# The Optimal Fin Shape For small rockets But will it work for supersonic ones?

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This is the transcript taken out of Apogee technical publications #16 which can be viewed here : https://www.apogeerockets.com/technical_publication_16.asp

Technical Publication #16
What Type of Fin Shape is Best?
By Tim Van Milligan

Many people have been told that the elliptical fin shape has the lowest induced drag. While that may be true for full size airplanes, it may not be necessarily true for small model rockets. The reason is buried in the very technical subject about something called the fin's "Reynolds Number." I'll try to describe this without getting too technical, because I want even young modelers to understand this (I've seen too many science fair projects with the subject being 'optimum fin shapes' -- which you won't find in my book: 69 Simple Science Fair Projects with Model Rockets: Aeronautics).

There are two types of drag on a rocket; induced drag, and profile drag. Induced drag only occurs when the fin creates lift. So if the rocket is flying along nice-and-stable, the fins don't have to create any lift forces to straighten out the flight path of the rocket. Hence, the induced drag on the rocket may be near zero. Therefore, it is highly likely that your rocket will have the same induced drag forces no matter what shape fin you use - because typically a model flies straight and true and the induced drag in the rocket is very, very small.

Profile drag on the other hand, is always present. It is a combination of friction drag and pressure drag. The profile drag force is determined by a number of factors, including the surface finish on the fin, airfoil used, area of the fin, the length of the fin chord, and the speed at which the rocket travels. The last two factors are also used with other parameters to determine the Reynolds Number for the rocket.

The Reynolds Number is often used to determine the Coefficient of Lift of the fin at various angle of attacks (AOA). You can see from the figure below, that the higher the Reynolds Number, the higher the fins Coefficient of Lift. Therefore, it will be more efficient at creating a restoring force to correct the path of a rocket.

So if your rocket is flying slow, and has very small fins, the Reynolds number might be so low that the fin will be very ineffective (because the Coefficient of Lift will be smaller). And if your rocket starts to stray from a vertical path, the model will cant much further over before the AOA is high enough to force a larger Coefficient of Lift. This will then start to bring the rocket back to vertical, but now the induced drag really starts to increase as does profile drag; because the side of the rocket is exposed to the airflow. This makes it highly desirable to have a fin that has a high Coefficient of Lift, so the model quickly restores to the correct flight path when the AOA is still small.

If you look around for data, you will find that the Coefficient of Lift is determined by the airfoil of the fin, not its shape. We will now see that the wrong shape can make the situation even worse.

So if your rocket is flying slow, and has very small fins, the Reynolds number might be so low that the fin will be very ineffective (because the Coefficient of Lift will be smaller). And if your rocket starts to stray from a vertical path, the model will cant much further over before the AOA is high enough to force a larger Coefficient of Lift. This will then start to bring the rocket back to vertical, but now the induced drag really starts to increase as does profile drag; because the side of the rocket is exposed to the airflow. This makes it highly desirable to have a fin that has a high Coefficient of Lift, so the model quickly restores to the correct flight path when the AOA is still small.

If you look around for data, you will find that the Coefficient of Lift is determined by the airfoil of the fin, not its shape. We will now see that the wrong shape can make the situation even worse.

The most efficient part of the fin is at the tips; where the airflow is nice and smooth because it is outside the turbulence caused by air flowing over the nose of the rocket. On elliptical fins, and on other shapes where the tip is reduced because
of tapering, the Reynolds Number is even further reduced - remember that Reynolds Number is a function of the chord length of the fin. So, because the Reynolds Number at the tip is lower, the tip is less effective at creating lift to restore the rocket to vertical if it should be disturbed. To compensate for this, you'll have to increase the size of the fin, which defeats the purpose of trying to make the model as small as possible to help reduce both weight and profile drag.

Changing the Airfoil on the fin affects performance too!
Another problem associated with tapered fin shapes is that the airfoil shape typically changes too. Why is this? Because the thickness as a percent of the chord length increases unless the fin thickness get progressively thinner toward the tip of the fin. Even people that sand an airfoil into the fin rarely make the tips thin compared to the root to keep a constant airfoil. This is because they are already starting with a thin fin, and it would be difficult and time consuming to sand the fin so thin that you could see through it. Well... this fatter airfoil makes the problem associated with low Reynolds Numbers worse! The tip of the fin is even less effective at creating a restoring force if it should become disturbed.

