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Because of the complex forces and moments resulting from the roll/yaw coupling (caused by the sail’s interference with the hull-induced upper vortex system), an approach to simplifying lateral control is to eliminate roll-angle in a tum and, subsequently, the snap role from a high-speed tum. A comparison to a modem fighter plane in a steep tum might be useful,

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Note, however, that the fighter plane has TWO half-wings, both pulling together to create a side force. This offsets the centrifugal force that is trying to pull the fighter plane out of it’s tum. Unhappily, the sub has only ONE half-wing which promptly rolls it over into a very difficult situation whenever it tries to tum at high speed. An obvious solution is to add another half wing, on the other side of the hull, directly opposite the sail. This will not only counter the sail’s rolling moment and keep the hull upright, but also adds a substantial side force to assist in tightening the turn.

The sail of today’s attack submarines typicaHy measures 400500 sq. ft. in size and – acting like a lifting wing on its side – generates a side force nearly 50% of that created by the two hull vortices that start at the bow and roll up on the lee side of the yawing body of revolution, Figure 2. This side-force, centered well above the center-of-gravity of the sub, is the cause of the infamous “snap roll” that has prevented routine,high-speed turning maneuvers by our submarines.

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Figure 3 illustrates one possible solution: “a keel-wing” (like a center-board on a sailboat) with a design similar to classic bow planes and utilizing a folding mechanism to retract the keel-wing for long transits or when going into port. By using modem computer-designed, multiple-element airfoils with endplates — analogous to the sophisticated rear wings on Formula 1 and Indy 500 race cars — the folding keel-wing can generate equal and opposite side forces to the sail, yet it need be only 1/3 to 1/4 the size of its topside counterpart. In addition, the two moving flap segments of this wing can be hydraulically linked to the rudder — at some appropriate ratio – to maintain an upright hull throughout the tum. This greatly simplifies the control task, and opens up the possibility of single-man control with existing hardware. Further work might even lead to the addition of a trailing flap on the sail, in the same control circuit, to complement the keel-wing.

Assisting this effort to minimize the size of the keel-wing will be the conventional metacentric stability, i.e. pendulosity, of the basic hull design. With the center of buoyancy (C.B.) above the submarine’s center of gravity (C.G.) for any rolling motion, this strong righting moment is the other major reason why the keel-wing does not have to be nearly as large as the sail in performing its task of keeping the hull upright through a high-speed tum.

Figure 4 describes a computerized simulation of the vortex flow field on a modem submarine hull that is yawed towards the viewer approximately 15 degrees. Figure 5 is a view of this same hull with the addition of the folding keel-wing. Note the difference in the position of the twin vortices.

The side-force generated by the “circulation” from the sail in Figure 4 shows its influence clearly. By countering this with the equal and opposite side force “circulation” from the keelwing, it is possible to contain the twin vortices at the same time that the “snap roll” rolling moment has been negated. (Both the sail and the keel-wing will also generate small “wingtip” vortices as a result of their side-forces but they are not shown here).

Containment and control of strong, bow-generated vortices is well known in the aerospace world. In fact, most of the published literature on vortex generation is for aircraft and missiles. For a beautiful and thrilling view of the prettiest vortices you will ever see, watch the Concorde land and takeoff on a damp day. You’ll see the vapor trail of its strong leading-edge vortex. The Concorde’s aerodynamicists spent many long hours in the wind-tunnel laboring over the refinement of this vortex structure to assist the SST take-off and landing with vortex-generated lift.

In the same manner that modem aerodynamics shaped the leading-edge of the Concorde to strengthen and control its vortex, one can also modify a similar area on the forward hull of a modern submarine to improve its vortices. Simple longitudinal strakes on the top and the bottom of the hull, per Figure 6, present an interesting possibility to improve the turning diameter radius in an upright underwater tum. These strakes — similar to the sharp leading edge of the SST — will promote an earlier and more positive creation of the two vortices seen in Figure 3. Calculations indicate that each vortex will be stronger and will be spaced further apart, allowing the hull to generate a higher side force. Higher hull side forces alJow the submarine to make tighter turns.

Why do we need to make tight turns? The following quotation from John Trotti’s excellent book, Phantom over Vietnam, may provide some insight if one substitutes “torpedo” for the “SA-2”, and “submarine” for the aircraft. “The main threat was a surface-to-air missile. The SA2 was the kind of missile that brought down Gary Power’s U-2 over the Soviet Union. It was a large missile ….. and the missile was guided through a pursuit curve (by ground-based track-while-scan radar), which differs from a lead collision profile in an important way. Whereas the lead collision approach calculates an aim point in front of the target, the pursuit curve vectors the missile to the rear of the target.

