Glide Ratio

This single property characterizes the performance of gliders, the sailboats of the sky

cot(ε) = L/D

A glider moves forward through the air as it descends because it produces much more lift than it does drag, as much as 60 times more, in fact. This high ratio of lift to drag, commonly called a glide ratio, is the single most important number in determining how long a glider can soar before needing to land. Knowing nothing else, this is how we compare the performance of one glider against another. And conveniently, a simple trigonometric relationship transforms the glide ratio L/D into a glide angle ε as illustrated and expressed above. Why do we care? Because it is this glide angle that leads us to the crucial insight expressed in The Beta Theorem, the governing equation of sailing.

The Beta Theorem

This insight is particularly critical to the design of high-speed sailboats

β = ε_A + ε_H

Whereas a glider has only one glide angle because it is moving through one fluid, air, a sailboat has two glide angles because it is moving through two fluids, both air and water. The minimalist diagram above illustrates how these glide angles apply to a sailboat's forward motion through the water: an aerodynamic glide angle ε_A captures the net performance of its sail(s) and superstructure, and a hydrodynamic glide angle ε_H captures the net performance of its hull(s) and foil(s). The Beta Theorem builds upon this duality by quantifying the relationship between a sailboat's glide angles and its relative direction through the two fluids, expressed by the apparent wind angle β. As Ross Garrett states in The Symmetry of Sailing, "the [apparent wind] angle β is simply the sum of the sail and hull [glide] angles." This "deceptively simple" (Garret) insight is the fundamental building block of the analytical expression we develop in our White Paper for comparing sailboat efficiencies.

Cavitation on Foils

This inevitable hydrodynamic phenomenon fundamentally influences the design

At boat speeds approaching 50 kn, the formation of vapor bubbles on the low pressure side of conventional hydrofoils (top) marks the onset of cavitation. And at modern record breaking speeds approaching 70 kn, these small vapor bubbles have combined to form a single cavitation bubble completely enveloping the low pressure side and extending past the trailing edge, reducing the glide ratio of the foil by nearly an order of magnitude. Supercavitating foils (bottom), on the other hand, have a strikingly different shape, with a sharp leading edge and a blunt trailing edge (or face), which causes the bubble to form and, therefore, collapse earlier while also reducing its dimension in the direction perpendicular to the flow (shown exaggerated in the illustration above). As a side note, the steep drag rise accompanying the onset of cavitation is why the one-of-a-kind boat Yellow Pages, a highly optimized yet conventionally ballasted sailboat, held onto a sub-50 kn outright speed record for over a decade starting in the early '90s, the longest continuous stretch of time since 1972, when the WSSRC began sanctioning records. More about this in our White Paper.

Aeroballast

A patented design with unmatched efficiency

Due to cavitation, the hydrodynamic glide ratio is significantly reduced at modern day record breaking speeds in excess of 60 kn. So in order to maximize overall efficiency, it becomes much preferable to use aerodynamics vice hydrodynamics to balance a sailboat, which was the driving motivation behind the development of aeroballast. The illustration above comparing aeroballast to other high-speed configurations is from our White Paper, where we introduce the notion of lost lift and how it is an inevitable consequence of the need to balance the heeling effect on real-world sailboats, ultimately revealing in detail why aeroballast is the most efficient balancing mechanism to date.

As shown in the snapshot above taken from Patent No. 7,568,442, aeroballast comprises sail-mounted ballast and a three degree-of-freedom pivot assembly. The pivot assembly allows for indepedent rotational control of the wing about the vertical, relative wind, and lateral axes. This level of control enables the sailor to align the wing precisely with respect to the apparent wind to maximize the aerodynamic glide ratio, as shown below.

Shown above—again from Patent No. 7,568,442—is how the aforementioned wing alignment would look on a starboard tack (i.e. wind off the starboard, or right, side) and port tack (i.e. wind off the port, or left, side). In both cases, the wing is leaning to windward to balance the heeling effect, and its leading edge is aligned for zero sweep, essential for maximizing the aerodynamic glide ratio.

Meet Cecilia

Our semi-autonomous research model for evaluating sailing performance in the real world

Early on, two foundational stability challenges unique to this high center of gravity configuration prompted an interest in real-world validation: 1. the launch of the sailboat from rest; and 2. dynamic control of the statically unstable sail-mounted ballast including basic sailing maneuvers. The solutions we have since developed are currently being tested on an approximately 1:10 scale research model, dubbed Cecilia.

Built around a simple tubular carbon fiber structure, Cecilia is designed to be robust and easy to reconfigure. The much simplified architectural view above highlights the five most important functional elements unique to this configuration: 1. a 'Brains' enclosure housing all of the controls electronics; 2. a 'Wind vane' sensor for maintaining alignment with the apparent wind; 3. 'Twin fore and aft hulls' for directional control and flotation at rest; 4. a 'Highly tapered wing' combining a high k_l value (see the White Paper for this definition) with the ease of flat-rolled construction techniques; and 5. an 'Aeroballast fairing' housing lead ballast. For the latest build and testing updates, please follow us on Instagram.

Meet Amelia

Our proof of concept designed to break records in the open ocean

The ambition to break the three major speed records ultimately boils down to designing a boat that can safely sustain supercavitating speeds in the open ocean. More specifically, it means exceeding 80 kn at times while maintaining speeds well over 50 kn for a full 24 hours. What we've shown in our White Paper is that the top speed of a sailboat is driven primarily by its overall efficiency, which in turn is driven primarily by the shaping of the three major wetted surface regions: 1. the superstructure; 2. the wingsail; and 3. the waterborne elements. So from the outset of conceptual design, the need for three key aerodynamic and hydrodynamic innovations was clear: 1. an 'Aerodynamic helm'; 2. a 'k_l optimized wing planform'; and 3. 'Precision supercavitating hulls'. The enclosed aerodynamic helm is shown here in a notional forward position where forward visibility is maximized and the overall diameter—and corresponding drag—of the enclosure is minimized by colocating the tallest frame of the cockpit with the tallest frame of an optimized teardrop shaped fuselage. And most importantly, this aerodynamic helm protects the sailor from the hurricane force winds experienced at supercavitating speeds. The k_l optimized wing planform is one chosen for its overall efficiency, a trade-off between the optimum aerodynamic efficiency of an elliptic planform and the optimum balancing efficiency of a high k_l value (more about this in our White Paper). The 'Precision supercavitating hulls' are designed to just barely plane at the air-water interface, necessitating a sophisticated trade-off between the aerodynamics and hydrodynamics. But the real brunt of the effort is focused below the waterline, on optimizing and fabricating supercavitating foils to a very high precision.

Just as shaping drives the boat's overall efficiency, robust control drives its practicality. And the aeroballast design is quite unique in this regard. Its high center of gravity is statically unstable, yes, but like a bicycle, the system as a whole can readily be stabilized dynamically while also allowing for incredible maneuverability. The need is clear, therefore, for a final key innovation, this time a mechanical one: a proven control scheme, one encompassing all aspects of launch and handling. To this end, we have begun validating and fine-tuning operating concepts on our small research model (shown here to scale). The test data gathered electronically informs the detailed design of manual controls (a requirement under WSSRC rules) for safe and practical operation in the heavy wind and sea states encountered in the open ocean.