This formula booklet is written for those who dedicated their lives to the merchant navy. For them this booklet will be a little “Treasure Chest”. For everybody else it is just another collection of formulas and tables.

Notice of Terms of Use

While the advice given in this formula booklet has been developed using the best information currently available, it is intended purely as guidance to be used at the user’s own risk. Neither the authors nor the editor accepts any responsibility for the accuracy of any information given in this document or any omission from this booklet or for any consequence whatsoever resulting directly or indirectly from compliance with or adoption of guidance in this booklet even if caused by failure to exercise reasonable care.

Table of Contents:

1.            Mathematics

1.1          Algebra

1.1.1       Fundamentals

1.1.2       Signed Numbers

1.1.3       Algebraic expressions

1.1.4       Exponents

1.1.5       Symbols of Grouping

1.1.6       Polynomials

1.1.7       Constants and variables

1.1.8       Functions

1.1.9       Factoring

1.1.10     Equations

1.2          Geometry

1.2.1       Figures in the plane

1.2.2       Solid bodies

1.3           Analytic Geometry

1.3.1       Cartesian Coordinate System

1.3.2       Straight Line

1.3.3       Triangle

1.3.4       Circle

1.3.5       Ellipse

1.3.6       Exponential Curve

1.3.7       Polar- Image1 Cartesian- Coordinates

1.3.8       Vectors

1.4          Spherical Trigonometry

1.4.1       Spherical Triangle Definitions

1.4.2       Great Circle through two points

1.4.3       Size of a Spherical Triangle

1.4.4       Equality of Triangles

1.4.5       Some useful geometrical properties

1.4.6       Formulae

1.4.7       Napier’s Rules

2.            Physics

2.1          Dynamic – Motion in one Dimension

2.1.1       Displacement

2.1.2       Velocity

2.1.3       Acceleration

2.2          Motion in one Dimension with Constant Acceleration

2.2.1       Velocity as a Function of Time

2.2.2       Displacement as a Function of Time

2.2.3       Velocity as a Function of Displacement

2.2.4       Free Falling Object

2.2.5       Motion in two dimensions

2.3          Law of Motion

2.3.1       Magnitude of Gravitational Force   Weight of Planet X

2.3.2       Forces of Friction   Static Friction   Kinetic Friction   Friction on the Inclined

2.4          Static

2.4.1       Hook’s Law

2.4.2       Young’s Modulus

2.5          Energy

2.5.1       Work Done on an Object

2.5.2       Work Done on an Object by a Constant Force

2.5.3       Net Work Done on an Object

2.5.4       Kinetic Energy

2.5.5       Potential Energy

2.5.6       Total Mechanical Energy

2.5.7       Elastic Potential Energy Associated with

2.5.8       Helical Spring (simple harmonic)

2.6          Power and Impulse

2.6.1       Power

2.6.2       Impulse – Momentum Theorem

2.6.3       Final Velocity of Two Objects in an One Dimensional Perfectly Elastic Collision

2.7          Rotational Motion and Law of Gravity

2.7.1       Objects Angular Displacement

2.7.2       Instantaneous Angular Speed

2.7.3       Average Angular Speed

2.7.4       Objects Angular Acceleration

2.7.5       Rotational Motion about a Fixed Axis, ‘α’ Constant

2.7.6       Tangential Speed

2.7.7       Tangential Acceleration

2.7.8       Centripetal Acceleration

2.7.9       Keppler’s 3rd Law

2.8          Rotational Dynamics

2.8.1       Torque

2.8.2       Rotational Kinetic Energy

2.8.3       Angular Momentum

2.9          Fluid

2.9.1       Variation of Pressure with Depth

2.9.2       Poiseuille’s Law

2.9.3       Bernoulli’s Equation

2.9.4       Flick’s Law

2.9.5       Reynolds Number

2.9.6       Stoke’s Law