Because the SA-2 had to continually respond to target position updates from the ground-based radar site as it sought to follow its target, it could be treated in much the same fashion as an enemy aircraft. Turning into the SA2 would throw it to a higher and higher angle-off, forcing it more and more to the outside of the tum. While it was capable of higher speeds than an aircraft, its turn radius was incapable of dealing with a fighter’s maneuverability. As the missile was forced to an everincreasing crossing angle, its closing rate decreased as it fell farther to the outside of the tum. The firing circuit in the missile warhead was designed to fire when the closing rate dropped off to a predetermined value. Regardless of the actual proximity of the missile to the target, when the Doppler value dropped below a certain level, the warhead exploded.”

The above scenario could very well happen at any time in the next few years if our submarines have the ability to tightly maneuver at high speed, and how to avoid torpedoes is learned.

The fighter aircraft analogy can also be applied to the fluid forces involved. Maneuvering any vehicle in a fluid medium, whether it be air or water, requires that the vehicle overcome its own inertia forces as well as the force of the fluid impinging on the hull or rudder, etc. To appreciate the magnitude of these fluid forces, imagine if you will, how the air pressure feels on one’s hand out the window of a car travelling at 60 mph. This pressure (engineers call it “q”), will be about 10 lbs per sq. foot.

For a submarine travelling at 20 knots, this pressure will be about 1140 lbs/ft2! Oddly enough, this same 1140 psf pressure is also experienced by an aircraft at Mach 2 and 40,000 feet – or 700 mph at 6,000 feet. To fly and maneuver at these speeds with these forces requires a stable, weii-built platform, whether it be an F-4 Phantom fighter or an SSN.

Today’s aircraft can maneuver aU over the sky at great speeds, while the “modem” submarine can only go fast in a straight line. To be sure, when the pilots of the P-47’s and PSl’s in WW ll found out about the “sound barrier” towards the end of the war, U.S. aircraft designers set to work in a big burry to investigate and solve the control problems due to the new aerodynamic characteristics at high speeds. Chuck Yeager was the first to break the “sound barrier” in the fall of 1947 in the X-1, and the U.S. aircraft industry soon mastered the pitch/yaw coupling hazards of supersonic forces and moments with new streamlining, new controls, and new control surfaces. But supersonic aircraft still had a fuselage, wings, and a tail structure, and they were simply arranged and coordinated together in a better way.

Less than 10 years after Yeager’s historic flight, the submarine community found its equivalent to the “sound barrier.” After their great WW ll success in the Pacific, American submariners saw a revolution in undersea warfare• with the simultaneous development of nuclear power and the “body of revolution” high-speed underwater shape. Nothing is free in this world, however, and after only a few flights the ALBACORE found the infamous “snap-roll… Several ALBACORE captains with skill and visionary thinking soon laid a solid database for the future of high-speed, maneuvering submarines. The rest of the engineering world was stunned and amazed at the submarine potential made possible by such foresight. By 1960 the 50 year-long German leadership in submarine design was but a distant memory. U.S. submarines were not only light-years ahead of the rest of the world, the multiplicity of different designs going to sea promised even more incredible ships in the future – but then it all stopped in the mid 1960s.

Today’s 688 class ships, with twice the power, can barely exceed the 1956 ALBACORE’s flank speed, and cannot even come close to turning with her. All work towards solving the pitch/roll/yaw coupling problems uncovered by the snap-roll came to a halt. American submarines became slow – but very stealthy – underwater blimps. Turning at high speed was ruled out.

After 30 years the Navy’s research people have a good theoretical understanding of these problems, and with new submarines costing nearly 1 billion dollars per copy, we should make every effort to make the small modifications necessary to allow all of our attack subs to maneuver freely. Certainly, it appears that keeping the hull vortices always in the lee of the turning hull – by maintaining an upright hull — offers a simple and potentially very reliable solution to the turning problem.


Finally, it should not be forgotten that an upright submarine in a fast turn is the world’s greatest “knuckle” generator. If you think a 700,000 odd pound jumbo-jet generates powerful long-standing vortices, what do you think a 14 million pound submarine will generate? There is no question that a rapid rudder change at 20 knots of a 688 submarine will generate a world-class vortex pair that would attract every enemy torpedo from 10 miles around. After generating such a knuckle, the generating sub can back down to stealth levels and skulk around for awhile to see who wants to sniff at his residue.

What about the classic “submerged operating envelope?” Giddings and Louis have already shown in a paper published in 1966 and again in 1988 how one could provide satisfactory jammed-plane safety margins by rearrangement of the stem planes. The “X” plane arrangement, first tested on the ALBACORE in 1960-61, is now being utilized by European submarines and provides a much larger operating envelope than the conventional cruciform used by U.S. ships. It would appear that the keel-wing, by eliminating the unstable snaproll, will provide an operating envelope nearly as large as that of the “X” stem. In fact, after a quick analysis, one suspects that the existing cruciform stem planes would actually be the optimum control structure for a folding keel-wing.

Henry E. Payne, III

Naval Submarine League

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