3 vs 4 fins in OpenRocket sim

[SolarYellow]

I've been reading the various old threads on 3 vs. 4 fins and decided to go A vs B in OpenRocket with the concept. Posting in this section of the forum because the question isn't unique to LPR/MPR/HPR, but is relevant to anyone designing their own rockets.

I took a few 3FNC designs I'd done in OR. Changed them to 4FNC by changing the fin count to four. In each case, when I scaled the fins to 80 percent of the 3FNC size, OR returned a stability factor that matched the 3FNC stability factor within a percent or so and apogee was increased by about 1 percent.

There's a lot of chatter that, all else being equal, 3 fins have less drag than 4. These results would seem to contradict that.

At 80 percent scaling, the planform area of each fin is 64 percent of the original fin area, which means the total area is 14.7 percent less than the three fins at 100 percent. However, the CP contribution of the fins is shifted rearward by ~20 percent due to their reduced size, making the smaller area equally effective in stabilization.

There are at least two other factors that seem important:

• Four fins induce less spin on the rocket, which ultimately leads to less rotational speed, and less drag because the fins are not sweeping the atmosphere at an angle. There's a post somewhere where a competition flyer says fins sweeping at an angle can easily be 10 percent of apogee if the fins aren't perfectly straight.
• Smaller fins will reach their flutter threshold at higher airspeed.

This is changing me into a four-fin kind of guy.

 

[neil_w]

Use the Component Analysis tool to show the different drag characteristics of the 3 vs. 4 fin sets.


It's usually informative.

See how it changes with different fin profiles.

 

[SolarYellow]

So I did that. Prompted me to go back and tune things up better.

One thing I noticed is that scaling the fins to 0.8 also scaled the thickness. Turns out that's where most of the apogee gain came from. So I changed that back to the same thickness as the 3F fins. I also tweaked the size a little bit (manually resetting the thickness each time) to match the stability factors to the three significant figures displayed.

The apogee difference shrunk quite a bit, but didn't go to zero. The drag still shows the 4 fin set as being less. With the induced spin and flutter differences, I still expect four fins will prove (infinitesimally) superior to three in the field.

Add a third advantage for smaller fins: They have less leverage when force is applied, so they should be slightly better able to resist breakage due to impact.

 

[neil_w]

So I did that. Prompted me to go back and tune things up better.

One thing I noticed is that scaling the fins to 0.8 also scaled the thickness. Turns out that's where most of the apogee gain came from. So I changed that back to the same thickness as the 3F fins. I also tweaked the size a little bit (manually resetting the thickness each time) to match the stability factors to the three significant figures displayed.

The apogee difference shrunk quite a bit, but didn't go to zero. The drag still shows the 4 fin set as being less. With the induced spin and flutter differences, I still expect four fins will prove (infinitesimally) superior to three in the field.

Add a third advantage for smaller fins: They have less leverage when force is applied, so they should be slightly better able to resist breakage due to impact.

What fin profile are you using? What do the actual drag values look like in Component analysis? Can you post screenshots for your 3- and 4-fin versions?

 

[SolarYellow]

I've actually built the three fin version, haven't flown it yet.

The component analysis window for the three fin version is on the left, four fins is on the right.

 

[neil_w]

Based on those numbers I assume you have the profile set to "airfoil". I admit I'm a little unsure why the 4-fin version is coming out with less pressure drag than the 3-fin version... But either way the reduced friction drag of the 4-fin version would be likely to outweigh it by a bit. Don't know how much fin/body effects are coming into play here.

 

[cls]

I think - but can't prove - 4 fins are better for stability at high alpha, angle of attack larger than (mumble make up a number ok 10 degrees). 3 fins just induce roll and little yaw.

Matters at launch (low velocity) vs crosswind, and near apogee (again low velocity) vs shear later crosswinds, so there more for HPR than LPR.

Why do I think this? Several days at Black Rock, serious shear layer (25 knots at say 6k ft), 3 fins all got knocked over, 4 fins wiggled at kept going. Anec-data, ymmv etc.