So we now see that the elliptical fin or the highly tapered fin may not be the optimum for lowest drag. These fins will require the model be further deflected before the forces acting on the fins are large enough to cause them to be effective in straightening out the flight of the rocket. And while the rocket is deflected, the nose and body tube are presenting a lot of side area to the on-rushing airflow; so the drag can be huge.

It would be better to use a shape that is more effective at low Reynolds Numbers, and that is easy to make without the hassle of thinning the thickness of the fin toward the tip. The better solution would seem to indicate that a rectangular or parallelogram would yield lower overall drag.

And there is a huge advantage to the rectangular shaped fin; you can cut and sand one long strip of balsa wood. Then you can just section it into the individual fins. All the fins now have the identical airfoil shape! This helps reduce the drag forces on a fin that might otherwise be non-identical with the others on the model.

There you have it. The best shape for a small competition model is a rectangle or the parallelogram. And it just happens to be the easiest fin to make!

WAIT HERES MY QUESTION!!
Will These fin shapes work for supersonic models? :dark:

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LOts of good info on this one but its stuff most pros already know

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Square is good for competition rockets, like duration and altitude rockets, that stay relatively slow and are already pretty stable.

For Machbusters, you need fins that can survive high-speed flight, and that will keep a model with most of the weight in the rear (motor) stable. Swept fins like delta ones are good for that.

would a fin shape like this work?

Not well. It'd probably shred. That nose is a poor choice too.

AtsWHAts wrong with the nc?

You should go straight to the Bible of model rocketry-- G. Harry Stine's "Handbook of Model Rocketry". He explains all about airfoils and nosecone shapes and what works and why, both at typical model rocket speeds as well as at/past Mach One.

Basically it boils down to this-- sharp, pointed CONICAL shapes are better at Mach speeds + because of the shock wave that is established at Mach One, which is basically a compression wave set up by the rocket breaking the sound barrier. Sharp, pointed shapes can penetrate this shock wave better than rounded shapes. Essentially what happens is, at Mach, the rocket's moving SO fast that the air can't get out of the way fast enough. If you have a rounded nosecone, the air will 'pile up' and compress on rounded shapes (nosecones and fin leading edges) and it takes energy to do that, which is wasted drag. The sharply pointed nosecone 'splits' the air easier and is more efficient. Fins on supersonic aircraft and rockets are also generally either wedge shaped (in profile) or have a sharp wedge-shaped leading and trailing edge. That is why missiles like the Trident II SLBM, which has a rounded nosecone about the same profile as a Big Bertha, actually has an extendable 'aerospike' much like a larger version of a car power radio antenna in the top of the nosecone. The rounded shape is best for launching underwater, as it moves the smoothest through the water, and at low speeds as the missile breaks the surface and starts to accelerate away. However, as it soon reaches Mach One, the aerospike sets up a shock wave ahead of the bulbous nosecone that ACTS like the nosecone is sharp and pointed!

When you look at strictly subsonic aircraft like commercial jets, their noses are distinctly rounded, as are their wings and stabilizers. This is the best shape at subsonic speeds. The rounded tip has less surface area than the long sharp tips, and the air flows more smoothly over it, and since there aren't any nasty 'shock waves' (but there are other aerodynamic effects like laminar and turbulent airflow, etc.) the rounded shape just works best.

Aircraft that spend most of their time supersonic are usually MUCH pointier at the nose and wings-- look at the Concorde, the F-104 Starfighter, B-58 Hustler, etc.

Hope this helps! OL JR

Ok it's final I'm getting the book

So at that speed the ogive and conical would be more efeective then say parabolic or an olipticoid oh but let's get back to the fins here : )

So at that speed the ogive and conical would be more efeective then say parabolic or an olipticoid oh but let's get back to the fins here : )

Did you ever consider tube fins?? I have a mach buster design using the D-21 that uses 3 -3/4in. long 10.5mm. tube fins.

Not well. It'd probably shred. That nose is a poor choice too.

That is my assessment. Great candidate for a shred when it is transonic, IMHO.

Greg

I will probobly change it to a delta

Did you ever consider tube fins?? I have a mach buster design using the D-21 that uses 3 -3/4in. long 10.5mm. tube fins.

