The effect of gas content on lift equilibrium of an inflatable wing

It is an oft-heard jest in a kiteboard launch zone: “Hey, dude, the wind’s too light—too bad we can’t pump our kites up with helium!” Conversely, 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!”. The latter idea would indeed help counteract too much wind but is obviously untenably dangerous (putting weights on your body when you need to be able to swim and not drown in water). However, the effect on a kite’s pull of replacing air with helium is not intuitively self-evident.

So . . . let’s do the calculations and find out!

What we want is to find the minimum wind velocity for lift equilibrium of a kite inflated with air versus for a kite inflated with helium.

To do that, we first calculate the mass of the gas inside the kite. Using the Ideal Gas Law Pv=nRT (where n=m/M), we solve for the mass (m) of either helium or atmospheric air.

Adding to that the mass of the kite itself to get a total mass (L), we can then solve for the requisite wind velocity (V) using the lift equation L=1/2*d*V^2*s* CL.

Fixed inputs and constants:

• Atomic mass of gas inside the kite (M): Assumes atmospheric air is 80% nitrogen and 20% oxygen and that helium is pure helium.
• Coefficient of lift (CL):  Since lift coefficients are determined experimentally and not available for kites, I have 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 (V) to maintain lift is highly sensitive to this lift coefficient assumption; however, the relative difference between results for different inflation gasses is unaffected (i.e., using the wrong CL will not change our conclusions as to the effect of replacing air with helium).
• Universal gas constant (R)

User-defined inputs:

• Kite
  • Total pressure in the kite (P): The sum of atmospheric pressure (pre-filled value is for sea level) and kite gauge pressure. Proper gauge pressure for the kite is a matter of heated debate among kiters. However, you will note that changing this number from the pre-filled value does not have a meaningful effect on theoretical lift (though it would indeed have an important practical effect on drag).
  • Volume of air inside the kite (v): Pre-filled value reflects my best estimated measurement of the total bladder volume in my 11.5 Best Kahoona kite.
  • Mass of the uninflated kite: Pre-filled value reflects my actual scale measurement of my 11.5 Best Kahoona kite. Add this value to the mass of the gas inside the kite (m)—which we solve for with the ideal gas law—to yield the total mass to be lifted (L).
  • Wing area (s): Pre-filled value reflects an 11.5 square meter kite size.
• Conditions
  • Ambient air temperature (T): Pre-filled value reflects standard temperature, to be consistent with the assumption for air density.
  • Ambient air density (d): Pre-filled value reflects standard temperature, pressure, and humidity at sea level. This value should be set consistently with the assumptions for atmospheric pressure and ambient temperature.

The calculated result indicates that inflating the kite with helium will not make a meaningful difference in lift. In other words, replacing air with helium does not meaningfully reduce the windspeed needed to fly your kite!

In the specific example case of my 11.5 square meter kite, I would save about 4 ounces of weight by using helium. However, those 4 ounces equate to just a 4% reduction in the total weight of the inflated kite (total weight = kite fabric plus gas inside). In order to keep the ever-so-slightly-lighter, helium-filled kite aloft, I could indeed accept the windspeed being a tiny bit less . . but only a measly 0.3 miles per hour less. And that slight difference in minimum kiteable windspeed is not noticeable or meaningful.

Play around with the inputs in the interactive calculator below!

You can change anything in a yellow square: the ambient temperature, your kite characteristics (size, weight, and volume), and the pump gauge pressure. You cannot change the assumption that this occurs at sea level, or the assumed coefficient of lift.

— October 2013