Dense Air

[NormanS]

Is there a measurable difference in the effect of cold dense air, as opposed to warmer lighter air?
Making south yesterday in a gusting westerly wind (max recorded 35 knots) in grey weather, and a temperature of 10°C, I commented to my wife, "This would be alright if it was 10 degrees warmer and the sun was shining".
Apart from being more pleasant, I would assume that warmer, less dense air, would apply less force. Is the difference significant?

 

[Fr J Hackett]

I was always under the impression that sailing in cold "heavy" airs the effect of the wind was stronger it may have been psychological though.

 

[wonkywinch]

https://www.noaa.gov/jetstream/atmosphere/air-pressure

 

[stranded]

There is definitely a spot in my personal sailing crapometer where more or less identical wind sea and temperature conditions are threatening on a dark cloudy day but exhilarating when the sun is sparkling off the water.

 

[flaming]

I was always under the impression that sailing in cold "heavy" airs the effect of the wind was stronger it may have been psychological though.

Yes. However I've never understood why the effect of the cold heavy air wouldn't also be felt by the anemometer that it's spinning so it would measure x% faster anyway.

 

[RunAgroundHard]

Definitely a measurable difference. One gets the donk used more than the other.

 

[jdc]

The lift associated with moving air in streamlined (ie not stalled) flow is given by Euler's formula, which states that the lift force is proportional to velocity squared and linearly proportional to the air density. This applies to the driving force of sails.

The drag from stalled objects is given by Rayleigh's formula, which similarly states that the drag force is proportional to velocity squared and linearly proportional to the air density. This applies to the boat's windage.

The density of air is proportional to the pressure, and inversely proportional to the absolute temperature. Thus when the temperature falls from 20°C to 10°C (293K to 283K) the density increases by 3.5%, which is the equivalent force increase of a wind speed increase of 1.7% (from 15 knots say to 15.3 kts). You'd not notice!

Of course other effects come in: a 35 milliBar increase of pressure would have the same minute effect, and humidity likewise changes the air density (more absolute humidity -> less dense, but on the whole cold air carries less humidity. The RH may be higher sure, but the absolute humidity contained in the air probably falls so actually this effect partly cancels the direct effect of temperature).

So for an explanation, you have to look elsewhere, it's not just simple density. Very plausibly the observed effect is caused by an increase in atmospheric turbulence and thus gust speed relative to average wind speed, which you might well experience more often in cooler climates, particularly when polar air masses meet tropical (which is stormy conditions anyway, just as we typically experience in autumn, and we've had all summer in Cornwall!).

 

[europe172]

Is there a measurable difference in the effect of cold dense air, as opposed to warmer lighter air?
Making south yesterday in a gusting westerly wind (max recorded 35 knots) in grey weather, and a temperature of 10°C, I commented to my wife, "This would be alright if it was 10 degrees warmer and the sun was shining".
Apart from being more pleasant, I would assume that warmer, less dense air, would apply less force. Is the difference significant?

This is why the Beaufort scale is good , regardless of measured wind speed the total power in the wind can be directly compared

 

[johnalison]

Yes. However I've never understood why the effect of the cold heavy air wouldn't also be felt by the anemometer that it's spinning so it would measure x% faster anyway.

I've often thought that too, but it might be that the spinning cups do measure real air speed with reasonable accuracy. In any case, heeling will affect the reading, so one really needs either a gimballed transducer or clever electronics that measure the heel and combine it with wind angle to give the real figure.

 

[flaming]

so one really needs either a gimballed transducer or clever electronics that measure the heel and combine it with wind angle to give the real figure.

Most integrated instrument systems do that. Mine certainly does.

 

[Roberto]

It's mostly a different vertical profile of wind speed / vertical gradient in the surface layer (the lowest layer, usually a few tens of meters thick; note, nothing to see with Ekman rotation etc which happens in an upper portion of the planetary boundary layer). The same measured speed at the conventional 10m has a very different distribution at say 5-7-12-15m height, usually a log-something function with different values for different degrees of air stability, cold air usually tending to be the least stable, a more vertical speed distribution with relatively higher low level speeds and forces exerted on sails.

