# optimizing fin shapes

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#### watermelonman

##### Well-Known Member
A friend of mine with a vast aerodynamic encyclopedia in his head was explaining how optimizing the leading edge of a fin is a simple matter of matching a mach number to an angle. Well, it is less simple considering how much our rockets vary speed throughout flight, but at least I can understand what is working where, and that gives me a good starting point.

As for the rest of the fin, it remains a mystery. Is the length typically a matter of how to get enough surface area out past the boundary layer or is there more to it than that? What about the trailing edge? I have no idea why a fin should or should not sweep back in, but I am sure it has an important effect.

This should be interesting conversation. I'm in. Have you used FinSim?

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Subscribed.

It all starts with "what do you want the rocket to do", and you use that as a basis to plan out your design. Since you don't have to worry about control, nor lift, it's mostly going to be about stability, drag, velocity, and thrust. But also, fin profiles are generally created (if you're doing that kind of work) around a velocity range, not a specific fixed velocity. It's when you start crossing from sub-sonic to super-sonic, and back again, that things get tricky. The worst thing you can do is keep a flight CLOSE to Mach 1.0 for any length of time. Trans-sonics are a confusing mess.

A thinner body, fins with shorter length and more chord, and more aggressive sweep and fin profiles, will go faster due to reduced drag but also NEED to go faster for stability.
Fatter body, longer and thinner chord fins, less sweep and taper, will be more stable at slower speeds but also much higher drag.
Barrowman equations give you your stability requirements.

Fin sweep angles at low speed is mostly for drag reduction. At higher speeds it becomes a factor to reduce trans-sonic and super-sonic shockwaves and other un-desired versions of turbulence. Other factors come into play with sweep angle in airplanes, but those are not as much a concern in rockets unless you get bad yaw going on.

Profile can be a huge factor but I rarely see much work other than a basic taper fore and aft on a fin. The trailing edge taper is generally going to be much more effective at drag reduction than the leading edge, but it's critically important to keep it as symmetrical as possible or you risk generating lift on one side of the fin.

Honestly ..... this topic may go a long while, entire books have been written on the topic. It's where you really do get things to be 'Rocket Science'.

Do remember too that all of this still applies to the body of the rocket as well, not just the fins. Every component exposed to airflow is an aerodynamic body. This is why boat-tails and variable body diameters are something you see more on higher performance rockets.

-Hans

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Great overview resource you've pulled up once again. I forgot about the divergence and flexure reasoning behind forward swept fins being a bad idea.

At the L3 performance level, the rocket science (or more aptly, rocket engineering) becomes so much more important unless you have an inordinate amount disposable income to burn figuring things out.

Hopefully the thread won't devolve into "I've done this forever so I know it works". I like seeing the tribal knowledge of the sport being challenged (or reinforced) by data.

We have a chart of NC shapes by mach number ranking. Is there such a resource for finforms?

We have a chart of NC shapes by mach number ranking. Is there such a resource for finforms?

Not that I have ever seen.

What would be interesting is running simulations in a wind tunnel with different fin shapes and comparing the data.

What would be interesting is running simulations in a wind tunnel with different fin shapes and comparing the data.

Unfortunately a mach+ windtunnel is a pretty rare bird to have available.

For subsonic, a couple of leaf blowers, some bt20, and plywood ought to do.

Next year when I'm at UAH I'll have acess to a supersonic wind tunnel where I will DEFINITELY be hanging out a lot

What would be interesting is running simulations in a wind tunnel with different fin shapes and comparing the data.

That would be if great use to the sport community. I cant shake the feeling that such tests have been done, but accessing and finding that data seems to be rare

A great resource to see drag and lift data in a relatively concise form is Chapter 13 of "Fundamentals of Aircraft and Airship Design- Volume I" by Leland M. Nicoai and Grant E. Charichner. It includes some mature methods for estimating the performance of lifting surfaces and the drag of axisymmetric bodies, based upon decades of empirical data. It is intended for airplanes but the data still applies.

Another good empirical source is the USAF DATCOM, which is available free of charge online.

As far as sweep choices versus mach go, there are essentially two design approaches: subsonic and supersonic leading edges. Subsonic leading edges generally have lower wave drag but need to be bigger due to sweep requirements, so the optimum option for each individual case takes some work to achieve. A rule of thumb for subsonic leading edges, mentioned in "Fundamentals", is to provide 5 degrees more sweep than the mach cone angle at the fastest intended speed.

Speaking of supersonic windtunnels, they have one at SDSU and I was lucky enough to run a drag study in it recently. They are quite expensive to build and run; operation of the tunnel impacts the grid voltage in the building, the wind destroys any and all sensor wires not covered with metal, and every 3 runs our models needed to be refinished from the erosion. As a result, at our school the faculty is pretty hesitant to let students use it. Took some nice pictures, here are a couple of the reference bodies we used to compare our results to:

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There are a couple Apogee newsletters on this topic, written in simple language (sometimes too simple). I remember one in particular that said fins with square trailing edges were low drag. I never got my head around that, but I use it to justify my lazy fin finishing techniques!

Speaking of supersonic windtunnels, they have one at SDSU and I was lucky enough to run a drag study in it recently. They are quite expensive to build and run; operation of the tunnel impacts the grid voltage in the building, the wind destroys any and all sensor wires not covered with metal, and every 3 runs our models needed to be refinished from the erosion. As a result, at our school the faculty is pretty hesitant to let students use it.

I would think that CFD is good enough these days to run comparison studies at much lower costs. The students can crank the numbers 24/7.

Not that I have ever seen.

Wiki has a good summary. Also has a nose cone summary vs mach.

https://en.wikipedia.org/wiki/Nose_cone_design

We have a chart of NC shapes by mach number ranking. Is there such a resource for finforms?

