(This article has been reproduced with the permission of the author and the Balloon Federation of America - Gas Division)

Introduction

            In this article I will try to help new gas balloonists achieve an intuitive feeling for the physics of their sport.  I will then show the equations behind these intuitions.  Finally, I will state some rules of thumb that can be remembered when these equations are just a vague memory.

            Four main factors are instrumental in determining lift:

1)   the type of lifting gas used (e.g. anhydrous ammonia, helium, or hydrogen),

2)   the amount of lifting gas in the envelope (usually equal to the envelope’s total capacity),

3)   the outside air temperature,

4)   the ambient barometric pressure (which is directly related to altitude).

Lift at Sea Level

At sea level under Standard Temperature & Pressure conditions (STP), one cubic meter of air weighs 2.702 pounds.  Also at STP, one cubic meter of helium weighs 0.3729 pounds.  Subtracting these two numbers gives the gross lift of a one cubic meter volume helium balloon.  This is because when the helium displaces the air the balloon gets lighter by the difference in these weights.

            Thus, this balloon has a gross lift of 2.329 pounds  (that’s 2.702 – 0.3729 pounds).  By multiplying 2.329 times the volume of helium in the balloon, the gross lift, under STP, is determined.

I will abbreviate this as:

Gross Lift (Helium) = Volume (cubic meters)* 2.329           [Equation #1]

 Likewise, hydrogen weighs 0.189 pounds per cubic meter and ammonia weighs 1.583 pounds per cubic meter.  Therefore to calculate gross lift for hydrogen use 2.513 to replace 2.329; for anhydrous ammonia use 1.119.  As compared to helium, ammonia has about 50% less gross lift and hydrogen has 8% more gross lift.

Lift at Altitude

As altitude increases, it is generally true that temperature, atmospheric pressure and gross lift all decrease.  This should not surprise any balloonist, but the next statement might.  Gross lift DECREASES as pressure decreases but it INCREASES as temperature decreases.  Thus, as a gas balloon rises in the atmosphere, the decreasing pressure and temperature oppose each other.  The decreasing temperature increases lift while the decreasing pressure decreases lift.  Atmospheric pressure changes are more significant than temperature changes.  Overall, lift decreases as altitude increases.

To calculate the effect of changing pressure and temperature it is only necessary to multiply the sea level lift by the ratio of pressures and temperatures.  For a non-standard ambient pressure, multiply the lift at STP either by: (pressure(in. Hg)/29.92). or (pressure(mB)/1013.25).  Use the first factor when expressing pressure in inches of Mercury and use the second for pressure in millibar.

The factor for temperature is a ratio of absolute temperatures, expressed in either degrees Kelvin or Rankine This is not as difficult as it sounds.  To get temperature in degrees Rankine, simply add 459 to the normal Fahrenheit temperature.  For a new temperature, multiply the lift at STP by the factor:

(59ºF+459)/(new temperature + 459).  When using temperature in degrees Centigrade add 273 to convert to absolute temperature (i.e. Kelvin).  This is: (15 ºC + 273)/(new temperature + 273).

So the equation for lift at altitude is our original Equation #1 times these two new factors

Note that in this equation Temperature (T) is in the denominator while Pressure (P) is in the numerator.  This causes T & P to have opposing effects on the calculated lift as discussed previously.

In the above example, the factor for non-standard temperature is greater than 1 while the factor for non-standard pressure is less than 1.  This means that the decrease in temperature by itself would increase the available lift while the decrease in pressure by itself would decrease lift.  Since the available lift does decrease, we see again that the pressure change has a bigger effect than the temperature change.

“Rules” to Remember

The following approximations generally apply to a balloon below 18,000 MSL.

1) Barometric pressure will decrease approximately 1 inch for every 1,000 feet of ascent.

2) Atmospheric temperature will decrease approximately 3.3°F for every 1,000 feet of ascent.

3) For a 1,000 cubic meter balloon at its pressure altitude, an ambient pressure decrease of 1 inch of mercury (Hg) causes a decrease in gross lift of about 80 pounds.

4) For a 1,000 cubic meter balloon at its pressure altitude, an ambient & gas temperature decrease of 3.3 °F causes a lift increase of about 16 pounds.

5) For a 1,000 cubic meter balloon at its pressure altitude, a discharge of about 64 pounds of ballast will result in approximately a 1,000 foot increase in altitude.

Note that the discharged 64 pounds equals the 80 pounds (step 3) minus the 16 pounds (step 4).

Additional factors that affect lift

1) A balloon flying below its pressure altitude (i.e. a flaccid balloon) will respond differently

2) When the lifting gas inside the balloon is warmer (i. e. super heating) than the ambient air additional lift is generated.  The reverse happens when the lifting gas is colder than the ambient air.

3) Non-standard atmospheric conditions such as inversions affect a balloon’s stability.

4) The atmospheric humidity has a small effect on lift with more humidity resulting in slightly less lift.

5) The purity of the lifting gas directly affects lift.  Most commercially produced gas is

assumed to be better than 99% pure but purity can be reduced as a result of improper filling technique.

References:

1) Technical Manual on Aerostatics TM 1-325 US War Department 1940

2) A Short Course on the Theory and Operation of the Free Balloon, C.H. Roth, Goodyear Tire & Rubber Flying School, 1917