# Calculating fin flutter using NACA TN 4197: Open Questions

#### grandcross

##### Well-Known Member
TRF Supporter
I've added fin flutter analysis to the FreeCAD Rocket Workbench based on the equations in NACA TN 4197. It works but there are improvements that can be made. I'm in need of advice from more knowledgeable aerodynamicists. I'll reference the paper here without link, but a quick google search shows many sites where it can be downloaded.

Question 1: The main formula is equation 18 on page 15 of the document. It assumes a value for epsilon of 0.25, which is to say the center of gravity is at the center point of the root chord. Epsilon is defined as the distance from the 1/4 chord (referenced from the forward end) to the center of gravity. As the fin sweeps back, the CG moves back and epsilon increases. As the fin sweeps forward, the CG decreases to 0 at 1/4 chord, and negative from there. Given that this is the distance from the 1/4 chord, is an absolute value correct for a forward swept fin? A negative value causes the velocity to enter imaginary space so that is a non-starter. Thoughts?

Question 2: FinsSim handles non-square fin profiles (airfoils, tapered leading and trailing edges, etc) by adjusting fin thickness to create a square profile fin of equivalent volume. I do a similar but different process. FinSim calculates based on the relative areas at the fin root profile, whereas I use the volume divided by the area of the fin side profile. FreeCAD provides the shape volume, so it's an easier calculation that works for all fin profiles. Thoughts?

Question 3: Elliptical fins. Formula 18 calculates an average chord (root chord + tip chord)/2. For an ellipse, the tip chord is 0 so would be approximated as a square fin with a chord of half of the root chord. Is this sufficient for handling elliptical fins, or non-trapezoidal shapes in general?

Question 4: I'm reasonably certain this method isn't up to it, but what about fins of tapered thickness root to tip? Given that thickness is one of the most important variables, is an approximation possible?

I'm also looking at other methods for calculating flutter, such as NACA TN 685, but let's start with this.

#### UhClem

##### Well-Known Member
Question 4: I'm reasonably certain this method isn't up to it, but what about fins of tapered thickness root to tip? Given that thickness is one of the most important variables, is an approximation possible?
The equations assume constant thickness ratio. (Used to justify equation 15.)

aka. tapered in a particular way.

#### grandcross

##### Well-Known Member
TRF Supporter
The equations assume constant thickness ratio. (Used to justify equation 15.)

aka. tapered in a particular way.
Yup. Just wondering if anyone had come up with any corrections that would allow for this. I knew the answer before I asked but it was worth a shot.

#### UhClem

##### Well-Known Member
Keep in mind that this paper was written long before computer modeling became possible so simplifying assumptions and approximations are required. These days you can simulate any fin geometry and composite layup you care to enter into a finite element model.

#### grandcross

##### Well-Known Member
TRF Supporter
Keep in mind that this paper was written long before computer modeling became possible so simplifying assumptions and approximations are required. These days you can simulate any fin geometry and composite layup you care to enter into a finite element model.
Yes, and I've already started looking into that. FreeCAD has FEM capabilities as well. But, starting with the simple first...

TRF Supporter
Keep in mind that this paper was written long before computer modeling became possible so simplifying assumptions and approximations are required. These days you can simulate any fin geometry and composite layup you care to enter into a finite element model.
Modeling the fins is easy... but is there an affordable simulation package available to look at the fin loading due to aerodynamic forces?

#### grandcross

##### Well-Known Member
TRF Supporter
Modeling the fins is easy... but is there an affordable simulation package available to look at the fin loading due to aerodynamic forces?
FreeCAD uses CalculiX for FEM, and it's included with the distribution. I've already started looking into creating a workflow specific to fin flutter, but that's going to take time. In the meantime, this method is available now, and it's been proven solid. It won't handle all possible cases, but if you have a trapezoidal fin it works just fine.

