinSim is an aeroelasticity
program that predicts flutter and divergence velocity for up to six sets of fins.
Fin flutter and divergence are vibrations of the fin caused by the coupling of
free flight aerodynamic forces with lightly damped structural modes of vibration, that can range from a slight
buzzing sound to instances where the oscillations are so severe
the fins are stripped off the rocket. In any case, fin
flutter and divergence will create excess drag, causing the rocket to
lose altitude and flight speed. FinSim will predict when flutter
occurs, so you can either beef up the fins or choose a different
rocket motor that limits the speed of the model. Please note that for flutter/divergence and fin stress analyses the user needs to manually enter only six
finrelated variables to determine flutter velocity, divergence velocity and maximum
allowable rocket velocity based on allowable material strength.
To
determine flutter and divergence velocity, FinSim
assumes each fin is mounted on bending and torsion springs located at the fin's
elastic axis (Xea) and the aerodynamic center is located at the 1/4 chord point for subsonic
flight and 1/2 chord point for supersonic flight. A critical velocity will cause either a static instability (torsional
divergence) or an oscillatory instability (flutter). FinSim computes divergence
velocity and flutter velocity for up to 6 fin sets.
FinSim models flutter and divergence using either
the simple Pine's flutter approximation method or the more complex
Theodorsen method and Ug method to model high speed torsionflexure
wing and fin oscillations. When using FinSim to estimate flutter velocity using
the Pine's method, one
should bound the flutter prediction by using the theoretical 2D lift coefficient
(2p) to
establish a lower flutter boundary and the 3D lift coefficient to establish an
upper flutter boundary. The true flutter velocity will fall somewhere between
the two flutter boundaries.
Third, In addition to flutter and fin
stress analyses, FinSim has the ability to determine the stability of spin
stabilized rockets that use canted fins to achieve rocket rotation. FinSim
computes the center of pressure location of a spin stabilized rocket by applying
the principals of gyroscopic motion. In addition, the SpinSim routine
computes precession angle, added moment coefficient due to spin stabilization,
total pitch moment coefficient with spin stabilization, rotary speed, precession
speed and total drag coefficient (Cd) due to spin stabilization. The SpinSim
routine takes information from either mass properties CSV export files or from
manually entered inputs. Both the FinSim Manual and the SpinSim Manual are
included during installation and are accessible from within the program's HELP
routine. Please note that for a spinstabilized rocket the center of pressure
location (XCp) should be at least one body diameter behind the center of gravity
(CG). This very same stability criterion is used to define the static stability
of all finstabilized rockets and is referred to as the static margin (XCpXcg).
Please note the SpinSim routine is and always was a subroutine in
FinSim and is not a separate computer program.
FIRST, SOME CONCEPTS ABOUT AEROELASTICITY
DIVERGENCE VELOCITY:
Fin or wing divergence
is an example of a steadystate aeroelastic instability. If a wing in steady
flight is accidentally deformed an aerodynamic moment will generally be induced
which tends to twist the fin/wing. Fin/wing twisting is resisted by the
restoring elastic
moment along the elastic axis (ea). However, since the elastic stiffness is
independent of the flight speed, whereas the aerodynamic moment is proportional
to the square of the flight speed, there may exist a critical speed, at which
the elastic stiffness is barely sufficient to hold the fin in the disturbed
position. Above such a critical speed, an accidental deformation of the fin/wing
will lead to a large angle of twist (torsion). This critical speed is called the
divergence speed, and the fin/wing is said to be torsionally divergent. Rocket
fins should be designed so the divergence speed is never exceeded at any
altitude during the flight.
Arbitrary crosssection, Sdesign = design area 
FinSim's Rectangular fin crosssection 
Planform geometry where b = fin semispan 
FINSIM FEATURES 1) Determine fin flutter critical velocity (UF) and fin divergence critical velocity (UD) using the Pines' approximate method. 
2) Define aerodynamic loads using either the 3dimensional Barrowman liftslope (CN_alpha) or the 2dimensional lift slope (CN_alpha). 
3) Define up to six finsets using only five variables to define fin geometry. 
