Ship Prestn

8/3/2019 Ship Prestn

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Mathematics In Ship

Designing

Presented By:

-Madhu H.B(0915002)

-Jeevan Anthony(0915028)

-Rajesh.G(0915018)


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Various Designs:


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Preliminary Design: Consists of features such as

-Dimensions(height,length)

-Displacement

-Stability

-Hull form-Propulsive characteristics

-Structural details.

Based on the usage, they are broadly

classified as: cargo,fishing,passengervessels & warships etc.


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Mathematics in Ship designing:

They are many formulas and techniques for shipdesigning.

Ship floating basically depends on Buoyancy(Physics)which is nothing but applied mathematics.

In this ppt,we deal with four of the important ones:

Taylors theorem.

Gross tonnage.

Navier-stokes Eqtn.

Froude Numbers.


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Definition: The Taylor series of a real or complex font (x) t

is infinitely differentiable in a neighborhood of

a real or complex numbera is the power series whi

can be written in the more compact sigma notation

where n! denotes the factorial of n and (n)(a)

denotes the nth derivative of evaluated at the

point a. The zeroth derivative of is defined to

be itself and (xa)0 and 0! are both defined to

be 1.

Taylors Theorem:
http://www.answers.com/topic/real-numberhttp://www.answers.com/topic/complex-numberhttp://www.answers.com/topic/smooth-functionhttp://www.answers.com/topic/open-neighborhoodhttp://www.answers.com/topic/real-numberhttp://www.answers.com/topic/complex-numberhttp://www.answers.com/topic/power-serieshttp://www.answers.com/topic/summationhttp://www.answers.com/topic/factorialhttp://www.answers.com/topic/derivativehttp://www.answers.com/topic/derivativehttp://www.answers.com/topic/factorialhttp://www.answers.com/topic/summationhttp://www.answers.com/topic/power-serieshttp://www.answers.com/topic/complex-numberhttp://www.answers.com/topic/real-numberhttp://www.answers.com/topic/open-neighborhoodhttp://www.answers.com/topic/smooth-functionhttp://www.answers.com/topic/complex-numberhttp://www.answers.com/topic/real-number


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Or in simple terms,the Taylor series

corresponding to a function (x) at a

pointx0 is the infinite series whose nth term

is (1/n!)(n)(x0)(x-x0)n, where (n)(x)

denotes the nth derivative of (x).

Resistance charts based upon model tests of aseries of ships derived by altering the

proportions of a single parent form.

Used to study the effects of these

alterations on resistance to the ship'smotion, and to predict the powering

requirements for new ships.


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Gross Tonnage:

It is a unit less index related to a ship's

overall internal volume. It was defined by The International Convention

on Tonnage Measurement of Ships, 1969, adopted

by the International Maritime Organization in

1969, and came into force on July 18, 1982. It is calculated by measuring a ship's volume

(from keel to funnel, to the outside of the hull

framing) and applying a mathematical formula. It

is based on two variables:1.V, the ship's total volume in cubic meters

(m), and

2.K, a multiplier based on the ship volume.


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The value of the multiplier Kvaries in

accordance with a ship's total volume (in

cubic meters) and is applied as a kind ofreduction factor in determining the gross

tonnage value - which does not have a unit

such as cubic metres or tons.Kranges from

0.22 to 0.32 and is calculated with a formula

which uses the common or base-10 logarithm:

Once Vand Kare known, gross tonnage is

calculated using the formula, whereby GT is a

function of V:
http://en.wikipedia.org/wiki/Common_logarithmhttp://en.wikipedia.org/wiki/Common_logarithmhttp://en.wikipedia.org/wiki/Common_logarithmhttp://en.wikipedia.org/wiki/Common_logarithm


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NavierStokes equations:

These equations describe how the

velocity, pressure, temperature, and density ofa moving fluid are related.

It consists of a time-dependent continuity

equation for conservation of mass, three time-

dependent conservation of momentum equations anda time-dependent conservation of

energy equation.

The differential equations are

therefore partial differential equations
http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/temptr.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/fluden.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/state.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/mass.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/conmo.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/conmo.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/mass.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/state.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/fluden.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/temptr.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html


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Froude NumberThe Froude number is a dimensionless number defined as

the ratio of a characteristic velocity to agravitational wave velocity.

In fluid mechanics, the Froude number is used to

determine the resistance of an object moving through

water, and permits the comparison of objects of

different sizesNamed after William Froude, the Froude number is based

on the speed/length ratio as defined by him.

The Froude number is defined as:

where Vis a characteristic velocity , and c is a

characteristic water wave propagation velocity. The

Froude number is thus analogous to the Mach number. The

greater the Froude number, the greater the resistance.
http://en.wikipedia.org/wiki/Dimensionless_numberhttp://en.wikipedia.org/wiki/Fluid_mechanicshttp://en.wikipedia.org/wiki/William_Froudehttp://en.wikipedia.org/wiki/Propagation_velocityhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Propagation_velocityhttp://en.wikipedia.org/wiki/William_Froudehttp://en.wikipedia.org/wiki/Fluid_mechanicshttp://en.wikipedia.org/wiki/Dimensionless_number


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Continued.

In Ship hydrodynamics

For a ship, the Froude number isdefined as:

where Vis the velocity of the ship, g is theacceleration due to gravity, and L is the

length of the ship at the water line level.

It is an important parameter with respect to

the ship's drag, or resistance, includingthe wave making resistance.
http://en.wikipedia.org/wiki/Drag_(physics)http://en.wikipedia.org/wiki/Wave_making_resistancehttp://en.wikipedia.org/wiki/Wave_making_resistancehttp://en.wikipedia.org/wiki/Drag_(physics)


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Thank You!!!

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