OPI™ - The Overall Performance
Index: An Introduction
Copyright © 1999 Richard
Boehmer
I first presented the Overall Performance Index (OPI™) at the May 1999 AYRS Forum held in Kennebunkport, ME as my latest tool for evaluating the performance of sailing vessels. The Index essentially consists of the area under the curve drawn through a set of points representing boat speed vs. wind direction (0-180° or 0-16 points) simply plotted on normal graph paper rather than using the polar format that one usually sees with VPPs, etc. Although most other indices appear without units, OPI™ can be expressed as knot-degrees or knot-points.
There are various ways to obtain the data, to cull/filter the unwanted values, to plot the selected choice few, to draw or fit a curve through them, and then to determine the area beneath the curve. The methods would depend on one's finances and mathematical abilities.
Of course, the OPI™ could not only be used to compare different boats in the same conditions (wind strengths), but also to compare their very best performances regardless of the conditions. Also, the OPI™ could be used with one boat to compare its overall performance in different conditions, or before and after making changes to hopefully improve performance. An example of this later case is shown in the accompanying plot of the best speed data of the Chapmans' hydrofoiled catamaran, Calliope (1).
As shown by this plot, the changes made to Calliope between sailing seasons resulted in an overall improved performance assuming that the measurements in both years were taken under similar environmental conditions. The difference of the areas under the two curves elegantly evaluates the overall improvement as being approximately 10%.
A similar approach could be taken when there is less data and/or much less precision in the measurements by making a simple tabulation.
As an example, the maximum speeds on four different general points of sail for the five-masted P-ships, Preussen & Potosi, as reported by Prager (2) can be tabularly presented as follows:
| Preussen | Potosi | ||||||
| point range | ∆ pts. | knots | kt-pts. | knots | kt-pts. | ∆ kt-pts. | |
| on the wind | 4-6 | 2 | 10.1 | 20.2 | 10.0 | 20.0 | 0.2 |
| near reach | 6-9 | 3 | 12.4 | 37.2 | 12.4 | 37.2 | 0.0 |
| broad reach | 9-15 | 6 | 14.7 | 88.2 | 14.6 | 87.6 | 0.6 |
| down wind | 15-16 | 1 | 13.8 | 13.8 | 13.2 | 13.2 | 0.6 |
|
Totals |
16 | 51 | 159.4 | 50.2 | 158.0 | 1.4 | |
From this less precise method,
we see that the performances of these two differently rigged vessels were almost
identical; the Pruessen was barely 1% (1.4/158.0) faster overall than the
Potosi.
References:
1. Chapman,
E.J.C. & G.C., Design and development of a 4.9m hydrofoiled catamaran,
Australian Science
of Sailing Conference Proceedings (1999 Jan. 04), in press.
(also in AYRS Catalyst 1:2, see below)
2. Prager, M.,
1905, Die Fahrtgeshwindigkeit der Segelschiffe auf großen Reisen, Annnalen der
Hydrographic und Maritimen Meteorologie XXXIII (January 1905), 1-17.
Other related material:
1. J. & G.
Chapman, "Design and Development of a Hydrofoil Catamaran", AYRS
Catalyst 1:2 (July 2000), 13-27.
3. J. Chapman, "CoolCat 26 Miu
Performance Measurement", Multihull International 375 (May'99), 129-132.
4. G. Chapman, "Calliope - update to end - 1994",
Inst. and Measure. of Performance, [AYRS 119] (1995), 29-30.
5. G. & J. Chapman, "Inst. performance measure. and
assess.", Inst. and Measure. of Performance, [AYRS 119] (1995), 7-28.
6. J. Chapman, "Small Craft
Instrumentation", Multihull International (Sep'94), 274-275.
7. G. Chapman, "Affordable
wind & water speed measurement", Foils and Hapas, [AYRS 108] (May'91),
24.C.A. Marchaj, 1979, Aero-Hydrodynamics of Sailing, p.71.
8. B. Wagner,
Fahrtgeschwindigkeitsberechnung fur Segelschiffe, Jahrbuch der
Schiffbautechnischen Gesellschaft, Vol 61 (1967) 14-33.