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HULL FORM AND GEOMETRY

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Title: HULL FORM AND GEOMETRY


1
HULL FORM AND GEOMETRY
Intro to Ships and Naval Engineering (2.1)
2
HULL FORM AND GEOMETRY
Intro to Ships and Naval Engineering (2.1)
  • Factors which influence design
  • Size
  • Speed
  • Seakeeping
  • Maneuverability
  • Stability
  • Special Capabilities (Amphib, Aviation, ...)

Compromise is required!
3
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Methods of Classification
  • 1.0 Usage
  • Merchant Ships (Cargo, Fishing, Drill, etc)
  • Naval and Coast Guard Vessels
  • Recreational Boats and Pleasure Ships
  • Utility Tugs
  • Research and Environmental Ships
  • Ferries

4
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Methods of Classification (cont)
  • 2.0 Physical Support
  • Hydrostatic
  • Hydrodynamic
  • Aerostatic
  • (Aerodynamic)

5
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
6
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Hydrostatic Support (also know as
    Displacement Ships) Float by displacing their
    own weight in water
  • Includes nearly all traditional military and
    cargo ships and 99 of ships in this course
  • Small Waterplane Area Twin Hull ships
    (SWATH)
  • Submarines

7
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Aerostatic Support - Vessel rides on a cushion
    of air. Lighter weight, higher speeds, smaller
    load capacity.
  • Air Cushion Vehicles - LCAC Opens up 75 of
    littoral coastlines, versus about 12 for
    displacement
  • Surface Effect Ships - SES Fast,
    directionally stable, but not amphibious

8
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Hydrodynamic Support - Supported by moving
    water. At slower speeds, they are
    hydrostatically supported
  • Planing Vessels - Hydrodynamics pressure
    developed on the hull at high speeds to
    support the vessel. Limited loads, high power
    requirements.
  • Hydrofoils - Supported by underwater foils,
    like wings on an aircraft. Dangerous in heavy
    seas. No longer used by USN. (USNA Project!)

9
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Hydrostatic Support - Based on Archimedes
    Principle
  • Archimedes Principle - An object partially or
    fully submerged in a fluid will experience a
    resultant vertical force equal in magnitude to
    the weight of the volume of fluid displaced by
    the object.

10
HULL FORM AND GEOMETRY
Categorizing Ships (2.2)
  • Archimedes Principle - The Equation

where FB is the magnitude of the resultant
buoyant force in lb ? (rho) density of
the fluid in lb s2 / ft 4 or slug/ft3 g
magnitude of accel. due to gravity (32.17
ft/s2) ? volume of fluid displaced by
the object in ft3
11
HULL FORM AND GEOMETRY
How are these vessels supported?
  • Hydrostatic
  • Hydrodynamic
  • Aerostatic
  • A combination?

12
HULL FORM AND GEOMETRY
13
HULL FORM AND GEOMETRY
14
HULL FORM AND GEOMETRY
15
HULL FORM AND GEOMETRY
16
HULL FORM AND GEOMETRY
17
HULL FORM AND GEOMETRY
18
HULL FORM AND GEOMETRY
19
HULL FORM AND GEOMETRY
20
HULL FORM AND GEOMETRY
Brain Teasers!
21
HULL FORM AND GEOMETRY
22
HULL FORM AND GEOMETRY
23
HULL FORM AND GEOMETRY
24
HULL FORM AND GEOMETRY
Representing Ship Designs
  • Problems include
  • Terms to use (jargon)
  • How to represent a 3-D object on 2-D paper
  • Sketches
  • Drawings
  • Artists Rendition

25
HULL FORM AND GEOMETRY
Basic Dimensions (2.3.3)
  • Design Waterline (DWL) - The waterline where
    the ship is designed to float.
  • Stations - Parallel planes from forward to
    aft, evenly spaced (like bread). Normally an odd
    number to ensure an even number of blocks.

26
HULL FORM AND GEOMETRY
Basic Dimensions (2.3.3)
  • Forward Perpendicular (FP) - Forward
    station where the bow intersects the DWL.
    Station 0.
  • Aft Perpendicular (AP) - After station
    located at either the rudder stock or the
    intersection of the stern with the DWL.
    Station 10.
  • Length Between Perpendiculars (Lpp) -Distance
    between the AP and the FP. In general the
    same as LWL (length at waterline).

