Design Report Guided Missile Submarine SSG(X) - AOE - Virginia ...

SSG(X) Design – VT Team 3 Page 92
4.10 Dynamic Stability and Maneuverability
Design of the SSG(X) hullform and control surfaces requires balancing stability and maneuverability. A
submarine’s stability is its ability to return to equilibrium without using the controls after some disturbance; its
maneuverability is its ability to perform specific maneuvers using the controls. Highly stable submarines require
greater control deflections to carry out these maneuvers. The SSG(X) should have control surfaces that provide
stability in the horizontal and vertical planes but this stability should be low enough that control deflections are
effective for maneuvering. Stability becomes more critical at higher speeds. Considerations of stability, speed, and
controllability determine the safe operating envelope (SOA). Concerns with vertical stability and control are
particularly important to prevent the submarine from going too deep or broaching.
Submarine stability is defined in the horizontal and vertical planes. Horizontal stability is the ability to maintain
a set course with little variation in heading; stable submarines will not need continuous changes in rudder deflections
to maintain a straight-line path. Stability in the vertical plane is its ability to maintain a constant depth without
continuous deflections of the hydroplanes. The submarine’s dynamic stability is critical in deep submergence when
little can be done to vary the hydrodynamic forces acting on the vehicle. This stability is expressed in terms of the
hydrodynamic stability coefficients in the horizontal and vertical planes, GH and GV respectively. These coefficients
are a function the submarine’s control surfaces and hullform. Stability is ensured by positive coefficients.
However, higher coefficients indicate less maneuverability. The SSG(X) control surfaces will provide low positive
values of GH and GV. The desired range for GH is 0.15 – 0.3; the desired range for GV is 0.5 – 0.7. Higher stability
is more critical in the vertical plane; it is undesirable for a ship to tend to surface or dive deeper without a controlled
deflection.
Submarines have forward and aft control surfaces. The forward surfaces are either sail or bow planes. They are
used primarily for diving and are most useful at low speeds. They provide a way to independently control pitch
angle and depth; the submarine can therefore remain level while changing depth. At higher speeds, pitch and heave
are coupled and must be controlled by the aft planes. The aft planes consist of horizontal stabilizers and vertical
rudders. The stabilizers provide stability in the vertical plane; the rudders give stability in the horizontal plane. The
surface area of the stabilizers must be large to ensure stability; flaps, or elevators, are generally added to provide
maneuvering ability. The size of the rudders must also be significant for stability. However, the whole surface is
allowed to move to produce fast maneuvers in the horizontal plane. The span of the lower rudder is constrained by
docking constraints. This asymmetry is also beneficial in counteracting the roll moment created by the sail.
Traditional aft plane configurations are cruciform. However, alternative designs have been explored to provide
planes that have more submerged area in the surface condition. The most common alternative is the x-stern. The
disadvantage of the x-stern is the symmetry of the forces generated in the horizontal and vertical planes. It is
therefore difficult to independently adjust the stability and maneuvering characteristics with an x-stern.
4.10.1 Control Surface Calculations and Response Surface Model (RSM)
Figure 93 shows the process used to determine the configuration, size, and location of the SSG(X) control
surfaces. Lisa Minnick of Virginia Tech developed a control surface database by measuring the control surfaces of
twelve submarines. This information was used to create a regression model that is a function of the submarine’s
diameter and length to diameter ratio. The regression model provided the size and location of the surfaces. A
Response Surface Model (RSM) was developed using NSWC Carderock stability code calculates GH and GV to
determine the feasibility of the calculated control surfaces. The SSG(X) is stable with sail planes and a cruciform
stern which is described in Section 4.10.2.
Figure 93 - Control Surface Calculation and RSM Flowchart