Maximum altitude of balloons / Physics of ballooning

I am an engineer and am interested in the physics of balloons. I am trying to derive an equation which would predict the maximum altitude reached by a balloon. The physics involved is quite simple. Buoyancy is maximum at sea-level. It decreases as atmospheric density decreases with altitude, so I solved the relevant differential equation and obtained a formula for the maximum altitude. But I am sure that someone has already done this. I want to check my work against that work. One result I get is that the bigger the balloon's volume, the greater the altitude it can reach. Is this correct?

Hello Sundar:

You are probably correct, its all been worked out. Having flown about 5000+ hours in U.S. Navy Blimps, I am just a little familiar with the problems you are trying to solve. I don't think there is any one formula as there are so many variables involved such as type of lifting gas, temperature etc. however: The is a great discussion group on all phases of LTA and I am quite certain one it's members can help you. I will try and attach the instructions on how to sign up. If I can't I will forward them on a separate e-mail. Basically it is called the 'Airship-List'. There are also many publications on the subject. Good Luck, Ford U. Ross, NAA, LTASOC, LTA Institute, ABAC, Airships LTD, ZCC/ AAMS, NLHS etc.

I'm not even close to being an expert on the issue but have been involved with hot air balloons for several years and I know that the colder the air is outside the envelope the longer the balloon can fly on the fuel it has. I would then assume that it is more bouyant at cooler temps? Would a larger balloon (with a larger volume of heated air) fly higher faster? But a smaller envelope could probably still fly as high as long as the fuel held out whereas a larger volume balloon can carry more fuel and thus fly longer (or higher). If bouyancy decreases with altitude does it actually cancel out the relationship between hot air and cold air or would that stay constant. If I'm at 20,000 feet above sea level with an air temp of 30 degrees, or whatever it might be, and the air inside the envelope is 200 degrees would it still be as bouyant at 40,000 feet with an air temp of -10 degrees? Most balloons set their gauges to AGL (above ground level) so is a balloon on the beach in Malibu (on the ground) more bouyant than a balloon on the ground in Jackson WY, the air temp in Ca is probably warmer than in WY so wouldn't the balloon in Wyoming be more bouyant? Interesting question I'll have to ask some of my balloon pilot friends?