27
HULL FORM AND GEOMETRY
Basic Dimensions (2.3.3)
  • Length Overall (LOA) - Overall length of the
    vessel.
  • Midships Station ( ) - Station midway
    between the FP and the AP. Station 5 in a
    10-station ship. Also called amidships.

28
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Lines Drawings - Traditional graphical
    representation of the ships hull form. Lines

Half-Breadth
Sheer Plan
Body Plan
29
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
Body Plan
Half-Breadth Plan
Sheer Plan
Lines Plan
30
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Half-Breadth Plan (Breadth Beam)

31
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Half-Breadth Plan (Breadth Beam)
  • Intersection of horizontal planes with the hull
    to create waterlines. (Parallel with water.)

32
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Sheer Plan
  • Parallel to centerplane
  • Pattern for construction of longitudinal
    framing.

33
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Sheer Plan
  • Intersection of planes parallel to the
    centerline plane define the Buttock Lines.
    These show the ships hull shape at a given
    distance from the centerline plane.

34
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Body Plan
  • Pattern for construction of transverse framing.

35
HULL FORM AND GEOMETRY
Hull Form Representation (2.3.0-2.3.3)
  • Body Plan
  • Intersection of planes parallel to the
    centerline plane define the Section Lines.
  • Section lines show the shape of the hull
    from the front view for a longitudinal position

36
HULL FORM AND GEOMETRY
Table of Offsets (2.4)
  • The distances from the centerplane are called
    the offsets or half-breadth distances.

37
HULL FORM AND GEOMETRY
Table of Offsets (2.4)
  • Used to convert graphical information to a
    numerical representation of a three
    dimensional body.
  • Lists the distance from the center plane to
    the outline of the hull at each station and
    waterline.
  • There is enough information in the Table of
    Offsets to produce all three lines plans.

38
HULL FORM AND GEOMETRY
Hull Form Characteristics (2.5)
  • Depth (D) - Distance from the keel to the deck.
  • Remember Depth of Hold.
  • Draft (T) - Distance from the keel to the
    surface of the water.
  • Beam (B) - Transverse distance across each
    section.
  • Half-Breadths are half of beam.

Flare
Tumblehome
39
HULL FORM AND GEOMETRY
Hull Form Characteristics (2.5)
  • Keel (K) - Reference point on the bottom of
    the ship and is synonymous with the baseline.

40
HULL FORM AND GEOMETRY
Centroids (2.6)
  • Centroid The geometric center of a body.
  • Center of Mass - A single point location of
    the mass.
  • Better known as the Center of Gravity (CG).
  • CG and Centroids are only in the same place
    for uniform (homogenous) mass!

41
HULL FORM AND GEOMETRY
Centroids (2.6)
  • Centroids and Center of Mass can be found by
    using a weighted average.

42
HULL FORM AND GEOMETRY
  • What is the longitudinal center of gravity of
    this 18 foot row boat?
  • Hull 150 lb at station 6
  • Seat 10 lb at station 5
  • Rower 200 lb at station 5.5

43
HULL FORM AND GEOMETRY
Center of Flotation (F or CF) (2.7.1)
  • The centroid of the operating waterplane.
  • (The center of an area.)
  • The point about which the ship will list and
    trim!
  • Transverse Center of Flotation (TCF) -
    Distance of the Center of Flotation from the
    centerline.(Often 0 feet)

44
HULL FORM AND GEOMETRY
Center of Flotation (F or CF) (2.7.1)
  • Longitudinal Center of Flotation (LCF)
    - Distance from midships (or the FP or AP) to
    the Center of Flotation.
  • The Center of Flotation changes as the ship
    lists or trims because the shape of the
    waterplane changes.

45
HULL FORM AND GEOMETRY
Center of Buoyancy (B or CB) (2.7.2)
  • Centroid of the Underwater Volume.
  • Location where the resultant force of
    buoyancy (FB) acts.
  • Transverse Center of Buoyancy (TCB) -
    Distance from the centerline to the Center of
    Buoyancy.

46
HULL FORM AND GEOMETRY
Center of Buoyancy (B or CB) (2.7.2)
  • Vertical Center of Buoyancy (VCB or KB) -
    Distance from the keel to the Center of
    Buoyancy.
  • Longitudinal Center of Buoyancy (LCB) -
    Distance from the amidships or AP or FP to the
    Center of Buoyancy.
  • Center of Buoyancy moves when the ship lists
    or trims (TCB).

