# sail aerodynamics

Discussion in 'Hydrodynamics and Aerodynamics' started by Guest, Mar 21, 2002.

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### RHoughRetro Dude

Tom,

Munk's theorem assumes that the total lift is the same? How do laterally offset foils (bi-planes) effect each other?, IIRC there is less induced drag for the pair than for the two wings separately (Prandtl Biplane Equation)?

In other words, if multiple foils are each trimmed to Cl max how do they interact?

In the case of a wing with a split flap the total CL seems to be higher than either foil can generate without the other. Is all Munk saying that the two can be considered as one at the same "impossible" CL?

Think Schooner!

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### masrapidoJunior forever

Are you saying that two sails have the same lift(performance) as one of the same height?
Would that apply to wing sails too?

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### masrapidoJunior forever

If Tom's statement is right, what about longitudinal configuration? one sail behind the other? Would that have better performance?

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### tspeerSenior Member

Yes. Just how that is accomplished isn't specified. For example, if you have two wings in tandem, widely separated, they may be producing the same lift. As you bring them closer while still maintaining their same attitudes, the lift on the forward wing will increase, the lift on the aft wing will decrease and the total lift may change due to their mutual interference. So you have to adjust them to continue to maintain the same lift. But given the lift, Munk's stagger theorem says the drag will be the same.

But this happens automatically with keels and rudders, because the total side force from the hull & foils has to equal the side force applied by the rig, and the leeway angle will adjust itself until this is true. Similarly for the sail rig, the boat's lateral stability will dictate the heeling moment that can be applied by the sail rig, and the crew will trim the sails accordingly. Or the designer will compare rig designs at the design angle of heel.

If you compare the biplane to the monoplane n the basis of equal span, the biplane has less drag. The Prandtl biplane equation also says that the interference of one surface on the other is the same as the second has on the first. In effect, you've split the tip vortex at each end in half, and moved one pair of half-strength vortices farther away from the surface where it has less effect.

But almost nobody uses biplane rigs that way. Instead, they split the area between the two masts and the keep the geometric aspect ratio for each demi-rig the same. So the span gets cut by 30%. If you compare the biplane rig on that basis, then it has more drag than the single rig unless the two demi-rigs are very far apart. Because as they come together, they act like a single rig with 70% of the span of the baseline single rig, resulting in twice the induced drag.

So a biplane rig could have less drag for a given center of effort height.

CLmax and induced drag are two different things! Clmax is determined by the boundary layer on the surface, while induced drag is determined by the wake.

Multiple surfaces properly shaped and arranged can produce a higher maximum lift than any single surface of the same chord. For a more in-depth discussion, search this forum for A.M.O Smith's "High Lift Aerodynamics".

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### RHoughRetro Dude

That CLmax and CDi are different leads me to conclude that for aircraft and the underwater foils of a boat Munk's applies directly, since both systems are automatically self adjusting to load.

Below the design wind speed there is "extra" RM on a boat. The CL needed so Heeling Moment = Righting Momentmax might be something like CL=9. In that case (all wind speeds below design point) the optimum sail plan is the one that can create the highest CL.

At and above the design wind, optimized for CDi makes sense.

Thanks for the reference to Smith's High Lift stuff.

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### jam007Junior Member

I don´t think so. RM is used when going to windward and to windward it is important to get the largest Cl/Cd ratio not the largest Cl at any Cd. It is the Cl/Cd ratio of the sails+rigg+superstructure that has to be minimized to maximize the speed going to winward. For reaching maximum Cl would be the optimum.

Anders M

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### RHoughRetro Dude

This is how I look at it:

For a given RM of x, the sails heeling force that the boat can use is sf * arm.
where sf=Area*CL*.0012*V^2
arm = distance from lateral force to sail force

100 lb.ft. RM = 10 lb SF * 10 ft arm

thus RM/arm=sail force

Sail force changes with V^2 while RM/arm is constant

At CL=y
V=z
we can calculate the area needed to balance RM at CLx and velocity z

When V changes and the area does not, CL must change so that sf*arm=RM at the new V

For V higher than the design point CL or Area must be smaller.

