You do the math

Now that the balloon is on order, it’s time to do some calculations. We’ll start with the easy stuff.

ItSONY DSC‘s recommended that the balloon be inflated with helium to a diameter of 6-8 feet. How much helium will be needed? Simple geometry says that the volume will be 4/3 pi r^2. For our first calculation we’ll pick the recommendation midpoint, 3.5 foot radius. That produces a needed volume of 180 cubic feet of helium. My source says that a size K tank provides 220 cubic feet, so that’s what we want to order. But will it be enough to fill the balloon to 8 feet? No, that would require 268 cubic feet. So how big can we make the balloon with 220 cubic feet of helium? A little under 7.5 feet in diameter.
Now it might be interesting to calculate lift. The formulae here are more complicated and I won’t try to present them. Since there are still several variables (amount of helium, payload weight, ascent rate being among the most important) I created a spreadsheet which shows a bunch of possibilities.
A 7.5 foot diameter balloon provides 14.4 pounds of total lift
A 6 foot diameter balloon provides about half that much lift, 7.4 pounds
A 5 foot diameter balloon provides 4.3 pounds of lift
And so on.
Our target is to have the payload weigh no more than 4 pounds.  Of course payload is only part of the total weight. Other contributors include: balloon (1200 grams), rigging, radar reflector, parachute, payload including case.
Let’s start with the rough estimate that total weight will be in the 5 pound range. The standard advice is to provide about one pound more lift, so six pounds of lift. My spreadsheet says that we need a starting balloon diameter of about 5.5-5.6 feet to provide this lift. Fortunately there’s a much easier way to figure lift than measuring balloon circumference: pre-weigh water in a gallon bottle to match the desired lift. Then attach the bottle to the balloon and when the pair are neutrally buoyant you are good to go.
The next thing to consider is why the standard advice on balloon lift is right. What if we choose to add a bit more helium, or not put so much in? There are a couple of things to consider here and I’ll provide the results in a subsequent post but for now the qualitative considerations are:
  • More lift means a faster ascent, a shorter flight, and a lower bursting altitude
  • Less lift means a slower ascent, longer flight, and higher bursting altitude

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