1. SUBMARINES Overview (10.1) 200+ Years Old (Turtle (1775) and Hunley (1864)) Navy mostly uses submarines (indefinite underwater endurance) Commercial industry uses submersibles (limited endurance) Expensive but stealthy! Share characteristics of both surface ships and aircraft CSS Hunley

2. SUBMARINES Submarine Structural Design (10.2) Longitudinal Bending - Hogging & sagging causes large compressive and tensile stresses away from neutral axis. A cylinder is a poor bending element. Hydrostatic Pressure = Major load for subs. Water pressure attempts to implode ship. Transverse frames required to combat loading. A cylinder is a good pressure vessel! Recall: hydrostatic pressure =

3. SUBMARINES Submarine Inner Hull (10.2) Holds the pressure sensitive equipment (including the crew!) Must withstand hydrostatic pressure at ops depth. Transversely framed with thick plating. Strength  = $ ,  , space , but depth . Advanced materials needed due to high .

4. SUBMARINES Submarine Outer Hull (10.2) Smooth fairing over non-pressure sensitive equipment such as ballast and trim tanks and anchors to improve vessel hydrodynamics. High strength not required so made of mild steels and fiberglass. Anechoic (“free from echoes and reverberation”) material on outer hull to decrease sonar signature.

5. SUBMARINES Submarine General Arrangements (10.2) Main Ballast Tanks Variable Ballast Tanks PRESSURE HULL

6. SUBMARINES Main Ballast Tanks (MBT) (10.2) Largest tanks. Alter  from positive buoyancy on surface (empty) to near neutral buoyancy when submerged (full). Main Ballast Tanks are “soft tanks” because they do not need to withstand submerged hydrostatic pressure. (Located between inner & outer hulls.)

7. SUBMARINES Variable Ballast Tanks (10.2) Depth Control Tank (DCT) – Alter buoyancy once submerged with little or no trim. Where is it located? – Compensates for environmental factors (water density changes). Rho*g*volume! – ‘Hard tank’ because it can be pressurized (has access to outside of pressure hull). Trim Tanks (FTT/ATT) – ‘Soft tanks’ shift water to control trim (internal)

8. SUBMARINES U.S. Submarine Types (10.2) Ohio Class Sub Launched Ballistic Missiles (SLBMs) aft of sail  greater than many surface ships (i.e. BIG)

9. SUBMARINES U.S. Submarine Types (10.2) Los Angeles Class (SSN688)

10. SUBMARINES U.S. Submarine Types (10.2)

11. SUBMARINES U.S. Submarine Types (10.2)

12. SUBMARINES U.S. Submarine Types (10.2) Virginia Class Displacement: 7,800 tons Length: 377 feet Draft: 32 feet Beam: 34 feet Depth: 800+ feet

13. SUBMARINES Submarine Hydrostatics (10.3) USS Bremerton (SSN 698)

14. SUBMARINES Submarine Hydrostatics (10.3) Static equilibrium and Archimedes Principle apply to subs as well. Unlike surface ships, subs must actively pursue equilibrium when submerged due to changes in density (  ) and volume (  ). Depth Control Tanks & trim tanks are used.

15. SUBMARINES Hydrostatic Challenges (10.3) MAINTAIN NEUTRAL BUOYANCY – Salinity Effects – Water Temperature Effects – Depth Effects MAINTAIN NEUTRAL TRIM AND LIST – Transverse Weight Shifts – Longitudinal Weight Shifts

16. SUBMARINES Hydrostatics (Salinity Effects) (10.3) Decreased  = less F B  sub weight > F B. Must pump water out of DCT Changes in salinity common near river estuaries or polar ice. Mediterranean salinity is higher from evaporation. Water density (  )  as salinity level .

17. SUBMARINES Hydrostatics (Temperature Effects) (10.3) Decreased  = less F B  sub weight > F B. Must pump water out of DCT to compensate. Changes in temperature near river estuaries or ocean currents (Gulf Stream, Kuroshio, etc.) Water density (  )  as temperature .

18. SUBMARINES Hydrostatics (Depth Effects) (10.3) As depth increases, sub is “squeezed” and volume (  ) decreases. The string demonstration! Decreased  = less F B  sub weight > F B. Must pump water out of DCT Anechoic tiles cause additional volume loss as they compress more.

19. SUBMARINES Neutral Trim - General (10.3) When surfaced, geometric relationships similar except that “G” must be below “B” for sub stability. Neutral trim on sub becomes extremely critical when submerged. Small changes to buoyancy can be mitigated with diving planes Note the positions of “G”, “B”, “M T ”, and “M L ” in the following figures!

20. SUBMARINES Neutral Trim - General (10.3) Recall: these relationships can be used in transverse or longitudinal directions to find KM T or KM L for a surface ship.

21. SUBMARINES Neutral Trim - General (10.3) Surfaced submarine similar to surface ship except G is below B. – For clarity, M T is shown above B although distance is very small in reality.

22. SUBMARINES Neutral Trim - General (10.3) When submerging, waterplane disappears, so no second moment of area (I), and therefore no metacentric radius (BM L or BM T )! Equation? “B”, “M T ” and “M L ” are coincident and located at the centroid of the underwater volume -the half diameter point (if a cylinder). Very sensitive to trim since longitudinal and transverse initial stability are the same.

23. SUBMARINES Neutral Trim - General (10.3) When completely submerged, the positions of B, M T and M L are in the same place.

