Density and sailing

[DeanDavis]

Okay now that we have hashed through some of the aerodynamics of our wonderful sport, and because the Air Sports Predictor showed more zeros than I think I have ever seen for Provo, lets tackle a simpler one, air density. As you all know, living in the high desert, we have thin air and that gives us less power (or force) in our sails. The beauty of air density is that we can talk both force or power and the outcome is the same, both equations have a linear relation to air density (i.e. if density decreases by 20% then power decreases by 20% and force decreases by 20%). I thought it might be interesting for everyone (myself included) to look at how air density changes with various parameters and then get feedback from the group on how other things might affect it.

So lets start with standard pressure and temperature (29.91 inHg, and 59°F) at sea-level this gives an air density of 1.225 kg/m^3. Now lets move to Utah and look at Utah lake (4,488 ft). At the same pressure (disregarding elevation*) and temperature we now have an air density of 1.035 kg/m^3 (we’ll call this Standard Utah Lake (SUL)) which is 15.5% less than at sea-level (we lost about 1/6th of our sail). A 16m^2 kite on the coast is now like a 13.5m^2 and a 20m^2 is a like a 17m^2 (or a 6.5m^2 sail is like a 5.5m^2). Deer Creek would be at (5,417 ft) which gives a standard density of 0.996 kg/m^3 which is an 18.7% decrease from sea-level (6.5m^2 is like a 5.3m^2). For the extreme lets go to Skyline and ride. Now we are at 9,900 ft and we have an air density of 0.806 kg/m^3 which is 34.2% less and the 16m^2 kite is now like a 10.5m^2. So as you can see elevation makes a big difference (ah, just another quirky thing about living in our (beloved) quirky state).

Lets move back down to Utah Lake and see what happens with temperature changes. Lets assume a hot day out at the lake 100°F. This would give us an air density of 0.959 kg/m^3 which is about 7.3% less than SUL. The 16m^2 kite is now like a 14.8m^2 kite because it is hot outside. If the temperature were 35°F then air density would be 1.085 kg/m^3 which is about 4.8% more than SUL. The 16m^2 kite is now like a 16.8m^2 kite.

What about atmospheric pressure? I don’t know the normal range (Craig?) but I found the world records which was 32.06 inHg for the high measured in Mongolia and 25.69 inHg in a Pacific typhoon (note that they said non-tornadic which I assume means the inside of a tornado can get pretty low). So I am going to assume that our extremes might be 1/3rd of these extremes (from normal). So I will use 30.6 inHg for the high and 28.5 inHg for the low and I will go back to Utah Lake as the reference. For the high pressure case we get 1.063 kg/m^3 which is 2.7% more than SUL. For the low pressure case we get 0.977 kg/m^3 which is 5.6% less than SUL.

So in summary we take about a 15-20% hit for typical sailing in Utah and as much as 34% when we snow kite up at Skyline. The temperature is a smaller difference (compared to elevation) but can fluctuate between 5% more or 7% less. Pressure would appear to make the smallest difference and typically I doubt it fluctuates very much.

Just for fun lets combine factors to see how high and low our density can get. Lets assume that we are out at Utah Lake (one of the lowest elevation sailing options in the state), the air temperature is 35°F (cold), and there is a monster high pressure (using the maximum from above). That would get us to a density of 1.115 kg/m^3 or about 9% less than sea-level. On the other end lets do some spring kiting up at Skyline. Assume it is pretty warm 80°F and a very low pressure system (using the maximum low from above). That would get us to a density of 0.719 kg/m^3 or about 41% less than sea-level.

So what about humidity? I know that water vapor is lighter than air but I have never heard of using humidity to calculate air density.

It is my understanding that wind monitoring equipment does not need to be adjusted for density. I think this is because they don’t produce any significant power (they just spin freely). That means they run at the no-load tip speed which means the tip speed is just some multiple of the wind speed. So when Marty and Jon hit south Texas they can read the wind as normal but if they read 13 mph they can think, not 20m^2 but 17m^2 kite.

*Elevation changes the pressure so when I say same pressure I am meaning the same pressure ignoring elevation changes. This is how the weather is reported, i.e. the pressure is report as if we lived at sea-level. If it weren’t reported that way then we would say “Rita, big deal we see pressures that low every day”.

[Marty Lowe]

Unfracking believably good stuff,

I knew there was undeniable differences,
but seeing the numbers is great.

-Marty

P.S. Reading between the lines,
I take it your not going to Texas with us?
Probably saving your $ for that new Rhino6.

[Ralph Morrison]

Hey Dean, thanks for the lesson. Something I've always wondered about is since air is less dense up here does it take a higher windspeed to produce whitecaps on the water? Or is water also less dense so it evens out? Since I've never owned a wind meter I've always used indicators like whitecaps, bending branches, blowing sand and liquid smoke to get an idea of wind speed. I figure the force it takes to bend something dense like a tree is similar at any elevation but how about water?

[Jon Manwaring]

Hey Dean,
What about the firiction, resistance, of an object pasing thru more dense air? Golf balls fly farther at altitude than at sea level. Also at the Oregon coast when It's blowing 12-15+ mph I fly a 17 M kite At ULSSB, at 12-15 mph, I also fly a 17 M kite!. Lots of fancy math demonstrating a thoretical difference but the kiting results are the same. IMO ??????. Also at the Gorge 300 ft + or - discounting for the current, usually a kite size, I will rig the same size kite as at home. WHAT'S UP ????