Hull Geometry

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Hull Geometry

• Jonathan R. Binns

Presented by THE ROYAL INSTITUTION OF NAVAL
ARCHITECTS Hosted by THE AUSTRALIAN MARITIME
COLLEGE
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The Lines Plan
From Larsson (1994) p 21
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Hull Lines on the Yacht
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Basic Measurements
From Larsson (1994) p 17
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Block Coefficient
From Larsson (1994) p 18
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Prismatic Coefficient
From Larsson (1994) p 18
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Starting Points

• From scratch
• use all the box measurements obtained from the
  concept/preliminary design stage, eg LOA, Bmax,
  BWL, Tc, DHKO etc
• From previous design
• use lines from previous design that are close in
  hull parameters mentioned

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Make Yourself Some Markers

• Either start point requires markers, which are
• Points in space either drawn on the paper to be
  used or modelled in the computer, showing either
  similar yacht or bounding box

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Two Methods

• By Hand
• Requires a LOT of work. Developing three views
  at once requires a lot of projection
• By Computer
• Takes much less work, but will always place
  restrictions on fairness.

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Some Computer Programs Available

• Autoship used by large ship builders
• Fastship used by Farr, Reichel Pugh
• Vicanti used by Jutson
• Maxsurf used by Prada, me
• In House Program used by Murray, Burns Dovell

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The Control Net in 2 Dimensions
A single curve represented by a NURB (Non-Uniform
Rational B-spline) control net
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The Control Net in 3 Dimensions
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Fairing

• There is no mathematical definition of fairing,
  therefore computers have to be pushed into
  fairing
• There is a trade-off between fairness and desired
  shape, this is the deciding factor in a good set
  of hull lines

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What is Curvature?

• The slope of a curve is the rate at which its
  plotted values are changing as we step through
  the curve
• The CURVATURE is the rate that the slope is
  changing as we step through the curve
• A smooth change in curvature is indicative of a
  fair hull

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How Can We Use Curvature

• Break everything down to two dimensional
  curvature
• By cutting in one plane, eg diagonals or buttock
  lines and looking at how curvature changes
• Maximum, minimum and Gaussian curvature, to be
  used sparingly

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What is Gaussian Curvature?

• At any point on a 3D surface put a plane cutting
  normal to the surface
• The intersection line now makes a 2D curve which
  has a curvature value
• Rotating the plane around the normal to the
  surface will change the curvature value for the
  point
• At different rotations there will be a unique
  maximum and minimum curvature
• Gaussian curvature max min curvature

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Consider the Bulb
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Cut it by a Plane
Profile
Intersection line
Normal point Change in slope, curvature is ve
Plan
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Rotate the Plane
Profile
Intersection line
Normal point Change in slope, curvature is -ve
Plan
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Shows up as -ve (red) Gaussian Curvature
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-ve Gaussian Curvature Means

• Principle axes have different curvature sign
• Yacht curves outwards in one dimension, inwards
  in another
• All -ve Gaussian curvature indicates a hollow
  (not all hollows have -ve though)

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Gaussian Curvature Tips

• Use to give overall rough picture, this will pick
  up some unfairness that you might not otherwise
  find
• Highly dependant on resolution, use as a check
  only, basic orthogonal curvature is more important