A ship performs well only when its hull, propeller and engine work together. This undergraduate marine engineering course explains how to achieve that match. It begins with resistance components, similarity laws and the extrapolation of model results to full scale, then compares the major empirical resistance prediction methods and the conditions under which each is valid. It develops open-water propeller characteristics from blade-element hydrodynamics, including four-quadrant operation, and applies the Bp-delta method to select propeller diameter and pitch. The heart of the course is propeller-engine matching at the design point and in off-design conditions such as fouling, multiple-shaft operation and reduced engine availability, followed by numerical matching exercises, the Admiralty coefficient and critical reading of software and spreadsheet outputs.
Course at a glance: Duration 20 hours · Self-paced online · 10 sections, 47 lessons, a 176-page downloadable course book
What you will learn
- Explain resistance components and the similarity laws used to extrapolate model results to full scale.
- Compare empirical resistance prediction methods and judge when each is valid.
- Interpret open-water propeller characteristics using thrust and torque coefficients and efficiency.
- Describe four-quadrant propeller operation for manoeuvring and astern conditions.
- Apply the Bp-delta method and hull-propeller coefficients to select propeller diameter and pitch.
- Determine design-point and off-design matching between propeller and engine, including margins.
- Audit numerical matching results from spreadsheets and propulsion software.
Inside the course: a high-level summary, section by section.
Resistance fundamentals and scaling
The course opens with the components of ship resistance and the similarity laws that link model and ship. Because Reynolds and Froude similarity cannot both be satisfied with water as the test fluid, model tests are run at the same Froude number as the ship. In Froude’s extrapolation, the total model resistance is measured, frictional resistance for model and ship is calculated from a friction line, and the residuary part is assumed to scale directly. The form-factor method refines this by treating viscous resistance as friction multiplied by a factor that depends on hull shape, so that only wave resistance is scaled by Froude’s law. Understanding these steps clarifies how towing-tank results become full-scale predictions.
Empirical resistance methods
In early design, model tests are often unavailable, so empirical methods are used. The course explains why methods differ: each was derived from a particular database of hull forms and speeds, and applying it to a different vessel type or outside its parameter range makes it invalid. Methods covered include Van Oortmerssen’s regression for small ships such as tugs and trawlers, Holtrop and Mennen’s method for a wide range of merchant ships, the Doust and Ridgely-Nevitt approaches for fishing vessels and Schneekluth’s compact method based on frictional and residuary resistance. A trawler case comparison shows how different methods can give different results for the same ship, and a worked example applies one method in detail.
Propeller hydrodynamics
The third section explains how a propeller generates thrust. Blade-element theory considers each section of a blade as a lifting foil, with the inflow angle determined by the ship’s advance speed and the blade’s rotational speed. Changes in ship speed or shaft speed alter the angle of attack and therefore the lift and drag on each section. The resulting thrust and torque are expressed non-dimensionally as thrust and torque coefficients plotted against advance coefficient, with open-water efficiency derived from them. The open-water diagram is more than a summary plot: it is the foundation of all later matching calculations.
Four-quadrant operation extends the picture beyond normal ahead running to conditions where the ship or propeller runs astern, such as crash stops and manoeuvring, which matter for safety and for engine and shaft loads.
Propeller design
Propeller design is introduced through design levels and cases, followed by the Bp-delta diagram. For a chosen propeller series, such as a Wageningen B-series propeller with a given blade-area ratio and number of blades, the diagram acts as a lookup map. You calculate a power coefficient from delivered power, shaft speed and advance speed, move through the family of pitch-diameter curves and identify the optimum diameter coefficient, pitch ratio and efficiency. Hull-propeller interaction coefficients, namely wake fraction, thrust deduction and relative rotative efficiency, are needed to convert between ship speed, advance speed, thrust and resistance. A design procedure, a tanker worked example and a Bp-delta worked example demonstrate the method.