 

[BABAR]

I think - but can't prove - 4 fins are better for stability at high alpha, angle of attack larger than (mumble make up a number ok 10 degrees). 3 fins just induce roll and little yaw.

clarification: better for STABILITY or LESS LIKELY TO WEATHERCOCK?

If latter, I have always wondered if Weathercocking is more a factor of Cross Sectional Area than absolute NUMBER of fins. For same stability by Barrowman (which I believe remains the core of most simulators?), larger number of smaller fins presents less surface area to cross winds than fewer larger fins. Tube fins are similar in reduced tendency to weathercock (much of the effective surface area is “shielded” from cross winds), although unless you are Larry Brandt tube fins tend to be less efficient.

As for efficiency of 3vs 4, not at all sure how to back it up mathematically, and maybe @BEC or other experienced competitors can correct or confirm, but I theeeenk most altitude and duration winners were and continue to be three-finned models. Since these folks seriously go all out to optimize performance, I suspect they would know. That would be more than anecdotal.

Following from

https://www.nakka-rocketry.net/fins.html#howmany

“How many fins?​

Clearly, at least three fins are required (for hopefully obvious reasons). And I can't imagine a need to have more than four fins, other than for aesthetic reasons. So the question becomes -- 3 or 4 fins? Nearly all my rockets had four fins. With such an arrangement, I found it simpler to form the root bend on the fins, and end up with fins that were neatly and symmetrically aligned. Three fins are best when designing a high performance, low drag rocket. This allows interference drag (drag caused by interference of the airflow over the body and fins at the junction) to be reduced by 25 percent. For this reason, the Cirrus One rocket was designed with a set of three fins.” (End quote)

Of course, he was wrong about 3 fins required. There are a number of ways to make 2 fins work, but they definitely are NOT performance hunters

https://www.rocketryforum.com/threads/2fnc-2-linear-fins-and-a-nose-cone-the-lucky-7.56426/

 

[bjphoenix]

I think - but can't prove - 4 fins are better for stability at high alpha, angle of attack larger than (mumble make up a number ok 10 degrees). 3 fins just induce roll and little yaw.

If stability is achieved by air pressure acting on a fin and creating a moment to restore orientation, then the question is what orientation does OR consider? With 4 fins you could have an orientation where 2 fins are fully exposed to the pressure, or you could have a situation with the rocket rotated 45 degrees where all 4 fins are exposed but they are angled 45 degrees to the axis of the rocket and the restoring force is less. Whichever orientation is considered, now apply that to a system of 3 fins. There is never an orientation where some of the 3 fins aren't at an angle to the wind direction so that affects the results. I think I could apply numbers to this comparison. I would be interested in the result.

I usually have a design in mind when I'm building so if the design requires 4 fins that's what I use, but if I'm the designer I'll use 3. I do this for 3 reasons- I think it makes the design look lighter, it is less work to build 3 fins, and alignment/installation of 3 fins is less critical. With 4 fins the opposing fins have to line up perfectly or it is obvious.

 

[jqavins]

A few quick numbers:

• If the semi-span of the larger fins is L, the frontal area of the 3FNC fins is 3L, while for the four 4FNC it's 4∙0.8L = 3.2L, so that contribution to friction is about 6.7% greater.
• If the area of the larger fins is A, the total surface area for the 3FNC is 3∙2A (two faces on each fin) or 6A, while for the 4FNC it's 4∙2(0.64A)=5.12A, so that contribution should be about 15% lower.
• With fixed fin thickness, the mass scales with the area, so that is also about 15% lower.

The area presented to wind is more complicated, because it depends on the extent to which one fin that's in the lee of another remains effective. Does the shadowing effect leave the fin that's behind unaffected? Surely not. But does it completely kill the shadowed fraction of the downwind fin? Probably not that either. And the planform will affect the answer, since the fraction of a downwind fin that's shadowed only changes linearly with the fraction of cord in shadow if the fins are rectangular (or parallelograms).

