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, Graphs, and Sketches (1.1) 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.

ENGINEERING FUNDAMENTALS Plots and Graphs (1.1)

ENGINEERING FUNDAMENTALS Sketches (1.1) – A Free Body Diagram

ENGINEERING FUNDAMENTALS Plots, Graphs, and Sketches (1.1) 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

ENGINEERING FUNDAMENTALS Area Under and Instantaneous Slope of a Curve (1.3) Dependent

ENGINEERING FUNDAMENTALS Units (1.4)   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 hour miles x 30 min 8 1 hour 60 min x = 4 miles

ENGINEERING FUNDAMENTALS Significant Figures (1.5) 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

ENGINEERING FUNDAMENTALS Forces, 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

ENGINEERING FUNDAMENTALS Static Equilibrium 1.7.5 If 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”)

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

ENGINEERING FUNDAMENTALS The Mathematical First, Second and Third Moments (1.7.7) These integrals are used in mathematical descriptions of physical problems Where: s = some distance db = some differential property = Summation

ENGINEERING FUNDAMENTALS The Mathematical First, Second and Third Moments (1.7.7) 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)

ENGINEERING FUNDAMENTALS Translational and Rotational Motion (1.8) 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)

Bernoulli’s Equation Along a line of equal energy (a streamline) in a fluid, the above is a constant. P = pressure r = fluid density V = fluid velocity Z = depth

ENGINEERING FUNDAMENTALS Bernoulli Equation (1.9) total pressure is constant in a fluid, if: inviscid flow (no viscosity) incompressible flow steady flow 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!