24. SUBMARINES Trim & Transverse Weight Shifts (10.3) Recall In Surface Ship Analysis: – GM T is found by equation (& Incline Experiment) to calculate the vertical center of gravity, KG. – Equation was only good for small angles (  ) since the metacenter is not stationary at larger angles. – Large  only available from analysis of Curve of Statical Intact Stability.

25. Submarines Recall for a Surface Vessel: From the geometry, we got: W t G M  B

26. SUBMARINES Trim & Transverse Weight Shifts (10.3) In Submarine Analysis: – The calculation of heeling angle is simplified by the identical location of Center of Buoyancy (B) and Metacenter (M) (BM=0). – Since GM=KB+BM-KG, then GM=KB-KG=BG – This equation is good for all angles:

27. SUBMARINES Trim & Transverse Weight Shifts (10.3) Surface Ship analysis complicated because vessel trims about the center of floatation (F) (which is seldom at amidships). Sub longitudinal analysis is exactly the same as transverse case since BM=0 for both longitudinal and transverse. For all angles of trim: Moment arm l   t, so trim tanks to compensate.

28. SUBMARINES Submarine Stability (10.4) USS Seawolf SSN-21

29. SUBMARINES Submarine Submerged Intact Stability (10.4)

30. SUBMARINES Submarine Intact Stability (10.4) Initial stability simplified for subs. The distance BG is constant (=GM) Righting Arm (GZ) is purely a function of heel angle. EQUATION IS TRUE FOR ALL SUBMERGED SUBS IN ALL CONDITIONS!

31. SUBMARINES Submarine Intact Stability (10.4) Since righting arm equation good for all , curve of intact statical stability always a sine curve with a peak value equal to BG.

32. SUBMARINES Submerged Stability Characteristics (10.4) Range of Stability: 0-180° Angle of Max Righting Arm: 90° Max Righting Arm: Distance BG Dynamic Stability: 2  S BG STABILITY CURVE HAS THE SAME CHARACTERISTICS FOR ALL SUBS!

33. SUBMARINES Submarine Resistance (10.5) Recall Coefficient of Total Hull Resistance – C V = viscous component, depends on Rn. – C W = wave making resistance, depends on Fn. – C A = correlation allowance, surface roughness and “fudge factor”.

34. SUBMARINES Submarine Resistance (10.5) On the surface (acts like a surface ship but with bigger wakes): – C V dominates at low speed, C W as speed increases (due to bigger bow and stern waves and wake turbulence). Submerged (acts like an aircraft): – Skin friction (C F  C V ) dominates. (Rn is the important factor when no fluid (air/water) interface). – C W tends toward zero at depth. – Since C T is smaller when submerged, higher speeds are possible.

35. Components of Total Hull Resistance Total Resistance and Relative Magnitude of Components Viscous Air Resistance Wave-making Speed (kts) Resistance (lb) - Low speed : Viscous R dominates - Higher speed : Wave-making R dominates - Hump (Hollow) : location is function of ship length and speed. Hump Hollow

36. SUBMARINES Submarine Propellers - Odd # of Blades (10.5) Stern planes could be rotated 45 o and called “X” or dihedrals

37. SUBMARINES Skewed Propellers (10.5) Advantages: – Reduced Vibration (eases into flow). – Reduced Cavitation as tip vortex is smaller. Disadvantages: – Inefficient backing. – Expensive & difficult to make. – Reduced strength. Operational need outweighs disadvantages !

38. SUBMARINES Submarine Seakeeping (10.6) Subjected to same as surface ships – 3 translation (surge, sway, heave) and 3 rotational (roll, pitch, yaw). – Recall heave, pitch, and roll are simple harmonic motions because of linear restoring force. If  e = resonant freq, amplitudes maximized (particularly roll which is sharply tuned). Roll motion accentuated by round shape. Why?

39. SUBMARINES Submarine Seakeeping - Suction Force (10.6) Water Surface Effect – Submarine near surface (e.g. periscope depth) has low pressure on top surface of hull causing net upward force. This is similar to squatting, but opposite! – Magnitude depends on speed, depth, and hull shape. – Minimize by reducing speed and having bow down trim. Wave Action – Top of sub has faster velocity due to similar lower pressure effect as above. – Minimize by going deeper or beam on to waves.

40. SUBMARINES Submarine Maneuvering and Control (10.7) Lateral motion is controlled with rudder, engines, and props. Note that in a fast turn the sail may create lift, heeling the boat outward in to a “snap roll”, particularly if the sail is forward of Cp. Depth control accomplished by: – Making the buoyant force equal the submarine displacement. – Finer and more positive control achieved by plane (control) surfaces.

41. SUBMARINES Fair-Water Planes (10.7) Primarily to maintain an ordered depth. – Positioning the planes to the "up" position causes an upward lift force to be generated. – Since forward of the center of gravity, a moment (M) is also produced which causes some slight pitch. The dominant effect is the lift generated by the control surface.

42. SUBMARINES Fair-Water Planes (10.7) Primarily DEPTH CONTROL

43. SUBMARINES Stern and Bow Planes (10.7) Primarily to maintain pitch because of the distance from the center of gravity. – Positioning the planes to creates a lift force in the downward direction creates a moment (M) which causes the submarine to pitch up. – Once the submarine has an up angle, the hull produces an upward lift force. The net effect is that the submarine rises at an upward angle.

44. SUBMARINES Stern and Bow Planes (10.7) Maintain Pitch (better control than with fairwater planes)

45. SUBMARINES FINAL THOUGHT... There are times when accurate control is nice!

46. Principles of Ship Performance Good Luck and Good “Boating”!