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      A Few Simple Rules   05/22/2017

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plenamar

Wind speed/sail area

20 posts in this topic

I read somewhere that wind force exerted  on sails is proportional to wind speed squared. 

My 30 ft half tonner carries a 32 sq mt sail area (mainsail = 14 + 100 % genoa = 18) in a 20 kt apparent breeze. This results in a "force" of:

32 x 20 x 20 = 12800 "units" of wind force

Does this mean that in a 50 kt storm I can carry a 5 sq mt storm jib ?

5 x 50 x 50 = 12500 "units" of wind force

 

Thanks

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But your windage (without any sails at all) will certainly affect the amount of sail you want to put up in a storm.

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Essentially yes. But the center of effort of the 5sq m storm jib  will be lower than that for full sail. And what Valis said is correct, there's still windage of the mast and rigging. 

A 5sq m storm jib is about right for a 30'er. You don't give boat type or details...IDK if you can carry that storm jib upwind in 50kn, but at least reaching and running should be ok.

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I'm fully powered with:

750 square feet @ 12 knots.

680 square feet @ 14 knots.

600 square feet @ 16 knots.

430 square feet @ 20 knots.

300 square feet @ 24 knots.

120 square feet @ 30 knots.

 75 square feet @ 40 knots.

Steve

 

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After thinking more about it, I'll adjust those last two figures:

120 sq. ft. @ 35 knots.

 75 sq. ft. @ 50 knots (a guess as most I've sailed in is 40).

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The dynamic pressure of wind is:

0.5 x air density x velocity^2, pick your units.

In Imperial (the only "correct" units):

0.5 x 0.002378 slugs/ft^3 x 33.75 ft/sec^2 = 1.35 psi for 20 knots. 

That is the force exerted by wind on a flat plate. The lift coefficient for sails is around 1.3, so well trimmed sails will produce 1.3 x the dynamic pressure in force. Drag coefficients vary from around 0.02 for a perfectly streamlined shape to 1.2 or so for something like a symmetric spinnaker. For round shapes in rigging, 0.4 - 0.6. 

Fun facts I thought you would like to know.

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Slugs shrivel up in salt environments, at least in my garden they do.  Suggest lb-f as the unit for sailing calcs ......

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9 hours ago, Panope said:

After thinking more about it, I'll adjust those last two figures:

120 sq. ft. @ 35 knots.

 75 sq. ft. @ 50 knots (a guess as most I've sailed in is 40).

Steve, I plugged your previous numbers into a spreadsheet and the 1/area vs windspeed squared plot was far from linear.  It would be interesting (for someone other than me) to add a windage constant to your sail areas to see if the curve gets any straighter.  These newer numbers do come a bit closer to a square-law relationship.

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That's cool, Paul.  I'd be interested to see the curve if you can post an image of it.

Yes, the windage factor makes for SMALLER sail areas than predicted (as  the wind increases).  However, the lower CE of the reefed/smaller sails will make for LARGER usable sail areas.   If someone is motivated to continue the calculation.  I could provide the CE heights for the various conditions.

Not sure how to explain a "bumpy" curve (besides errors in my data).  A possible explanation could be transition from the gaff main to jib headed sails.  

Steve

(Note: my definition of "fully powered" is when my side rail submerges (flat water) when beating or beam to the wind.  Rail will probably submerge with BARE POLES at about 60 knots.)

 

  

 

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panope.png.a16111291ac88d3b5cca32502c8d5d0c.png

Steve, here are your latest sail sizes vs windspeed squared.  The X axis is windspeed, and the y axis is windspeed squared times sail area, normalized so that your 12Kt / 750 sq ft sail = 1.  I tried adding various static windage constants to the sail areas, but that didn't look too enlightening.  If anything, it looks like your light-air sails are too small, or the heavy-air sails are too big.  But, as you mention, this doesn't take into account the sail location and height.

Anyway, it's fun to play with this stuff.  I don't pretend that it's valuable or correct.

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If we massage the "50 knot" point down to wind 44 knots (remember, I guessed at that one), and add the "0 sq ft/60 knot" point, we get a (sorta) smooth arc.

The light air condition's "too small sails" can be explained by the CE height being very high (top sails).

