Every ship design, loading plan and stability booklet rests on a small set of principles: what holds a vessel up, how its underwater shape is described, and how it responds when weight is added, removed or moved. This introductory course rebuilds those principles from first principles for engineers who want a structured refresher. You move from the four modes of vessel support and Archimedes’ Principle, through hull-form coefficients, curves of form and Simpson’s Rule, to metacentric height, the inclining experiment, trim about the centre of flotation and practical weight-shift problems. Each idea is tied to the kind of calculation naval architects and ship operators actually perform, with worked examples that show every step, so that by the end the mathematics connects directly to the physical ship floating at its waterline.
Course at a glance: Duration 20 hours · Self-paced online · Level: Introductory · 6 sections, 23 lessons, a 76-page downloadable course book
What you will learn
- Classify the main ways vessels are supported (hydrostatic, hydrodynamic, aerostatic and aerodynamic) and relate each to real craft.
- Calculate displacement, buoyancy and simple loading effects in both seawater and freshwater.
- Read the key reference points on a profile plan, including the keel, centre of buoyancy, centre of flotation, midships and length between perpendiculars.
- Use block, midship, prismatic and waterplane coefficients to describe and compare hull forms.
- Apply Simpson’s Rule to estimate areas and volumes from tabulated offsets.
- Determine GM, KM, BM and KG, and explain how the inclining experiment reveals a ship’s actual vertical centre of gravity.
- Predict heel, sinkage and trim caused by adding, removing or shifting weights, including grounding and jettison cases.
Inside the course: a high-level summary, section by section.
Vessel support and buoyancy
Naval architecture begins with a deceptively simple question: what force is keeping the vessel up? The course opens by sorting craft into four support modes. Hydrostatic support relies on buoyancy alone, as with a conventional displacement monohull. Hydrodynamic support uses lift generated by flow, as on planing hulls and hydrofoils. Aerostatic support uses a cushion of air, and aerodynamic support uses lift from moving air. Recognising which mode dominates tells you which force balance governs the design, and it explains why most of naval architecture concentrates on the floating, hydrostatic case.
From there, Archimedes’ Principle becomes a working tool rather than a schoolbook statement. A floating body displaces a weight of water equal to its own weight, so displacement, draft and fluid density are tightly linked. You work through applications such as estimating how a vessel’s draft changes when it moves between seawater and freshwater, and how much weight must be added or removed to keep a body at a required waterline. The section then introduces the vocabulary of ship geometry: the keel as the baseline for vertical measurements, the centre of buoyancy as the centroid of the underwater volume, the centre of flotation as the centroid of the waterplane, midships as the halfway point between perpendiculars, and length between perpendiculars as the standard reference length for hydrostatic work. Being able to place these points confidently on a profile plan is the foundation for every later calculation.
Hull form analysis
A hull is a complex three-dimensional shape, and naval architects need compact ways to describe it. The form coefficients do exactly that. The block coefficient compares the underwater volume with a rectangular box of the same length, beam and draft. The midship-section coefficient compares the immersed midship area with its circumscribing rectangle. The prismatic coefficient describes how volume is distributed along the length, and the waterplane coefficient measures how full the hull is at the waterline. Each coefficient isolates one aspect of fullness, and together they allow a full-bodied cargo ship, a fine-lined fast vessel and a simple box-shaped barge to be compared on equal terms.
The course then shows how hydrostatic properties change with draft by introducing curves of form, the family of curves that record displacement, centres of buoyancy and flotation, tonnes or tons per unit immersion and the moment to change trim. These quantities are what an engineer reads off when assessing a loading condition.
The practical engine behind all of this is numerical integration. Simpson’s Rule turns a series of station measurements, such as half-breadths or sectional areas, into a reliable estimate of a continuous area or volume. You learn why the method is so widely used in hull calculations, how the multipliers are applied, how to check that the result is sensible, and where its limitations lie for very irregular shapes. A worked capacity problem for a garvey-type craft brings these steps together, moving from tabulated offsets to waterplane area and then to displaced volume.
Initial stability
Once a vessel floats, the next question is whether it will return upright when disturbed. The course explains initial stability through the relationship between the keel, the centre of buoyancy, the centre of gravity and the metacentre. KB locates the centre of buoyancy above the keel, BM depends on the geometry of the waterplane and the displaced volume, and KM is their sum. Subtracting KG gives the metacentric height, GM, which governs the ship’s restoring tendency at small angles of heel. A positive GM means the ship tends to right itself; a small GM shows up as a large heel for a modest weight shift.