For V lower than the design point CL or area must be higher.

Area is hard to change with every change in V, so we change CL to a new value.

For all values of V below the design point the CL must be higher
For all values of V above the design point the CL must be lower

The V range of the design is bounded by CLmax at low V and CLmin at high V.

V=5 will need CLdesign * 4 if the boat is to use all the available RM

Sails can't do CL=4 so after CL max is reached the boat is underpowered at V < design.

The ideal sail plan needs to have the highest CLmax value below design V and highest L/D at and above the design point until CLmin is reached and the sail area must be reduced.

High L/D at design point V looses races at V<design if the sail plan cannot produce high CLmax values.

Since multiple elements can produce higher CLmax, the multiple element sail plan should win below design V

Compare two sail plans:

Set span = 20
Set total area = 100
Set CLmax = 1.5
Set V = 10

Single sail:
Lift = 18
Drag = 2.86
L/D = 6.28
aoa = 24.11 degrees

Now split the area into 2 sails of 50:
Lift = 22.20
Drag = 2.18
L/D = 10.19
aoa = 24.11 degrees

More lift and less drag!

At the same aoa as the single sail each of the two sails would have CL=1.85

If we force them to have CL=1.5:

Lift = 18
Drag = 1.43
L/D = 12.56
aoa = 19.56

the total lift is the same as the single sail (area and speed are the same), but the aoa and L/D change to be even better than the single sail case.

Same lift, lower drag, higher pointing angle.

The split rig has higher L/D and higher lift. Unless they interact some way to reduce the performance of each sail.

Munk assumes Lift is equal for the multiple elements. On a sail boat this is true only when RMmax is reached.

Below the design speed we can use all the CL we can get, since boat speed depends on available force.

The comparison above is 3D lift line theory and does not include profile drag (which is assumed to be the same for each sail).

If we keep the same span, each time we split the rig the AR of each element goes up and induced drag goes down.

If profile drag is the same and the parasitic drag from the rig scales linearly with area, the more elements the better until the rig looks like a row of turbine fins.

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### RHoughRetro Dude

Just for fun I plotted the effect of multiple sails as I understand the theroy.

The sail area is constant
The CL is constant
The Span is constant
The wind speed is constant
The Profile and Parasite drag is constant (CDp = 0.1)
Since Lift is constant the induced drag is the same per Munk's theorem so total CD=CDi + CDp
Since Lift and Span are constant the RM needed is also constant if each sail has the same planform.

The Trim angle is calculated so the CL based on 3D lift line is 1.5

More elements should point higher?

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### jam007Junior Member

As the velocity is created by the sails and the relative windspeed increases with boatspeed any boat with sufficently low drag (mostly hyrodynamic) can reach a speed high enough to generate maximum sideforce for its optimum RM at any windspeed.
This shows that you can´t separate rigg construction and sailplane from boat design.
A high drag boat will benefit from generating a lot of lift even at the expence of extra drag. A low drag boat benefits from high L/D ratio at the expence of lift.
This can be seen in sailboat construction. As the drag of the boats decreases the rig gets more and more wing like trading max lift for L/D ratio.

Anders M

PS Cl/cd ratio has to be maximized, not minimized as I managed to write in my last post at one place. Sorry

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### tspeerSenior Member

That may be true if the height of the rig and planform shape are held fixed. But CDi is still important at low speeds. If you aren't pushing the hull's righting moment, your rig is too short. If you look at 18' skiffs, they have multiple rigs - the light air rig not only has more sail area, it's taller, too. This is an arguement for putting a very tall mast on a boat and reefing at comparatively low wind speeds.

I suspect one reason tall rigs perform well in light air is not just because the rigs can reach up into stronger winds, which is the typical explanation. But since induced drag for a given amount of lift is inversely proportional to velocity squared, it's even more important to minimize induced drag at low speeds than it is at high wind speeds.

Most boats have so much windage that the maximum L/D occurs above stall onset. So that's a big reason why you want to raise the maximum lift as high as possible.

