Disgusted from Cornwall. said:
We've got a 50m shaft to bolt climb and I was thinking about a go pro on a helium balloon. It's the sort of thing that if it goes, it will be utterly incredible.
I've just done some maths, assuming 15 degrees Celcius (density air 1.2250 g/l, helium 0.1693 g/l) and using the lightest GoPro Hero 4 Session (74g) - many GoPros are quite a bit heavier.
You need approximately 70l of helium, not accounting for the weight of the balloon itself or guide line. That is a sphere 50cm across.
I have tried to look up party balloon data; this study
http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/36.%20PartyBalloons.pdf of a 25cm x 20cm balloon (more like what we usually see in the UK, I think) had a balloon mass of 1.3g and a volume of 5.5l. This gives each balloon a lifting capacity of 4.5g (accounting for the balloon mass), and so we need 17 balloons.
I can't find line densities for skinny cords/fishing lines, so I am going with 1.15 g/cm^3 for nylon and assuming a 0.5mm diameter cord, giving ~0.23 g/m. With a 60m guideline, I get ~13.5 g. Total mass is then ~88g (GoPro and cord).
I've just discovered there is a Hero Session 5 which is 73g and I need to include the mass of the microSD card which is about 0.5g. Conveniently these errors cancel each other out, rounding up
With the same balloons as earlier, we now need 20 balloons. To account for incomplete fill, temperature changes, miscalculations or estimates and (potentially significantly) draughts, I would have at least 50% extra balloons if not double.
That's a lot of balloons! Try and do it with an original GoPro (~150g?) and you will need yet more balloons...