RG 65 Sail Area MeasurementRequest For Comments Version 0.1Comments to boebert@swcp.com

Background

Earlier this year, the Class Secretary for the RG 65 class in the United States was contacted by the International Radio Sailing Association (IRSA) who expressed their intent to establish a new set of rules to govern international RG 65 events. One justification for their doing this was the asserted inadequacy of the current RG 65 method of measuring sail area, which was to be replaced in its entirety by one of IRSA’s devising. The purpose of this document is to examine that assertion, and answer two questions:

• What are the problems with the current method?

• If problems exist, can they be overcome by less radical steps than a completely different method?

Policy and Intent of the RG 65 Class

The IRSA web site contains a “Policy and Intent” document for the classes it manages. The role of this document is described in its preface.

When a problem of interpretation of class rules occurs people almost inevitably discuss the intention of those who wrote them. In practice this is unimportant as the class rules can only ever be interpreted, in the formal sense, according to their meaning. In any case the original rules were often written fifty or more years ago and it may be impossible to correctly gauge the original intent. Even if that was possible it may have been intended to change the rules subsequently. However it is useful to know something of the intent and the reason for this intent if only because it brings the nature of each class into clearer focus. Knowledge of the intent at those crucial times in a class's history i.e. when class rules are revised, may help to establish where the class rules are failing to work properly and may assist in bringing the rules back into line. *

The IRSA document is dated 1995 and does not fully reflect the effect of commercial interests on the IRSA classes. No draft or official version of a Policy and Intent document for the proposed IRSA version of the RG 65 class rules has been made available to the author. The notion of a Policy and Intent document is still useful, and although one has not been produced by the existing RG 65 International Class Authority it is possible to review the history of the Class and determine what would be included.

https://www.radiosailing.org/documents/category/150-administration?download=58

The policy of the RG 65 Class as it exists today is captured in the policy section of the U.S. class owners association: “friendly competition in the Corinthian Spirit.” The essence of the Corinthian Spirit is self-policing of rules and encouraging amateur participation in design and construction as well as competition. A second policy, not formally stated but evident in the current class rules and their management by the current International Class Association, is to permit the widest possible range of innovation in the design and construction of a monohull racing yacht.

Effective application of the Corinithian Spirit requires that class rules be simple enough in both definition and process to be understood by nonprofessionals. Complex rules favor the professionals because of the investment in time required to negotiate a thicket of restrictions. The ability to offer a guaranteed measurement certificate becomes a value added to a purchased boat for which there is an associated cost to the purchaser. Professional builders already have the advantage of bulk purchase of material and access to specialized equipment and it is the policy of the existing RG 65 ICA to avoid, wherever possible, giving them the advantage conferred by a complex rule set.

The combination of support for Corinithian conduct and innovation has influenced the Class rules in the direction of extreme simplicity: three objective measurements of overall length (65cm), mast height (110cm) and sail area (2250 sq cm). It is the adequacy of the latter that we examine in this paper.

The Current RG 65 Method of Sail Area Measurement

The relationship between measured sail area and sail performance is far from simple.* In particular, it should not be assumed that small percentage differences in sail area correlate in any way with differences in performance. This is especially true for the RG 65 class, whose sails operate in the bottom one meter or so of the atmosphere and are subject to significant turbulence from ground effect.

Sail area has been measured, or to be more accurate approximated, by a variety of techniques since sail area values were included in measurement rules over 100 years ago. The basic technique, described books such as the second edition of Skene’s Elements of Yacht Design (1909) is to divide the sail into triangles and add up the areas

* See, e.g., the long discussion of sail aerodynamics at http://www.boatdesign.net/forums/hydrodynamics-aerodynamics/sail-aerodynamics-457.html

of each one, as shown in the diagram from the book:

In general, rules makers for both full size and model yachts accepted the fact of approximation and considered a method to be fair if it was uniformly applied.

The use of polygons could be exploited by adding unmeasured area in the form of a curve at the edges of the sail. The three methods for dealing with curves are to ignore them, limit them (as was done in the original Marblehead rules for “roach,” or curved trailing edges to sails) or approximate its measure. The RG 65 ICA method of measurement includes the latter, yielding the method shown below, in which curves of greater than 2 mm must be “bridged” by a straight line and its area calculated by the formulae given. Measurements are to be taken on the actual sail and recorded on a full-size paper template. Vertices of the partitioned shapes are to be marked on the sail.

This formula applies to curved edges that may appear anywhere on the perimeter of the sail, and is the same as used in the original Marblehead class rule. The formulae for trapezoidal and triangular segments depend on all edges of the segments being straight lines.

The latter requirement gives the measurer freedom in choosing a partitioning that minimizes the number of measurements and the resulting possibility for error, as shown below:

IRSA Requirements for Sail Area Measurement

No publicly available requirements for sail area measurements have been found by the author. Private correspondence with the Chairman of the Technical Committee yielded a requirement that sail area approximations be accurate to 0.25 percent of “actual” area. For the RG 65 class this produces a tolerance of approximately 6 square centimeters.

This number was established by social process 26 years ago in conjunction with an update to the 10 Rater rule. No aerodynamic justification for this number has been provided.

The USA NCA has collaborated with an aerodynamicist who also designs and builds Moth class foils. This individual has adapted the Michlet codes and developed a simple model of an RG65 to produce a first-generation Velocity Prediction Program (VPP). The very preliminary results of this exercise show that for a swing-rig RG65 running downwind, a one percent increase in sail area yields between 2 and 4 tenths of a percent increase in velocity. This essentially negligible effect is consistent with informal observations of large numbers of RG65 heats sailed with mixed rig selections, e.g., some running A rigs, others running B rigs, or B rigs of varying sizes.

