Wind, Pressure, Temperature and effective force

[fireball]

The discussion turned to Wind speed after our mornings race ....

One argument is:
In the winter, the wind is colder, colder air is more dense therefore for the same wind speed you get more air to be deflected by your sails - so a F5 in the winter is stronger than a F5 in the summer (same wind speed though)

and the Other:
Air density is measured in pressure, we have similar pressure in the summer and winter, so the effective force of the wind is the same for similar speed and pressure and no account has to be taken of the wind temperature....

 

[DJE]

I'm sure this has come up before. It's a good excuse for capsizing more in the winter.

Volume of a fixed mass of gas varies with temperature and pressure. But the changes in volume, and hence density, are pretty small.

(P1 x V1)/T1 = (P2 x V2)/T2

So new volume V2 = old volume V1 x P1/P2 x T2/T1

But temperatrue is measured relative to absolute zero (-273 degrees C)

Increase pressure from 980 mb to 1030 mb and volume decreases by 5% so density increases by 5%.

Decrease temperature from 20 degrees C to zero degrees C (293 degrees K to 273 degrees K) and volume decreases by 7% so density increases by 7%.

If both act together then you get 12% more force in your sails.

But how are you measuring the windspeed? Cup anemometers are largely independent of air density but anything that measures stagnation pressure by bringing the airflow to a standstill will read higher speeds in denser air.

 

[gandy]

[ QUOTE ]
.. and the Other:
Air density is measured in pressure, we have similar pressure in the summer and winter, so the effective force of the wind is the same for similar speed and pressure and no account has to be taken of the wind temperature....

[/ QUOTE ] That part is incorrect. Density is affected both by temperature and by pressure.

Tony S

 

[fireball]

Wind speed that we link into (Chimet and Cambermet) is cup measured ....

Are you saying that ... if the pressure is the same, a drop in temperature by 20C would result in a 7% effective force increase ???

any slight change in effective force is noticable when your racing a dinghy .... especially when it is cold!

 

[peterb]

It's a little bit more complicated than that. First, the density of the air also changes with humidity. Surprisingly, wet air is lighter than dry air (water vapour is lighter than oxygen or nitrogen). Air near the sea surface will not be far off saturation, and hot air holds more moisture than cold air. The effect is to amplify up the density differences, giving a difference closer to 8% than to 7%.

But what causes the wind in the first place? Generally it will be caused by the pressure gradient between high and low pressure areas, and the wind speed resulting from a given pressure gradient will depend inversely on the density. The sail forces will depend on the density multiplied by the square of the velocity. So for a given pressure gradient the wind speed should be lower in winter than in summer, and then because of the squared velocity term the forces should be lower in winter than in summer even though the density is higher.

For a given wind speed, the sail forces will be higher in winter. For a given meteorological pressure gradient, the winter forces will be lower. As so often, the answer depends on how you ask the question!

 

[DJE]

Yes a drop in temperature from 20C to 0C (at constant pressure) gives 7% more density so 7% more force on the sails. But as PeterB says wind speed is far more important than density, because pressure varies with the square of the wind speed. So an increase of wind speed of 3.5% (15.0 knots to 15.5 knots) will have the same effect as the 20 degree drop in temperature. How accurately do you record the windspeed?

 

[fireball]

wind speeds are gathered from www.chimet.co.uk and associate sites ... but generally it is an experience ... u know - a feeling

 

[Fin]

[ QUOTE ]
Are you saying that ... if the pressure is the same, a drop in temperature by 20C would result in a 7% effective force increase ???


[/ QUOTE ]

A drop in temp of 20C would result in an effective force increase of me staying at home.

/forums/images/graemlins/smile.gif

 

[nigelhudson]

[ QUOTE ]


Increase pressure from 980 mb to 1030 mb and volume decreases by 5% so density increases by 5%.

Decrease temperature from 20 degrees C to zero degrees C (293 degrees K to 273 degrees K) and volume decreases by 7% so density increases by 7%.

If both act together then you get 12% more force in your sails.



[/ QUOTE ]

Unfortunately it doesn't work that way - the force on the sail is not a function of the air density. The sail is acted on by pressure, that is the differential pressure caused by the airflows on each side of the sail travelling at different speeds. As the air is effectively the same temperature on both sides there is no effect.

 

[DaveNTL]

 

[DJE]

[ QUOTE ]
the force on the sail is not a function of the air density.

[/ QUOTE ]
What??

So Bernoulli was wrong all the time then.

 

[boomerangben]

However you measure wind speed (apart from any modern dopler/ultrasound thingy) there is always a 1/2 rho v squared, in other words, you are always measuring dynamic pressure, which of course is what the sails experience. So 15kts of wind in the summer will make the boat tip as much as 15kts in the winter.

How the forecasters account for the temperature/humidity/pressure I don't know, but I would expect that they are predicting what they think their anemometers are going to tell them.

 

[gandy]

[ QUOTE ]
However you measure wind speed (apart from any modern dopler/ultrasound thingy) there is always a 1/2 rho v squared, in other words, you are always measuring dynamic pressure, which of course is what the sails experience. So 15kts of wind in the summer will make the boat tip as much as 15kts in the winter. ...

[/ QUOTE ] Not all wind instruments work that way. Rotating cups or turbines don't read pressure. They read how fast the air is moving (less a little bit of slip). You could confirm this by imagining how they would measure water velocity.

Something like a pitot or venturi will work as you describe, and maybe a Ventimeter as well.

Tony S

 

[boomerangben]

Correct me if I am wrong, but aren't the cups on an anemometer rotating due to drag which is proportional to 1/2 rho V squared? The cup shape means that there is a drag differential front to back so that they can rotate. Turbines use a combination of drag and lift, which is also related to 1/2 rho V squared.

 

[DJE]

I did the maths on this last time this question came up. You are right that it's the difference in drag of the convex and concave cups that matters but the density term "rho" cancels out and all that matters is the difference in drag coefficients between the cups facing in opposite directions. You have to ignore friction in the bearings for this to be accurate but in theory if you stick the masthead unit in the water it will read boatspeed.

 

[fireball]

So is there a higher drag in cold wind???

All this on Dynamic pressure has not convinced me yet ...

Sails do work by air sucking them forwards ... but I believe there is also an element of pressure on the windward side PUSHING the sail ... and this is when the "denser" air has a greater healing force.