3 vs 4 fins; Why do space programs prefer 4?

From what little I know, if three fins are properly sized and shaped, it will work just the same, and maybe better than four. Yet, all of the NASA/military designed rockets seem to use four fins. Is it because they are active control surfaces and its easier along an axis? But even sounding rockets that don't seem to have any guidance typically have four, so why?

Trooper said:

From what little I know, if three fins are properly sized and shaped, it will work just the same, and maybe better than four. Yet, all of the NASA/military designed rockets seem to use four fins. Is it because they are active control surfaces and its easier along an axis? But even sounding rockets that don't seem to have any guidance typically have four, so why?

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You pretty much nailed it... controlling pitch and yaw with opposing PAIRS of fins is easier when you're pairing them up... with three it gets a little more complicated since you have to move pairs of adjoining fins and throw the surfaces in opposite directions to "push" the rocket the direction you want it to go...

Roll is relatively easy-- pitch all the fins the same way to roll one way, or pitch them the opposite direction to roll the opposite direction...

Later! OL JR

PS... most "space program" rockets don't even have fins, especially nowdays... they simply gimbal the engines/nozzles to steer the rocket and push it the way they want it to move... The early sub-launched solid rocket propellant SLBM's and big solids like the Titan III SRM's used "fluid injection thrust vector control" (fluid injection TVC) for steering the thrust, rather than moving the nozzles. This was because a fluid injection system was more compact for a tight-fitting SLBM with a limited amount of space in a sub launch tube, and for the big solids, swiveling gas-tight joints that could stand up to the incredibly high temperatures in a burning solid rocket motor hadn't been perfected yet. Fluid injection TVC used a series of valves arranged around the periphery of the rocket nozzle, like the positions of the numbers on a clock face (if you looked straight up into the nozzle). These valves opened under the control of the guidance system, and sprayed a high-pressure "steering fluid" into the exhaust stream, vaporizing it and deflecting the rocket exhaust toward the other side of the nozzle... thus the exhaust stream would "turn" toward one side of the nozzle or the other, exerting a rotational force in the opposite direction (toward the valve that was opened). The steering fluid was usually nitrogen tetroxide, which of course would usually burn in the nozzle or behind it with anything oxidizable left in the exhaust stream... The downside of this system is, that you have to carry a tank of steering fluid sufficient to maintain control of the vehicle until the rocket motor burns out and the vehicle stages...

The Titan III carried its TVC fluid in the large red pencil-shaped tanks bolted the sides of the SRM's about halfway up-- each SRM had a tank bolted to it, but the tanks were clocked on opposite sides of the vehicle on the opposing SRB's...

Later! OL JR

Thanks for the quick reply! It made sense to me why four fins would be better if they were control surfaces, but the sounding rockets without guidance that still baffle me. I suppose its habit for the experts...

I was reading about the vectored thrust a few weeks ago, and the extra steering fluid did seem like extra weight. Of course the experts have done the research and decided it was a tradeoff they can live with. Its a fascinating system to be able to apply the right amount of fluid at the right moment and duration to get the right reaction. Somebody kinda smart must have come up with that...

Really going to a different topic, but wouldn't that red pencil on the Titan III create a little parasite drag?

Yep, any 'extraneous structure' on the outside of a cylindrical vehicle would create drag.

But the IIIC solids kicked out enough thrust they figured it was worth it.

Trooper said:

Thanks for the quick reply! It made sense to me why four fins would be better if they were control surfaces, but the sounding rockets without guidance that still baffle me. I suppose its habit for the experts...

I was reading about the vectored thrust a few weeks ago, and the extra steering fluid did seem like extra weight. Of course the experts have done the research and decided it was a tradeoff they can live with. Its a fascinating system to be able to apply the right amount of fluid at the right moment and duration to get the right reaction. Somebody kinda smart must have come up with that...

Really going to a different topic, but wouldn't that red pencil on the Titan III create a little parasite drag?

