rocket stoves and hot air balloons

I was watching a you tube video on the first hot air balloons on nature's lost vault. A thought came while watching it has anybody tried to use a rocket stove to propel a hot air balloon?

Hot air balloons use liquid propane to power them.

I feel a rocket stove would require too much fuel and would weight down the balloon.

Hey you are not the only person to have this thought:

https://permies.com/t/39501/Rocket-Stove-Powered-Hot-Air

So the Montgolfier brothers used wood to heat their balloons, and had issues in an early flight with sparks threatening to burn the balloon.

A J-tube rocket of lightweight insulating material could provide more heat for the fuel used, and with full combustion may give less danger of sparks. A complication would be inflating the balloon to start with, as the rocket would not be able to blow hot air into the flattened balloon; not sure how modern balloonists do this, with just a fan or with the propane flame directed sideways...

One of the main challenges would probably be the low energy density, as Anne was commenting. The following graph shows that quite obviously.

For the same energy you need almost 3 times the mass of wood compared to natural gas. On the other hand you're not bringing a pressurized container...

I suppose it depends on the kind of wood fuel, too. Would charcoal be more heat-producing for its weight?

It looks like charcoal is about twice as energy dense as wood, so that would be a step in the right direction - Wikipedia gives a value of 30 MJ/kg for charcoal's specific energy content.