4) Easily define rocket angle of attack, flight altitude, fin fillet radius and buttjoint or thruthewall fin mounts using simple options buttons. 
5) Specify from a list of 25 standard and composite materials or manually enter modulus of elasticity, material density, poissons ratio and bending yield strength. 
6) Specify from a list of 12 common adhesives or manually enter the adhesive allowable strength. 
7) Fin allowable and adhesive allowable is displayed for comparison purposes. 
8) Plot fin stress verses rocket velocity and see the maximum allowable velocity as limited by either the fin material or adhesive material strength. 
9) Plot each fin set by simply clicking one of up to 6 finset option buttons. 
10) By clicking SHOW or HIDE in the Additional Results menu in the toolbar, display Stress Concentration Factor due to fillets, Torsional Frequency, Bending Frequency, FinTip Deflection and Maximum Fin Bending Moment. 
11) Determine the stability margin (XCpXCG) of spin stabilized rockets using canted fins to achieve rotational velocity. 
12) FinSim instructions and SpinSim instructions are included with purchase and are accessible from within the program's HELP routine. 
13) Specify a title on the main screen to differentiate between the various input data files. NOTE: Fin flutter and stress analysis files have the .FIN specification 
14) Use the Classical 2D Lift Slope, Barrowman 3D Lift Slope or the new Supersonic Airfoil Lift Slope to define fin loads for flutter and stress analyses. 
15) Location of the aerodynamic center (A.C.) automatically changes to the 25% chord length position for subsonic airfoils (Classical 2D Lift Slope and Barrowman 3D Lift Slope) and automatically changes to the 50% chord length position for supersonic airfoils (Supersonic Airfoil Lift Slope). Mach number is inserted or modified in the STRESS routine. 
NEW FinSim 4.0 Features 16) Added the ability to model unsteady torsionflexure wing oscillations using the Theodorsen method or Ug method to determine critical flutter velocity and divergence velocity. Also, included six test cases with reference pages. 
17) Manually enter experimentally derived aeroelastic data on the Theodorsen and Ug method screen. 
18) Increased the altitude corresponding to atmospheric density and pressure from 10K feet to 50K feet greatly increasing the atmospheric affect on flutter and divergence velocity. 
19) In the Additional Results section on the main screen added output of material properties including Modulus of elasticity (E), Shear modulus (G), Poissons ratio, and Material density (r) in addition to the uncoupled bending frequency (w_{h}) and torsion frequency (w_{a}) of fin/wing vibration. 
20) Improved accuracy of the Pines' approximate method for determining critical flutter and divergence velocity. 
21) Fixed a few errors in the material properties data base, specifically the Polystyrene material. 
22) Save 1/k, F(k), G(k), X1r(k), X2r(k), X1i(k), X2i(k) for the SQR(X) verses 1/k analysis to a CSV file. Also, Save k, F(k), G(k), U_{F}(k), g(k) for the U verses g analysis to a CSV file for later use in Excel or other spreadsheet programs. The Theodorsen aerodynamic function is F(k) + i G(k). 
NEW FinSim 4.5 Features 23) For the User Defined Materials option in the Fin Materials pull down menu, added the option to save user defined modulus of elasticity (E), density (r), poissons ratio (n) and bending yield strength in material files having an .MAT extension. New material data can be opened or saved in the Fin Materials section by selecting File and then Open New Material in MAT Format or Save New Material in MAT Format and then clicking Insert New Data. 
24) Increased altitude corresponding to atmospheric density and pressure from 50K feet to 200K feet for stress analyses, flutter velocity and divergence velocity. 
25) Increased numerical accuracy and speed of the flutter velocity and divergence velocity calculations. 
26) Under the CNAlpha pulldown menu, the option Supersonic Airfoil Lift Slope has been replaced by a method from NACA TN 4197 (see description) for determining main screen flutter velocity and divergence velocity. The new flutter velocity and divergence velocity method is called the NACA TN 4197 METHOD and is located in the CNalpha pulldown menu. 
NOW, SOME FINSIM
TEST CASES
Please Note: Click the
icon
located on the main FinSim Flutter screen to access the new
TorsionFlexure (2D) Unsteady Flutter analysis screen for modeling
unsteady torsionflexure wing oscillations using the Theodorsen method or
Ug method to determine flutter and divergence velocity.