It should also be noted that in any class that permits cambered sails, the “true” sail area is generally not measured, but rather the projected sail area defined by the perimeter of the sail laid on a flat surface. If a sail is cut to a typical camber of 4% or so, the actual sail area will exceed the projected sail area by about 1.5 percent.

In response to inquiries, the IRSA Technical Committee furnished nine examples of what they viewed as erroneous partitionings using the current RG 65 ICA rule. Several of these involved cases where “cuts” produced shapes that had curved edges, in violation of the rule. The fact that such partitionings existed “in the wild” suggests that an interpretation and/or tutorial document should be produced as the popularity of the class grows.

Other partionings submitted by the IRSA Technical Committee raised issues that needed to be addressed. These are treated in the next section.

Methodology of Analysis

Hundreds of RG 65 designs have been produced since the current method of sail area measurement was introduced in 1999. A common sailplan configuration is roughly 70 percent main and 30 percent jib. In the interest of economy, the analysis is restricted to approximations of mainsail area of the largest (“A”) rig, since it is only necessary for the smaller (“B”, “C”) rigs to be shown to exhibit less area and there is no need to measure them otherwise.

An elliptical planform was chosen because analytic methods exist to compute the “actual” or “perfect” perimeter and area of such a shape. Elliptical planforms are also aerodynamically efficient so the shape is also a plausible one. The resulting sail is one-quarter of an ellipse with a submajor axis of 103 cm and a subminor axis of 19 cm, yielding an “analytic” area of a few square millimeters in excess of 1537 square centimeters. This value was used as the reference value for comparisons.

The values for the width W of the quarter ellipse at any height were also calculated analytically and plotted at one centimeter intervals of H on a piece of dimensionally stable material as shown below. The width values are given in the Appendix to permit interested parties to replicate our results. The plotted values were then faired to form the shape of the sail for measurement purposes.

Approximation by the IRSA Method

The proposed IRSA method for approximating sail area requires the construction of a measurement template with parallel lines every 10 cm. The sail is aligned on this template and measurements taken at each line. The area is then calculated using the trapezoidal rule. If there is a fraction of the sail above the uppermost line, the area is approximated by a bounding trapezoid. The application of this rule to our elliptical planform is shown below:

The calculations shown used the analytic values for width W at each station and measurement with a metric dial caliper for the fraction above the top station. The resulting “best case” approximation was 1533.68 sq cm, for a deviation of 0.2% of the tolerance allocated to the mainsail.

A “worst case” calculation was made by truncating the analytic values to one millimeter accuracy as a means of approximating maximum plausible measurement error. The resulting approximation was 1529.9 sq cm, or 0.46% of the mainsail’s allowed tolerance. This indicates that the 0.25% tolerance required by the IRSA will be difficult to achieve with their method.

A curious inclusion in the IRSA method is the requirement to measure any curved or triangular foot of the sail using the trapezoidal rule at an interval of 4 cm. In our example, this would add five measurements to the thirteen already mandated by the method. The inclusion is curious because the imposition of a limit on rig height effectively eliminates the possibility of unmeasured area in the foot of a sail:

The IRSA method also does not exploit the simplicity of many RG 65 sailplans, and imposes the use of a measurement template and eighteen or so measurements on a sailplan consisting of a simple trapezoid and a triangle whose area can computed to the limit of measuring error with four linear measures:

Approximation Error in the ICA Measurement Method

One of the “erroneous” partitionings submitted by the IRSA points out an exploitable shortcoming in the current ICA method. This is illustrated using our elliptical example by partitioning the sailplan into one triangle and one curved or “roach” segment:

The left hand diagram shows the roach segment with a measured chord of 7.77 cm. This yields an approximation of just over 1521 sq cm, which provides about 16 sq cm of unmeasured area, or about 1%. The right hand diagram is an exercise in “adversarial analysis,” in which we deliberately set out to maximize the unmeasured area. This is done by “squeezing” a curve into a tangent that maintains the 7.77 cm chord length. The resulting curve was measured with a planimeter and seen to add roughly 28 sq cm to the unmeasured area, for a “worst case” of 44 sq cm or approximately 2.8%

The amount of unmeasured area using the ICA method can be reduced significantly by imposing a limit of 3 cm on the chord length of roach segments:

This yields a (rounded) area of 1536 sq cm, for a deviation of 1 sq cm, a smaller number than that produced by the propose IRSA method. The reduction in “worst case” error suggests that a 3 cm limit on chords of roach segments should be considered for the 2017 RG 65 rules update.

Conclusions and Recommendations

1. The IRSA should produce a policy and intent document to support their proposed rewrite of the current RG 65 rules, so that the hundreds of RG 65 class members can understand the rationale for IRSA’s changes. This policy and intent document should address, at a minimum, the issues of complexity of the rule, bias toward commercial interests, and aerodynamic justification for the asserted requirement of 0.25% maximum approximation error.

2. The proposed IRSA method for sail measurement is more complex than that currently in use and unfamiliar to the current class members. Even if the 0.25% approximation error is imposed, it can be achieved by a much simpler, one-line change to the rule that class members are familiar with.

Appendix

Below is the table of widths for each station. Station intervals are 1 cm and Station 1 is the foot of the sail.Station Width Station Width Station Width Station Width