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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-number8/3/2019 Ship Prestn
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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_logarithm8/3/2019 Ship Prestn
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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.html8/3/2019 Ship Prestn
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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_number8/3/2019 Ship Prestn
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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)8/3/2019 Ship Prestn
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Thank You!!!
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