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Yeah, but they needed a LOT of steering fluid for a vehicle that size, and where else were you gonna put it?? I SUPPOSE they could have created a cylindrical section and put it under the nosecone and piped it down the side to the nozzle end, but then that's extra weight and expense to fabricate... drag isn't that big an issue for rocket designers, especially when you've got connecting struts and stuff sticking out into the wind like most big rockets do, like retros and antennas and propellant feedlines and cable fairings and stuff like that which all creates a certain amount of drag anyway...

I'm sure someone sharpened up their pencil and looked at "performance lost to additional drag" from a small external steering fluid tank parallel mounted on the booster with a short feedline, versus 'additional cost to design and build a forward full-diameter short steering fluid tank under the nosecone and run a long feedline back to the nozzle end of the SRM" and quite quickly figured out any performance gained wasn't worth the expense... extra weight cuts into performance more than drag anyway...

Later! OL JR

luke strawwalker said:

Yeah, but they needed a LOT of steering fluid for a vehicle that size, and where else were you gonna put it?? I SUPPOSE they could have created a cylindrical section and put it under the nosecone and piped it down the side to the nozzle end, but then that's extra weight and expense to fabricate... drag isn't that big an issue for rocket designers, especially when you've got connecting struts and stuff sticking out into the wind like most big rockets do, like retros and antennas and propellant feedlines and cable fairings and stuff like that which all creates a certain amount of drag anyway...

I'm sure someone sharpened up their pencil and looked at "performance lost to additional drag" from a small external steering fluid tank parallel mounted on the booster with a short feedline, versus 'additional cost to design and build a forward full-diameter short steering fluid tank under the nosecone and run a long feedline back to the nozzle end of the SRM" and quite quickly figured out any performance gained wasn't worth the expense... extra weight cuts into performance more than drag anyway...

Later! OL JR

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That's interested. How about missiles used on air fighters. I see they still use pins

Stability is extremely important for unguided missiles. A 4 fin rocket will be more stable than a 3 fin rocket (if the individual fins have the same area) and all unguided sounding rockets are required by range safety rules to spin to minimize trajectory dispersion so the operators know where the ballistic impact zone will be. There are several sounding rockets that can use either 3 or 4 fins. 3 fins on a heavy payload rocket can provide equivalent stability to 4 fins on a light payload rocket as the CG will move forward and the weight is reduced by removing the 4th fin so the performance is not degraded as much as it would be if you didn't remove the extra fin.

Bob

luke strawwalker said:

You pretty much nailed it... controlling pitch and yaw with opposing PAIRS of fins is easier when you're pairing them up... with three it gets a little more complicated since you have to move pairs of adjoining fins and throw the surfaces in opposite directions to "push" the rocket the direction you want it to go...

Roll is relatively easy-- pitch all the fins the same way to roll one way, or pitch them the opposite direction to roll the opposite direction...

Later! OL JR

PS... most "space program" rockets don't even have fins, especially nowdays... they simply gimbal the engines/nozzles to steer the rocket and push it the way they want it to move... The early sub-launched solid rocket propellant SLBM's and big solids like the Titan III SRM's used "fluid injection thrust vector control" (fluid injection TVC) for steering the thrust, rather than moving the nozzles. This was because a fluid injection system was more compact for a tight-fitting SLBM with a limited amount of space in a sub launch tube, and for the big solids, swiveling gas-tight joints that could stand up to the incredibly high temperatures in a burning solid rocket motor hadn't been perfected yet. Fluid injection TVC used a series of valves arranged around the periphery of the rocket nozzle, like the positions of the numbers on a clock face (if you looked straight up into the nozzle). These valves opened under the control of the guidance system, and sprayed a high-pressure "steering fluid" into the exhaust stream, vaporizing it and deflecting the rocket exhaust toward the other side of the nozzle... thus the exhaust stream would "turn" toward one side of the nozzle or the other, exerting a rotational force in the opposite direction (toward the valve that was opened). The steering fluid was usually nitrogen tetroxide, which of course would usually burn in the nozzle or behind it with anything oxidizable left in the exhaust stream... The downside of this system is, that you have to carry a tank of steering fluid sufficient to maintain control of the vehicle until the rocket motor burns out and the vehicle stages...

