Polars and Density of Air

[rgleason]

From Ross Gerrett Symmetry of Sailing
Upwind Sailing page 69

From the example

FT = 1/2 As Va(squared) Ct P

As = sail area 10 meters squared
Va = wind speed 6 m/sec or about 12 knots
Ct = Use angle of incidence (28 degrees between boom and apparent wind) and Sail Polar Diagram to read off lift and drag coeff. Ct(sq) = Cl (sq) +Cd (sq) (Ct= 1.6)
P = Air Density is about 1.2 kg/m(cubed)

Thus

FT = 1/2 * 10 * 6(sq) * 1.6 * 1.2 =
FT = 50 * 36 * 1.92 = 3,456 = 346 newtons force.

The example is for a boat that points better than our boat, thus the forces on the sail going upwind are less than our boat.

Next I need to evaluate what are reasonable Air Densities to use
including the effect of humidity for the two conditions, Spring and Summer.

--
At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 1.2754 kg/m3. At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m3. At 70 °F and 14.696 psi, dry air has a density of 0.074887lbm/ft3.
--
At sea level and at 15 °C air has a density of approximately 1.225 kg/m3 according to ISA (International Standard Atmosphere).

More later.

[seandepagnier]

I wanted to say that my rig gets loose in cold weather. This is because the mast gets shorter, but the dyneema rigging doesn't change (at least not nearly as much as metal)

Maybe it's different with stainless rigs.


I agree that the difference from 13 to 16 knots (50%) seems a little high. I would suspect the anenometer to be inaccurate as well as as many other possible factors.

In any case, I know rain improves power downwind, but not sure it can help sailing upwind. Maybe it does but I'm not sure because the direction of the rain is much more vertical than the direction of the wind, so it has also a lot of down force.



I think for weather routing in areas that are dry vs wet would be more about comfort and avoiding as much sail change than improving speed in most cases. We can easily find examples where the fastest route is wet, or it is dry depending on the situation. So maybe yes, the computer could route around these, or very slightly alter course to give another day or 2 of steady conditions before entering the areas with the dark clouds.


What becomes increasingly difficult with complexity is not implementing the algorithms and applying various formulas, but receiving and presenting the information to the user in a useful and meaningful way.

[tom_BigSpeedy]

This is not direcly linked to the initial question of this post, but I think you might find it interesting :
I used to fly hanggliders in the past, and in hot desert conditions e.g. of California and Nevada the local airports always reported the density altitude of their runways. Differences were quite significant, lets say on a runway which is at a sea level altitude of 1000m, we had density altitude reports of 2500 to 3000 m.
That means a plain behaves like landing on 3000m. And I can tell ya from own experience that you hit the deck quite hard, if you miss the stall speed ...
Stall speed increases significantly in higher altitude and the wing also needs much more altitude to recover from a stall.

So there is a non-neglectible effect of temperature on the wing of a plain or hangglider -- or sail.

There is also a big impact of rain on a hangglider, but other than discussed here, it's not the force of the rain, but the raindrops heavily influencing the airflow on the profile. We always put liquid soap on the (mylar sailcloth) leading eadges as precaution if rain was forecasted for the day.

PS: you wouldn't believe it on the first guess, but the sail of a hangglider and sailing boat follow almost exaclty the same design principles. There is also designed twist, which can be adjusted while flying and the materials are the same. The only difference is, that it's 2 asymmetrically designed half-wings being used horizontally instead of one vertical sail used on sailboats.

Anyway, in sailing I think the wind gradient between water surface and mast head is more important that the temperature influence. From my experience, this differs from day to day. We have a north easterly wind phenomenon here, blowing down from the mountains and gusting out on the sea. 12 knots of (cool) NE-"Bora" are way not comparable to 12 knots of (warm ) south easterly, but from my experience it is not the temperature which makes the difference, but the NE wind gusts blowing very strong near the water surface.

This is easily visible when you're at anchor in these NE conditions and watch your wind instruments on the mast top. Sometimes gusts hit the boat and it starts already to heel while the instrument at 16 m height records only 10 knots. On other gusts, the boat is quiet and stable, but I see 30 knots on the instruments ...

In contrast, the warm south easterlies (here) generally have a long fetch on the water and therefore a strong gradient.

