Hey, you actually want to see the math! Good for you. Pat yourself on the back for being an intelligent, curious person, and then go through this and make sure I didn't make any mistakes.
Weather balloon: 6ft diameter, 15 dollars Helium: tank fills approximately 500 12inch diameter balloons, 60 dollars Harness: between free and 100 dollars
The first thing I did was figure out the volume of a weather balloon:
volume of a sphere=4/3(pi*r^3)
converted the volume to liters:
v=195333.12in^3*(1 liter/61 in^3)= 3202.2 liters
Helium floats because it is lighter than the air it is surrounded by. By determining the difference in weight between the filled balloon and the air it would be displacing, you can determine the force with which it will rise. I used the Ideal Gas Law to figure out the mass: m = PVM/RT, where:
m = mass of the gas, grams P = pressure iside the balloon, atmospheres V = volume, liters M = Molecular weight of the gas (helium= 4.00, "air"=28.97) R = a constant = 0.082 T = Absolute temperature, Kelvin (273.15 + celcius temperature).
Air pressure is 1 atmosphere at sea level (P=1) and room temperature (T = 298K)
Mass of helium in weather balloon = m = 1 * 3202.2 * 4.00/0.082 x 298= 524.18 grams
Mass of air displaced = m =1 * 3202.2 * 28.97/0.082 * 298 = 3796.35 grams
Subtract the mass of the helium from the mass of the displaced air, and you get the buoyant force that will provide lift:
3272.18 grams of lift, or since 1 gram = .0022 lbs, 3272.18*.0022= 7.2 lbs.
So, one weather balloon will take approximately 7.2 lbs off of my 185 lb. weight. I figure I won't have any fun until my effective weight on earth is cut in half, so I would need 13 balloons full of helium.
If a tank can fill 500 12inch diameter balloons, that is approximately 450,000 in^3 per tank. At 195333.12in^3 a pop, that is only 2.3 balloons a tank.
Thus, I would need
13 balloons * 15 dollars= 195 dollars 6 tank rentals * 60 dollars= 360 dollars and a harness, for let's say 50 dollars.
Grand total= 605 dollars.
Now, that isn't much in the grand scheme of things, but it is more than I have to throw around. I need to cut costs down with some creative bargaining, you can read about that next week. But thanks to math, I now know what I am dealing with. As soon as I raise the money, I'm leaving the ground.