EN400 – Principles of Ship Performance

An Introduction to Naval Architecture(Alias “Boats”)

Associate Professor Paul H. Miller

INTRODUCTION

•Course Objectives (Why Study Boats?)

•Personal Introductions–Name–Major–Service Selection

•Syllabus/Course Policy

•Lecture #1! - Engineering Fundamentals

Some of my projects…

ENGINEERING FUNDAMENTALS

• Plots or Graphs - Generally the most effective format for displaying and conveying the interrelation of experimental variables.

• Sketches - Quick and informal method of sharing ideas with others or clarify concepts for yourself. Free body diagrams (FBDs) are an example.

Plots, Graphs, and Sketches (1.1)

ENGINEERING FUNDAMENTALSPlots and Graphs (1.1)

ENGINEERING FUNDAMENTALSSketches (1.1) – A Free Body Diagram

ENGINEERING FUNDAMENTALS

• Means of Communicating Ideas Concisely– Axes

X-axis (horizontal (independent variable))

Y-axis (vertical (dependent variable))

Divide major axes into divisions of 1, 2, or 5 times 10 to the nth power

Label with words, symbols, and units

Minor axes should be distributed evenly

Plots, Graphs, and Sketches (1.1)

ENGINEERING FUNDAMENTALSArea Under and Instantaneous Slope of a Curve (1.3)

Area UnderCurve

Slope

Dependent

ENGINEERING FUNDAMENTALS

Units (1.4)

System Length Time Force Mass gcSI meter

(m)second

(s)newton(N)

kilogram(kg) 2sN

mkg 1

pound –slug(BG)

foot(ft)

second(s)

pound(lb)

slug(slug) 2sl

lug 1

b

fts

pound force –pound mass

foot(ft)

second(s)

poundforce(lbf)

poundmass(lbm)

2f

m

sbl

ftbl 2.23

the unit system used in EN200

Engineering Fundamentals

Unit Analysis (1.4.1)• A “fool proof” method of determining

the correct units!

• Example: Speed x Time = Distance

= 4 mileshour

milesx 30 min 8

1 hour60 min

x

ENGINEERING FUNDAMENTALS

• The number of accurate digits in a number– Example: 2.65 has 3 significant figures– Example: 10 has 1 or 2 , 10.0 has 3– Example: 0.25 has 2 (note 0.25, not .25!)

• Multiplication / Division: Use the same # of significant figures as the number with the least # of significant figures– Example: 20 x 3.444 = 69

• Addition / Subtraction: Use the same # of decimal places as the number with the least # of decimal places– Example: 3.6 + 1.212 = 4.8

Significant Figures (1.5)

ENGINEERING FUNDAMENTALSForces, Moments, and Couples (1.7)

• FORCE - a vector quantity (i.e. a magnitude and a direction)

• MOMENT – a force times a distance with respect to a given origin (M=FxD)

• COUPLE - A special case of moment causing pure rotation and no translation

Static Equilibrium 1.7.5If an object is neither accelerating or

decelerating then it is because…• Sum of the forces = 0• Sum of the moments = 0

• Why?• F=ma • (This is very important in “hydrostatics”)

ENGINEERING FUNDAMENTALS

Hydrostatic Pressure 1.7.6• “Pressure” is the amount of force

applied to a given area (p=F/A)

• In English units it is pounds/sq. ft. or pounds/sq. in., or “psi”

Air pressure is ~ 15 psi.

At 440 ft below sea level it is ~ 195 psi!

Quick Physics Review

Static: No accelerationDynamic: Has acceleration

Question: If a ship follows this path, at a constant speed, is it static or dynamic?

ENGINEERING FUNDAMENTALSThe Mathematical First, Second and Third

Moments (1.7.7)

• These integrals are used in mathematical descriptions of physical problems

dbs

dbs

dbs

3

2

Where:s = some distance

db = some differential property = Summation

ENGINEERING FUNDAMENTALSThe Mathematical First, Second and Third

Moments (1.7.7)

dAy

dmx

2

• In Naval Architecture:– “b” could represent length, area, volume, or mass– “s” is a length or distance

First Moment of Mass

Second Moment of Area

ENGINEERING FUNDAMENTALS

Weighted Averages (1.7.7)

In Naval Architecture we use the simplified form:

to find the Longitudinal Center of Flotation (LCF), Longitudinal Center of Buoyancy (LCB),

Center of Gravity (LCG, TCG, VCG)

1i i

1i iiave

F

FXx

321

332211ave FFF

FXFXFXx

ENGINEERING FUNDAMENTALS

• A ship (or plane) has 6 degrees of freedom (DOF)

– Three are Translational Heave (z) (up and down) Sway (y) (side to side) Surge (x) (fore and aft)

– Three are Rotational Yaw (z) Pitch (y) Roll (x)

•

Translational and Rotational Motion (1.8)

Bernoulli’s Equation

• P = pressure = fluid density

• V = fluid velocity

• Z = depth

2

2

221

2

11 21

21

gzVpgzVp

Along a line of equal energy (a streamline) in a fluid, the above is a constant.

ENGINEERING FUNDAMENTALS

Bernoulli Equation (1.9)

• total pressure is constant in a fluid, if:

inviscid flow (no viscosity) incompressible flow steady flow

2

2

221

2

11 21

21

gzVpgzVp

This gives us hydrostatic and hydrodynamic pressure. These are the water loads on the vessel.

Pressure Prediction• Vertical pressure supports the vessel

(lift versus weight)

• Horizontal pressure is thrust and drag

These are the same as an aircraft!