2.10         Thermal Physics

2.10.1      Temperature from C° to Kelvin

2.10.2      Temperature from C° to Fahrenheit

2.10.3      Heat

a)   Specific Heat Capacity

b)   Latent Heat

c)   Thermal Conduction

d)   Energy Transfer by Conduction through a Compound Slab

2.11          Expansions

2.11.1       Linear Expansion

2.11.2       Cubical Expansion

2.11.3       Superficial Expansion

2.12          Gases

2.12.1       Ideal Gas Equation

2.12.2       Gas Equations

a)   Boyle’s Law

b)   Charles’s Law

c)   Marriot’s Law

d)   Law of Amonton

e)   Law of Gay-Lussac

2.12.3       Increase of Pressure

2.12.4       Increase of Volume

2.12.5       General Gas Equation

2.12.6       Total Pressure

2.12.7       Isothermal and Adiabatic Expansion

2.13.         Magnetism

2.13.1       Magnetic Field

2.13.2       Magnetic Force on a Current–Carrying Conductor

2.13.3       Torque on a Current Loop and Electric Motor

2.13.4       Ampere’s Law

2.13.5       Cyclotron Equation

2.13.6       Magnetic Field in a Solenoid

2.13.7       Magnetic Force between two parallel Conductors

2.13.8       Magnetic Field of Current Loops

2.13.9       Magnetic Field inside a Solenoid

a)   Energy Stored in a Magnetic Field

2.13.10     Magnetic Flux

2.14          Electric

2.14.1      Ohm’s Law and Faraday’s Law

a)  Ohm’s Law

b)  Faraday’s Law

2.14.2      Capacity Reactance

2.14.3       Inductive Reactance

2.14.4       The RCL Series Circuit

2.14.5       Phase Angle Φ between Current and Voltage

2.14.6       Resonance Frequency

2.14.7       Power in an AC Circuit

2.14.8       RMS current in a series RLC circuit

2.14.9       Transformer

2.14.10     Ratio Electric Field to Magnetic Field

2.14.11     Speed of Waves

2.14.12     Electromagnetic Spectrum

2.14.13     Resistor

2.15           Lights / Optics

2.15.1       Nature of Lights

a)  Angle of Refraction

2.15.2       Law of Refraction

a)  Index of Refraction

b)  Total Internal Refraction

c)  Polarisation of Light Waves

2.15.3       Convex Mirrors and Lenses

2.15.4       Mirror Equation

2.15.5       Images Formed by the Refraction

2.15.6       Magnification of a Refracting Surface

2.15.7       Magnification of a thin Lens

2.15.8       The Lens Equation

2.15.9       Angular Magnification of a Lens

2.15.10     Maximum Angular Magnification of a Lens

2.16          Wave Optics

2.16.1       Angular Magnification of a Telescope

3.              Formulae for Stability Calculation

3.1           Basic Principles: Density, Mass, Volume

3.1.1       Density

3.1.2       Mass

3.1.3       Displacement

3.1.4       Hull Depth

3.2           Form Coefficient

3.2.1       Waterplane Area Cw

3.2.2       Block Coefficient

3.2.3       Midships Area Coefficient

3.2.4       Longitudinal Prismatic Coefficient Cp

3.2.5       Calculation of Mid Rip Area

3.2.6       Calculation of Mid Rip Coefficient

3.3.          Freshwater- and Dockwater- Allowance

3.3.1       Freshwater Allowance

a)          TPC

b)          WPA

3.3.2       Dockwater Allowance

3.4          Centre of Gravity; Buoyancy

3.4.1       GZ

3.4.2       KG

3.4.3       RM [t-m]

3.4.4       GM

3.4.5       BMbox

3.4.6       KB

3.4.7       KMbox

3.4.8       KM for a Triangular Shape Type

3.4.9       GM calculated in accordance to an Inclining Test

a)  Rolling Period

3.5           Reduction of GM: shifting of Centre of Gravity

3.5.1       Vertical Shift of Centre of Gravity

3.5.2       Horizontal Shift of Centre of Gravity

3.5.3       Loss of GM during Dry Docking

3.5.4       Effect of Bilging

3.5.5       Angle of List resulting from an amidships side compartment becoming bilged

3.5.6       Loading Weight using Ship’s Gear