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This question is restricted to post-WWII submarines designed to have a greater speed while submerged and to cruise underwater (unlike WWII U-boats).

As highlighted in this question, there is no need to have 2 rudders (one on the upper side, the other on the lower one) and 2 fins for pitch control (stern plane?) (one on the left and one on the right side). As I don't know the exact vocabulary, for the rest of the question I'll name all those fins "rudder", whatever axis they control.

As highlighted by the Zeppelin NT, 3 independent rudders offset at an angle of 120 degrees are enough to control rotation along all axis on a vehicle based on equality between buoyancy and weight. (Note that with 2 independent fins, you can have a 2-axis control (e.g. roll and pitch)*)

I see several possible advantages of using fewer rudders:

  • fewer links between rudders and the hull, easing stealth (less hydrodynamic interaction, smoother shape)
  • shallower draft (even shallower than X-shaped discussed in that question) **
  • maintenance costs (fewer moving parts)

Of course, rudders' dimensions should be adapted to provide enough authority.

As I failed to find submarines with fewer than 4 rudders, I would like to know if it has already existed.

* I think some ship uses 2 fins for roll control
** some submarines already uses smaller bottom rudder, I suppose for this purpose.

Manu H
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  • What is your definition of “modern”? After 1900? After the end of WW1? After WW2? Or after nuclear subs? Or last 7 years only? – Solar Mike May 07 '20 at 11:22

3 Answers3

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In modern submarine design, the rudders and aft planes are set far enough ahead of the propellers so as not to interfere with them and thereby generate turbulence and flutter that could be heard by another sub.

Because subs do not have the roll stability of a surface vessel, the rudder surfaces must be symmetrically disposed so that rudder action will not produce a moment about the longitudinal centerline and thereby roll the boat during a turn.

This means that the default design for subs is 4 fins at the rear.

niels nielsen
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    Can't tell if this answer says "yes" or "no". – Wyck May 08 '20 at 03:25
  • 3 fins are OK to provide roll stability. – Manu H May 08 '20 at 06:17
  • Do you mean submarines are statically roll unstable when submerged? i.e. if they stop when submerge otherwise they would roll out of control? – Manu H May 08 '20 at 06:30
  • I fear your answer has false assumption: 2 fins are enough to have 2-axis control (e.g. [elevon](https://en.wikipedia.org/wiki/Elevon) as on the F-22 stabilator), compensating any rolling moment, whatever its cause (e.g. a vertical fin) – Manu H May 08 '20 at 06:48
  • subs are almost unstable in roll when submerged because their centers of mass and buoyancy are close together. Let's imagine a sub with a single rudder fin below the propeller shaft centerline, entering a right turn, the rudder pivots left, pushing the rear of the sub leftwards and simultaneously applying a right roll moment to the hull. Similarly, if the sub had a single rudder above the CL, a right turn movement of the rudder would roll the hull over to the left. – niels nielsen May 08 '20 at 08:05
  • @ManuH How fast does the F-22 go in water? or are you making a false assumption? – Solar Mike May 08 '20 at 08:53
  • @SolarMike You should compare Reynolds number, not speed. By the way, my point is that 2 fins are enough to control roll and counteract rolling moment, and it is done in other fluids like air. The assumption is that rotation control by fins is comparable whatever the fluid you are working in. – Manu H May 08 '20 at 10:44
  • @nielsnielsen do you have any further reading for the center of mass position? It sounds weird to put it so that the sub is unstable as for boats you try to put it as low a possible to improve stability. – Manu H May 08 '20 at 10:46
  • @ManuH you should compare more than just Reynolds number, geometric similarity is just one - hmm have not seen a sub with the shape of the F-22... – Solar Mike May 08 '20 at 10:48
  • @SolarMike I agree, Blimp are closer in shape (that's why I cited the zeppelin NT in the question) – Manu H May 08 '20 at 10:49
  • submarine rudders actually do produce a twisting moment because the upper section is larger than the lower because there is more room above the shaft. – Tiger Guy May 09 '20 at 22:52
  • Subs are relatively unstable in roll because the center of buoyancy is above the center of gravity. This means they are self righting, but the righting moment is relatively small. – Tiger Guy May 09 '20 at 23:12
  • While two planes could manage roll, we still need direction control on a sub because subs don't turn by banking. – Tiger Guy May 09 '20 at 23:12
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Searching for "submarine tail" I found this image. It seems to use the configuration you are looking for, even if it is some kind of modular unmanned submarine.

sub (source)

What's interesting with unmanned submarine is the fact that 2 tail fins are enough for attitude control. Since there is no reason to keep some human standing on its feet inside the submarine, changes in attitude can be decomposed.

