cat ketch downwind

No, it's much more fundamental to sailing performance than that. The basic sailing performance equations are:

Vb/Vt = sin(gamma - beta)/sin(beta)

Vmg/Vt = sin(gamma - beta)*cos(gamma)/sin(beta)

beta = atan(D_aero/L_aero) + atan(D_hydro/L_hydro)

Vt = true wind speed, relative to the water
Vb = boat speed through the water
Vmg = speed in the upwind/downwind direction
gamma = course sailed to the true wind. 0=head to wind.
beta = apparent wind angle, measured between apparent wind vector and boat's velocity through the water
D_aero = component of total aerodynamic force (sails, hull, rigging windage, etc.) parallel to the apparent wind
L_aero = component of total aerodynamic force perpendicular to apparent wind wind and parallel to the water surface
D_hydro = component of total hydrodynamic force parallel to boat's course through the water
L_hydro = component of total hydrodynamic force perpendicular to boat's course through the water

These equations are exact, with no approximations, and come directly from the wind triangle and the definition of lift and drag.

If the rig produces no lift, then its "drag angle", atan(D_aero/L_aero), is 90 degrees. Since the hull produces a side force that opposes the side force from the rig (and hull), there is no lift from the hull, either, and the boat is restricted to sailing DDW, at a comparatively low speed.

Producing lift with the rig does two things. It reduces the aerodynamic drag angle, reducing the apparent wind angle (beta), and improving boat speed. It also loads up the keel, increasing the lift on the keel and improving the hydrodynamic L/D as well, which further reduces the apparent wind angle and improves boat speed.

The lower the apparent wind angle, the faster the boat goes, because of the sin(beta) term in the denominator of the boat-speed equation. So long as the lift does not produce so much additional drag that the L/D actually decreases, producing more lift is always going to be faster.

At high lift/drag ratios, it is more productive to reduce drag than it is to increase lift - a small change in a small beta has a huge effect on speed. But at low lift/drag ratios, it is easier to add lift. That's why you see symmetrical spinnakers used on low performance craft, asymmetrical spinnakers used on higher performance craft, and only headsails or unarigs used on very high performance craft. Not only do the sails have to operate at lower and lower apparent wind angles as the performance improves, but the emphasis becomes more and more on reducing drag rather than producing pure force.

If beta is held constant (fixed L/D ratios), the course (gamma) to sail for best Vmg upwind is 45 deg + beta/2, and the best Vmg downwind is at 135 deg + beta/2. Maximum speed is obtained at 90+beta. Very few craft can sail fast enough for this to be their best point of sail upwind because L/D drops off as they foot or pinch too much. But it does show that the magic numbers 45 deg, 90 deg, and 135 deg are quite fundamental in themselves.

The more drag a boat produces (larger beta), the deeper it needs to sail downwind for best Vmg. But the Vmg it attains will be less than the boat that has a better L/D and sails a hotter course. I can easily see that a cat ketch would sail much better by letting out the sail so as to operate at high L/D downwind. The same goes for ballestron boom rigs.

 

Thanks for that, Eric. My post was indeed just meant to keep the wild-*** stuff down to a minimum.

 

"If the rig produces no lift, then its "drag angle", atan(D_aero/L_aero), is 90 degrees. Since the hull produces a side force that opposes the side force from the rig (and hull), there is no lift from the hull, either, and the boat is restricted to sailing DDW, at a comparatively low speed. "

This is not true; with "drag only" sail it is possible to sail broad reaching and almost crosswind; for so long as aerodynamic force of hull + rig has a reasonable component forward relative to boat, the boat will move forward, if not with sprightly performance;

more mathematically, with "drag only" above water part:

beta = atan(D_aero/L_aero) + atan(D_hydro/L_hydro)=90deg + atan(D_hydro/L_hydro);

if we assume a very modest underwater part L/D ~3, than :

atan(D_hydro/L_hydro)=18deg, and :

beta = 90deg + atan(D_hydro/L_hydro)= 90deg+18deg=108deg.

i.e. boat will be able to sail almost crosswind;

Of course, in this case, best VMG downwind will be made dead running.


"The more drag a boat produces (larger beta), the deeper it needs to sail downwind for best Vmg. But the Vmg it attains will be less than the boat that has a better L/D and sails a hotter course. I can easily see that a cat ketch would sail much better by letting out the sail so as to operate at high L/D downwind. The same goes for ballestron boom rigs."

I never doubted THIS in my post. Of course, with lifting instead of dragging sails (~1.5 times more pure force), cat ketch WILL sail significantly faster. I am told firsthand about Aerorig boats speeding away at beam reaching point of sail. However, speed will never be TWICE. Even when sailing dead downwind (i.e. no side force on sails and consequently no induced resistance on the hull) 1.5 times driving force will mean 1.5^0.5=1.22 times (+22%) the speed at very best, with easily driven hull, when far below the hull speed; closer to hull speed additional speed could be 1.5^0.33=1.14 (+14%) to 1.5^0.25=1.11 (+11%). When sailing hotter angle for best VMG, other two important factors came in to play:
1)what maximum sideforce underwater hull could carry efficiently, i.e. with small (D_hydro/L_hydro)
2)what maximum sideforce a boat can accept, without heeling to mutch i.e. transversal stability.