Can I see the plans for that?

The delta shape, or clipped delta, are better fin shapes for what you are trying to attempt.

Fins will long spans are prone to experience the phenomena called fin flutter, especially at transonic speeds. Oscillations cause the fin to move back and forth until they snap off the airframe. On YouTube, there is a clip from a video cam mounted on a rocket that shows this phenomena, until the fin is ultimately ripped off.

My fin test: If I lay the rocket horizontal and take Vise Grips and attach it to the tip of the fin (which is also in the horizontal plane), will I lose the fin? If I think that I will the fin, the fin and joint are probably not strong enough for a Mach attempt. That is just an "armchair" test, but it is at least something to start with.

As far as the nosecone is concerned, read and study the link provided by Microspeed before you settle on your nosecone design. Once you digest that material, it will aid your decision on finding a nosecone tuned to parameters of your flight envelope.

Greg

Out of couriousity where does one get a Von karmon nose cone?

Out of couriousity where does one get a Von karmon nose cone?

AFAIK, they are all custom made, which is to say I do not know of one vendor that supplies them in any size. They can either be turned by hand or on a CNC lathe. Cost is a function of size (volume), material and labor.

The designer determines the base and the fineness ratio, then it is just a matter of getting the calculations right, with the desired level of granularity between data points to establish the nose cone profile.

Greg

Oh joy more math!

Oh joy more math!

Come now! What's rocket science without a little F=ma?

Seriously, it's not so bad with Excel. You just make it do the heavy lifting.

Greg

Out of curiousity again why doesn't anyone carry Von karmon nose cones?

Out of curiousity again why doesn't anyone carry Von karmon nose cones?

The market has determined that the demand is not sufficient to incur the costs associated with production.

Is there a demand? Yes. But it would be mostly in the MPR and HPR arena. The Von Karman is a COOL looking nose cone, and, in my judgment, one of the finest aerodynamically in the transonic regime. But really, who knows this stuff unless you have have studied it and have a rocket that can take advantage of it?

If a boutique vendor makes them, he can probably sell them. But I would expect to only see them in sizes 2.60" OD or greater.

Greg

I always need stuff the market has deemed inprofitable

Where did you find the 10.5 mm body tubes?

BMS sells it

Does this mean the ogive is poor for everything?

Remember, this is a guide. Unless you have wind tunnel tests with different configurations of NCs so that you can gather empirical data, it is hard to say for instance what performance drop one cone has when compared to another. Ogives at least look great and they do work.

I would like to see NC tests to evaluate CDs using the available minimum diameter airframes (starting at the 29mm motors), at different velocities (say Mach 0.4 to Mach 2). Another variable is the atmosphere. Perhaps some NCs work better at sea level in the denser air than the thinner air out in Mile High country. Maybe a study like this could be a thesis for an Aero. Eng. major. A well thought out study would take away a lot of mystery in this area, at least it would benefit those who want to fly fast.

Here is something to think about, one of the US Army's missiles chose a Von Karman (at least as best as I can determine). I figure they have a wealth of resources that we hobbyists don't have and the physics haven't changed much since then.

Aren't cones ogives and parabolics th only ncs that are commerically availible?

I can't speak to that, but it would not surprise me. Unless you have the engineering drawings or the specifications of the nc, it is hard to know unless you take the physical measurements, yourself.

Greg

AFAIK, they are all custom made, which is to say I do not know of one vendor that supplies them in any size. They can either be turned by hand or on a CNC lathe. Cost is a function of size (volume), material and labor.

The designer determines the base and the fineness ratio, then it is just a matter of getting the calculations right, with the desired level of granularity between data points to establish the nose cone profile.

Greg
Would either of these be in the ballpark?

https://www.semroc.com/Store/Scripts/prodView.asp?idproduct=581

https://www.semroc.com/Store/Scripts/prodView.asp?idproduct=2258

MarkII

Does this mean the ogive is poor for everything?
Aren't cones ogives and parabolics th only ncs that are commerically availible?

I don't know if Ogives and Parabolics are the only one available, but are they poor for everything? NO. As the write-up explained, all the nosecones are about the same below 0.8 Mach. It's only when you get into and above the Mach transition speeds with the associated shock wave that the nosecone shape starts to play a large part in the drag generated.

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