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The effect of gas content on lift equilibrium of an inflatable wing
It’s an oft-heard jest in a kiteboard launch zone: “Hey, dude, the wind’s so light – we should pump our kites up with helium!” I was very intrigued the first time I heard this, and was curious to know exactly how ridiculous the idea is. Similarly, when the wind is blowing hard and someone is stuck with a too-large kite for the situation, one can hear the joking recommendation to “strap on some ankle weights.”
After doing the calculations below, it turns out that inflating the kite with helium will not help. And, while strapping weight to one’s feet will actually help counteract too much wind, it creates a dangerous situation as soon as the kiter winds up in the water needing to swim to safety!
The pre-filled default assumptions below reflect sea level conditions, and actual measurements of my 11.5m Best Kahoona kite. Since lift coefficients are determined experimentally and not available for kites, I’ve estimated the coefficient of lift from known coefficients of other airfoils and then backfit to known approximate windspeed required to keep a kite in the air. The end result of requisite velocity to maintain lift is highly sensitive to the lift coefficient assumption; however, the difference between results for different inflation gasses is unaffected. Proper gauge pressure for the kite is a matter of heated debate among kiters, but does not have a meaningful effect on theoretical lift (though it would indeed have an important practical effect on drag).
In order to find the minimum lift equilibrium velocity, we first calculate the mass of the gas inside the kite. Using the ideal gas law Pv=nRT , where n=m/M, we find the mass (m) in grams of helium and of atmospheric air (which is 80% nitrogen and 20% oxygen). Then, knowing the mass of the kite itself, we can calculate requisite velocity in each case, using the lift equation L=1/2*d*V^2*s*CL.
|Effect of gas content on lift equilibrium of an inflatable wing|
|Constants and environmental assumptions:|
|Atmospheric pressure (default reflects sea level)||psi (pounds per square inch)|
|Ambient temperature||degrees fahrenheit|
|Density of air (default reflects sea level, std temp, pressure, humidity)||d||slugs per cubic foot|
|Wing area:||square meters|
|Mass of uninflated kite:||kilograms|
|Volume of air in kite:||cubic inches|
|Gauge pressure in kite||psi (pounds per square inch)|
|Coefficient of lift (at zero angle of attack)||CL||0.15|
|Total pressure in kite (gauge+atmospheric)||P||atmospheres|
|Inflated with atmospheric air (80% N2/ 20% O2)||Inflated with helium|
|Atomic mass of gass inside kite||M||29||4||grams / mole|
|Mass of gass inside kite||m||grams|
|Total mass of inflated kite||kilograms|
|Velocity required to maintain lift equilibrium (i.e. apparent windspeed, or windspeed plus kite movement)||V||feet per second|
|miles per hour|