FIN FLUTTER AND DIVERGENCE VELOCITY FOR SUPERSONIC FLIGHT
Fin flutter analysis for the Don't Debate This rocket, the correct way
Copyright © 1999-2015 John Cipolla/AeroRocket


| MAIN PAGE | SOFTWARE LIST | AEROTESTING | MISSION | RESUME |

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 high-aspect-ratio wings for subsonic flight not low-aspect-ratio 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.

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.
 
UF METHOD (Use Table-2) 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 %

Table-1, 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, high-aspect-ratio 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 small-aspect-ratio 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 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 Supersonic Airfoil Lift Slope 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 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 (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.)

0.50

Attachment centroid, main screen

Center of gravity location (C.G.)

0.658

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