ToolBar located on the main screen
(1) FLUTTER VELOCITY FOR THE 2ND STAGE FINS OF THE
QUANTUM LEAP:
BACK
The following FinSim analysis predicts flutter and divergence velocity
for the second stage fins of the PML Quantum Leap. This FinSim
unsteady TorsionFlexure flutter analysis indicates the Quantum Leaps'
second
stage fins will flutter at approximately 0.76 Mach (see Figure4) and become fully
divergent at 0.96 Mach. Inflight video seems
to indicate the second stage fins of the Quantum Leap will flutter at
0.90 Mach when fiber glassed. The FinSim critical flutter velocity
result of 0.76 Mach defines the earliest possible onset of flutter
when the oscillations can just maintain themselves at small steady amplitude and
the divergence velocity of 0.96 Mach completely bounds the observed result. Above the critical
flutter velocity any
accidental disturbance can
initiate oscillations of great amplitude. Therefore, the large oscillations
observed at 0.90 Mach were probably triggered by an accidental disturbance of
the airflow (gust of wind?) after exceeding the critical flutter velocity,
explaining why the oscillations were observed at 0.90 Mach although flutter may
have been occurring earlier in the flight as predicted by FinSim's result.
Figure1: Main FinSim analysis screen
displaying the Pines' approximate flutter results (Windows 10 image displayed)
Figure2: FinSim Input geometry screen
Figure3: FinSim fin stress analysis
screen
Click the
icon located on the main
FinSim toolbar to access the
new TorsionFlexure (2D) Unsteady Flutter
analysis
Figure4: Flutter and divergence velocity
using the Ug method
(2) FLUTTER
VELOCITY COMPARISON WITH MSC/NASTRAN SOLUTION:
BACK
The following is an unsteady TorsionFlexure
flutter validation of an airfoil mounted on bending and torsion springs
located aft of the aerodynamic center of a fin or wing. A
critical velocity will be found that will cause either a static instability
(torsion divergence) or an oscillatory instability (flutter). Both divergence
and flutter speeds of the airfoil are determined and compared to exact
theory and a separate MSC/NASTRAN finite element analysis (FEA) technique using the Kmethod based on the
exact Theodorsen function. The following table illustrates the usefulness of FinSim for
accurately determining critical flutter and divergence velocity of
typical cruciform model rocket fins. This example uses the Theodorsen and Ug
methods to predict flutter and divergence velocity as described in NACA Report
685, Mechanism of Flutter by Theodorsen and Garrick on page 542 of the report.
Comparison between FinSim results and the paper's results are excellent.
Fin Aeroelastic Data
g
(structural damping) = 0.0
m
(mass ratio) = 20.0
a (elastic axis location) = 0.2
x_{a}
(c.g. location) = 0.1
r_{a}
(radius of gyration) = 0.5
w_{a}
(torsion frequency, rad/sec) = 25
w_{h}
(bending frequency, rad/sec) = 10
b (half chord, inches) = 36.0
Results 
Flutter Velocity (UF) 
Difference 
Divergence Velocity (VD) 
Difference 
Exact Theory 
169 ft/sec 
 
216 ft/sec 
 
MSC/NASTRAN 
166 ft/sec 
1.8% 
216 ft/sec 
+ 0.0% 
FinSim 4.0 
166 ft/sec 
1.8% 
217 ft/sec 
+ 0.5% 
Click the
icon located on the main
FinSim toolbar to access the
new TorsionFlexure (2D) Unsteady Flutter
analysis
Figure5: Flutter and divergence velocity
using the Ug method
Click the
icon located on the main
FinSim toolbar to access the
new TorsionFlexure (2D) Unsteady Flutter
analysis
Figure6: Flutter velocity using the
Theodorsen method (SQR(X) verses 1/k)
(3) FLUTTER VELOCITY OF A WING FOR A LARGE MODERN
AIRPLANE:
BACK
This example uses the Ug method to predict
critical flutter velocity for a wing described in NACA Report 685 as being for a
large modern airplane. Please reference, NACA Report 685 Mechanism of Flutter by Theodorsen and Garrick
on page 108 of the report. The parameters supplied by the report are as follows.