The Titan III carried its TVC fluid in the large red pencil-shaped tanks bolted the sides of the SRM's about halfway up-- each SRM had a tank bolted to it, but the tanks were clocked on opposite sides of the vehicle on the opposing SRB's...

Later! OL JR

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Actually you can efficiently vector thrust by injecting a small additional propellant flow asymmetrically into a rocket nozzle. It still provide propulsive force, however a shock wave is created by the injection and that moves the thrust vector just like it would if you had an engine gimbal. You save a lot of weight and cost by eliminating the gimbal so you can afford to carry a little more propellant and plumbing.

Bob

Actually you can efficiently vector thrust by injecting a small additional propellant flow asymmetrically into a rocket nozzle. It still provide propulsive force, however a shock wave is created by the injection and that moves the thrust vector just like it would if you had an engine gimbal. You save a lot of weight and cost by eliminating the gimbal so you can afford to carry a little more propellant and plumbing.

Bob

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I remember seeing technical papers showing the several injection points around the circumference of the Titan SRB's in the nozzle diverging (or supersonic flow) section and they did create shock waves, which helped the nozzle vectoring. In addition the Titan's injection fluid was nitrogen tetroxide, which reacted with the exhaust gases further enhancing the pressure distribution in the nozzle. The Chemical Systems Division of UTC did studies of several candidate liquids and decided that N2O4 was the best. (I am thinking one candidate might have been a permanganate solution. Probably, easier to handle than N2O4, but not as good as performance.)

How do gimbals work for the big solid motors (like the Shuttle SRB's, iirc)?

CarVac said:

How do gimbals work for the big solid motors (like the Shuttle SRB's, iirc)?

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Let's see. The attached photos do not show everything. The aft segment (case) with propellant fits into the nozzle on the lower left. The aft segment fixed housing is dome shaped (you can see a very small portion of the aft segment dome attached by the nozzle-case joint). Attached to the aft case dome iss the aft skirt (not shown) that fits like a truncated cone on the far outside. There is a hydraulic piston attached to the aft skirt, which is called an actuator. The other end of the actuator is pinned to the large hole fixture that you can see on the diverging nozzle section. At the end upstream of the actuator attach point you can see a large massive object made up of a series of metal plates with rubber sandwiched in between the plates. This is the flex bearing. You can see that the flex bearing is in contact with the nozzle (near the throat) by way of a sort of shoe. As the actuator moves the aft diverging nozzle the flex bearing takes up the load at the other end. Keep in mind that this is a cross section and the actual device is 3-dimensional. Just aft of the flex bearing is a boot cavity space and a thick flexible rubber boot. (There are vent holes going through a lower phenolic part that allow the boot cavity to breath as the boot flexes.) This boot cavity space and flexible boot distort and shape around the circumference as the nozzle is vectored.

aerostadt said:

Let's see. The attached photos do not show everything. The aft segment (case) with propellant fits into the nozzle on the lower left. The aft segment fixed housing is dome shaped (you can see a very small portion of the aft segment dome attached by the nozzle-case joint). Attached to the aft case dome iss the aft skirt (not shown) that fits like a truncated cone on the far outside. There is a hydraulic piston attached to the aft skirt, which is called an actuator. The other end of the actuator is pinned to the large hole fixture that you can see on the diverging nozzle section. At the end upstream of the actuator attach point you can see a large massive object made up of a series of metal plates with rubber sandwiched in between the plates. This is the flex bearing. You can see that the flex bearing is in contact with the nozzle (near the throat) by way of a sort of shoe. As the actuator moves the aft diverging nozzle the flex bearing takes up the load at the other end. Keep in mind that this is a cross section and the actual device is 3-dimensional. Just aft of the flex bearing is a boot cavity space and a thick flexible rubber boot. (There are vent holes going through a lower phenolic part that allow the boot cavity to breath as the boot flexes.) This boot cavity space and flexible boot distort and shape around the circumference as the nozzle is vectored.
View attachment 159491 View attachment 159492

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So the layered-looking portion is what transmits loads and allows it to rotate, and the black curved-looking thing is what actually seals the gases in? That makes sense.