Add. A couple of figures, the lower one relates the vertical gradient to the difference between Air and Sea Temperatures as simple approximation of air stability

 

[johnalison]

Most integrated instrument systems do that. Mine certainly does.

Yours corrects for angle of heel? I've not heard of that.

 

[flaming]

Yours corrects for angle of heel? I've not heard of that.

Yes it does.

Measured Wind Speed. On Hercules systems equipped with a Heel Angle sensor the Apparent Wind Speed is corrected for the Heel Angle of the yacht.

 

[greeny]

Always seemed that way when windsurfing. I always seemed to need bigger sail when abroad in the hot climes than when in UK for equivalent wind speed. I often tried to rationalise that, but was unable to come up with any method of calculating why that should be.

 

[Roberto]

It's mostly a different vertical profile of wind speed / vertical gradient in the surface layer (the lowest layer, usually a few tens of meters thick; note, nothing to see with Ekman rotation etc which happens in an upper portion of the planetary boundary layer). The same measured speed at the conventional 10m has a very different distribution at say 5-7-12-15m height, usually a log-something function with different values for different degrees of air stability, cold air usually tending to be the least stable, a more vertical speed distribution with relatively higher low level speeds and forces exerted on sails.

Just for fun, I once made some very rough calculations about the difference in force upon my mainsail with two different vertical profiles, I sliced it into three superposed horizontal parts, calculated the force over that section in the two different cases Stable/Unstable air vertical velocity profiles.
With a 20m True wind (masthead) of 10kt, unstable air yields 20% more force. With 15kt the difference is 23%, with 20kt a 25% difference. The other way around: given the force developed by unstable air at 20kt, a stable air will need 3-4 more knots to give the same force.
No pretention whatsoever of being accurate, but that sort of differences (add some tiny percent for density) can be felt by anyone with a little helming experience.
The lower half was for apparent wind angle at different heights, the stable air needing considerable more twist if one wishes to keep the same angle to the apparent wind along the mast. Again, it's a situation one might have sometimes felt, the mainsail being "untrimmable" or very difficult to trim because of the large variation in apparent angle along the vertical.

 

[NormanS]

Wow! This become much more technical and complicated than I expected.
I hesitate to introduce the touchy subject of anchoring, but consider a boat anchored (any anchor, let's not go down that road), with its anemometer reading 30 knots of wind at 10°C. Would the wind force (thrust) acting on the boat be less if with the same wind strength, the temperature became 20 or 30°C?

 

[rogerthebodger]

Wow! This become much more technical and complicated than I expected.
I hesitate to introduce the touchy subject of anchoring, but consider a boat anchored (any anchor, let's not go down that road), with its anemometer reading 30 knots of wind at 10°C. Would the wind force (thrust) acting on the boat be less if with the same wind strength, the temperature became 20 or 30°C?

IMHO it would not as the force on both the windward side and the leeward side of the anemometer would have the same density as it would have the same temperature

The anemometer on my boat gives the same reading at sea level as it does at my home at 6000 ft above sea level but the air density is quite different

 

[Metalicmike]

No one sees the Elephant in the room...........When Air is Heavy the barometric pressure goes up and that is in fair weather because warm air can hold more water than cold air

 

[AngusMcDoon]

.

 

[thinwater]

It's mostly a different vertical profile of wind speed / vertical gradient in the surface layer (the lowest layer, usually a few tens of meters thick; note, nothing to see with Ekman rotation etc which happens in an upper portion of the planetary boundary layer). The same measured speed at the conventional 10m has a very different distribution at say 5-7-12-15m height, usually a log-something function with different values for different degrees of air stability, cold air usually tending to be the least stable, a more vertical speed distribution with relatively higher low level speeds and forces exerted on sails.

Add. A couple of figures, the lower one relates the vertical gradient to the difference between Air and Sea Temperatures as simple approximation of air stability

View attachment 182745

View attachment 182746

^^ This. The difference in density is trivial compared to the differences in boundary layer thickness when the air and water temperature differ significantly. I've been sailing when the telltales at deck level pointed at 180 degrees from the masthead.

Actually, though, I think it's just a difference in hold a cold blast feels, to most of us. Most of it is in our heads.