Comparison between FinSim results and the report's results are excellent.
Fin Aeroelastic Data
g (structural damping) = 0.0
m
(mass ratio) = 4.0
a (elastic axis location) = 0.4
x_{a}
(c.g. location) = 0.2
r_{a}
(radius of gyration) = 0.5.
w_{a}
(torsion frequency, rad/sec) = 90
w_{h}
(bending frequency, rad/sec) = 22.5
b (half chord, inches) = 72.0
Results 
Flutter Velocity (UF) 
Difference 
SQR(X)  Difference  1/k  Difference 
NACA Report 685, page 108 
567.0 mph 
 
1.594    2.460   
FinSim 4.0 
568.65 mph 
+0.29% 
1.592  .0125%  2.460  0.0% 
Click the
icon located on the main
FinSim toolbar to access the
new TorsionFlexure (2D) Unsteady Flutter
analysis
Figure7: Flutter and divergence velocity using
the Ug method
FINSIM USES THE FLUTTER VELOCITY METHOD FROM NACA TN 4197 (FINSIM 4.5.3 OR LATER):
BACK
Under the CNAlpha pulldown menu, the
option Supersonic Airfoil Lift
Slope has been replaced by Equation18 from NACA TN 4197 for
determining main screen flutter velocity and divergence velocity. The Classical 2D Lift
Slope and Barrowman 3D Lift Slope methods are not affected and are
very accurate over a wide range of Mach numbers. This
modification was necessary to more accurately estimate high subsonic and supersonic flutter and
divergence velocity. The Theodorsen and Ug flutter velocity results are not
affected and are extremely reliable. An extensive investigation represented by
the following table (Table1) and plot was conducted to validate the method from NACA TN
4197. Because the results from NACA TN 4197 reasonably matched the Theodorsen
and Ug flutter velocity methods, the decision was made to replace the Supersonic Airfoil Lift
Slope option. The new flutter velocity and divergence velocity method
is called the NACA TN 4197 METHOD and is located in the CNalpha
pulldown menu. In the illustration below please note that FinSim_Ug has
excellent correlation between results using NASTRAN FEA and actual wind tunnel
measurement (ASROC Test38).
One by product of this effort has been the development of a divergence velocity
estimate based on methods presented in NACA TN 4197. The AeroRocket derived
expression for divergence velocity (UD) and the expression presented in NACA TN
4197 for flutter velocity (UF) appears in FinSim as a new option to compute
divergence velocity. The discussion below explains in more detail how the new
expression for divergence velocity was derived. This new equation for divergence
velocity will appear in future versions of AeroRockets Excel flutter velocity
and divergence velocity spreadsheet,
NACA TN 4197
(33.8 KB).
FinSim 4.5 Project Name 
Aspect Ratio (AR) 
MF NACA TN 4197 
MF POF291 
MF FinSim Ug 
MF FinSim Main 
CNalpha Main Method 
Rocket Altitude 
Velocity UNITS 
E.A.  C.G.  Fin Materials 
NASTRAN EXAMPLE  0.167  0.604  0.855  0.15 (0.15*)  0.24  Classical 2D  Sea Level  MACH  0.50  0.50  Steel 
ASROC Flutter (Test 38)  0.446  1.319  1.866  1.20 (1.3**)  1.33  NACA TN 4197  29K FT  MACH  0.50  0.694  Aluminum 
N5800 Project (Don't debate This)  0.561  3.891  5.504  3.28  3.89  NACA TN 4197  11K FT  MACH  0.50  0.658  Aluminum 
Apogee Test  0.704  0.504  0.713  0.48  0.52  Classical 2D  3K FT  MACH  0.50  0.50  User Defined Balsa Wood 
Tomahawk Rocket (2.933 span)  0.875  1.493  2.112  0.93  1.49  NACA TN 4197  1K FT  MACH  0.50  0.50  User Defined Balsa Wood 
Quantum Leap Flutter  0.972  0.437  0.618  0.38  0.44  Classical 2D  15K FT  MACH  0.50  0.64  G10 Fiberglass 
Tomahawk Rocket (5" span)  1.492  0.739  1.045  0.62  0.74  NACA TN 4197  1K FT  MACH  0.50  0.50  User Defined Balsa Wood 
Table1, FinSim input data and output flutter velocity results compared to supplementary information. * NASTRAN FEA flutter result, ** Wind tunnel test result. 
