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HULL FORM AND GEOMETRY

Intro to Ships and Naval Engineering (2.1)

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!

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

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Categorizing Ships (2.2)

- Methods of Classification (cont)
- 2.0 Physical Support
- Hydrostatic
- Hydrodynamic
- Aerostatic
- (Aerodynamic)

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Categorizing Ships (2.2)

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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

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

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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!)

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.

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

HULL FORM AND GEOMETRY

How are these vessels supported?

- Hydrostatic
- Hydrodynamic
- Aerostatic
- A combination?

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Brain Teasers!

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Representing Ship Designs

- Problems include
- Terms to use (jargon)
- How to represent a 3-D object on 2-D paper
- Sketches
- Drawings
- Artists Rendition

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.

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).

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.

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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

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Hull Form Representation (2.3.0-2.3.3)

Body Plan

Half-Breadth Plan

Sheer Plan

Lines Plan

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Hull Form Representation (2.3.0-2.3.3)

- Half-Breadth Plan (Breadth Beam)

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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.)

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Hull Form Representation (2.3.0-2.3.3)

- Sheer Plan
- Parallel to centerplane
- Pattern for construction of longitudinal

framing.

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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.

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Hull Form Representation (2.3.0-2.3.3)

- Body Plan
- Pattern for construction of transverse framing.

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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

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Table of Offsets (2.4)

- The distances from the centerplane are called

the offsets or half-breadth distances.

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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.

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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

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Hull Form Characteristics (2.5)

- Keel (K) - Reference point on the bottom of

the ship and is synonymous with the baseline.

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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!

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Centroids (2.6)

- Centroids and Center of Mass can be found by

using a weighted average.

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- 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

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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)

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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.

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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.

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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).

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Center of Buoyancy (B or CB) (2.7.2)

Which way is it moving? Fwd or Aft?

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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)

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Fundamental Geometric Calculations (2.8.1)

Example Waterplane Calculation (Trapezoidal)

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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)

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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...

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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.

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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!

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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).

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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.

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Waterplane Area (2.9.1)

- Numerically integrate the half-breadth as a

function of the length of the vessel.

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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!

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Section Area (2.9.2)

- Numerical integration of the half- breadth as

a function of the draft.

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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

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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

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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?

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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

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Submerged Volume Longitudinal Integration (2.9.3)

So, the volume if using Simpsons is

Ques where is the 2?

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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.

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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

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)

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

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.

HULL FORM AND GEOMETRY

Curves of Form (2.10)

- Curves of Form Include
- Displacement
- LCB
- VCB
- Immersion (TPI)
- LCF
- MT1
- And some others...

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Curves of Form (2.10)

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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!

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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.

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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.

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Curves of Form (2.10.1.4)

- An approximate formula for TPI based on the

area of the waterplane can be derived as

follows

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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.

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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?

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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.

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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.

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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.

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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.

The End of Chapter 2

Did you meet all the chapters objectives?! In

one word buoyancy!