Steampunk Airship Design

Given the time I've spent on a modern airship design it seems an appropriate moment to look at the commonly seen airships of steampunk.  Since the genre is largely governed by a what-might-have-been look at industrial revolution technology, particularly steam power, airships are a large factor.  The "Golden Age" of airships began in 1900 with the launch of Count von Zeppelin's LZ-1 and the beginning of the Zeppelin Airship Company.  His designs used diesel engines and aluminum for dope and structure, and neither was available in the mid 19th century.  It is reasonable to ask if 19th century practical airships would even be possible.  If so what would they look like?

The first question that must be asked is: what would lift an industrial age airship?  In the 1920's, during the time of the great airships, lift was provided primarily by hydrogen gas and later by helium.  Modern airships exclusively use helium, however the rarity and expense would not allow widespread use even now.  Additionally industrial production of helium wasn't discovered until the early 20th century.  A 19th century airship could not in any way be said to have easy access.  So a look at industrial age lifting gas options is in order.  Recall cold air has a density of 1.225 kg/m3.

• Hot Air: Frequently used in recreational balloons.
• Advantages: Cheap, safe, easy to obtain.
• Disadvantages: The biggest disadvantage is that the air has to be constantly heated, which limits range by heating fuel availability.  This essentially negates the airship's primary advantage, that it can remain aloft indefinitely.
• Hydrogen: Commonly used in early 20th century airships.  First use in an airship in 1783. (0.0898 kg/m3)
• Advantages: Industrial production involves methane and steam, both were available in the 19th century.  Lightest of all lifting gases.
• Extremely small molecules can easily leak through container.  Highly flammable.
• Methane: Sometimes used as a lifting gas if hydrogen or helium not available. (0.656 kg/m3)
• Advantages: Occurs naturally, so no production process is needed.  Can be tapped in situ if deposit is found.  Can be produced by industrial processes if no natural deposit is available.
• Disadvantages: Highly flammable.  Heaviest option.
• Coal Gas: Was also used before widespread availability of natural gas. (0.58 kg/m3)
• Advantages: Produces as a byproduct of coking processes and later developed for industrial production.  Was widely available well before methane.
• Disadvantages: Flammable, also toxic and an irritant.  Primarily composed of carbon monoxide. Heavier than hydrogen.

Since hot-air can be easily discounted as a likely lifting gas all of the likely options have one common characteristic: they are flammable.  Industrial production of hydrogen depends on the availability of methane and steam.  So if natural gas is available, then the more efficient hydrogen is an option.  Early natural gas production occured as a byproduct of oil drilling (although the earliest oil drills appear in China for the purpose of extracting natural gas).  The biggest advantage of coal gas is that by the mid-19th century nearly every sizeable town had a small coal gasification plant to provide for streetlights.  Interestingly byproducts of this process were widely used in WWI for explosives.
If a large scale airship production system were to rise based on industrial age technology hydrogen would be a likely option.  Hydrogen would be produced at, or very near, to oil fields using the natural gas that is found in oil wells.  As the infrastructure grew dedicated natural gas production might arise.  Airship production and maintenance facilities would likely also be found near to these sites, as transportation of the gas would be difficult.  The conversion of methane gas to liquid was not discovered until the 1920's, liquid hydrogen was first produced in the laboratory slightly earlier in 1898.
The question then becomes could an airbag capable of containing the hydrogen for long periods be constructed in the 19th century?  Ease of use and design demands a non-rigid fabric envelope.  The earliest balloons, designed by the Montgolfier brothers and the Roberts brothers, used silk airbags coated in a mixture of rubber soaked in turpentine.  Mass production of both silk and rubber was possible in the 19th century and may have expanded greatly if a practical airship were developed during that period.  As neither silk nor rubber is flammable this makes a suitable cover.  The mixture should also be able to contain hydrogen gas effectively even over a long period.
In order for the airship to reasonably move itself a propulsion system will be needed.  This is where difficulty begins.  Since the internal combustion engine was not available during the period in question, the much bulkier steam engine is the only option.
Before considering the limitation of steam engine power-to-weight ratio it will be beneficial to consider another drawback: it requires both fuel and water to function, instead of internal combustion engines which need only one.  However all airships also require ballast, a counter-weight to adjust the center of gravity of the vehicle and control altitude.  Early airships used water for this purpose, if steam from the engine were condensed it could be recycled back into the ballast, which reduces the weight penalty.
Going back to the power-to-weight issue, the diesel engines intended for the R101 airship produced 450 W/kg.  A steam engine produced around the same time, around 1930, the BR Class 8 Duchess produced only 11.3 W/kg.  A relatively simple analysis will tell if it is even possible to lift such an engine.  The famous cigar shape of early airships, which has a 5:1 length to diameter ratio, was experimentally determined to have the optimal drag profile.  Using this best case scenario for drag, the power to weight ratio of the engine, and the excess lift of the gas:

The majority of these terms are constants that we have already found.  We'll use the BR Class 8 mass to power ratio, k, which is overly optimistic, and assuming 70% engine power to thrust power efficiency, again optimistic.  Solving gives a relation between envelope size and velocity:
 
For a length in meters and velocity in m/s.  Thus to move a pace of just 35mph (15.65 m/s) requires an airship to be at least 100m long.  That is without any structure or payload.  An industrial age airship would need to be huge, or based on technology developed after that period.
One possibility is the gas turbine (otherwise known as a jet engine).  Possible fuels were available as were materials that would work and the idea was patented in 1791.  Since this is a what if scenario, what if an effective gas turbine was invented well before the airplane?  Electricity would be common much earlier, since the steam turbine generator is built on similar principles.  But beyond that even a simple jet engine burning kerosene is much more efficient than a steam engine or diesel engine.  So inputting a much later turboprop (a relatively simple design where a gas turbine spins a propeller, first built in 1940) and their early power to weight ratio of 43.4:

So for the same 35mph airship a length of only 22m is needed.  That tells us something else about a steampunk airship and its world: they have turboprops and thus the capability to make jet engines and electric generators.  This does not, oddly, require the ability to build an effective internal combustion engine.  It is likely the structure will be composed primarily of wood, as wood construction was used widely on airships of the early 20th century.
We'll use as a sample carriage something the approximate size and weight of a longship, which weighed 18 metric tonnes and carried 10 tons of cargo and personnel, was 25m long, 6m wide, and had a 2m interior height.  Lifting this mass requires 25,000 m3 of hydrogen, or about 100m length.  To travel at 35mph requires turboprop engines weighing 20tons and an additional 17,000 m3, or 80m length.  With additional volume for envelope mass, rigging, and control systems the envelope for the 25m long 17m wide carriage would be about 200m long 40m wide.
So for a steampunk airship we need one major technological discovery, one that would be the end of the steam age.  And still it would be sizeable vehicle, as all airships are.  As for a steam-powered airship, it is quite clear why they never got off the ground.