FinSim flutter velocity compared to NACA TN 4197,
POF291 and NASTRAN FEA/experimental data.
Discussion of flutter velocity from NACA TN 4197 and derivation of the new AeroRocket equation for divergence velocity.
DEFINING COMPOSITE
MATERIAL PROPERTIES IN FINSIM:
BACK
FinSim has a builtin library of
standard materials, adhesive materials and composite materials. The list of
materials are located in FinSim_Theory.pdf, which tabulates E,
r,
n and
S for the provided materials. Also, user defined materials may be specified
in the Fin Materials pulldown menu where modulus of elasticity, material
density, Poissons ratio and yield strength in bending can be inserted into the
analysis. However, occasionally the user may need to determine composite
material properties based on specific properties of the fiber and matrix
materials used for fin construction. In this case the Rule of Mixtures or
the volume fraction rule is
used to estimate composite material properties as a function of the fiber and
matrix constituents and their volume fractions. The volume fraction rule can be
stated as follows. The modulus of elasticity of a composite material equals the
modulus of elasticity of the first phase times the volume fraction of that phase
plus the modulus of elasticity of the second phase times the volume fraction of
that phase. A similar rule applies to the other properties of a composite
material. Using the
Rule of Mixtures the relationship for longitudinal modulus of elasticity
(E), material density (r),
Poissons ratio (n)
and allowable stress (S) are specified as follows:
Composite material modulus of elasticity
E = f E_{f} + (1f) E_{m}
Which says that the longitudinal modulus of elasticity (E) is proportional to
the volume fraction of the fiber material (f) and the volume fraction of the
matrix material (1f).
Composite material density
r = f
r_{f}
+ (1f) r_{m}
Composite material Poissons ratio
n = f
n_{f} + (1f)
n_{m}
Composite material allowable stress
S = f S_{f} + (1f) S_{m
}NEW DOWNLOAD: To illustrate
how to define E,
r,
n and
S for FinSim,
a new Microsoft Excel spreadsheet based on
the Rule of Mixtures
(49 KB) is provided as a free download. The
user simply inserts results from the spreadsheet into the User Defined
Material section of the Fin Materials pulldown menu on the
FinSim main screen. The example illustrated in the
spreadsheet is for the construction of Glass Fiber Reinforced Plastic (GFRP)
fins that use epoxy for the matrix material and fiberglass for the fiber
material. This spreadsheet analysis uses GFRP an example so it is recommended the user
consult other sources for more exotic constituent material properties.
DESIGNING SPIN STABILIZED
ROCKETS (SPINSIM):
BACK
In addition to flutter and fin stress analyses,
FinSim has the ability to determine the stability
of spin stabilized rockets that use canted fins to achieve rotation. FinSim computes the center of
pressure location
of a spin stabilized rocket by applying the principals of gyroscopic
motion. In addition, the SpinSim routine computes precession angle,
added moment coefficient due to spin stabilization, total pitch
moment coefficient with spin stabilization, rotary speed, precession
speed and total drag coefficient (Cd) due to spin stabilization. The SpinSim
routine takes
information from either mass properties CSV
export files or from manually entered inputs. Both the FinSim Manual and the
SpinSim Manual are included during installation and are accessible from within the
program's HELP routine. Please note that for a spinstabilized rocket the center
of pressure location (XCp) should be at least one body diameter behind
the center of gravity (CG). This very same stability criterion is used to define the
static stability of all finstabilized rockets and is referred to as the static margin (XCpXcg).
SpinSim uses fins, fixed at a constant angle of inclination, to induce
rotation during flight. Spin stabilization is achieved when external aerodynamic
forces change the rocket's angular momentum, L in time dt by an amount, dL.