In the end I believe the gradient has more impact on the reef point in daily sailing practice than the temperature ...

Thomas

[rgleason]

By the way, in the example below, I misplaced a decimal (50 should be 5).

FT = 1/2 * As * Va(squared) * Ct * P

FT may (12 knots) = 1/2 * 53.7m2 * 6.2 m/sec (sq) * 1.6 L-D coeff * 1.261 kg/m3
= 42.96 * 6.2 m/sec (sq) * 1.261 kg/m3 = 2082 newtons

FT aug (17 knots) = 1/2 * 53.7m2 * 8.7 m/sec (sq) * 1.6 L-D coeff * 1.167 kg/m3 =
= 42.96 * 8.7 m/sec (sq) * 1.167 kg/m3 = 3794 newtons

FTmay should equal FTaug if everything was calibrated and measured properly.
It appears that FTaug is 3794/2082 or 82% more than it should be.

Lets try this another way:
FTmay = 2082 newtons
What wind speed is needed in August using the August density assumed above?

2082 newtons = 1/2 * 53.7m2 * Wind Speed m/sec (sq) * 1.6 L-D coeff * 1.167 kg/m3

2082 / (1/2 * 53.7m2 * 1.6 L-Dcoeff * 1.167 kg/m3) = Wind Speed m/sec (squared)

Wind Speed m/sec = Sq Root of (2082/50.134) = Square root of 41.5287 = 6.44 m/sec
Which converts to 12.51836 knots!

So the difference from May to August in Rhode Island due to air density would be at most 1/2 knot!

What would account for my observations?
1. Perhaps we were healing 2-3 degrees more in August.
2. Perhaps the headstay was not as tight in May.
3. The biggest factor might be that the cold NE wind has less gradient, as Sean, Tom and others have suggested.

-----------
Total force on the sails (Newtons)
As = sail area 578 sf = 53.7 sq meters
Va = wind speed 12 knots = 6.2 m/sec and 17 knots=8.7 m/sec
Ct = Use angle of incidence (28 degrees between boom and apparent wind) and Sail Polar Diagram to read off lift and drag coeff. Ct(sq) = Cl (sq) +Cd (sq) (Ct= 1.6)
P = Air Density (Rhode Island May and August)
Spring (May) 1.261 kg/m3
Summer (August) 1.167 kg/m3

===============

17 knots = 8.7 m/s
16 knots = 8.2 m/s
13 knots = 6.7 m/s
12 knots = 6.2 m/s
11 knots = 5.7 m/s
---------
The boat has 135% Jib =328 sf + Main 250 sf
Total 578 sf = 53.7 square meters

-----
(Picked some extreme values from May and August on the NOAA website.)
Spring (May)
1016.5
Air Temp 6.8
Dew -2.4
Wind 14.9
Gust 17
At 10 meters altitude
1.261 kg/m3
Used https://wahiduddin.net/calc/calc_da.htm

----
Summer Aug
1003
Air temp 23.1
Dew 22.0
Wind 8.8
Gust 10.1
At 10 meters altitude
1.167 kg/m3
Used https://wahiduddin.net/calc/calc_da.htm


Delta is 1.261 - 1.167 = .094 kg/m3
-------

[rgleason]

So the stall speed changes quite a lot depending on air density. Would the the corollary to that be that a sail would want a higher angle of incidence in lighter density air so as not to stall? IE: Don't pinch in lighter density air (same applies in light air too).

Thomas, as you have said and Expedition has determined, the wind gradient is what really counts. Perhaps I have encountered some of those days when there is not much gradient from sea level to the top of the mast in the spring.

I guess there is no way to determine those conditions from NOAA data for weather-routing...

[rgleason]

Wind Speed Gradient https://en.wikipedia.org/wiki/Wind_gradient

[Jman]

As far as adjusting polars, it would only help with routing, and I think it would be so negligible as to not bother with, given all the other uncertainties that exist in routing calculation.

The 13knot vs 16knot reefing is far more likely to be wind sheer. Sheer affects both the wind speed at ground level and the top of your mast, but it can be a huge difference the two directions. With less shear you are more effectively using your whole sail plan. I believe that this could more than explain the difference between summer and spring reefing wind speeds.