If pitch and roll are ok with 2 fins, yaw becomes: 1/4 roll + pitch - 1/4 roll. (or 90deg bank left + pitch + 90deg bank right)

EDIT: this configuration would still require natural yaw stability, using fixed vertical fins.

enter image description here

At some point submarines could live without fins, yet fins are also meant to counter propeller's torque, like wings do on one single engine aircraft.

Coaxial contrarotative gimballed propellers could be one way to get rid of any hydrodynamic control surface, even if propeller's blade itself is tautologically one hydrodynamic surface.

user721108
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You can do whatever you want on an un-staffed sub because the requirements are different. Nuclear submarines are warships and have warship requirements: speed, maneuverability, and reliability.

  1. Rear horizontal planes on subs are called stern planes. Vertical planes are called rudders. The rudder does no extend below the hull, because submarines are already very deep draft vessels, and increasing draft while exposing the rudder to damage in a grounding would be unwise.

  2. Submarines change depth primarily by putting an angle on the boat. Both stern planes and bow planes do this. Stern planes do this best because they can be quite large and also they are at the max moment arm to put an angle on the boat. The angle of this change is limited by depth excursions, not by humans. Nuclear submarines can only operate in a relatively narrow depth band near the surface (relative to the depth of the ocean).

  3. I cannot come up with any practical advantage from moving from four control surfaces to three. Most of the noise produced by a submarine will be machinery noises, screw noise, and flow over the hull. Reducing the planes would be negligible. The three would also need to be larger than existing because the two now at 120 degree angles would be less effective than at 90 degree placement. We still need high rates of maneuverability on a warship.

  4. Using the offset planes as both rudder and depth control means they need to operate independently. This is now an additional failure point, which is a problem when the consequences of any failure while submerged are dire. We would need either a complicated mechanical linkage to allow the two to move differently, or do it via software. Regardless, we now have a new failure mode, which would be what to do when they fail opposite or singly.

In summary, no warship is changing its plane design just to reduce from four to three

Tiger Guy
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  • I fail to understand the point #4. this problem has been solved [long ago in aviation](https://aviation.stackexchange.com/questions/3741/), and [this answer](/a/21058/2817) states [Collins class](https://en.wikipedia.org/wiki/Collins-class_submarine) rudders operates independently (so it is feasible, and already implemented) – Manu H May 10 '20 at 09:18
  • for the point #3, reducing number of planes would smooth the hull reducing the noise produced by the flow over the hull. – Manu H May 10 '20 at 09:21
  • @ManuH, it was "solved" in aviation and promptly disregarded for the vast majority of builds. Reducing planes reduces flow over planes, but you need proportionally larger planes to give the same level of force in the desired direction. It's trig. It does nothing to the hull. Flow over the hull is unchanged. – Tiger Guy May 10 '20 at 21:40
  • does it mean it is better to add more smaller fins? e.g. putting 8 or more fins? (it seems the Virginia class goes in that direction). For me, adding more mobile pieces increase maintenance costs and umber of failure modes. (BTW in aviation it was mostly lack dynamic coupling that made this solution not popular, but it still exists in more modern aircraft such as the [RQ4](https://en.wikipedia.org/wiki/Northrop_Grumman_RQ-4_Global_Hawk), fly-by-wire helping reducing the mechanical complexity) – Manu H May 11 '20 at 08:13
  • @ManuH, I believe the extra planes on Virginia subs are for streaming towed array sonar sensors. – Tiger Guy May 11 '20 at 16:13