What about a hot air blimp with the membrane being quilted, and filled with aerogel. The super light, super insulating aerogel combined with the large volume to surface ratio would make it pretty efficient to keep hot.
https://en.m.wikipedia.org/wiki/Thermal_airship
With aerogel insulation, the hot air plus steam idea seems quite plausible. Claude s3.6 says:
With modern aerogel insulation (U-value ~0.015 W/m²K):
For 10m radius: Heat loss = 0.015 × 1,257 × (100-15) = 1,602 W ≈ 5,500 BTU/hr
For 20m radius: Heat loss = 0.015 × 5,027 × (100-15) = 6,409 W ≈ 22,000 BTU/hr
Converting to fuel consumption (using propane as example):
Propane contains ~91,500 BTU/gallon
Assuming 80% heating efficiency:
10m radius: ~0.08 gallons/hour 20m radius: ~0.30 gallons/hour
The efficiency improves dramatically with size due to the cubic/square relationship. Each doubling of radius:
Increases volume (and lift) by 8×
Increases surface area (and heat loss) by 4×
Improves fuel efficiency per kg of lift by ~2×
What about a hot air blimp with the membrane being quilted, and filled with aerogel. The super light, super insulating aerogel combined with the large volume to surface ratio would make it pretty efficient to keep hot.
https://en.m.wikipedia.org/wiki/Thermal_airship
With aerogel insulation, the hot air plus steam idea seems quite plausible. Claude s3.6 says:
With modern aerogel insulation (U-value ~0.015 W/m²K):
For 10m radius: Heat loss = 0.015 × 1,257 × (100-15) = 1,602 W ≈ 5,500 BTU/hr
For 20m radius: Heat loss = 0.015 × 5,027 × (100-15) = 6,409 W ≈ 22,000 BTU/hr
Converting to fuel consumption (using propane as example):
Propane contains ~91,500 BTU/gallon
Assuming 80% heating efficiency:
10m radius: ~0.08 gallons/hour 20m radius: ~0.30 gallons/hour
The efficiency improves dramatically with size due to the cubic/square relationship. Each doubling of radius:
Increases volume (and lift) by 8×
Increases surface area (and heat loss) by 4×
Improves fuel efficiency per kg of lift by ~2×