[lyner]

Cheers for the correction - I was into fatigue by the time I pressed 'POST'.

Adiabatic expansion of the air in the balloon will cause temperature drop as it rises. It's a gas law thing. PV = RT and all that. The burner offsets this, when required, of course.

I didn't mention a fan; the expansion of the fuel + air on the way in acts like a jet. I imagine that the burner is actually designed with this characteristic accentuated so that it will inflate fast, when setting the thing up on the ground.

Without any explicit temperature measurements they need to leave plenty of headroom in order to avoid damage. that must account for the 120 Celsius design limit when the melting point of nylon is a lot higher. I guess it is important to avoid hot spots!

This 25% increase in lift would apply all the way up; the details just get more complicated and depend on conditions changing on the ascent.

So; problem solved? Near enough for Jazz?

[another_someone]

I didn't mention a fan; the expansion of the fuel + air on the way in acts like a jet. I imagine that the burner is actually designed with this characteristic accentuated so that it will inflate fast, when setting the thing up on the ground.

Not disagreeing with anything here, but the point was if the expansion has already taken place near the burner, then there is little capacity for extra expansion once the exhaust gasses have entered the canopy.

Without any explicit temperature measurements they need to leave plenty of headroom in order to avoid damage. that must account for the 120 Celsius design limit when the melting point of nylon is a lot higher. I guess it is important to avoid hot spots!

It is conceivable that a small patch at the very top is more resistant to heat than the rest; but even allowing for that, if all of this is happening with wide margins applied, then one can imagine there might be some variation in temperature allowed simply because temperature is not that tightly regulated.  I am not trying to predict what effect this may have, only that the notion that the temperature is a constant 120°C is probably not totally accurate (although it may work as an approximation - I cannot say).

This 25% increase in lift would apply all the way up; the details just get more complicated and depend on conditions changing on the ascent.

So; problem solved? Near enough for Jazz?

Yes, as a rough approximation, I think it works.

[paul.fr]

What about convection? As the skin of the balloon is heated, the layer of air surrounding it is also heated, Conduction. This gives the balloon bouyancy and causes it to rise beacasue the colder air sinks forcing the warmer air to rise.

The density of the air surrounding the skin of the ballon decreases, which causes the air to rise, this then gets replaced by colder air. This gets heated, decreases its density, rises and so on and so on...

[lyner]

But if the air surrounding the envelope is warmer than it was it will produce less upthrust on the balloon. I doubt that the resulting upwards currents of the surrounding air due to convection would produce enough force to overcome this reduced upthrust.
I think that the less heat loss from the skin the better, in fact.