RockSim gives a nice polar coordinate plot of stability margin vs. wind angle as seen from the rocket's base, but I don't know what shadowing assumption is used. (The overall margin shown on the design screen is the minimum one would see on that plot.) Does OR have such a feature?

 

[SolarYellow]

The area presented to wind is more complicated, because it depends on the extent to which one fin that's in the lee of another remains effective. Does the shadowing effect leave the fin that's behind unaffected? Surely not. But does it completely kill the shadowed fraction of the downwind fin? Probably not that either. And the planform will affect the answer, since the fraction of a downwind fin that's shadowed only changes linearly with the fraction of cord in shadow if the fins are rectangular (or parallelograms).

I think the "shadowing" issue can be safely ignored for most cases.

Say we take a worst-case example. A rocket leaves the rod at about 30 mph in a 20 mph cross-wind, the angle of attack will be about about 34 degrees. If the wind flowed in a straight line, like light, past the upwind fin, the tip of the LE would begin to impinge on the root of the downwind fin at 3/2 of the lateral distance between them. If we have a clipped delta fin planform, I would expect most of the downwind fin to be non-shadowed. (Something like an Alpha fin would be worse, but Alphas are way over-stable, so it's not an issue.) Further, the wind will actually tend to follow the lee side of the upwind fin, so the actual shadowing will be less.

However, in such a situation, we probably actually want reduced stability so as to reduce the weathercocking that would be expected under the circumstances. If we had more common sense and were launching a zippier rocket more appropriate for the conditions, or flying in less silly conditions, it takes care of the shadowing issue.

You do raise a good point about the relative contributions of frontal area vs. surface friction drag. Thin fins make the relative importance of frontal area less. Less-perfect surface finish leans in the direction of the reduced surface area of four fins being advantageous.

However, as @neil_w pointed out, there must be something else going on in OR, as OR is assigning approximately a 1/3 drag reduction to both pressure drag and friction drag on the four-fin version of the model. Curious what @JoePfeiffer can add.

 

[jqavins]

I totally agree that there is something else going on. I'm only offering the geometrician's perspective.

 

[OzHybrid]

I've been reading the various old threads on 3 vs. 4 fins and decided to go A vs B in OpenRocket with the concept. Posting in this section of the forum because the question isn't unique to LPR/MPR/HPR, but is relevant to anyone designing their own rockets.

I took a few 3FNC designs I'd done in OR. Changed them to 4FNC by changing the fin count to four. In each case, when I scaled the fins to 80 percent of the 3FNC size, OR returned a stability factor that matched the 3FNC stability factor within a percent or so and apogee was increased by about 1 percent.

There's a lot of chatter that, all else being equal, 3 fins have less drag than 4. These results would seem to contradict that.

At 80 percent scaling, the planform area of each fin is 64 percent of the original fin area, which means the total area is 14.7 percent less than the three fins at 100 percent. However, the CP contribution of the fins is shifted rearward by ~20 percent due to their reduced size, making the smaller area equally effective in stabilization.

There are at least two other factors that seem important:

• Four fins induce less spin on the rocket, which ultimately leads to less rotational speed, and less drag because the fins are not sweeping the atmosphere at an angle. There's a post somewhere where a competition flyer says fins sweeping at an angle can easily be 10 percent of apogee if the fins aren't perfectly straight.
• Smaller fins will reach their flutter threshold at higher airspeed.

This is changing me into a four-fin kind of guy.

Also, the "4 fins induces less spin" applys to after ejection when the body is coming down flat-ish and rotates, twisting up the lines. With 4 fins the air sees the fin area more evenly and does not spin as much. With 3 fins it sees an uneven amount on one side or the other. Starts spinning and tangles the lines. This has resulted in securing eyebolts getting unscrewed and the rocket separating. (Not mine) This is one of the reasons why you need to judiciously use swivels.