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### RHoughRetro Dude

Good points made, maybe I'm not posing the question properly.

I'm only considering boats that sail upwind in displacement mode.

The design point for the boat is 12 knots VTW. The sail plan is designed for maximum L/D with enough area to use max RM. Say we managed to get L/D max at CL=.5 with a wing sail.

Now sail the boat in 6 knots, we need 4 times the area or 4 times the CL.

The wing can't grow, so it needs to make CL=2.0 to use the available RM.

If the CL max of the wing is 1.5 the boat will be underpowered, if we trim for max L/D CL = .5 the boat may not move at all.

The question is:

What combination of sails will give the highest CLmax of a given area without giving up a high L/D?

Historically, it's been a large main and a fractional height jib.

The only sail driven vehicles that have not ended up with this sail plan are ice boats, landsailers, A-Class cats, and windsurfers.

Skiffs, where boat speed is equal to or greater that VTW on all points of sail, use the large main, fractional jib upwind.

Why?

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### redcoopersMember

I haven't been watching this post for a while, so please forgive me if my comments are not very applicable!

However, the design of sailforms is very much a practical nature. Almost every normal racer is designed to race in ~5kts to +50kts windspeed. This means that first and foremost, the sails must be easily handled.

If you've ever raced in <5kts, you know that you're praying for some smooth laminar winds near the top of the sail. Most of your crew are lying flat on the leeward side to try not to disturb any air at all. Hence, we want the tallest rig we can to both 1) develop a righting moment to lengthen our LWL and 2) catch any undisturbed air which is above the competition.

Many sailboats feel like they get in the "groove" in about 10-12 kts. At this point, the sails are trimmed in what we consider the optimum condition. However, nearing ~18kts, most boats need to start spilling air. The DELFT works point to this as well. In many VPPs, there are variables having the naming convention alike to "REEF". This has nothing to do with truly reefing the sails, but instead imply mostly to easing out the mainsail to reduce the righting moment.

In terms of sailing, the feel is that our jib supplies the driving power - and wind tunnel tests also show that it has a very large Cl compared to the main. The main on the other hand, is very responsible for the righting moment and general tuning of the boat. Skippers know that if they constantly communicate with their mainsail trimmers while sailing upwind they'll do well - the jib trimmers are mostly left to following their tales.

So ultimately, what I am saying is that for a sailboat, instead of thinking of a design point for a Cl, think instead of a large plateau in which you can spill enough wind out of your sails to maintain a stable platform. In 8kts of wind, you may be able to get 5kts of boatspeed. In 15kts of windspeed, you may need to start easing out the main to get 6kts of boat speed. What most designers want is a boat which quickly gets up to near designed boatspeed and then gradually increases afterwards.

So the reason many boats use a frac rig is because all sailing is a compromise. A nice roach on a main will supply power at very low wind speeds. In high winds, you can simply ease the traveller and let the jib with its lower CE do the work. Furthermore, when running / cracked-off, the extra mainsail area is very beneficial. Remember that all inshore is 0.5 offwind, and most offshore racing can be usually 0.7 offwind.

-Jon

Last edited: Dec 13, 2005
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### brian eilandSenior Member

Something different...a gentleman wrote to me recently;

I have been interested in the idea of a forward raked mast with an
unusual sail layout for quite some time now, originally seeing the
idea at a student design show. The boat looked like the sailboat
equivalent to a future speculating auto show "Concept Car", with wild
ideas that gave little concession to practicality.
Kyle

Have a look at this futuristic design

Last edited: Jan 17, 2006
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### saildogJunior Member

So, do the same sail aerodynamics apply to square rigger sails? For example, as the foremast, main and mizzen are turned against the ratlines wouldn't the principal be one more of thrust than aerodynamics of high and low pressure areas? I'm building a model square rigger to test some of these theories....anyone with thoughts, ideas on this? I not an expert here but would love to hear thoughts and opinions...

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### RHoughRetro Dude

Stanford has done some work on a modern square rig

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