47
HULL FORM AND GEOMETRY
Center of Buoyancy (B or CB) (2.7.2)
Which way is it moving? Fwd or Aft?
48
HULL FORM AND GEOMETRY
Fundamental Geometric Calculations (2.8)
  • A ships hull is a complex shape which cannot
    be described by a mathematical equation!
  • How can centroids, volumes, and areas be
    calculated? (Hint you cant integrate!)
  • Use Numerical Methods to approximate an integral!
  • Trapezoidal Rule (linear approximation)
  • Simpsons Rule (quadratic approximation)

49
HULL FORM AND GEOMETRY
Fundamental Geometric Calculations (2.8.1)
Example Waterplane Calculation (Trapezoidal)
50
HULL FORM AND GEOMETRY
Fundamental Geometric Calculations (2.8.1)
  • Simpsons Rule - Used to integrate a curve
    with an odd number of evenly spaced ordinates.
    (Ex. Stations 0 - 10)

51
HULL FORM AND GEOMETRY
Fundamental Geometric Calculations (2.8.1)
  • Area under the curve between -s and s
  • Solving this equation for the given
    endpoints
  • A simple example with a rectangle...

52
HULL FORM AND GEOMETRY
Fundamental Geometric Calculations (2.8.1)
  • If the curve extends over more than three
    points the equation becomes
  • s is the spacing between ordinates.
    Usually will be the spacing between stations or
    waterlines.

53
HULL FORM AND GEOMETRY
Section (2.9)
  • Using Simpsons 1st Rule, you must be able
    to calculate
  • Waterplane Area
  • Sectional Area
  • Submerged Volume
  • Longitudinal Center of Flotation (LCF)

meaning this will be on the homework, labs,
quizzes, and exams!
54
HULL FORM AND GEOMETRY
Applying Simpsons Rule (2.9)
  • Methodology
  • Draw a picture of what you intend to
    integrate.
  • Show the differential element you are using.
  • Properly label your axis and drawing.
  • Write out the generalized calculus equation
    in the proper symbols (optional).

55
HULL FORM AND GEOMETRY
Applying Simpsons Rule (2.9)
  • Methodology (cont)
  • Write out Simpsons Equation in generalized
    form (if a curved shape).
  • Substitute each number in the generalized
    Simpsons Equation.
  • Calculate the final answer.

56
HULL FORM AND GEOMETRY
Waterplane Area (2.9.1)
  • Numerically integrate the half-breadth as a
    function of the length of the vessel.

57
HULL FORM AND GEOMETRY
Waterplane Area (2.9.1)
  • Writing out the Simpsons equation
  • where
  • Awp is the waterplane area in ft2
  • s is the Simpsons spacing
  • y(x) is the y offset or half-breadth at each
    value of x in ft
  • Example for a ship!

58
HULL FORM AND GEOMETRY
Section Area (2.9.2)
  • Numerical integration of the half- breadth as
    a function of the draft.

59
HULL FORM AND GEOMETRY
Section Area (2.9.2)
  • Determine how to find the area(s) by using which
    methods (Simpsons must be an odd number of
    points!)
  • Writing out the generalized Simpsons Equation
    and the triangle equation

60
HULL FORM AND GEOMETRY
Recall that the goal of us using the Lines
Plan And the Table of Offsets was to find the
Volume, and hence the buoyant force!
  • Archimedes Principle - The Equation

And, if in static equilibrium, then
FBWeight! But so far, we can only calculate the
section and waterplane areas
61
HULL FORM AND GEOMETRY
Submerged Volume Longitudinal Integration (2.9.3)
  • Integration of the section areas over the
    length of the ship. Curve of Areas

Curve of Areas
Stn4
What is a barges section area, volume and curve
of areas if is 100 ft long, 25 feet beam and 10
feet draft?
62
HULL FORM AND GEOMETRY
What is a barges section area, volume, curve of
areas and displacement?
Section Area Beam x Draft
Volume Section Area x Length 100 ft long, 25
feet beam and 10 feet draft
63
HULL FORM AND GEOMETRY
Submerged Volume Longitudinal Integration (2.9.3)
So, the volume if using Simpsons is
Ques where is the 2?
64
HULL FORM AND GEOMETRY
Longitudinal Center of Flotation (LCF)
(2.9.4) (Centroid of Waterplane Area)
  • Point at which the vessel ___ and ___?
  • Distance from the Forward Perpendicular to the
    center of flotation (or from MP).
  • Found as a weighted average of the distance
    from the Forward Perpendicular multiplied by the
    ratio of the half-breadth to the total
    waterplane area.