4 fins will be smaller and therefore stiffer. Less liable to fluttering. But you will get more parasitic drag from the root fillets. A Mach+ rocket will have some coning of the airflow. With smaller height fins, the air could partially bypass sufficient of them to make the rocket unstable as your Cp would start to move forward.
Good luck with the build
Norm

 

[SolarYellow]

4 fins will be smaller and therefore stiffer. Less liable to fluttering. But you will get more parasitic drag from the root fillets. A Mach+ rocket will have some coning of the airflow. With smaller height fins, the air could partially bypass sufficient of them to make the rocket unstable as your Cp would start to move forward.
Good luck with the build
Norm

Good point about the swivels for recovery.

I bolded the bit about fillets. I recently became unconvinced that that is true. See my post over here https://www.rocketryforum.com/threads/the-whys-of-fillet-radius.124576/#post-2422716 where I investigated that a little.

Figure 26 indicates that the interference drag becomes very small for t/c ratios below 0.1, with a zero crossing around t/c = 0.5-0.6. With smaller t/c ratios, the interference drag is graphed as negative and there is no differentiation below the zero crossing between with and without fillet.

There are plenty of PDFs of the Hoerner book around. Easy to find. A good read.

 

[OzHybrid]

Good point about the swivels for recovery.

I bolded the bit about fillets. I recently became unconvinced that that is true. See my post over here https://www.rocketryforum.com/threads/the-whys-of-fillet-radius.124576/#post-2422716 where I investigated that a little.



There are plenty of PDFs of the Hoerner book around. Easy to find. A good read.

With 4 sets of fillets, you've got 33% more fillets than 3 sets of fillets. Now the fillets might be slightly smaller, but that's still likely to be more parasitic drag from 4 fillets.

 

[SolarYellow]

Are you talking frontal area drag due to the fillet cross section? Usually when people talk type about fillets and drag, they are referring to interference drag. The Hoerner book indicates that interference drag goes negative on a fin that's long and thin enough. Many model rocket fins fit the criteria.

 

[OzHybrid]

Are you talking frontal area drag due to the fillet cross section? Usually when people talk type about fillets and drag, they are referring to interference drag. The Hoerner book indicates that interference drag goes negative on a fin that's long and thin enough. Many model rocket fins fit the criteria.

Let's just say that having 4 sets of fillets instead of 3 will be on the negative side of your performance equation. Due to the increased frontal area produced....

 

[Gus]

The issue is sim vs. reality.
No one flies 4 fins in either national or international altitude competition.

 

[BEC]

This discussion just makes me want to make one of my models for NARAM — either the A Altitude or the A Payload Altitude model — with four smaller fins. Since I've only built one of each so far, I could do it.

BUT... my Apogee tower is set up for 3-fin rockets and I don't really want to make a dedicated tower for a 4-fin model.

I was amused at @BABAR calling me out as out as an "experienced competitor" up there in post #8. I am an occasional competitor whose had a couple of successes and lots of mediocre results. Steve (@Gus ) on the other hand, is literally a world-class competitor and multi-NAR-record-holder. I've used three fins on all my competition models (except B cluster altitude and gliders of various sorts) because it's generally believed 3 is a better choice than four for overall performance. And, the aforementioned GSE constraint.

Setting up a flight test regime where the variable was three or four fins with equal total area and similar planforms would be an interesting project perhaps....but not until after the TARC finals, the WSMC and NARAM, at least for me. But it would be fun to validate (or not). That said, getting real world performance in real weather and with real-world motors measurable to within a consistent 1% seems a bit of a stretch, at least for what I have access to.

Added: this discussion does make me want to ask Bill Saindon why the BMS School Rocket has four fins, though. That model is very reliable in the hands of just about anyone and performs without drama even under less-than-ideal conditions. I wonder why he opted for the additional parts (and manufacturing time with his laser cutters) making four fins and four fin slots for that model....

 

[Gus]

Steve (@Gus ) on the other hand, is literally a world-class competitor and multi-NAR-record-holder.

Bernard,

Thanks for the compliment. As I mentioned above, I believe what the OP has found is a simulation anomaly with little correspondence to actual flight models. There is a good reason altitude competitors don't fly 4 finned rockets, they don't perform better.