As the wind builds past 30 knots, the CE heights remain somewhat constant (low).  However, windage becomes dominant (boat is flattened under bare poles), thus explaining the plot 'curving' back to zero.

It would be interesting to overlay a couple more boats on the curve an see it the pattern repeats (If anyone posts their numbers, remember to use "close hauled" sails only).

Yep, fun stuff to play with.  

Steve

 

 

 

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8 hours ago, valis said:

panope.png.a16111291ac88d3b5cca32502c8d5d0c.png

Steve, here are your latest sail sizes vs windspeed squared.  The X axis is windspeed, and the y axis is windspeed squared times sail area, normalized so that your 12Kt / 750 sq ft sail = 1.  I tried adding various static windage constants to the sail areas, but that didn't look too enlightening.  If anything, it looks like your light-air sails are too small, or the heavy-air sails are too big.  But, as you mention, this doesn't take into account the sail location and height.

Anyway, it's fun to play with this stuff.  I don't pretend that it's valuable or correct.

You could also plot it on semilog (log of speed against linear size).  . I know you do the same thing by incorporating that "log" into the squaring before plotting. But semilog plots are so engineerie :-)

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You can go a bit further and calculate the heeling torque: Foresail area Centroid was calculated using Euler method and then the values for various LP's roughed out and pasted in. Heel angles are not far off from what has been observed. 

Base above CG 5 headstay top angle   Wind density Forestay Length   Height above Cg   10       Height above CG 10           Righting moment    
Hoist "I" 42 20.38   0.02 44.80   "P"   37       PY 22           4000    
Foot "J" 15.6           "E"   17       EY 8                
  Jib Area LP Deck Point past mast LP up  forestay   Centroid Y Heel area* moment Heel Torque Main Area Centroid Y Heel moment Heel Torque Mizzen Area Centroid Y Heel moment Heel Torque Sum Heel Torque Heel Degree Wind Shedding heel Cos 
wind Kts LP/reef               reef depth         reef depth           0 0 1
2 160% 524.2 11.0 9.3   18 9429 754 0 315 22.3 7020 562 0 88 17.3 1524 122 1438 0.4 2 0.999
6 160% 524.2 11.0 9.3   18 9383 6756 0 315 22.3 6985 5029 0 88 17.3 1517 1092 12878 3.2 6 0.995
10 160% 524.2 11.0 9.3   18 9229 18457 0 315 22.3 6870 13741 0 88 17.3 1492 2984 35182 8.8 12 0.978
14 140% 458.6 7.7 8.1   16 6896 27031 0 315 22.3 6600 25873 0 88 17.3 1433 5619 58523 14.6 20 0.940
18 120% 393.1 4.4 7.0   15 5387 34908 4 250 21.0 4799 31101 0 88 17.3 1393 9030 75038 18.8 24 0.914
22 95% 311.2 0.2 5.5   14 4040 39105 4 250 21.0 4871 47153 4 59 16.0 874 8459 94717 23.7 22 0.927
26 75% 245.7 -3.1 4.3   14 3189 43120 4 250 21.0 4871 65858 4 59 16.0 874 11815 120793 30.2 22 0.927
30 50% 163.8 -7.3 2.9   10 1519 27337 8 193 19.7 3523 63414 4 59 16.0 874 15730 106481 26.6 22 0.927
34 50% 163.8 -7.3 2.9   10 1519 35113 8 193 19.7 3523 81451 8 36 14.7 485 11204 127768 31.9 22 0.927
38 30% 98.3 -10.6 1.7   10 911 26317 12 144 18.3 2441 70486 8 36 14.7 485 13995 110798 27.7 22 0.927
42 30% 98.3 -10.6 1.7   10 911 32148 12 144 18.3 2441 86106 22 0 10.0 0 0 118254 29.6 22 0.927
46 30% 98.3 -10.6 1.7   10 911 38564 24 39 14.3 516 21835 22 0 10.0 0 0 60399 15.1 22 0.927
50 30% 98.3 -10.6 1.7   10 911 45562 24 39 14.3 516 25798 22 0 10.0 0 0 71360 17.8 22 0.927

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6 hours ago, fastyacht said:

You could also plot it on semilog (log of speed against linear size).  . I know you do the same thing by incorporating that "log" into the squaring before plotting. But semilog plots are so engineerie :-)

True, but we are supposing that the sail area should be a function of the square of the windspeed.  Squares, inverse squares, etc, don't plot straight on a semilog(10) graph.  And that's the only kind of semilog that my OpenOffice Calc spreadsheet does.