#### FredA

##### Well-Known Member
FinsSim handles non-square fin profiles (airfoils, tapered leading and trailing edges, etc) by adjusting fin thickness to create a square profile fin of equivalent volume.
And these are supposed to resonate/flutter the same???? Call me dubious.

TRF Supporter
FreeCAD uses CalculiX for FEM, and it's included with the distribution. I've already started looking into creating a workflow specific to fin flutter, but that's going to take time. In the meantime, this method is available now, and it's been proven solid. It won't handle all possible cases, but if you have a trapezoidal fin it works just fine.

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#### grandcross

##### Well-Known Member
TRF Supporter
So the free cad looks at air flow?
Fin flutter is more about resonance within the fin. and FEM is used to model that resonance. FreeCAD can also do CFD but that's not typically how flutter is analyzed.

Obviously that's an extremely simplified answer. Others may be able to explain it better.

#### QFactor

##### L2 - NAR & TRA
TRF Supporter
With all this modeling & math, do you have access to wind tunnel data or flight data to verify the model's predictions ?

Eqn. 18 in the NACA report makes a number of assumptions, based on earlier reports. There were subsequent studies that
added to the body of information on Fin Flutter, but I have not seen a report where all these findings went back into the
improvement of Eqn. 18.

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#### grandcross

##### Well-Known Member
TRF Supporter
And these are supposed to resonate/flutter the same???? Call me dubious.
The NACA 1497 is based on many simplifying assumptions. This one is no less reasonable.

#### grandcross

##### Well-Known Member
TRF Supporter
With all this modeling & math, do you have access to wind tunnel data or flight data to verify the model's predictions ?
For straight or symettrically tapered fins yes. In particular, NACA TN 685 has a lot of wind tunnel data. It also has a more generalized model for calculating flutter, but as you can imagine it's much greater effort to implement than this simplified model. So I started here first.

I don't have access to data for swept or elliptical fins, hence this post.

#### QFactor

##### L2 - NAR & TRA
TRF Supporter
For straight or symettrically tapered fins yes. In particular, NACA TN 685 has a lot of wind tunnel data. It also has a more generalized model for calculating flutter, but as you can imagine it's much greater effort to implement than this simplified model. So I started here first.

I don't have access to data for swept or elliptical fins, hence this post.

Attached is NACA RM-L57L10. This is from 1958, and they looked at using a "strip" analysis for fin flutter; swept & unswept, subsonic & supersonic.

It's a tough but interesting read if you're going to dive into fin flutter.

#### Attachments

• NACA-RM-L57L10-1958-Flutter-Strip-Anaylsis.pdf
3.2 MB · Views: 1

#### QFactor

##### L2 - NAR & TRA
TRF Supporter
There is a thesis from 2009. The gentleman that wrote it did a nice job of reviewing Eqn. 18. He presents a fin flutter analysis method,
and then generated some wind tunnel data too. It's worth a read if you have the time.

I could not download the file. It was too large. Here's info that should allow you to find it on the web.

Air Force Institute of Technology
AFIT Scholar
Theses and Dissertations Student Graduate Works
6-9-2009
Aeroelastic Optimization of Sounding Rocket Fins
Joseph R. Simmons III

#### G_T

##### Well-Known Member
You can use Xfoil or XFLR5 to model some of the fin aerodynamics.

Gerald

#### QFactor

##### L2 - NAR & TRA
TRF Supporter
You can use Xfoil or XFLR5 to model some of the fin aerodynamics.

Gerald

Thanks for posting those programs. I had not come across them before.

#### grandcross

##### Well-Known Member
TRF Supporter
Wow. I knew this thread would have either no response or be a treasure trove of knowledge. Luckily it's the latter.

Time to brush up some atrophied math skills. Thanks everyone!

#### shockie

##### High Plains Rocketeer
Keep in mind that this paper was written long before computer modeling became possible so simplifying assumptions and approximations are required. These days you can simulate any fin geometry and composite layup you care to enter into a finite element model.
I just love it when you talk technical

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