Sweet Spot Part 2

Rerunning the Numbers

In light of observations over the season and the 'below expectations' performance results, Martin has decided to check and optimise the foil setup on Paradox.

Using updated software he plans to compare optimised setups for S foils and for hypothetical C foils similar to ones used by the current generation of A Cats. 

The calculations will be set up to arrive at the lowest drag combination for a given sideforce.

Interestingly, vertical lift as a percentage of boat mass (lift fraction) will be left as a variable. 

The calculations will be repeated for several boatspeeds. The result for each boatspeed being the lowest drag combination of foil immersion, toe-in angle and lift fraction. 

Computing a series comprising different boatspeeds (sideforce values) for each foil type will give a level comparison between the two configurations over a range of conditions.

Since lift fraction will be a free variable, the calculations will effectively compare total drag for foil assisted sailing against full foiling. Foil assisted will naturally have a bit more hull drag as the lift fraction will be smaller. However the number that interests us is total drag - being made up of both hull drag and foil drag.
For the same speed, the lowest drag combination for C foils might involve carrying, say, 50% of displacement on the foils while, at the same speed, an S foil boat would be happier carrying 60% of total weight on the foils.
If foil drag is higher, the gain to be had by lifting the hulls out of the water will be more expensive so carrying a lower lift fraction on the foils will give a lower total drag value.

What interests us is how that optimised lower total drag figure compares to the analogous lowest number for the alternative foils at the same sideforce value, even if the lift fraction might be different.

As described in part 1, the second round of calculations will be closer to representing reality as it will be informed by observations on the water. 

Leaving aside stability when foiling, it is thought that the span-wise lift distribution on S foils is inherently less biased toward the tip so their induced drag should be less (we will soon find out).
This incidentally would explain why it does not pay to set up C foils with aggressive rake (large angle of attack at the tip). Something many sailors have observed on existing boats.

Toe-In Angle

The biggest question mark right now is toe-in angle.
As explained previously, toe-in is an important variable as it has two effects:

1) Upwind it ‘feathers’ the windward foil which is surface-piercing so less efficient. At the same time it loads up the leeward foil which is working under the hull so effectively has a rigid ‘end plate’ above it. To understand this effect, think of the angle of each foil with respect to leeway. Toe-in aligns the windward foil with the true course through the water and gives the leeward one more 'bite'...

2) Downwind, toe-in causes the windward foil to pull up and to leeward, contributing additional vertical lift and, crucially, adding sideforce to allow the leeward foil to make even more lift.

More toe-in effectively decreases the ‘takeoff speed’. The question is whether taking off ‘early' gives a net gain. Meaning, is foil drag in fact less than the hull drag reduction may buy us... 

We found that aggressive toe-in is definitely slow upwind (slower than initially predicted) and not helpful downwind, especially so below about 15 knots of boatspeed. Yet it is necessary to foil but that is now thought to only pay at very high speeds. 

So it may be that toe-in should change at the end of every leg! In fact it should increase with increasing speed downwind.

Rather than adding another control, we plan to solve this conflict by machining new foil bearings with an angled slot: When the foil is pulled back the slot in the top bearing will guide the trailing edge outboard. When eased forward, the leading edge will rotate outboard. The range is from 0.5 degrees when fully forward to just more than 2 degrees (exact value pending) when fully back.

This solution in theory should give us the best of both worlds.
More importantly, it will not require an additional control.

Exploitability

The only extra control on Paradox (compared to other As) for now is the foil fwd/aft line. 

You pull it and cleat it to move the top of the relevant foil aft, or release it to allow the top of the foil to go forward (it should go forward automatically, aided by a bungee and by the drag of the foil in the water).

When the top of the foil is all the way back, the horizontal part below the hull is at the greatest angle of attack so lift is maximised. 

When the top of the foil is forward, the lift is actually pulling down (this can help upwind by sucking the windward hull down, giving a bit more power). 

Half way along and the foil is neutral.

Going upwind you tug on the windward foil control line as you come in off the wire, then release the new windward one as you complete the tack.

Downwind, both foils are set with the top fully aft to give maximum lift (and soon max toe-in) so you don’t need to do anything with them between top mark and bottom mark.

In the design brief we imposed the constraint that foil depth be set for the conditions: In anything over 8 knots TWS they are cleated in the ‘reaching position’. This is when the top part sticks out about 150 mm (as you can see in most pictures of the boat underway). In this position dihedral angle is maximised. 

In light winds there are two options: Pull both foils half way up so that they become upright (but each with halved immersed area) or always have the windward one up completely and the leeward one down completely such that it is vertical (no dihedral so no upward lift). 

Having the leeward one fully down and the windward one up gives an advantage in theory but requires an additional adjustment at every tack.

Handling

Our last observation is that having the foils so far forward, which must necessarily load up the rudders to keep the boat balanced, does require some getting used to. 

The reason for having the rudders hydrodynamically loaded is so they share with the foils the task of generating sideforce. 

This is a principle used on big boats such as CBTF maxis and is at the root of the tandem keel solution seen on several IACC boats. It is also why conventional IACC boats had such deep rudders.

If the rudder were completely neutral it would be ‘coming along for the ride’, contributing only drag. If the rudder is working to help resist leeway, it reduces the lift-induced drag being generated by the foils. 

This hydrodynamic load is felt through the tiller as a bit of weather helm. It is something that does reduce the margin for error, especially when tacking.

Conclusion

At the last regatta our setup may have been too aggressive, taking us past the optimum lift fraction. 

With excessive toe-in the foils were working too hard, giving a lot of lift but adding more foil drag than what is being saved in hull drag.

As with any new concept, there is a process of learning, to optimise both setup and sailing technique to exploit the advantages on offer. Martin points out that any comparable innovation (such as the foiling Moth) has an associated learning curve. Perseverance could be the key to getting it right and several design improvements may be required along the way. Our plan is to see this process through but also test different alternatives in pursuit of the best all-round solution.

In summary, the S foil and L rudder solution is still thought to have potential. 

It is arguably more demanding to exploit fully than a conventional setup but it might be more correct to say that it requires an adaptation in technique and a deeper understanding of foil dynamics than is sufficient on boats where the foils play a less crucial role. 

It is vital to understand where the gains lie and work through the solutions without ‘throwing the baby out with the bathwater’. An objective analysis is the only way to draw meaningful conclusions and make progress.

Going Forward

We will continue to tune and test the system on our existing prototype and work to fully understand what makes it tick. We will compare the best version of this concept with other ideas worth testing, then decide what to put into production.