FORCES ACTING ON A TORPEDO WHILE ENTERING

INTO WATER

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Weight downwards

Hydrodynamic Drag

Hydrodynamic Drag

Buoyancy ForceHydrofoil Lift and Drag + Turning Moment

Hydrofoil Lift and Drag + Turning Moment

Hydrodynamic Drag

Force due to Wind and Waves

Added Mass

• Various Forces– Object Drag– Propulsion– Waves – Control Surfaces– Buoyancy– Weight

Hydrostatic Forces and Moments

The torpedo experiences hydrostatic forces and moments as a result of the combined effects of the torpedo weight and buoyancy.

The hydrostatic moment is stabilizing in pitch and roll, meaning that the hydrostatic moment opposes deflections in those angular directions.

BGHS ffF

The branch of Fluid Mechanics that studies fluids at rest is referred to as ‘Hydrostatics’.

Hydrostatic Force

• Gravitational Force-The net force produced by gravity is the weight of the torpedo acting vertically downward at the center of gravity.

• Buoyancy Forces- The net force of the hydrostatic pressures is buoyant force acting at the center of buoyancy of the torpedo.

• Thrust Force. The thrust of the propulsion system will be assumed to act along the longitudinal axis of the torpedo with no resultant torque.

Hydrodynamic Force

• Hydrodynamics is the branch of Fluid Mechanics that studies the motion of fluids (liquids) and the forces acting on solid bodies immersed in them.

Examples:• Forces acting on an AUV / Torpedo submerged in

water • Flow of water around submersibles • Forces acting on a buoyHydrodynamic Drag (fluid resistance) is the forces that opposes the relative motion of

an object through a fluid.

1. Radiation Induced Forces.These forces arise when the body is forced to oscillate with the wave excitation frequency and there are no incident waves. These forces are mainly composed of four components:-

Added mass and Inertia- Added mass forces arise due to the inertia of surrounding fluid. A body having an accelerated motion in a continuous medium of fluid experiences a force that is greater than the mass of the body times the acceleration. Since this increment of force can be defined as the product of a body acceleration and a quantity having the same dimension as the mass, it is termed added mass.

Hydrodynamic Force

Hydrodynamic damping forces- Hydrodynamic damping forces arise mainly due to the viscosity of the fluid hence also called real fluid forces. As the name implicates, these forces are dependent on velocity There are two major mechanisms responsible for this force. They are:-

a) Skin friction due to boundary layer b) Shedding of vortices Restoring forces- Hydrostatic pressure forces arise due to the

action of weight and buoyancy forces. Restoring forces for a submerged body depend upon the centre of gravity and centre of buoyancy.

Control surface forces- Control surfaces are generally lift producing hydrofoil sections. The lift force generated varies linearly with the angle of attack over the practical range of operation of the lifting surfaces.

2. Environmental Forces.These forces arise when the body is restrained from oscillating and there are incident regular waves. There are two major sources of environmental disturbance forces:-

Surface wavesCurrent

Hydrodynamic Force

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Skin Friction

Skin friction arises from the friction of the fluid against the "skin" of the object that is moving through it. Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the wetted surface, the area of the surface of the body that is in contact with the fluid

• Unsteady motion of bodies underwater or unsteady flow around objects, an additional effect (force) resulting from the fluid acting on the structure needs to be considered when formulating the system equation of motion. This added effect is added mass.

• Most floating structures can be modeled, for small motions and linear behavior, by a system equation with the basic form similar to a typical mass-spring-dashpot system described by the following equation:Where, m is the system mass, b is the linear damping coefficient, k is the spring coefficient, f(t) is the force acting on the mass, and x is the displacement of the mass.

• In a physical sense, this added mass is the weight added to a system due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. The added mass force opposes the motion and can be factored into the system equation as follows

m x b x kx F t

Archimedes Principle“The up thrust (buoyancy force) on a body immersed in a

fluid is equal to the weight of the fluid displaced” Buoyancy Conditions

Positively Buoyant Neutrally Buoyant Negatively Buoyant

Stable Unstable

CB

CG

CG

CB

Fig 2.2 Center of Gravity CG- The center Gravity is the mean location of all the mass in a system.

Center of Buoyancy CB- The center of buoyancy is the point that coincides with the centroid of the volume of water displaced by the boat / submersible.

Vortex Shedding• Vortex shedding is caused when a fluid flows

past a blunt object. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

• Vortex gets created at the back of the body.• Is an Unsteady flow that takes place in special

flow Velocity (depends on size and shape of the cylindrical body)

http://upload.wikimedia.org/wikipedia/commons/b/b4/Vortex-street-animation.gif

Reference

• Admiralty Research Establishment Research Paper, 1998• Torpedoes ancient and Modern, Frank B Anderson,

Lieutanent and signal officer, Brigade staff, Naval Milittle, N.Y, The New york Times, 03 April 1898

• Hydrodynamic Forces, www.wikipedia.com• Hydrostatic Forces, www.wikipedia.com• B.R. Munson, D.F. Young and T.H. Okiishi, Fundamentals of

Fluid Mechanics, 4th Edition, 2002, Wiley and Sons, New York

• An Introduction to Fluid Dynamics, G.K. Batchelor, F.R.S, Professor in University of Cambridge, 1993