During this time interval the aerodynamic forces applied at the center of
pressure (Cp), exert a restoring torque given as M = dL/dt around the center of
gravity. The incremental moment caused by the restoring torque moves the
effective Cp aft by an amount determined by the separation of the Cg and Cp and
the value of the incremental moment. For more information about the technical
aspects of spin stabilization and a stepbystep procedure please read the Spin
Stabilization pdf instructions.
GENERAL PROCEDURE TO RUN SPINSIM
To generate the SpinSim results illustrated in Figure8 use the
following general procedure.
1) To use SpinSim the rocket's fin geometry must first be defined. On the
main FinSim screen click the left icon with ToolBar description,
Open FinSim Project in FIN format. For this example click
Saturn Rocket.FIN which is a file that describes the fin geometry for Apogee's spin
stabilized Saturn model rocket.
ToolBar located on the main screen
2) Click the forth icon from the left with
ToolBar description, SpinSim  Spin stabilization analysis to enter
the SpinSim analysis screen. Then, under File click Open
SpinSim data in TXT format. For this example click Saturn Spin Data1.TXT
to open a file that further describes the spin stabilized characteristics of Apogee's spin stabilized Saturn model rocket. Required data for
a SpinSim analysis is summarized in the Basic SpinSim Data and
Rocket Properties sections. Most of the information required for a
SpinSim analysis is pretty simple to determine except for Radial moment
of inertia (Ixx) and Longitudinal
moment of inertia (Izz) which are rather complicated. The rocketeer has two
options to determine Ixx and Izz. The most accurate way to determine Ixx and Izz is to use a
torsional pendulum as detailed in the
Sprint Assembly Instructions report
(no longer available) describing how John Cipolla used a torsional pendulum to measure Ixx and Izz for
his exact scale Sprint ABM model
rocket. The other method involves using one of the commercially available model
rocket simulation programs that produce values for Ixx and Izz that may or may
not be accurate enough for a typical SpinSim analysis. In this author's
opinion these programs were not accurate enough to determine Ixx and Izz for the
Saturn rocket and Sprint ABM spin
stabilization analyses.
Figure8: SpinSim Spin Stabilization Screen
DRAG COEFFICIENT OF SPIN
STABILIZED ROCKETS:
BACK
SpinSim determines the zero lift drag coefficient (Cd) for finless
projectiles based on experimental results from Fluid Dynamic Drag,
page 313. As defined in SpinSim drag coefficient is a function of circumferential
velocity ratio (u/V). Where, projectile circumferential velocity (u) around an axis
parallel to the direction of flight and projectile speed (V) define the velocity
ratio.
Projectile rotation has the following influences on finless projectile aerodynamics.
a) Projectile rotation causes additional drag because the added speed component,
u thickens the boundary layer. Where, u =
p
D n_{x} and n_{x} is the
speed of projectile rotation (rev/sec).
b) The thickened boundary layer causes flow to separate from the aft end of
the projectile causing additional form drag.
c) Centrifugal forces in the rotating boundary layer around the projectile
increase base flow separation and base drag. Boat tail designs can help mitigate
this situation.
d) Depending on projectile shape the critical Reynolds number may be reduced
decreasing the velocity of transition from laminar to turbulent flow.
The equation displayed in Figure9 is a curve fit approximation for
Cd verses u/V based on experimental data for a finless projectile. Where, Cd_{0} is
finless projectile drag
coefficient for zero rotation and u/V is circumferential velocity ratio.
SpinSim uses this equation to determine the total drag coefficient of a
finned rotating projectile that includes canted fins and base drag. Figure10
displays experimental data from Fluid Dynamic Drag (red
dots) plotted verses the curve fit equation displayed in Figure9
over a very wide range of velocity ratio (u/V).
Figure9: Curve fit approximation for Cd verses u/V based on Fluid Dynamic Drag
experimental data
Figure10: Drag coefficient (Cd) of spin stabilized projectiles as a function of circumferential velocity ratio (u/V)
MODIFICATIONS AND REVISIONS:
BACK
FinSim 4.5.3 Features (10/26/2014)
1) Under the CNAlpha pulldown menu, replaced Supersonic Airfoil Lift
Slope with the NACA TN 7149 Method for determining main screen
flutter velocity and divergence velocity. The existing Classical 2D Lift
Slope and Barrowman 3D Lift Slope methods were not affected. This
modification was necessary to more accurately estimate supersonic flutter and
divergence velocity. The Theodorsen and Ug flutter velocity results were not
affected.