65
HULL FORM AND GEOMETRY
Longitudinal Center of Flotation (LCF)
(2.9.4) (Centroid of Waterplane Area)
  • Drawing of the LCF

Recall For most normal vessels LCF is between
Stn 5 and 6.7
66
HULL FORM AND GEOMETRY
Longitudinal Center of Flotation (LCF)
(2.9.4) (Centroid of Waterplane Area)
  • Writing the general calculus equation and the
    general Simpsons form (for 4 Simpsons spaces in
    a 10 station ship)

67
Sample Quiz Questions!
  • To calculate the submerged volume of a ship, one
    would
  • Integrate half-breadths from the keel to the
    waterplane
  • Integrate half-breadths longitudinally at the
    waterline
  • Integrate section areas longitudinally
  • Use Simpsons Rule to integrate waterplane areas
    at each station
  • The Center of Flotation is
  • Centroid of the underwater volume
  • Point at which Fb acts
  • Centroid of the waterplane
  • Point at which the hydrostatic force acts

68
HULL FORM AND GEOMETRY
Curves of Form (2.10)
  • WHAT THEY ARE Graphical representation of the
    ships geometric-based properties.
  • WHY When weight is added, removed or shifted,
    the underwater shape changes and therefore the
    geometric properties change.
  • DETAILS
  • Based on a given average draft.
  • Unique for every vessel.
  • The ship is assumed to be in seawater.

69
HULL FORM AND GEOMETRY
Curves of Form (2.10)
  • Curves of Form Include
  • Displacement
  • LCB
  • VCB
  • Immersion (TPI)
  • LCF
  • MT1
  • And some others...

70
HULL FORM AND GEOMETRY
Curves of Form (2.10)
71
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.2)
  • Longitudinal Center of Buoyancy (LCB)
  • The distance in feet from the longitudinal
    reference position to the center of buoyancy.
  • The reference position could be the FP or
    midships. If it is midships remember that
    distances aft of midships are negative!

72
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.3)
  • Vertical Center of Buoyancy (VCB)
  • The distance in feet from the baseplane to the
    center of buoyancy.
  • Sometimes this distance is labeled KB with a
    bar over the letters.

73
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.4)
  • Tons Per Inch Immersion (TPI)
  • TPI is defined as the tons required to obtain
    one inch of sinkage in salt water.
  • Parallel sinkage is when the ship changes its
    forward and after drafts by the same amount so
    that no change in trim occurs.

74
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.4)
  • An approximate formula for TPI based on the
    area of the waterplane can be derived as
    follows

75
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.6)
  • Longitudinal Center of Flotation (LCF)
  • The distance in feet from the longitudinal
    reference point to the center of flotation.
  • The reference position could be the FP or
    midships. If it is midships remember that
    distances aft of midships are negative.

76
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.7)
  • Moment to Trim One Inch (Moment/ Trim 1 or
    MT1")
  • The ship will rotate about the (?) when a
    moment is applied to it.
  • The moment can be produced by adding,
    removing, or shifting a weight some distance
    from the center of flotation.
  • The units are?

77
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.7)
  • Trim is defined as the change in draft aft
    minus the change in draft forward.
  • If the ship starts level and trims so that the
    forward draft increases by 2 inches and the aft
    draft decreases by 1 inch, the trim would be -3
    inches.

78
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.7)
  • Since a ship is typically wider at the stern
    than at the bow, the center of flotation will
    typically be aft of midships.
  • This means that when a ships trims, it will
    typically have a greater change in the forward
    draft than in the after draft.

79
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.8)
  • KML (A measure of pitch stability)
  • The distance in feet from the keel to the
    longitudinal metacenter.
  • This distance is on the order of one hundred
    to one thousand feet whereas the distance from
    the keel to the transverse metacenter is only
    on the order of ten to thirty feet.

80
HULL FORM AND GEOMETRY
Curves of Form (2.10.1.8)
  • KMT (A measure of roll stability)
  • This is the distance in feet from the keel to
    the transverse metacenter.
  • Typically, we do not bother putting the
    subscript T for any property in the transverse
    direction because it is assumed that when no
    subscript is present the transverse direction is
    implied.

81
The End of Chapter 2
Did you meet all the chapters objectives?! In
one word buoyancy!
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