# Introduction

The resistance and propulsion analysis tools in PolyCAD fill a gap in the naval architecture analysis tools beyond stability that can be introduced without becoming a major focus of the software. The original plan was to present methods covering typical commercial ship, yacht and planning hull forms by implementing Holtrop and Mennen, Delft Series and Savitsky approaches. Presently only the first two have been finalised and validated. All calculations in this discipline as based on SI Units and only work with Design Units set to metres.

# A Little Bit of History

The implementation of resistance and powering analysis represented to me personal unfinished business from my undergraduate degree. This topic is, of course, a major element of any university course on ship design and often taught by the eminent academics of your institution. It is, however, a complex topic where introduction of first principle theory contributes little to the ability of an undergraduate to calculate the size of installed power required to drive a ship at trial speed. For this, we can use a range of empirical methods but the models of these bear little relationship to first principles physics. I scraped a pass on this module. I was disappointed. 20 years later, with the benefit of having been trained to deliver learning, I look back at my notes and the problem is clear. The knowledge I expected was not covered in the course. The minds of the eminent academics were perhaps focused on their more eminent research than the challenge of devising a successful learning process through which undergraduates could be introduced to this complex topic.

To resolve this unfinished business the action was clear. Pick up any renown naval architecture textbook covering the methods I need, learn the process and validate through worked examples. But I found that even these good textbooks, individually, struggled to convey the knowledge and process I needed to implement a solution that produced acceptable results. PolyCAD's Holtrop and Mennen implementation was first coded in 2013 and released for evaluation. However, it took the help of a couple of users, original papers and the combination of several textbooks to release a version that, in 2020, could be considered validated. I am now satisfied that the implementation is correct but expect to get the occasional objections from users who may disagree with results. Coding these methods is a challenge and simple mistakes may produce completely different predictions. The validation process identified bugs not only in my code but also in the spreadsheets of those that queried the results of my implementation. The code used to validate these methods is retained and is available to support enquires in the future.

# Integrated Resistance and Powering Analysis in PolyCAD

Like many algorithms used in ship design, almost all empirical resistance and propulsion methods can be implemented using spreadsheet style calculations. You can create your own design tools. Spreadsheets implementations, however, do not lend themselves to particularly flexible analysis. You almost will always need to update the input values which model the characteristic of your design as it changes which brings a chance of data entry mistakes.

An integrated modelling and analysis solution, like PolyCAD, eliminates the need to enter hull form characteristics because these can be directly measured from the design. In fact, PolyCAD is designed so that any analysis performed on a design project persists in the background, tracking changes, until the results are displayed. This will invoke an update if needed. In addition to hull surface geometry, the characteristics of appendages can often be included as part of resistance and powering analysis, referencing the dimensions, area and centroid of these elements. In PolyCAD, any element defining these characteristics can be referenced into the analysis in addition to the hull surface. This allows something as simple as a polyline to outline the physical dimension of a keel and rudder. These elements remain referenced into the calculation during the modelling process, updating the analysis if changed.

PolyCAD presents a wide range of outputs from each analysis in both graph and table formats. This provides a window into the intermediate results of the calculation as well as the indication of overall performance characteristics. Given the abundance of results, limitations in the formulations of these empirical methods can be easily detected. This is usually observed where different equations are used in specific ranges of speed, a feature of Holtrop and Mennen, and the initial Delft Series (I & II). All characteristics which parameterise each analysis are presented on the left of the analysis form with options and graphical indications of whether values are read-only or override by the user. All tables and charts can be copied into the Windows Clipboard allowing preparation of reports and other presentations.

# Holtrop and Mennen

For many decades, Holtrop and Mennen has been the principle empirical resistance method for most commercial ship configuration hull forms, although it is certainly not the only method for this type of vessel. I had intended to deliver a "vanilla" implementation, creating a solution that was exactly as the original papers had been written but user feedback and access to a wider range of options through the various textbooks I used saw the inclusion of the Gawn Segmented Propellers in addition to Wageningen B and various Air/Wind Resistance models.

