Andrew Mason of VIRTAC provides an excellent and in-depth analysis of the upwind sailing aspects of the AC62′s, the recently-unveiled boats to be used in the 35th America’s Cup:
In Part 1 of this article we discussed the likely shape of the AC62 polar curve and how it affects the viability of upwind foiling in shifting wind conditions. In this article we will look at the decision making process of when and where to foil, and the tools and techniques that can be used to help predict these situations.
AC62 Foiling Evolution
America’s Cup designers such as Pete Melvin and Paul Bieker have talked about making the AC62 foil in lower winds than was feasible with the AC72. However, when the dimensions for the AC62 are compared with a scaled down AC72, the boat is heavier relative to its righting moment and sail area. This does not indicate a boat that will be more likely to foil in light winds than the AC72.
It is possible that the teams may reduce aerodynamic drag on their AC62s even more than was achieved by the Oracle team with their Cup-winning boat, but paradoxically, this may not make upwind foiling more advantageous, as it would improve the lift/drag ratio of the boat and make the high, non-foiling mode even more efficient.
Unlike the AC72, the AC62 allows dynamic control of rudder foil angle of attack. As a result, it may be possible to improve the efficiency of the main foils of the AC62 as they will not need to be as self-regulating in the heave axis. This may deliver some gains in the upwind foiling mode, as side-force can be generated more effectively when flying height can be precisely controlled. But how much more efficient upwind foiling will become is unclear, and whether upwind foiling mode can improve on the VMG available in the high-pointing displacement mode is also uncertain.
Some America’s Cup designers now believe that hulls are simply “foil delivery systems” and that hull design is no longer important, but this may be a naive view. It is a safe bet that the AC62s will be able to foil upwind in most conditions, but it is far from guaranteed that they will do so the majority of the time while racing.
Performance Prediction Difficulties
In order to accurately predict the behavior of the AC62 upwind it is necessary to use a Velocity Prediction Program (VPP) that can balance the forces and moments involved and determine the boat speed for a given true wind speed and direction. The problem is that for the 34th America’s Cup, many of the VPPs used by the teams were not able to do this satisfactorily for an AC72.
One of the primary reasons for this is the shape of the AC72 polar curve. It not only has multiple upwind VMG peaks, but for some wind angles it also has multiple boat speeds for the same wind angle, due to the hysteresis loop.These multiple solutions cause difficulties for the solvers used in conventional VPPs, which are designed to find a single equilibrium point. As a result of this limitation, a common problem for the conventional VPPs was getting different results when different starting conditions were used for a calculation.
Just because a force and moment equilibrium exists for a given wind speed and angle does not mean that it is achievable. The AC72 polar curve is “path dependent” in nature; that is, the performance achieved for a particular point of sail and wind speed is dependent on what headings and boat speeds preceded the current state. As a result there may be multiple equilibria possible for a given wind speed and direction.
For example, with the idealized AC72 polar curve shown above there are two stable boat speeds possible at 60 degrees true wind direction: 21 knots and 29 knots. Which of these speeds the boat adopts depends on the path it has taken. The 29 knot speed is only achievable if the boat has previously borne away beyond 60 degrees, risen up on foils, then luffed up back to 60 degrees.
In some cases a force and moment equilibrium may exist for which there is no path available for a give wind speed. For example, it is likely that a wind speed exists for an AC72 where foiling can be maintained, but not initiated. An example of this may be where the boat has been foiling happily in 15 knots of wind but where the wind speed then drops to 12 knots. Even though the boat may not be able to get onto foils when the breeze is a steady 12 knots, it may be able to maintain foiling in that wind strength if it is already on foils.
This situation also occurs with planing boats, in that it is often possible to maintain planing when the wind drops slightly below the wind speed needed to initiate planing. However, in the case of foiling cats, the issue is more pronounced and causes significant issues for conventional VPPs, as these are designed to find a single equilibrium for forces and moments, not trace out the path to that equilibrium point to see if it is achievable.
The behavior described above is not just restricted to the AC72. Smaller foiling catamarans such as the Flying Phantom and GC32 also have sawtooth shaped polar curves upwind, with their high-pointing displacement mode having slightly better VMG than their low foiling mode. This makes it very likely that the AC62 will have similar behavior, and have similar problems with VPP predictions. The inability of conventional VPPs to resolve path dependencies and the resulting inaccuracy of their predictions has resulted in several of the teams for the next America’s Cup committing to new VPP development.
The benefits of Wallying on foils in an AC62 will be substantial, but the penalties for getting it wrong will also be great. For example, if forced to sail a header for any period of time due to the proximity of a boundary or a competitor, the VMG obtained from sailing on foils will be dramatically worse than would be available from sailing in high mode.
The decision of whether or not to pull away and foil is a complex one based on how much the current tack is lifted, how far it is to the layline or boundary, and how soon a heading shift is expected. The maximum benefit occurs if the wind direction is headed just before the boat reaches the boundary or layline, but if this period is not long enough or the lift hasn’t been big enough, the gain may still not be greater than the distance lost pulling away to get onto the foils.
The mathematics required to calculate the the risks and benefits is complex, having many similarities to the methods used to value financial derivatives, such as the Black-Scholes model for options pricing. But these methods are complex and computationally expensive, and there is currently no on-board instrument system that is capable of weighing the future probability of lifts and headers versus the time available and the cost of initiating foiling. In the meantime, the decision when and where to foil upwind needs to be based on the intuition of the sailors.
The complexity of the trade offs involved in the decision to foil upwind makes it essential for the helmsman and tactician to have an instinctive sense of when and where to Wally, and the only way of training this intuition is repeated race practice in different wind conditions. Although this may be possible with training boats such as foiling AC45s, SL33s or GC32s, these will not necessarily replicate the trade-offs required for the AC62, nor will they provide a controlled environment where their decisions can be measured and compared to the optimal course.
This is one situation that is ideally suited to a simulator, as scenarios can be repeated many times in a short period, course options can be compared to optimal outcomes, and sailors can benefit from an ideal learning environment. VIRTAC is specifically set up to foster this learning process, with the inclusion of Artificial Intelligence (AI) based opponents who are capable of evaluating and executing wallying strategies based on intelligent routing algorithms.
In this way helmsmen can compete against a synthetic competitor that always makes optimally informed decisions based on the probabilities, making the quality of a helmsman’s choices and their effect on the position in the race immediately apparent.
Postscript: Why is it called Wallying?
Several readers have asked where the term Wallying came from. The idea behind the technique has been around for some time, most commonly referred to as “footing to the header”, but the 1987 America’s Cup was first time that a yacht’s instrumentation system automated the calculations and provided recommendations based on the yacht’s polar curves.
To avoid the on-board TV cameras and microphones revealing a new technique that the Stars & Stripes crew considered a key competitive advantage, the crew referred to a fictitious crew member, Wally, when course adjustments were relayed to Dennis Conner, the helmsman. Messages from the navigator such as “Wally suggests two tenths faster than target, Dennis” were clear to those on-board, but baffling to those unaware of the technique being used. Wally helped win the America’s Cup and has been immortalized ever since.