Sent from my iPhone using Cruisers Sailing Forum

[Stumble]

Originally Posted by boat_alexandra

I wanted to say that my rig gets loose in cold weather. This is because the mast gets shorter, but the dyneema rigging doesn't change (at least not nearly as much as metal)

Maybe it's different with stainless rigs.


I agree that the difference from 13 to 16 knots (50%) seems a little high. I would suspect the anenometer to be inaccurate as well as as many other possible factors.

In any case, I know rain improves power downwind, but not sure it can help sailing upwind. Maybe it does but I'm not sure because the direction of the rain is much more vertical than the direction of the wind, so it has also a lot of down force.



I think for weather routing in areas that are dry vs wet would be more about comfort and avoiding as much sail change than improving speed in most cases. We can easily find examples where the fastest route is wet, or it is dry depending on the situation. So maybe yes, the computer could route around these, or very slightly alter course to give another day or 2 of steady conditions before entering the areas with the dark clouds.


What becomes increasingly difficult with complexity is not implementing the algorithms and applying various formulas, but receiving and presenting the information to the user in a useful and meaningful way.

Actually it's weirder than that. Where metals shrink when they get cold dyneema expands as the temprature drops. So as it gets colder your mast gets shorter and dyneema rigging gets longer. It's not much but on a closely tuned rig it can be enough to matter. A temprature swing of about 40-50F is enough to justify a retune with dyneema standing rigging.

[mrohr]

F=MA......force equals mass times acceleration . Cold air is denser than warm air (i.e. greater mass) so greater force as many here have observed including myself.
And,yes moist air is less dense than dry air( at the same temp of course).
Am I missing something here?

.................luv you all.......................mike.................... .....................................

[seandepagnier]

mrohr,

Yes you are missing something.

We need a formula to adjust polar speeds based on temperature and humidity. As I pointed out the wind sheer might be affected in non-linear ways making this problem difficult or impossible.

[rgleason]

Yes that is also true, but the calcs are here.
http://www.cruisersforum.com/forums/...ml#post2185896

Probably no more than a 0.5 knot difference betweeen spring and fall in Rhode Island.

The difference noted is most likely due to there being no wind gradient in the spring (IE: the wind speed at the surface was very close to the same as the top of the mast on the spring day that I observed.) --as Thomas, Cagney and others suggested earlier.

As OP I think this discussion can end. I certainly learned that the effect I noticed was only slightly due to change in the density of air between spring and fall and was more likely due to differences in wind speed gradient between sea level and the top of the mast.

Thank you everyone for your forbearance and understanding. Many of you were right trying to look for other factors ...Viking, Sean, etc.

[Alan Mighty]

Originally Posted by rgleason

Probably no more than a 0.5 knot difference betweeen spring and fall in Rhode Island.

The difference noted is most likely due to there being no wind gradient in the spring (IE: the wind speed at the surface was very close to the same as the top of the mast on the spring day that I observed.) --as Thomas, Cagney and others suggested earlier.

Exactly! The magnitude of wind shear (or wind gradient) as captured by the concept of "wind weight" is greater than the magnitude of differences associated with different densities of air.


Look again, if you will, at the graphics I posted in #14 and #15 of this thread.


Or consider this example: the masthead wind instrument of Led Myne is about 14 m above waterline. The geometric centroid of the mainsail + jib combination of Led Myne is about 6 m above waterline. The aerodynamic centre of effort of those sails is likely a tad higher than the geometric centroid.


On a day with little or no mixing of the air column, such as an overcast day with light steady wind, the wind shear is high. To the extent that if Led Myne's masthead wind instrument reads 5 knots, the wind at the centroid can be only 0.8 knot. That's what is called 'low wind weight'.


On another day with a clear sky and bright sun, the air column can be unstable, meaning that higher velocity upper level air is mixed or brought down to the surface - the result being gusty conditions instead of a steady wind and relatively low wind shear or wind gradient. To the extent that when the masthead wind instrument reads 5 knots, the wind at the sail centroid is about 4 knots. Hence 'high wind weight'.


VPP generated polars assume an 'average wind weight', with air mixing such that if Led Myne's wind instrument reads 5 knots, then the wind at the sail centroid is about 3.3 knots.


