The flutter velocity
performed for the “Don’t Debate This” high power rocket was
incorrect because the user did not specify the correct supersonic lift
slope (CN_alpha) and center of gravity (CG) location for the fins and
other errors to be discussed.
When proper inputs for airfoil lift slope and CG location are input, the
resulting flutter velocity (UF) of the rocket is determined to be Mach
3.29 and the divergence velocity is Mach 4.30. Therefore, the statement on page 3 of "Taming the N5800: Don't
Debate This" that "FinSim predicted the potential onset of flutter
and divergence well below Mach 3” is totally incorrect.
Also, the value presented on page 3 for flutter velocity (Mach 3.245) in
the report does not provide enough safety margin for flutter considering the equation used from NACA TN 4197 is
intended for highaspectratio wings for subsonic flight not
lowaspectratio fins for supersonic flight. Another error considered
"in the noise" indicates the successful Mach 3 flight of the "Don't
Debate This" rocket was a lucky coincidence. Specifically, the user
input the incorrect value for pressure (P) at the point of maximum Mach
number. The user assumed a simulation altitude of 4K feet that is the
altitude at the launch point in the Nevada desert. Actually, the correct
simulation altitude should be 11K feet or the altitude above the launch
point at which maximum rocket velocity occurs during launch.
Table1 presents a comparison between flutter velocity methods discussed
and the Ug method used by FinSim. Notice the other methods that rely on
simplified equations over predict flutter velocity by a wide margin
compared to FinSim and should only be used as estimates.
UF METHOD (Use
Table2) 
FLUTTER VELOCITY
(UF) 
DIFFERENCE 
FinSim_Ug 
Mach 3.29 
NA 
NACA TN 4197
equation 
Mach 3.89 
+ 18.2 % 
POF 291 equation 
Mach 5.50 
+ 67.2 % 
Table1, Flutter
velocity computation methods compared to the FinSim Ug
method 
NOTE: The flutter velocity equation presented in How to Calculate
Flutter from Issue 291 of the Peak of Flight (POF) Newsletter
is based on results from the Appendix in NACA TN 4197
where the derivation of the simplified flutter criterion is described as "an
empirical expression for flutter speed as given by Theodorsen and
Garrick for heavy, highaspectratio wings (AR > 5) with a low ratio of
bending frequency to torsional frequency..." Therefore, using the
flutter velocity equation presented in POF and NACA TN 4197 should be
avoided for smallaspectratio rocket fins operating at high subsonic
and supersonic speeds and not used at all for low subsonic designs. Sometimes these simplified flutter equations work
and sometimes they do not depending on the aspect ratio correction,
frequency ratio assumed in NACA TN 4197 and the actual Mach number. In
this case the aspect ratio of the Don't Debate This rocket is
0.561 meaning the AR correction used in the derivation is meaningless
for subsonic and supersonic flight outside the Mach number range
intended for these equations. Previous work indicates these equations
are simply an approximation and should not be used for determining the
fin flutter velocity of subsonic and supersonic vehicles without a
massive safety factor.
Use the values displayed in Table2 to
populate the FinSim main screen and fin geometry screen for performing a
flutter velocity and divergence velocity analysis. Make sure to select Supersonic Airfoil Lift Slope
under the CNalpha pull down menu to automatically specify the
aerodynamic center (AC). Also, to avoid a common mistake be sure to
input the correct values for fin elastic axis (AE) location and fin
center of gravity (CG) location. Please refer to the screen shots below
for performing a flutter velocity and divergence velocity analysis for
the "Don't Debate This" rocket. Use a similar procedure for other
supersonic fin flutter velocity analyses.
FINSIM INPUT DESCRIPTIONS 
VALUES 
NOTES 
Semi span (b) 
4.0 in 
Fin input geometry screen 
Root chord (c_{r}) 
12.0 in 
Fin input geometry screen 
Tip chord (c_{t}) 
2.25 in 
Fin input geometry screen 
Sweep length 
9.75 in 
Fin input geometry screen 
Fin thickness (t) 
0.195 in 
Fin input geometry screen 
Maximum body diameter near fins 
4.0 in 
Fin input geometry screen 



Fin Materials 

Aluminum, main screen pull down 
Shear modulus (G) 
3759398 psi 
Fin material, aluminum 
Elastic modulus (E) 
10E6 psi 
Fin material, aluminum 
Poissons ratio 
0.33 
Fin material, aluminum 
Material density 
0.098 lb/in^{3} 
Fin material, aluminum 



Rocket simulation altitude (P) @ max Mach 
11,000 ft 
Pressure, main screen pull down 



Supersonic Airfoil Lift Slope 

CN_alpha, main screen pull down 
Aerodynamic center location
(A.C.) 
0.50 
0.5 for supersonic, main
screen 



Aeroelastic input variables 

E.A. and C.G. main screen inputs 
Elastic axis location (E.A.) 
0.50 
Attachment centroid, main
screen 
Center of gravity location
(C.G.) 
0.658 
Measured or computed, main
screen 



FinSim Results 


TorsionFlexure flutter velocity (UF) 
Mach 3.29 
See Figure5 and Figure6 
Ug TorsionFlexure divergence velocity (UD) 
Mach 4.30 
See Figure5 and Figure6 
Table2, FinSim input variables for performing supersonic flutter velocity
analysis 
The following screen shots are intended to help FinSim users predict
supersonic flutter velocity and divergence velocity simply and easily.
Use the values presented in Table1 to perform the flutter and
divergence velocity analysis. 
Methods to Determine Fin Center of Gravity (CG)
and Elastic Axis (EA)
Figure1, Fin model method to determine center of
gravity location (xcg = Xcg/2b)
Figure2, Determine elastic
axis location (xea = Xea/2b) using the Excel spreadsheet
The elastic
axis (xea) for fins formed from uniformly thick materials
(thickness = constant) are located at the 50% normalized location (B/2)
measured from the leading edge. Where, the
normalized elastic axis location, xea = Xea/2b is the
ratio of the elastic axis (Xea) location to the chord (2b) measured at the fin root. A Microsoft
Excel spreadsheet analysis
for determining
elastic axis
location (57 KB) is
presented that determines the normalized elastic axis location
for the case of a DoubleWedge crosssection fin. Where, the maximum
crosssectional thickness (H1, H2) of the fin is located an
arbitrary distance (C1, C2) from the leading edge and the fin
chord (B = 2b) is used to normalize the locations. If your fins
use some other arbitrary shape simply inscribe the DoubleWedge
geometry in the crosssection of the fin and proceed as usual. 