Thanks.

3 fins are more efficient than 4 fins, if you size 3 fins and 4 fins for a rocket with the same CP, you'll find that the 3 fin configuration has less fin area and thus less drag.

One disadvantage of 3 fins is that almost any combination of angle of attack and yaw creates roll. 4 fin rockets have much less roll. The MIT Topics in Advanced Model Rocketry book goes over this in some detail.

As noted, when moving fins or control surfaces on fins, it's a lot easier to keep track of the response to control surface deflections with 4 fins; 2 for pitch, 2 for yaw, differential for roll. In fact I can't think of a guided rocket with movable fins or fin control surfaces that has 3 fins; US, Russian, etc., they all have 4 fins.

Many military systems are volume limited, and often have folding fins to fit in canisters. 4 fins have shorter fin spans than 3 fins, again for equivalent stability.

Attitude control for solid rocket motors was a major problem. The early systems (examples, Sargent, Scout first stage) used jet vanes (usually combined with fin elevons) like the V-2 and the Redstone. Other systems were tried, none (Scout, separate peroxide RCS for the upper stages), single axis per nozzle (Minuteman I, II, and III first stages, nozzles only gimbal in one axis), and liquid injection (Minuteman II and III stage 2, Titan III).

Then the big breakthrough, the Lockheed Lockroll (or named something like that) followed by the Thiokol flex seal nozzle (both very similar). The flex seal nozzle is the current definitive solution for solid rocket motor thrust vectoring. The drawing previously shown was a flex seal nozzle.

Then large solid rocket motors went from multiple nozzles (4 nozzles on Minuteman I, II, III first stages, Minuteman I and II third stages), to single nozzles as used on the Peacekeeper. One big nozzle has lower nozzle internal drag, and lower weight, than 4 smaller nozzles. Moves in 2 axes for pitch and yaw. But how do you do roll with a single nozzle? You don't. The rocket actually rolls very little (it's asymmetric), and modern missile systems are not guidance gimbal limited, so the missile can roll to whatever angle. The final stage which has 3-axis attitude control takes out whatever roll has developed (because now it does matter), and lines up the final stage in the correct attitude for the next phase of the mission.


Chuck Rogers

aerostadt said:

I remember seeing technical papers showing the several injection points around the circumference of the Titan SRB's in the nozzle diverging (or supersonic flow) section and they did create shock waves, which helped the nozzle vectoring. In addition the Titan's injection fluid was nitrogen tetroxide, which reacted with the exhaust gases further enhancing the pressure distribution in the nozzle. The Chemical Systems Division of UTC did studies of several candidate liquids and decided that N2O4 was the best. (I am thinking one candidate might have been a permanganate solution. Probably, easier to handle than N2O4, but not as good as performance.)

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Over 50 years ago Titan already used hypergolic Aerozine/N2O4 propellant, so handling the nasty N2O4 for the injection wasn't a big deal.

I did a quick Google search before this post and didn't realize how old injection induced shock thrust vectoring was. I first became aware of it in the mid-2000s as an element of an inexpensive rapid response launch system for small satellites. I was invited to call into a telecom where a small Mohave based aerospace company was presenting it as a replacement for a 400K+ gimbal and I think I heard something about it at some aerospace meeting I was attending. I believe the rocket was a self-pressurize liquid or hybrid that employed N2O as the oxidizer and that ~2% of the flow was all that was required to obtain effective thrust vectoring.

