Fin flutter analysis for a supersonic high power rocket
Copyright © 1999-2022 John Cipolla/AeroRocket


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 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.

Table-1 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.
FinSim_Ug Mach 3.29 NA
NACA TN 4197 equation Mach 3.89 + 18.2 %
POF 291 equation Mach 5.50 + 67.2 %

Table-1, Flutter velocity computation methods compared to the FinSim Ug method

Use the values displayed in Table-2 to populate the FinSim main screen and fin geometry screen for performing a flutter velocity and divergence velocity analysis. Make sure to select NACA TN 4197 Method under the CN-alpha 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. Use a similar procedure for other supersonic fin flutter velocity analyses.




Semi span (b)

4.0 in Fin input geometry screen

Root chord (cr)

12.0 in Fin input geometry screen

Tip chord (ct)

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/in3 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.)


Attachment centroid, main screen

Center of gravity location (C.G.)


Measured or computed, main screen


FinSim Results


Torsion-Flexure flutter velocity (UF)

Mach 3.29 See Figure-5 and Figure-6

U-g Torsion-Flexure divergence velocity (UD)

Mach 4.30 See Figure-5 and Figure-6

Table-2, 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 Table-1 to perform the flutter and divergence velocity analysis.

Methods to Determine Fin Center of Gravity (CG) and Elastic Axis (EA)

Figure-1, Fin model method to determine center of gravity location (xcg = Xcg/2b)

Figure-2, 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 Double-Wedge cross-section fin. Where, the maximum cross-sectional 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 Double-Wedge geometry in the cross-section of the fin and proceed as usual.


Figure-3, FinSim main screen


Figure-4,  Fin input geometry screen


Figure-5,  Flutter velocity (UF) computed using Theodorsen method


Figure-6,  Flutter velocity (UF) and divergence velocity (UD) computed using U-g method