Principle geometric characteristics are taken from the hydrostatics of the selected hull surface with the opportunity to reference additional geometry representing underwater appendages and projected area of the hull and superstructure to parameterise Wind Resistance.

Specific notes on the implementation are as follows:

- Holtrop and Mennen power prediction implemented in accordance with the methods described [1, 2], supported by general references [3, 4].
- Wageningen B-Series Propeller implemented in accordance with methods described in [4], with validation from [3, 5]. Polynomial values taken from [6].
- Gawn Propeller Series implemented as described in [7] using Polynomial values taken from [6].
- Taylor and Hughes Air resistance methods taken from description in [4].
- ITTC method of Air resistance taken from [3], modified to account for relative wind speed.
- Air Drag coefficient values as suggested by [4].
- Hull Transverse area for air drag taken from the calculation section with maximum area above the waterline.
- Burrell Cavitation limits implemented as described in [4, 3].
- Service Margin implemented as described in the AVEVA Marine Initial Design Hydrostatics Documentation.
- Entrance Angle calculated taking the breadth of the waterplane, 30% back from the forward point to the point of maximum breadth or beginning of parallel waterline.

# The Delft Series

The implementation of the Delft Series in PolyCAD can be traced back to the original software implementation of YachtLINES, from 1997, where an optimisation was provided to find the prismatic coefficient (Cp) and longitudinal centre of buoyancy (LCB). This was based on the Delft Series characterised as version 1 & 2 [8]. Since then, two further versions have been presented and are now made available in PolyCAD. This implementation is based on the approach documented in [11] and incorporates upright and heeled resistance of the hull, keel and rudder. Keel and Rudder are defined as additional appendages and may reference surface geometry or closed outline polyline elements. Heeled resistance is defined as part of the Delft Version 1 & 2, and Version 3 [9], which is also presented when Version 4 [10] is chosen. Lift Slope is only defined in Version 1 & 2 but is available for all versions. The frequency of coefficients across Froude number is more limited for later versions and it should be noted that any requested speed will not be calculated if it is not within the range of the chosen version of the analysis.

# References

- An Approximate Power Prediction Method, Holtrop and Mennen, International Shipbuilding Progress, Vol 29, No 335, pp. 166-170, July 1982.
- A statistical re-analysis of resistance and propulsion data, Holtrop, International Shipbuilding Progress, Vol 31, pp. 272-276, 1984.
- Ship Resistance and Propulsion: Practical Estimation of Propulsive Power. Molland, Turnock and Hudson, Cambridge University Press, 2011.
- Principles of Naval Architecture, Volume II Resistance, Propulsion and Vibration, Lewis, SNAME, 1988.
- Basic Ship Propulsion, Ghose and Gokarn, KW Publishers Pvt. New Delhi 2015.
- Marine Propellers and Propulsion, Carlton, Elsevier, 2007.
- Sizing Segmental Section Commercially Available Propellers for Small Craft, Blount and Hubble, Propellers'81 Symposium, SNAME, Virginia Beach, USA, 1981.
- Sailing Performance in Calm Water and Waves, Gerritsma, Keuning and Versluis, The 11th Chesapeake Sailing Yacht Symposium (11th), Annapolis, MD., January 29-30, 1993.
- Approximation of the hydrodynamic forces on a sailing yacht based on the "Delft Systematic Yacht Hull Series", Keuning and Sonnenberg, 15th International HISAS Symposium on "Yacht Design and Construction", Amsterdam, Delft University of Technology press, Amsterdam 1998.
- A Bare Hull Resistance Prediction Method Derived From the Results of the Delft Systematic Yacht hull series extended to higher speeds, Keuning and Katgert, International Conference on Innovations in High Performance Sailing Yachts, RINA, Lorient, 2008.
- Aero-Hydrodynamics and the Performance of Sailing Yachts, Fabio Fossati, Adlard Coles Nautical, 2009.