h a l f b a k e r y
Assume a hemispherical cow.
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I've never seen a blimp or dirigible that used the waste heat of the thrust engines. Water-cooled aircraft engines aren't too hard to come by, and it should be a fairly simple matter of placing the radiator inside the lift gas bags.
As heat inside the gas bag goes up, either pressure or volume must
increase; the volume will increase to the limit of the lift ballonet's elasticity, then pressure increases until a failsafe switch operates a compressor to scavenge excess lifting gas from the ballonet to a high-pressure cylinder for later use. In this way, the lifting gas' density is minimized, and its lift thus maximized, making the best possible use of expensive helium (or some other gas that expands a suitable amount when heated).
The temperature increase can't be all that great, and will have an absolute upper limit equal to the maximum operating temperature of the engine. If material tolerances will allow it, further gains can be had by also running the exhaust through an air-to-air heat exchanger inside the ballonets. At this point we're talking about pretty serious temperature increases, raising the temperature inside the ballonets to something like what is experienced inside a hot air balloon. The radiator will continue to function well if the system is engineered to appropriate ratios of heat transfer through the skin of the gas bag yielding an appropriate ambient operating temperature for the radiator. If the temperature should rise too high, then an external radiator is switched into the loop and heating is provided by the exhaust only. If a hot air balloon can work as well as it does using just hot air, imagine then the increase in performance when expanding an LTA gas such as helium or a nonflammable helium-hydrogen mix.
In a funny way, this brings the engine into the job of directly providing lift, and obviates my blue-sky fantasy of solar-electric powered dirigibles.
||I flubbed the category earlier, sorry.
||A typical hot-air balloon burner is rated at probably 20 million BTU - what sort of power engine were you thinking of fitting?
||Dunno. Too many variables are in play: the length and diameter of the dirigible haven't been specified, nor has desired cruising speed. Hindenburg, at over 800' l x 135' d. was served by 4800hp worth of diesels, and did 80+ mph. In my opinion, structure could weigh a lot less with materials advances; that factor combined with heated lifting gas could allow a smaller envelope to achieve the same lift. It's conceivable that a vehicle with Hindenburg's capacity could be constructed of similar length but considerably less diameter, maybe only 100'. This significant reduction of frontal area would permit a much cleaner airflow around the body, and raise the airspeed considerably for the same power rating, or allow similar speeds with much smaller engines, maybe on the order of 3000hp. I'm a big fan of multiple redundancy, so I'd spread that out over at least six engines. Zoche has models in the works, but they're air-cooled. I have no idea what kind of heat these things shed in use.