Math/ Science of Hot air ballooning?

Hi, I was wondering if any of you could help me figure out the math/ science behind hot air balloons. Specifically: 1) How do you figure out when to start your descent (and if you use fancy electronics for this, is there a way to do it without technology?) 2) How do you know how high you went? (again, any non-technology based ways would be helpful... especially any related to trigonometry ratios)

Thanks for any help you're willing to give me!!!

Thanks,

In the US this is true, in the UK it is perfectly legal to fly in uncontrolled airspace without any instruments and I often do! It's great fun to fly using only natural senses without all the crap of an altimeter, vario, temp gauge, gps etc.

To take off I keep the burner going while jumping up and down in the basket, you can feel the moment when it's becoming buoyant. Then short steady burns until you achieve lift off.

To fly level you simply watch the horizon - if you look directly down you can't be sure if it's the ground rising because you're flying over a hill or whether you're descending.

Altitude may be approximated by how much noise from the ground reaches you! You can't hear the dogs barking at 1500'. At around 1000' the ground looks very much looks like the 50000 scale map I fly on.

Envelope temperature is a smell thing! I get a distinctive smell from my envelope the moment it gets toward 120C! And it's not just my envelope, I've been able to smell all envelopes I've flown. In truth it is probably more the composition of air at the mouth of the envelope rather than the fabric which produces the smell.

If while descending the balloon starts to rotate I'm dropping in excess of 500' per minute.

I think that just about covers all the senses - feel, sight, hearing,