I was referring to a similar item for fin shapes. I am familiar with the nosecones.

I like this comparison/properties figure from Mccord's reference:

I would think that CFD is good enough these days to run comparison studies at much lower costs. The students can crank the numbers 24/7.

CFD is advanced, but running High-velocity (Mach +) and turbulence analyses is incredibly taxing on a system. The pros use custom built machines for specific aspects, and a friend of my uncle was telling me about a case for the Orion capsule descent that took 10 days to mesh and converge. (they had 4 more variables with ~12 cases each to finish the package)

There are a couple Apogee newsletters on this topic, written in simple language (sometimes too simple). I remember one in particular that said fins with square trailing edges were low drag. I never got my head around that, but I use it to justify my lazy fin finishing techniques!

Here's something about square edges. Honestly, at the lo-power low velocity level, the differences are probably minimal. But
https://www.princeton.edu/~asmits/Bi...eparation.html
I find it weird that TimvanMil would say square edges are low drag because PoF 305 says the exact opposite
:Most model rocket kit photos today show the rocket finswith &#8220;squared&#8221; edges (perhaps because it&#8217;s the easiest and
fastest to do). However, this is generally the worse (by far!)
trailing edges can reduce the &#8220;fin drag&#8221; dramatically (up to
75% less than squared edges).

can further reduce fin drag up to 85% less than that of
round edge fins (or up to 96% less than fins with squared
edges). This means your model rockets will fly faster and
much higher!

I think those numbers are extremely optimistic and likely won't be achieved by hand sanding.
Plus, Mach+ flights run into the aforementioned Mach angle issue which makes elliptical leading edges a bad idea.

I was referring to a similar item for fin shapes. I am familiar with the nosecones.

This would still be correct for the aerodynamics of the leading edge, but says nothing about the aerodynamics or flutter resistance of a particular fin shape. Maybe it's as simple as having the least amount of area that is still effective at supersonic speeds. I honestly don't know.

Steve Shannon

Yup, fin LAYOUT. NACA 6dig has plenty to say about airfoils. Materials science for flutter I'm good on. Leading edge angle as function of mach number, fillet as percent of root chord no problem.

What trailing shape is optimal for a given airspeed on the aft end?

How long should the tip chord be?

The previously referenced presentation on nosecones, and fin shape and flutter is interesting however it is rather simplistic and dated on it's conclusions on fin flutter. https://www.rocketryforum.com/attachment.php?attachmentid=307472&d=1481900239

Calculating the minimum drag shape for a nosecone is simple and it is easy to make a nosecone sufficiently stiff so that aeroelastic structural response is not an issue, however that is not the case for fins and the current concerns about fin flutter illustrate this fact. I can't find any data that shows 3 fins are better than 4 fins because it's just not that simple. To exert the same corrective authority, the total fin area would have to be the same for 3 larger fins or 4 smaller fins. A larger fin would have to be stiffer and more massive that a smaller fin for the same flutter velocity, so in practice, 4 smaller fins may well be the better solution, and indeed, many if not most unguided sounding rockets have 4 fins not 3.

The fin flutter part of the presentation has only 2 references more recent than 1990! https://www.dtic.mil/dtic/tr/fulltext/u2/a502110.pdf is an excellent reference from an AFIT Master's thesis defended in 2009 that portraits the difficulty. Not only is the size and shape of the fin important but the internal structure and material make an important difference due to mass, stiffness and aeroelastic response. Unlike the NC, the fin structure significantly effects the CG, the CP and the lift/drag of the aft section of the rocket.

CFD is advanced, but running High-velocity (Mach +) and turbulence analyses is incredibly taxing on a system. The pros use custom built machines for specific aspects, and a friend of my uncle was telling me about a case for the Orion capsule descent that took 10 days to mesh and converge. (they had 4 more variables with ~12 cases each to finish the package)

10 days on how many CPUs? That doesn't sound too bad for such a detailed and lengthy simulation. The fin designs in question here would be much less time consuming. I do automotive (subsonic) aerodynamics with CFD (often more difficult than aerospace applications because of ground effects, turbulence, and bluff shapes), and we get one to two day turnaround on a couple hundred cores per job.

If a university can afford to build and maintain supersonic wind tunnel labs and fab shops, they can easily purchase (or rent on the cloud) a few thousand cores in a High Performance Computing system and still come out ahead.

If someone wants me to use my fairly beastly rig to do some intense CFD work, just say the word .

Related: hexagonal or tetrahedral wing tips between, say, M 1.2 and M 4?

10 days on how many CPUs? That doesn't sound too bad for such a detailed and lengthy simulation. The fin designs in question here would be much less time consuming. I do automotive (subsonic) aerodynamics with CFD (often more difficult than aerospace applications because of ground effects, turbulence, and bluff shapes), and we get one to two day turnaround on a couple hundred cores per job.

If a university can afford to build and maintain supersonic wind tunnel labs and fab shops, they can easily purchase (or rent on the cloud) a few thousand cores in a High Performance Computing system and still come out ahead.

As someone that only uses CFD for insight into a hobby, I completely defer to your experience here.

I wish my old engr. department had the funding for stuff like that.

If someone wants me to use my fairly beastly rig to do some intense CFD work, just say the word .

Related: hexagonal or tetrahedral wing tips between, say, M 1.2 and M 4?

Went and re-read and remembered that folks around here call those "diamond" airfoils, such as DSMix, SpaceCowboy, APE 54's, etc. I have my answer

As someone that only uses CFD for insight into a hobby, I completely defer to your experience here.

I wish my old engr. department had the funding for stuff like that.

Sure, no worries. The devil is always in the details. Full disclosure: I am a simulation hawk. :wink:

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