Optimization mindia fins - advice needed on semi-span

[ghostfather]

I'm suffering from the altitude bug, and I am designing a minimum diameter rocket for a personal altitude record. Optimization of the fins is my present challenge.

I've decided to go with a clipped delta fin, with about a 70 degree sweep angle. The rocket will probably go 2 - 2.5 mach.
I'm playing with the semi-span, the width of the fin that sticks out from the rocket. Reducing the semi-span results in less wetted area, and higher altitudes.

Is there a "rule of thumb" as far as the semi-span of the fin in relation to the airframe diameter? Presently, I am using 2/3 of the airframe diameter as the semi-span on my fins, based on rockets that I have flown successfully.
The fin has to stick out enough to stabilize the rocket, but at mach 2+ still be small enough to minimize drag. Rocksim tells me that it is stable, even if I use minimal fins at 20% of the airframe diameter, but then the fillets are about a third of the fin, which doesn't seem right.

Sorry, I don't have a wind tunnel, but there must be some wisdom out there as far as how far a fin must stick out from the airframe to be effective and safe.

 

[SDramstad]

My general rule of thumb is at least 1 cal of span on the fin. 38 mm airframe equals a 38mm or 1.5 inch span minimum. YMMV

 

[ghostfather]

at least 1 cal of span on the fin.

Thanks. Rules of thumb are usually based on some sort of real-life wisdom, like the aerodynamics of the fin needing at least "this much" clean air to function.

I also use a rule of thumb for the size of my fin joints - radius between 4% and 8% of the root chord - based on recommendations from a paper from the 40's or 50's describing the influence of wing fillet size on transonic behaviour. It doesn't matter much at subsonic speeds. Too small a fillet, and there is increased interference drag between the body tube and fin. Fillets too big, then the fin (wing) doesn't steer as well.
I don't bother calculating anything, I just use this rule of thumb based on an old NACA paper.

That being said, most of my rockets follow your rule of thumb of the semi-span at least 1 caliper, and most between 1 and 2 calipers, but many of my minimum diameter models have flown well enough with a semi-span of about 70% caliper. It's not based on any research that I can find, they've just survived and flown true.

>> First rule of aerodynamics. Push anything hard enough and it will fly.
Probably more applicable for mindia rockets at 2+ Mach, even with 70% caliper fins

I do check and calculate fin flutter for anything going very fast, and shorter fins flutter less easily.

Again, thanks for your input.

 

[G_T]

One thing that should really reduce the flutter issue is to get the stiffness distribution of your fins appropriate for the aerodynamic loads. I ran some numbers on that recently. For fairly conventional fins for high performance rockets, the appropriate taper ratio is going to be very close to having the tips be 1/3 the thickness of the root.

If concerned about flutter, make the root a little thicker. Keep the tips down to around 1/3 the root thickness. Then the stiffness profile will be a close match to the aero loads applied. Such a fin won't suffer from being too wimpy at the root compared to the tips. And of course, anchor the root well, so they can take some serious loading without breaking off.

Aero loads are generally a function of the square of the speed.

 

[ghostfather]

One thing that should really reduce the flutter issue is to get the stiffness distribution of your fins appropriate for the aerodynamic loads. I ran some numbers on that recently. For fairly conventional fins for high performance rockets, the appropriate taper ratio is going to be very close to having the tips be 1/3 the thickness of the root.

If concerned about flutter, make the root a little thicker. Keep the tips down to around 1/3 the root thickness. Then the stiffness profile will be a close match to the aero loads applied. Such a fin won't suffer from being too wimpy at the root compared to the tips. And of course, anchor the root well, so they can take some serious loading without breaking off.

Aero loads are generally a function of the square of the speed.

I generally use finsim to check flutter, which only accepts flat fins geometries That gives me a good minimum thickness to work with.

On smaller rockets I have used 3D-printed fins with airfoils and tapering from the root to the tip. I might try to do something like that with a fiberglass G10 core and fiberglass over the 3D-printed part, and taper it to 1/3 the root thickness, as you suggest. I may need to address the heating on the leading edge, for which 3D-filament under fiberglass can't stand up to very long, even with high-temp PET filaments. Don't want my fins melting off.

 

[UhClem]

One thing that should really reduce the flutter issue is to get the stiffness distribution of your fins appropriate for the aerodynamic loads. I ran some numbers on that recently. For fairly conventional fins for high performance rockets, the appropriate taper ratio is going to be very close to having the tips be 1/3 the thickness of the root.

The classic paper on fin flutter assumes a constant value for the ratio of t/c which is the thickness to chord.

 

[G_T]

And that would yield the same results if the tip chord is 1/3 the chord of the root. However if the tip were the same chord as the root, the paper will be way off the ideal thickness distribution. Not that most would choose a tip chord the same as the root chord on our scale minimum diameter rockets, but hopefully the point is noted.

I've attached a picture of essentially what the bending load on typical fins would be. Admittedly, taken from a higher aspect ratio wing (a highly optimized reference wing design I published a few years back). The principle and pattern is substantially the same.

If you want, take that bending load pattern and figure out the simplest thickness distribution that matches the stiffness to the bending load. That's what I did, and then suggested the 1/3 tip thickness to root, with a linear thickness taper. Of course the tips then end up slightly thicker than necessary (at the tips, bending load is zero so thickness could be zero if you didn't want to keep an airfoil).

But it is a HUGE improvement on what is typically done on hobby rocket fins. What the 1/3 rule of thumb does is give you a thickness of 2/3 the root, halfway out, which is going to be very close to correct. So if you don't want to run the aero sims to generate the bending moments along the span, then figure the required stiffness distribution, that rule of thumb will save you time and get you in the ballpark.

What the paper most likely does is start from a hypothesis that the airfoil is held constant across all span stations, thereby forcing thickness to be proportional to local chord. It need not be. But, if I've read that paper, it's been a while!