Altitude, superpressure and Volume Calculations

It is important to know the volume of a balloon in order to run the calculations in the spreadsheet float1g. That spreadsheet does all the math for you and you need to know the payload weight, the balloon weight, the free lift and the volume of the balloon.

The weight of the balloon and the payload are pretty simple, just weigh them with the scale you bought for free lift. The volume of the balloon is another. It can be simply assumed to be what others have found and things will be close enough. The chinese balloons are .17 cubic meters each and the SBS-13 according the SBS is .5 cubic meters. You can just use those numbers.

For the chinese balloons, you might want to measure things as you stretch the balloon. That way you can be sure you know what is going on. The measurements can be simple. Tape a metric stick to the floor, put a box on one end at zero and tape it to the floor to stay put. Place the balloon next to the box, use another box to hold the sides agains the cardboard on both sides and then read the meter stick. Do this for the distance across the seam and across the faces. A good approximation is to us the formula for an oblate spheroid.

Vol= 4Pi*a^2*b

Where a is the radius between the seams and b is the radius across the faces.

There is a formula for mylar balloons that is an interesting formula and the math was quite a task to put together. It has the restriction that the film is inelastic which ours is not so it will not work.

If you really want to get into the weeds and verify how good the formula is, inflate a balloon to the pressure you will tolerate. Take a photo so the seam forms a straight line. Print the photo as large as you can. Make sure you measure the balloon. Draw a line across the seam, find the center, divide the line into convient segments and, knowing the scale, find the dimensions of each line. Since the balloon has radial symmetry, calculate the volume of your annular rings, add them up and compare it to the volume of the oblate spheroid. I think they will be pretty close.

The math used to calculate the float altitude and superpressure is in the spreadsheet float1g. The complete expaination can be found at https://ukhas.org.uk/projects:splat. It includes a massive table of atmospheric parameters for a standard atmosphere. We never have a standard atmosphere but it is the best we can do and does a very good job.

Published by WB6TOU

Retired chemical engineer

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