does anyone know the formula for expansion and lift at different altitudes for hydrogen helium filled balloons

Question

i am launching a few baloons to collect insects at different altitudes and need to know how much gas i need to start with so that they will popp at the correct altitude

Answer 1

Questions like this one display what science is all about. Thank you so much for asking this question. Although explaining something on paper and doing it out in the field are two different things but, let's see how close can we get:

First of all, decide what gas you're gonna use. Hydrogen or Helium? Hydrogen can go higher than Helium because it is lighter than helium. So, if you want to collect insects from outer space, hydrogen is your choice. (lol)

Helium is commonly used these days because hydrogen although lighter than helium, lights pretty easily... in other words, hydrogen is highly inflammable.

Now, how much pressure would the balloon be able to bear depends on the "Bulk modulus of elasticity" of its rubber.

Here is how you should go with your experiment:

1- Take some identical balloons, a helium pump and choose a suitable location.

2- Take a balloon and find out its maximum volume by inflating it untill it explodes. Note the maximum volume of Helium it can carry. Please realise that the "maximum volume" would be different for different heights because atmosphereic pressure decreases as the balloon moves up.

3- Now, take readings of pressure at the levels of height where you're gonna conduct your experiment. I mean, at ground level, the pressure is 101300 Pa or 0.76 m of Mercury.

As we move up, the pressure decreases. In broad terms, it becomes half of its orignal value at 6 kms of height. You'll have to observe atmospheric pressure of the range of heights where you are going to conduct your atmosphere.

Tip: If you don't want to record pressures at different heights, use this link- http://www.csgnetwork.com/pressurealtcalc.html

4- Now, determine the ground-level pressure of the place where you're conducting this experiment. It is usually 0.76m of Hg.

5- Multiply the ground-level atmospheric pressure with the "maximum volume" at ground level obtained in Step 2 above. The number you get now as the product is a CONSTANT. No matter what the values of pressure and volume are, their product will always be this number.

6- Now, take a height (say 5 meters). As you already have recorded the atmospheric pressure at 5 meters in step 3, all you need is to divide the constant obtained in step 5 by the pressure at 5 m.

7- By dividing, what you get is the MAXIMUM volume that can be carried by the balloon at that height i.e. 5 m.

8- Repeat the experiment for different heights and atmospheric pressures.

Good Luck!