Optimizing altitude for a given motor is an interplay between rocket length, nose weight, and fin size and critical assumptions about stability caliber, among a number of other variables. For a given rocket length (shorter with less skin drag is better) fin size should be continually reduced until, eventually, the additional nose weight needed to reach the desired stability caliber exceeds optimal mass thereby reducing altitude. Adding additional fins of smaller size at that point would not be helpful. Of far more importance is deciding what is the minimal stability caliber you are willing to accept (is 1 necessary, how about 0.7 or 0.6?).

Also, in the original post the statement that 3 fins are more likely to induce rotation than 4 is incorrect. Properly placed fins should induce no rotation but with 4 fins you have more chance of messing one up than with 3.

Again, thanks for the compliment and looking forward to seeing you at WSMC and NARAM this summer.

Steve

 

[jqavins]

Setting up a flight test regime where the variable was three or four fins with equal total area...

Make that equal CP. That should be close to the same thing, but what with one thing and another it might not be exactly the same.

 

[SolarYellow]

Optimizing altitude for a given motor is an interplay between rocket length, nose weight, and fin size and critical assumptions about stability caliber, among a number of other variables. For a given rocket length (shorter with less skin drag is better) fin size should be continually reduced until, eventually, the additional nose weight needed to reach the desired stability caliber exceeds optimal mass thereby reducing altitude. Adding additional fins of smaller size at that point would not be helpful. Of far more importance is deciding what is the minimal stability caliber you are willing to accept (is 1 necessary, how about 0.7 or 0.6?).

Anyone playing seriously with the available variables in a simulation program such as OR will arrive at the optimization process you describe.
You state the bolded part as a simple, unsupported assertion. That is actually the question under discussion in this thread. The point is to pull on every available thread and try to figure out whether it's a valid assumption or not.
The minimum acceptable stability factor is obviously of critical importance in the optimization process. I've written elsewhere about why I believe discussing stability in calibers rather than percentage of airframe length is an error in denominator selection.

Also, in the original post the statement that 3 fins are more likely to induce rotation than 4 is incorrect. Properly placed fins should induce no rotation but with 4 fins you have more chance of messing one up than with 3.

In a perfectly still atmosphere without any disturbances to the flight, this would be true. There is extensive discussion and even published literature about four fins having less roll moment than three fins when angle of attack is not equal to zero, due to the asymmetry (varying periodically with rotation) of three fins.
With robust fin tooling, I am not worried about messing one up. Doing everything by hand, it may be nearly impossible to get them close enough to right (even just the same) that fewer fins isn't the best answer.

Make that equal CP. That should be close to the same thing, but what with one thing and another it might not be exactly the same.

As far as I can tell, this is the source of the advantage I'm seeing in OR for four fins. Making the fins smaller (equal area) moves their contribution to CP farther aft, which allows them to be made even a little more smaller and arrive at the same CP. It's a small difference, on the order of a small single digit percent.

Smaller fins generate smaller moments due to landing impacts and should have an edge in durability.

There should be an additional advantage for high-speed rockets in that smaller fins have a higher flutter velocity for the same material thickness/stiffness, so it may be possible to reduce fin thickness and stay clear of flutter.

There is another thread with currently ongoing discussion of the aerodynamic virtues of fillets on model rockets.

Testing the difference between fully optimized three- and four-fin designs (otherwise as close to identical as can be built, obviously) to a level of statistical significance acceptable in various engineering fields would require 30 flights of each configuration in conditions as close to the same as possible. That is likely the biggest barrier to getting it done. It's likely that the total difference between the two would be less than production variation in motor output and variation in conditions from launch to launch that defied measurement and normalization against a sim (bringing sim accuracy back into it, if one went that way).

I won't deny the possibility that, as a practical matter, the real-world performance difference that might be available due to the theoretical difference between fully optimized three- and four-fin designs for model rockets is less than the real-world performance differences of reduced potential for performance-inhibiting variation and reduced construction labor that lie in the three-fin court, especially with low-power altitude competition models.

Further questions (probably best addressed in a different thread) are, how good are we at really optimizing our models with construction technique, and how consistent are we from build to build? How much maintenance is required on an ongoing basis to keep models at peak performance? i.e., filling scratches/dings from landings, maintaining polish, cleaning out ejection charge material buildup, etc.

