A DATA PROCESSING FRAMEWORK FOR POLAR PERFORMANCE DIAGRAMS - VALENTIN DANNENBERG, ROBERT SCHULER, AND ACHILL SCHURMANN

Oct 26, 2026

Polar performance diagrams are widely used to predict the speed of sailing vessels under given wind conditions, especially for robotic sailing systems and weather-routing algorithms. The paper presents a new framework and an open-source Python package that builds polar performance diagrams from measurement data. It supports multiple diagram representations, visualization methods, and generalizes weather-routing needs by computing trip costs via custom cost functions, deriving optimal steering through convex hull calculations, and flexibly calculating isochrone points using custom weather models.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages28

Reading Time1 h 11 min

AccessFree to download

Introduction

Polar performance diagrams in sailing and routing

Velocity Prediction Programs (VPPs) and measurement-based alternatives

Proposed framework and Python package features

A DATA PROCESSING FRAMEWORK FOR POLAR PERFORMANCE DIAGRAMS 􀁿 VALENTIN DANNENBERG, ROBERT SCHULER, 􀁿 AND ACHILL SCHURMANN Abstract. Polar performance diagrams are commonly used to predict the performance of a sailing vessel under given wind conditions. They are, in particular, an essential part of robotic sailing vessels and a basis for weather routing algorithms. In this paper we introduce a new framework for scienti􀀌c work with such diagrams, which we make available as an open source Python package. It contains a model for the creation of polar performance diagrams from measurement data and supports di􀀋erent representations of polar performance diagrams for di􀀋erent tasks. The framework also includes several ways of visualization of polar performance diagrams, for example for scienti􀀌c publications. Additionally, the presented framework solves basic tasks for the future development of weather routing algorithms in a way more general manner than other methods did before: it provides the calculation of costs of a sailing trip using custom cost functions, suggestions of optimal steering using convex hull calculations and a more 􀀍exible calculation of isochrone points, using custom weather models. Altogether, the presented framework allows future researchers an easier handling of polar performance diagrams. The corresponding Python package is compatible with various established 􀀌le formats. 1. Introduction A natural occurring task when steering a sailing vessel is to predict the speed over ground (SOG) in a given direction and in a given situation. This prediction is a di􀀎cult physical problem ([1], [2]) and depends on various factors, among them wind, current, waves, the shape of the vessel, but also the competence of the crew and others. For simpli􀀌cation, one can assume idealized conditions for some of these factors (e.g. that there is no current and no waves) and 􀀌nitely many possibilities for others (e.g. the used set of sails or the shape of the hull) . In this way the complicated physical dependencies can be simpli􀀌ed to 􀀌nitely many di􀀋erent functions depending only on Key words and phrases. polar performance diagram, sailing vessel, weather routing, automated sailing, Python package, data processing framework. 2 V. Dannenberg, R. Sch􀁿uler, A. Sch􀁿urmann Figure 1 . Example of a polar diagram as polar plot. a few parameters. Traditionally, this method is used to describe the performance of a boat in dependency of strength and direction of the wind, yielding a polar (performance) diagram. These polar diagrams are also a fundamental part of computer assisted and robotic sailing (see for instance [3] , [4]) and a basic tool used in routing software for sailing vessels ([5], [6]) . They predict the performance (boat speed/ speed through water / BSP) of a sailing vessel under 􀀌xed circumstances (usually using a 􀀌xed set of sails) and under idealized conditions (usually no current and wave e􀀋ects are captured, in this case BSP 􀀙 SOG) . In their most common form, they predict BSP for a given true wind angle and true wind speed (TWA/TWS) . Often, a polar diagram is visualized as atable or as a polar plot of BSP in dependency of TWA, with di􀀋erent curves indicating speci􀀌c values of TWS (see Figure 1 or [7, Figure 5]) . Sometimes, apparent wind is used instead of true wind (for example in [8]), but for the purpose of this paper, a polar diagram always uses true wind. For a better understanding of the di􀀋erent terms, see Figure 2 or [1], [2] . Polar diagrams given by manufacturers or by o􀀎cial sailing organisations like the O􀀋shore Sailing Congress (ORC) are mostly obtained by Velocity Prediction Programs (VPPs) that use computer simulations to predict the boat performance under idealized theoretical conditions [9] . For an overview over naval architecture, VPPs and alternatives refer to [10],[11] or [12] . However, it is not always reasonable to use a VPP, since real conditions can di􀀋er a lot from t

FAQs

What is the purpose of polar performance diagrams in this work?

They are used to predict a sailing vessel’s speed under specific wind conditions and serve as a foundation for robotic sailing and weather routing algorithms.

How does the proposed framework create polar performance diagrams?

It introduces a pipeline model that creates polar diagrams from real-world measurement data, supporting multiple representations for different tasks.

Which additional capabilities are provided for weather routing beyond diagram visualization?

The framework computes travelling costs with custom cost functions, suggests optimal steering using convex hull calculations, and calculates isochrone points with flexible custom weather models.

Oct 26, 2026

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