2) When performing a Fin Bending Stress Analysis, the
flutter velocity computed on the main screen is now inserted into the Maximum
rocket velocity input box in selected units of FT/SEC, MPH, M/SEC or MACH.
Previously, a fixed velocity was inserted which was confusing when MACH units
were also selected. In addition, fixed an error which caused confusion when the
displayed Lift Slope (CNa) on the main screen would change by simply changing
the Maximum rocket velocity when the Supersonic Airfoil lift Slope option was
selected. The Theodorsen and Ug flutter velocity results were not affected.
3) By clicking Additional Results and then SHOW, FinSim now
displays local speed of sound for the selected flight altitude. Speed of sound
information is necessary for being able to double check results when changing
units.
4) Double checked that fin bending stress, fin deflection, bending frequency and
torsion frequency were correct by using MathCAD for several test cases.
FinSim 4.5.2 Features (10/23/2014)
1)
For the User Defined Materials option in the Fin Materials pull
down menu, added the option to save user defined modulus of elasticity (E),
density (r), poissons ratio
(n) and bending yield strength
in material files having an .MAT extension. New material data can be
opened or saved in the Fin Materials section by selecting File and
then Open New Material in MAT Format or Save New Material in MAT
Format and then clicking Insert New Data.
2) Fixed an error that occurred in the
Fin Bending Stress Analysis
section when velocity in Mach units and Supersonic Airfoil Lift Slope
(CLa) caused a feedback situation with the Pines method flutter analysis on the main screen causing flutter
velocity results and stress analysis results to be totally inaccurate. The Theodorsen
and Ug flutter velocity results were not affected.
FinSim 4.5.1 Features (03/27/2013)
1)
Increased altitude corresponding to
atmospheric density and pressure from 50K feet to 200K feet for stress analyses,
flutter velocity and divergence velocity.
2) Increased numerical accuracy and speed of the flutter velocity and divergence
velocity calculations.
FinSim 4.0.3 Features (10/05/2009)
1) At a purchasers request added display of
fin force due to flight angle
of attack and canted fins for each finset selected in the Fin Stress
plot. Also, added display of fin moment due to angle of attack and canted
fins for each finset selected in the Fin Stress
plot. Fin forces and fin moments were required for designing a rocketmotor spin
stabilized rocket. The new display of fin forces and fin moments are located on
the Fin bending stress analysis screen and are accessed by clicking
Additional Results then selecting SHOW.
FinSim 4.0.2 Features (09/14/2009)
1) For
FinSim, fixed all input data text boxes for 32 bit and 64 bit
Windows Vista. When operating earlier versions of FinSim in Windows Vista the input data
text boxes failed to show their borders making it difficult to separate each
input data field from adjacent input data fields.
FinSim 4.0.1 Features
1)
Added the ability to model
unsteady torsionflexure wing
oscillations for determining flutter and divergence velocity.
2)
Increased the altitude corresponding to
atmospheric density and pressure from 10K feet to 50K feet.
3)
In the Additional Results
section added output of material properties in addition to the uncoupled
bending frequency and torsion frequency.
4) Improved accuracy of the Pines' approximate method for determining critical
flutter and divergence velocity.
5) Fixed a few errors in the material properties data base specifically the
Polystyrene material.
6) Save SQR(X) verses 1/k, U verses g and the Theodorsen aerodynamic
coefficients to a CSV file.
FinSim 3.1 Features
1) Included a Supersonic Airfoil
Lift Slope for the analysis of fins in supersonic flow (above Mach 1).
2) Corrected an error in the computation of fin bending frequency.
3) Added a colorful and more descriptive illustration describing the aerodynamic
center (A.C.), elastic axis (E.A.) and center of gravity (C.G.).
FinSim 3.0 Features
1) Made FinSim a stand alone computer
program that no longer relies on output files (either XML or CSV) from other
flight simulation programs.
2) Displayed several variables that are useful for aeroelastic evaluations.
AeroFinSim
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