Submarine Mechanics

This is a brief overview of some technical details related to the design and construction of submarines

Length to Bow Ratio:

The optimal ratio for the length to bow of a submarine is 7:1, which is a result of the trade-off between two types of drag forces: pressure drag and skin friction drag. The pressure drag is caused by the width of the vessel and can be represented by the formula:

$D_p = \frac{1}{2} \rho V^2 C_p S$,

Where $\rho$ is the density of the fluid, $V$ is the velocity of the fluid, $C_p$ is the coefficient of pressure drag and $S$ is the wetted area of the vessel. On the other hand, skin friction drag is caused by the length of the vessel and can be represented by the formula:

$D_{sf} = \frac{1}{2} \rho V^2 C_{sf} L$

where $C_{sf}$ is the coefficient of skin friction drag and $L$ is the length of the vessel.

By minimizing one drag force, the other drag force increases. To minimize both of these drag forces, an optimal ratio is established. The ratio of 7:1 for the length to bow of a submarine has been found to effectively balance these two forces and minimize the overall drag, represented by the formula $D_{total} = D_p + D_{sf}$. This is why a ratio of 7:1 is considered as the optimal ratio for the length to bow of a submarine.

Neutral Buoyancy:

Neutral buoyancy is a crucial aspect of submarine design, as it allows the vessel to remain at a constant depth without sinking or rising.

$\rho_{seawater} = f(S,T,p)$

where $S$ is the salinity, $T$ is the temperature, and $p$ is the pressure. The density of seawater is affected by its salinity, depth, and temperature. The salinity of seawater is dependent on the amount of dissolved salts it contains, which can vary depending on the location and the time of year. The density of seawater also changes with depth, as the pressure increases with increasing depth. Temperature also affects the density of seawater, as colder water is denser than warmer water. Submarines are designed to be able to adjust their buoyancy by controlling the amount of water in their ballast tanks, which can be filled or emptied as necessary to maintain optimal buoyancy. Additionally, submarines are equipped with sensors that can measure the density of the surrounding water and make adjustments to the ballast tanks accordingly.

Ideal Shapes:

For submarines, the ideal shape for the stern is a parabolic shape while the ideal shape for the bow is an elliptical shape. These shapes are slightly altered during the manufacturing process to make the vessel cheaper and easier to construct.

Submarine Sails:

The sail, or dorsal fin, of a submarine is located at the top of the vessel and helps prevent rolling. The sail can contribute up to 30% of the resistance faced by the submarine. On real submarines, the sail also serves as an observation tower. It is important for dynamic stability, but the sail should be as small and slim as possible to minimize drag. Additionally, the sail fairing should also be as slim as possible.

Submarine Propellers:

The number of blades on a submarine's propulsion motor can have a significant impact on propulsion efficiency. The blades take on a fan shape and more blades typically lead to greater efficiency. The blades can be made of aluminum or stainless steel and are either forged or welded together. Submarines typically use three, four, or five blades. Blade pitch can be fixed or controllable, with controllable pitch propellers allowing for greater maneuverability but fixed pitch propellers being easier to design and manufacture.

Submarine Rudders:

Submarines use rudders to control direction. There are several types of rudders including balanced, spade, full skeg, semi-balanced skeg, semi-balanced aft of skeg or deadwood, unbalanced aft of keel or deadwood, and transom bung surface piercing. The choice of rudder type will depend on the specific design and needs of the submarine.