Both of them are quite fundamental.

Both of them quickly put the limit on speed increase of conventional boats, more so for monos, less for multis.

Most important (hardest to improve) appears to be transversal stability.

Increasing stability dramatically (twice and more) by moving ballast (canting keels, crew on wings wider as hull length and trapezes (skiffs)) or increasing stability together with dramatic improve of (D_hydro/L_hydro) (Hydroptere, foiling Moth) are the only ways so far discovered, which enable to exploit lifting sails with low (D_aero/L_aero) for DOUBLING, instead of SIGNIFICANTLY IMPROVING the speed and VMG.

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To return to "twice the speed".
Races in competitive fleets of monotype boats are won or lost by few boatlengts, i.e. with time difference of 0.2% and less. This have fundamental influence to speed perception of racing sailors. They constantly tune their perception to notice VERY SMALL increase or decrease in speed and VMG. Very small I mean much less than 0.2%. So when racer gain, say 2% or 3% of speed, he could easily say "my speed has doubled!" and grin from ear to ear.

I think real meaning of "double the speed" is worth a separate tread.

 

Did not visit this thread for a few days and things got sort of over the wall. Surely Eric was just being a bit of that with the "twice the speed" comment, reported second hand. I just assigned that comment to the same bin that holds "blazing speed", "shifting gears" and all the other things that sailors say to emphasize a claim.

Has anyone ever actually taken data to show the effect of letting cat ketch sails forward of 90 degrees? Most of the small sailboats we build locally are unstayed cat ketches and have learned that the rig offers many advantages. I do try to stay out of pointing duels with sloops of equal speed potential. I agree with the comments of importance of lift in downwind sailing and often take advantage of downwind tacking, whether under spinnaker or wing and wing..

 

Years ago, I did a VPP with account on sheeting limits for sails; on broad reaching points of sail limiting mainsail to 80-90 degrees out cut the speed by ~5% if I remember well. If you are interested, I could retrieve this data.

One point to consider is that any sail, when let out past 90degrees, start to heel boat to windward. To me it is scary (memories from Optimist in strong winds).

 

I'm not sure I understand what you mean there. Cut the speed from what?

Yes, your point is well taken and I have been subjected to windward capsizes in Lasers more times than I care to remember. In a cat ketch, this tendency is balanced by the mizzen and I've never tried it in really high wind.

 

Cut the speed from sail positioned for maximum driving force.

 

I don't mean to be a bother but what was the angle of max speed or driving force? I assume this would depend somewhat on the draft, draft position and vang tension in the mainsail.

 

I mean VPP can assume a sail so positioned as to have maximum force component forward, regardless of anything else, or some limits could be introduced, like maximum acceptable heeling moment, or sheeting out limit (as first approximation spreaders angle to CL is a natural limit).
If sheeting out is limited, at broad reaching and running points some potentially available driving force will be lost.

Below are two polar diagrams of imaginary 2 mast bermuda schooner, sailing in 6 and 8 m/s wind, with foresail and mainsail sheeting out limits of 65, 75, 85, 95 and 120 degrees respectively.

As could be seen, advantage of unlimited sheeting out do not look so great.

However, VPP calculation do not account for dynamic effects: when sail is over sheeted on broad reaching or running points of sail, not only driving force is lost. This would be not so damaging, as could be seen from diagrams. Important is that flow over such sails became either reversed (from leach towards mast) or unstable (from leach to mast for few seconds, than from mast to leach for few seconds, and so on). In either case, only the aftermost sail work "properly", while flow over the forward sails is destroyed. This way, large proportion of forward sails area is NOT exposed to anything resembling organized flow and effectively "dissapear" from the boat. I.e. we have 100m2 "hanging" and only 50 or 60 of them "working". It is not easy to account for in VPP. So driving force and speed loss could be greater as VPP predict it.

Further, with unstable flow over the sails, the boat start to roll back and forth. Rolling do increase resistance in many ways: large ant constantly changing angles of attack of keel and rudder, additional wave making, constantly changing underwater shape of hull, etc., etc.. All this further exaggerate speed loss from lost driving force.

On the other side, wing-and-wing'ed sails, let out forward of the beam, always have stable flow over them; this mean, the driwing force is not only greater, it also naturally stable in magnitude and direction, and whole setup is naturally course-stable in the sense that boat is returned to its course by aerodynamic forces, without (almost) any action from the rudder. This again greatly reduce resistance, and consequently, increase the speed. More as pure force calcuations would suggest.