 

[BEC]

Testing the difference between fully optimized three- and four-fin designs (otherwise as close to identical as can be built, obviously) to a level of statistical significance acceptable in various engineering fields would require 30 flights of each configuration in conditions as close to the same as possible. That is likely the biggest barrier to getting it done. It's likely that the total difference between the two would be less than production variation in motor output and variation in conditions from launch to launch that defied measurement and normalization against a sim (bringing sim accuracy back into it, if one went that way).

I won't deny the possibility that, as a practical matter, the real-world performance difference that might be available due to the theoretical difference between fully optimized three- and four-fin designs for model rockets is less than the real-world performance differences of reduced potential for performance-inhibiting variation and reduced construction labor that lie in the three-fin court, especially with low-power altitude competition models.

Sixty flights…so 2 1/2 bulk boxes of motors with the same date code (and maybe start with more motors and select the test motors by weight), rapid turnaround between flights with respect to flight prep and downloading/saving altimeter data, and either doing it all on one day with static weather conditions or very similar days weather-wise (definition of “very similar“ TBD). Launch out of a tower or use a rail that’s undisturbed for angle once set up. Yeah….that’s likely not really practical. And as you suggest (and I implied earlier) motor variations and flight condition variations even so will probably wash out whatever small advantage the better fin configuration will have.

It’s fun to talk about, though.

Steve and I both use examples of the Rose-Harrison fin jig to build our models, and using it helps with consistency there. But even with that elegant tool, things aren’t perfectly repeatable (at least in my case).

However, if I get a wild hair to actually try this, I’ll take Joe’s suggestion about equal CP. Don’t anyone hold your breath, though.

 

[SolarYellow]

As you well know, good testing is expensive and often difficult.

 

[BABAR]

I think Tim Van Milligan’s daughter got access to one of the wind tunnels at USAFA (I think they either have or are working toward one that goes to Mach 6.). I believe there is a rocketry group that used to fly at NASA Ames research facility near Silicon Valley.

So there are other more consistent objective ways to test this theory.

 

[BEC]

The wind tunnel idea (and one of the Van Milligan girls having gotten access to one) came to my mind as well. I doubt I could talk either UW or Boeing to let me use one of their local facilities for this, so I will leave that approach to someone else…..

 

[SolarYellow]

A&M has a wind tunnel. Maybe I can get a conversation going with the rocket team that shows up at local launches.

 

[jqavins]

Make that equal CP. That should be close to the same thing, but what with one thing and another it might not be exactly the same.

I've been thinking more about it, and what I should have written is "Make that equal CG to CP distance." Using four fins will add a little (probably miniscule) mass at the aft end, even if CP locations are equal. So the CG will shift ever so slightly aft, meaning that the total fin area can't be reduced as much as it might seem.

And yes, these are all tiny, tiny effects.

 

[jqavins]

I doubt I could talk either UW or Boeing to let me use one of their local facilities for this...

Don't be so sure of that. Universities exist in part to do research, and often they love stuff like this. The van Milligans got access to a tunnel as the USAFA by the simple expedient of asking. They had to work around other projects' schedules, but other than that the Academy saw it as a form of community engagement and a way to keep a grad student busy.

 

[SolarYellow]

I've been thinking more about it, and what I should have written is "Make that equal CG to CP distance." Using four fins will add a little (probably miniscule) mass at the aft end, even if CP locations are equal. So the CG will shift ever so slightly aft, meaning that the total fin area can't be reduced as much as it might seem.

And yes, these are all tiny, tiny effects.

If the fin area is kept equal, the mass should be the same, so any rearward CG shift would be limited to the fact that the CG of the smaller fins is farther back, keeping the TE/BT intersection point unchanged. Downsize the fins that little bit further to account for the rearward shift of the CP due to their smaller size, and you may get that back. Reduce thickness to keep the thickness/chord ratio the same, and you should come out ahead, due to ^3 effect beating out ^2 effect.