Bob

A lot of interesting stuff on this thread. Going back to vectored solid rocket nozzles, the Minuteman 1st stage motor had 4 nozzles that used something that might be called a ball and socket for turning the nozzle. This was before the flex bearing concept was perfected. Thiokol did not call the Minuteman design a ball socket nozzle. They referred to it as a split-line design. The 2 nozzles on a diagonal were connected by rods and could only move back and forth in one direction perpendicular to the direction of the other two nozzles. In this way pitch and yaw movements were covered. I believe that this old technology is still being used, because nothing can be changed according to the SALT agreements. Thiokol came up with a single vectored nozzle for the Minuteman on paper, but it cannot be used, because of the SALT agreement.

Going back to the Shuttle SRB design, it was expensive to make the nozzle flex bearings, because it was difficult to get the plates of steel to bond to the layers of rubber. After the booster were recovered at sea (The aft exit cone was blown off by a shaped charger just before water impact to reduce impact loads.), the charred phenolic nozzle parts and flexible boot were stripped off. Since the flex bearing was expensive to build, it was re-used along with nozzle metal parts lying underneath the phenolics.

bobkrech said:

I was invited to call into a telecom where a small Mohave based aerospace company was presenting it as a replacement for a 400K+ gimbal and I think I heard something about it at some aerospace meeting I was attending. I believe the rocket was a self-pressurize liquid or hybrid that employed N2O as the oxidizer and that ~2% of the flow was all that was required to obtain effective thrust vectoring.

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Whittinghill/WASP? Man it's a small world

My space program prefers 3 fins. In order to keep the technical details to a minimum, it’s primarily because I don’t like to do fillets.

View attachment 2007PSI-PEG Thruster PhII.pdf

daveyfire said:

Whittinghill/WASP? Man it's a small world

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Quite possibly. Most likely.

See the above attached page from a 2012 NASA Ames investment presentation.

The 2007 Whittinghill contract is listed on the left hand side of the page and my 2007 PulsedElectroGasdynamic Thruster contract is listed on the right.

It's a very small world.

Bob

I think it was pretty far into the rocketry development that they figured out 3 fins would work at all. I remember reading (in Rockets of the World) about how some sounding rocket (the Aerobee?) "proved" that 3-fins were sufficient. (I'm not at home to check the reference.)

I found it interesting that in the early days, rocket science was just as empirical as our hobby rockets are today.

JohnCoker said:

I found it interesting that in the early days, rocket science was just as empirical as our hobby rockets are today.

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I suppose the early rocket scientists didn't have much more capability to test designs in the early 20th century, than we can test our own amateur creations today. Trial and error still works if its done safely. But, we have the benefit of their research. With the internet, knowledge spreads so much faster, like this guy who I've learned so much from before I registered on this forum.

That makes sense.

A few years back while visiting a secret government wind tunnel facility. I asked an aerodynamic engineer the 3 vs 4 fin question. He explained it to me that it all has to do with angle of attack. Rockets never fly straight. It's a constant push on one axis or another. Like trying to balance a pencil in the palm of your hand. The fins provide the stabilization instead of your hand motion. So now imagine the angle of attack changing do to transonic shock waves, wind sheers, etc.. It's much easier to balance out these forces with an even number of fins (axis) as opposed to an odd number. Four just happens to be the sweet spot. Six, Eight, etc. work well too. So the answer is 3 fins work fine but 4 are optimal especially in transonic, supersonic flight or guided missiles where angle of attack changes are more severe.

FWIW

I believe NRL's Aerobee-Hi was one of the very early 3 Fin designs along with The Wac-Corporal. Both used Tower Launcher that were a bit less expensive or complicated to construct.

Chuck Rogers said:

The MIT Topics in Advanced Model Rocketry book goes over this in some detail.

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Thanks for reminding me of that book. I've always meant to check it out via inter-library loan before possibly purchasing a copy, but forgot. According to Worldcat, 167 libraries own it.

Great question, Trooper, along with some great answers here.