Because KG cannot be guessed from the hull shape once a ship is built, the course explains the logic of the inclining experiment. A known weight is moved a known distance across the deck, the resulting heel angle is measured, and from that response the actual GM and then KG are derived. This is the step that turns a design estimate into a verified stability baseline. The section closes by linking small-angle stability to practical loading: how adding deck cargo, filling tanks or moving equipment changes KG, and why that matters for the safety margin a vessel carries into service.
Trim and weight shifts
The final technical section deals with longitudinal attitude. Small trim motions occur about the centre of flotation, not the centre of buoyancy, and this distinction underpins every trim calculation. Weight added directly at the centre of flotation produces pure parallel sinkage. Weight added forward or aft of it causes the ship to trim, and weight placed off the centreline produces list. You learn to separate these effects and combine them into a predicted final condition, with forward and aft drafts.
Applied problems extend the method to situations engineers and operators encounter: how much ballast must be removed to reduce draft by a given amount, how a vessel responds when it takes the ground and part of its weight is supported by the seabed, how jettisoning cargo changes the condition, and where tanks should be placed to achieve a desired trim. Each problem is reasoned from the loading condition to the likely change in trim, sinkage, buoyancy location or grounding response before any numbers are calculated, which builds the habit of checking whether an answer makes physical sense.
Bringing it together
The course closes by drawing the threads together: support and buoyancy, hull-form description, initial stability and trim form one connected toolkit. Worked examples walk through each calculation step by step, short self-checks inside the lessons let you test your understanding as you go, and a graded quiz at the end of each technical section confirms that you can apply the methods. You finish with a clear, practical understanding of how ships float and how they respond to the loading decisions made every day at sea and in port. Along the way, the course stresses the habits that separate a reliable stability assessment from a quick estimate: always identifying the reference point a quantity is measured from, keeping track of units and fluid density, sketching the expected response before calculating it, and checking results against physical intuition. These habits matter as much in a design office as they do when reviewing a loading plan on board, and they prepare you for more advanced work on large-angle stability, damage stability and hull-form design.
How you study
The course is delivered fully online and is self-paced, so you can fit roughly 20 hours of study around professional commitments. Lessons combine clear explanation with examples, diagrams and short interactive checks, and the main sections end with graded quizzes (4 in total) so you can confirm you can apply each method before moving on. A 76-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Vessel Support & Buoyancy: Modes of Support; Archimedes’ Principle; Ship Geometry Basics; Support and Buoyancy Review
- Hull Form Analysis: Form Coefficients; Curves of Form; Simpson’s Rule; Garvey Capacity
- Initial Stability: GM, KM, and BM; Inclining Experiment; Loading and Stability; Stability Review
- Trim and Weight Shifts: Trim About F; Weight Shift Effects; Grounding and Jettison; Tank Placement; Trim Review
- Summary: Key Takeaways
Who this course is for
This course is designed for engineering graduates and practising engineers who want a structured refresher in the fundamentals of naval architecture, whether they are moving into ship design, marine surveying, offshore support or vessel operations from another discipline. The source course recommends an engineering degree or equivalent experience, basic algebra and trigonometry (including small angles and the tangent of an angle), and familiarity with centroids, moments and fluid density. No prior naval-architecture study is assumed. It also suits those preparing for further study in hydrostatics, ship stability and ship design.
Frequently asked questions
How long does Principles of Naval Architecture: Support, Form, and Stability take?
The course is designed for about 20 hours of study. It is self-paced and fully online, so you can spread it over a few weeks or complete it more quickly.
What is covered?
The course is organised into 6 sections with 23 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 76-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (4 in total). The quizzes test understanding of the concepts and methods explained in the lessons rather than memorisation, and you can review the relevant lessons before attempting them.
Can I record this study for my own professional development?
Yes. The course notebook includes a self-assessment of the course objectives before and after study, a reflection page and a learning log, which you can use to keep your own record of professional development.
Level: Introductory
Duration: 20 hours
Related courses: A02 – Ship Hydrostatics and Stability Foundations; A18 – Naval Architecture Fundamentals; B01 – Introduction to Marine Engineering & Naval Architecture; A04 – Project Introduction to Hydromechanics
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Study at your own pace and work through the full course material, worked examples and section quizzes. Enrol in A01 – Principles of Naval Architecture: Support, Form, and Stability →
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