Propeller-engine matching
Matching brings resistance, propeller and engine together. The inputs are the resistance curve, the propeller characteristics and the engine layout diagram. At equilibrium, the propeller thrust must equal the hull resistance adjusted for thrust deduction, and the propeller torque must equal the torque the engine supplies through the shafting. Plotting the propeller’s power demand against speed on the engine diagram gives the propeller curve.
Margins and allowances are essential. A sea margin accounts for weather, fouling and ageing, so the propeller is usually designed for a light-running condition at trial, ensuring that the engine is not overloaded when the hull becomes rougher in service. An engine margin keeps continuous operation below the maximum rating. Finding the design point combines these allowances, and a worked example illustrates their effect.
Off-design operation
Ships rarely operate exactly at their design point. Off-design drivers include hull fouling, heavy weather, changes in displacement and towing. Single-shaft and multiple-shaft arrangements behave differently when one shaft is trailing or when engines are shared, and reduced engine availability, such as running with one engine out of service on a twin-engine gearbox, moves the operating point. Shifted load lines show how heavier propeller loading pushes the operating point towards the engine’s torque limit, and how a controllable-pitch propeller or a different gear ratio can restore a safe operating margin.
Numerical matching and software
The final technical sections work through a complete numerical matching example, from resistance to power demand, the choice of gear ratio and engine operating point, and reduced-power cases, with a spreadsheet cross-check. The Admiralty coefficient is introduced as a quick tool for estimating power changes with speed and displacement. A propulsion software case study, using NavCad outputs, teaches how to read program results critically. Spreadsheet auditing and lessons from flawed spreadsheets emphasise checking units, assumptions and formula logic, because a professional-looking output is not necessarily correct.
Key takeaways
You leave able to predict resistance with appropriate methods, interpret propeller open-water data, select propeller dimensions with the Bp-delta method, match propeller and engine at design and off-design conditions and audit numerical and software results with confidence.
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 (8 in total) so you can confirm you can apply each method before moving on. A 176-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Fundamentals of Resistance: Resistance Components; Similarity Laws; Froude Extrapolation; Form-Factor Method
- Resistance Prediction Methods: Why Methods Differ; Van Oortmersen Method; Holtrop and Mennen; Doust and Ridgely-Nevitt; Schneekluth Method; Trawler Case Comparison
- Propeller Hydrodynamics: Blade Forces and Angles; Speed Change Effects; KT KQ and Efficiency; Four-Quadrant Operation
- Bp-δ Propeller Design: Design Levels and Cases; Reading the Bp-δ Diagram; Hull-Propeller Coefficients; Design Procedure; Tanker Worked Example
- Design-Point Matching: Matching Inputs and Curves; Thrust and Torque Balance; Margins and Allowances; Finding the Design Point
- Off-Design Matching: Off-Design Drivers; Single and Multiple Shafts; Engine Availability; Shifted Load Lines
- Worked Matching Example: Example Setup; Resistance to Demand; Gear Ratio and Engine Point; Reduced-Power Cases; Spreadsheet Cross-Check
- Power Estimation Tools: Admiralty Coefficient; NavCad Case Study; Software Output Reading; Spreadsheet Auditing; Broken Spreadsheet Lessons
- Summary: Key Takeaways
Who this course is for
This course is for engineering graduates and practising engineers in marine engineering and naval architecture who specify propulsion plants, design propellers or analyse ship performance, including superintendents investigating speed loss or engine overload in service. A background in fluid mechanics and basic ship resistance is assumed.
Frequently asked questions
How long does Propeller-Engine Matching & Ship Resistance 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 10 sections with 47 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 176-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (8 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.
Duration: 20 hours
Related courses: B06 – Resistance & Propulsion; B02 – Marine Engineering 1; B04 – Marine Propulsion Systems and Thruster Design; A12 – Naval Architecture and Ship Production Technology (Part 3 of 4)
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Study at your own pace and work through the full course material, worked examples and section quizzes. Enrol in B07 – Propeller-Engine Matching & Ship Resistance →
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