That is why some software, such as Expedition, has a factor to represent wind weight and modify your target speeds depending on the wind weight.


Note well: VPP generated polars will differ from polars generated from actual sailing data. So if you are generating polars from actual sailing data you need to pay attention to wind shear (or wind weight or wind gradient, whichever concept tweaks your buttons). You also need to pay attention to on which tack you are sailing and logging data. Here in Australia (S hemisphere) the vertical wind gradient is usually most marked when on port tack (i.e. the twist in the wind, the apparent wind speed at the masthead, is higher when on port tack than stbd). One would expect the opposite in the N hemisphere: on an overcast day with low wind speed and steady (not gusty) wind, one would expect noticeably higher apparent wind gradient on stbd tack to port tack.


That tack-to-tack difference disappears on a high wind weight/low wind shear day. On relatively calm low wind weight days, I find it difficult to find the upwind groove on port tack. Your mileage likely varies.


One easy way to convince a doubter is to construct a Shear-O-meter to measure the wind gradient. Here's a pic of a Shear-O-meter constructed by Mike Ruhland on his father's Dolphin, on one of the Great Lakes. And a pdf documenting how to make one.


Here also is that graphic, from Ockam, of wind gradient on low wind weight, average wind weight, and high wind weight days.


And a link to an Ockham page on how to measure wind gradient/wind weight effects by keen attention to differences between port and starboard tacks in the N hemisphere: Determine Shear


If your copy of Marchaj, <Aero-hydrodynamics of sailing>, is to hand, turn to pp. 530-535 and look at the ilustrations on p. 535 in particular. Marchaj focuses on wind gradient, but does not address the differences between high wind weight/low wind shear and low wind weight/high gradient conditions well.

[mrohr]

Originally Posted by boat_alexandra

mrohr,

Yes you are missing something.

We need a formula to adjust polar speeds based on temperature and humidity. As I pointed out the wind sheer might be affected in non-linear ways making this problem difficult or impossible.

Well, I was not attempting to explain how to sail,why I sail, or the meaning of life,.... but rather some simple observations .
If you were expecting me to suggest ways to adjust polars to reflect unmeasurable wind shear vis a vis humidity etc., I'm not your man. I just adjust twist by looking at my tell- tails and hope that it will suffice without consulting NASA. I'm still having trouble keeping my beer cold.

Interesting thought experiment tho...

BTW: there must also be a humidity gradient since the air at the very bottom is rubbing against the water while the air higher up is not and this must be a function of the difference between sea temp and air not to mention relative humidity.
Wait a minute! How a about factoring in wave height because wave motion
surely affects the mixing of the lowest air layers and must also contribute to shear.
All this has proven too much for me; my head hurts, I need to finish my beer......Damn! ,warm again.

.............................luv you all....................mike....................... .....

[rgleason]

Thanks, Alan, yes you were one of the ones who advised me.
How did I miss these pages on Ockham's website?
Wind Shear and Gradient - Ockam Sailing Instruments
Wind shear

Certainly have known about this but not thought about it as much as perhaps I should have.

We should have the Wind sensor down at the level of the Center of Effort of the Sail, but that would not work due to the sail changing airflow. Something simple without masses of wires to allow us to quantify. I guess that's why sailing is a Art too.

Thanks for piping up again.

Shear is as simple as keep those telltails on the leach flowing, but no really that simple if you want to calculate stuff.

Gradient needs some way to sense sea level and masthead, but my masthead instrument is ancient, and needs calibration anyway. For down at the cockpit, I threw out that Venturi Wind sensor because the ball always got stuck, infuriating.

[rgleason]

I have some more information and example calculations to support my original observations that the density of air in the spring creates a significant difference in the power in the sails. These example calculations by a good friend and Sikorski Engineer show that many variables simply drop out and we are left with a % of relative density. The example uses 59 deg f and 90 deg f. The values for Rhoe should be checked however because he was doing this from memory.

It appears there could be a 15-20% difference between spring and summer. This supports big_tom_speedy glider observations.

Many thanks to my Sikorski engineer friend for his help in understanding this factor.

It seems that boat polars should use this variable and there might be an easy way to calculate the boat polars in various temperatures, simply by adjusting the percentage of wind!

Please see the attached photo for the calculation. Can't find the attachment button... next post I hope.