Speaking of engineerie, I still buy 10 squares per inch "Engineering pads" for use at home (I'm retired).  Some people call these "quadrille" paper, but that's the stuff with a uniform 4/inch grid.  Real Engineering paper has five per inch, with darker major divisions on the inch.  And it's green.  That's important to me.

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Fastyacht: "semilog" scale compresses one variable, why do this ?

Lioness: Please explain the table results.....I get the following graph of jib+main torque ("y") as a function of windspeed ("x"):

 

 

Is this the heeling moment as a function of windspeed given succesivelly deeper reefing? Why is it strongly concave for wind speeds >25 kts?

Am I graphing the correct variables?

 

wspeed.pdf

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19 minutes ago, valis said:

True, but we are supposing that the sail area should be a function of the square of the windspeed.  Squares, inverse squares, etc, don't plot straight on a semilog(10) graph.  And that's the only kind of semilog that my OpenOffice Calc spreadsheet does.

Speaking of engineerie, I still buy 10 squares per inch "Engineering pads" for use at home (I'm retired).  Some people call these "quadrille" paper, but that's the stuff with a uniform 4/inch grid.  Real Engineering paper has five per inch, with darker major divisions on the inch.  And it's green.  That's important to me.

I have that paper. K&E .

I can still get 5 sq to the inch (albeit without the major minor thick thin) form, of all places, walmart. Staples has forsaken it.

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1 hour ago, valis said:

True, but we are supposing that the sail area should be a function of the square of the windspeed. 

And here is why, said SemiSalt pedantically...

Suppose we put up a piece of sailcloth 1 ft square, rather like the top example in the diagram below. Suppose that the wind is 1 foot per sec. Then in one second, the sailcloth will to exert some f to force 1 cubic foot of air around the sides.

Now, second case, the wind increases to 2 feet/sec. In this case, in one second,  the sailcloth has to move 2 cu ft of air (which by itself would double the force to 2f). But each cubic foot of air must be moved in 1/2 second, i.e. twice as fast as in the original example. So the force required is 4f.   2 times the air, 2 times as fast, 4 times the force.

As if you'all didn't know that.

30.jpg 

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20 hours ago, plenamar said:

 

Fastyacht: "semilog" scale compresses one variable, why do this ?

Lioness: Please explain the table results.....I get the following graph of jib+main torque ("y") as a function of windspeed ("x"):

 

 

Is this the heeling moment as a function of windspeed given succesivelly deeper reefing? Why is it strongly concave for wind speeds >25 kts?

Am I graphing the correct variables?

 

 

wspeed.pdf

That was a quick exercise in figuring out if simple modeling would match observations and projections from the US SAILING Performance package VPP. 

  • Wholly arbitrary "density" number to fit the speed to observed heel
  • Use of a "shedding" angle to reflect the reduced projected area normal to wind
  • Simplified Righting moment (one value, not a function of heel)  
  • Presumption that the lift/drag vectors can be resolved into force/heel
  • Calculated for beam reach with sails strapped in as worst case
  • Sails were calculated as simple triangles, no roach, no windage from rig & superstructure
  • Headsail centroid assignment was as noted, a bit arbitrary,
    • calculating it accurately is tedious and not readily parameterized in a compact spreadsheet to reflect "reefing" on furler 
    • Storm jib likely there would be a pennant to get it up above the waves a bit. 
  • The "Reef Depth" columns for Main and Mizzen are the height of the successive reefs, then show the replacement of the Main with the Trysail and dropping mizzen. 

Intention was at sufficiently high wind speeds, (implying resulting higher sea states,) to no longer be heeling as aggressively,  in more of a survival/comfort > 30 kts vs best VMG mode < 30 kts, which is why the torque is reduced, both by smaller areas and carrying lower due to reefing.

 

 

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