Hydrogen has to be made. There are three probable methods: electrolysis of water, the action of acid on metal, and by forcing steam over red hot iron.
Electrolysis of water has a specific energy per m^3 of hydrogen produced of 4.5 to 5.45 kWh [LookChem], which suggests that electrolysis is not the way to go.
The Union Balloon Corp during the American Civil War [Wiki: Union Balloon Corp] used a pair of wagon mounted sulfuric acid- iron filings hydrogen generators per observation balloon. The reaction formula Fe + H2SO4 ‹=› FeSo4 + H2 indicates that one mole of iron will produce one mole of hydrogen gas. At STP (standard temperature and pressure) one mole of gas occupies 22.4 liters. Therefore, to produce one m^3 of hydrogen, we need (1000/22.4=) 44.64 moles of iron. Iron is 55.85 grams per mole, so one m^3 of hydrogen gas at STP needs the reaction of 2.493 kg (44.64 x 55.85) of iron filings (and 4.375 kg pure acid). Each of the civil war hydrogen generators could produce about 60 m^3 per hour (2166 ft^3) [EB9th: Vol.1 p200]
The steam over red-hot-iron method has the reaction equation 3Fe + 4H20 ‹=› Fe3O4 + 4H2. Three moles of iron produces 4 moles of hydrogen, or 2.493 x 0.75 = 1.870 kg of iron per m^3 of hydrogen gas. Normally the iron has to be recharged after use, but there is a hydrogen generator that can reuse the iron. The Lane producers used after 1909 could recycle the iron. They were available in models with production rates of 14 to 284 m^3 (500 to 10,000 ft^3) per hour [Lane].
Using the largest Lane producer, the hydrogen vented after the crossing the Atlantic to allow landing (up to 5,410 m^3), would take about 19 hours to replace. However, that size plant is likely to be exceedingly expensive. Something able to replenish the lost hydrogen in about 48 hours is more likely
The lifting cells
There are several options for gas bag construction, but I'll only consider the two actually used on rigid airships before the advent of modern polymers. There is the tried and proven "gold beater's skin," and then there is elastomer coated fabric-basically rubber, sometimes mixed with gelatin, spread over cotton or silk (Although it wasn't unknown for people to use a combination of goldbeater's skin and rubber.).
Gold beater's skin is well described in the article by Chollet, and after reading that article, you'll understand why it isn't still used. The process is drawn out, and labor intensive. You get two skins per animal, and an airship such as the ZR-1 Shenandoah (gas capacity: 60,915m^3) needs about 750,000 skins [Wiki: Goldbeater's skin; Steadman]-Remember, the Sao Martinho has a gas capacity of 47,092 m^3, so it would need something of the order of five hundred and eighty thousand skins (And only you get two skins per fully grown cow).
An acceptable alternative is to dissolve the raw rubber and mix it with gelatin, and spread it on cotton fabric. This was the material used for the gas bags on the Hindenburg and many other airships. The weight of this material was about 180 gsm, compared with a standard goldbeater's skin gas cell, which weighed about 145 gsm. Simply spreading rubber over fabric produced gas tight cells that weighed 240 gsm [Cooper].
Gold beater's skin is considered "tight". That means the diffusion of hydrogen through the layers is slow-only a few liters per m^2 per 24 hours. On the Sao Martinho, with gas bag surface area of 19,116 m^2, that's a loss of 38-134 kg of lift per day. The latex coated cotton is good for less than 9 liters per m^2 per 24 hours [Woodhouse, p.211], or no more than 172 kg per day. Generally, lift freed by burning fuel will be enough to counter this loss on a voyage, but hydrogen will need to be replenished on a regular basis.
Through his relationship with the Duke of Braganza, it is hoped the Duke of Medina Sidonia can obtain natural rubber from the Amazon for his airship.
Fuel
What fuel is to be used? Well, the final design for the Sao Martinho has assumed we'd use hot-bulb engines that can burn nearly any flammable liquid. However, no matter what propulsion system is used, the fuel will be in liquid form. This is a simple matter of energy density and ease of handling.
The steam engine variant is the only propulsion system that might consider solid fuel, but that involves using a much less efficient boiler system-one that needs constant stoking, and clearing away of the ashes. There are also problems with the fuel. Solid fuel has to be manually moved, or you use heavy automated systems. It is also heavier for its energy content. Coal is about half the energy per pound of petrol, and as for wood, that's about a third the energy per pound. A cord of wood (3.6 m^3) has about as much energy as a 450 kg of petrol, and it weighs about 1360kg. Using solid fuel doubles or triples the mass of fuel required for a steam propulsion system. Worse yet, moving the mass of fuel around the airship will cause significant trim management problems.
One thing to remember with liquid fuels aboard an airship is that, as the airship climbs, the ambient air temperature drops. That means fuel will thicken. Air temperature hits freezing at about 8,000ft. Heaters, or something may have to be added to allow the fuel to flow if the airship is to regularly fly at higher altitudes.
Engines:
We have stated that the Sao Martinho will use hot-bulb engines. These are heavy and not very economical compared with petrol or diesel engines. However, they are being made down-time in the desired power range (at least 40 HP) as early as 1634 ("The Boat" By Kerryn Offord, GG#30).
We could use petrol spark-ignition or diesel engines, but the Spanish are unlikely to be able to purchase up-time built engines. There are currently no new diesel engines being built, which leaves new build petrol fueled spark-ignition engines. The best bet would be new-build variations on the radial engines in "The Spark of Inspiration" by Gorg Huff and Paula Goodlett (GG#13), or "The Boat" by Kerryn Offord (GG#30). These are nominally 125 hp engines, and they will tend to be less economical than the water cooled inline Maybach engines we've been basing our petrol engine calculations on. However, they have significantly better power to weight ratios than the Hot-bulb engines. Two such engines could easily provide all the propulsion the Sao Martinho needs, releasing the weight of 4 gondolas and engines (1,510 kg) and removing the drag of four gondolas-something to look forward to when the Hot-bulb engines are upgraded to petrol spark-ignition engines sometime in the future.
Operating Ceiling
When you research airships, you might see a value called "static ceiling". This is the altitude at which an airship's gas capacity is at 100%, and it is only lifting the deadweight.
For the Sao Martinho, that happens where air density is 60% of sea level. From tables we can find that this happens at about 14,000 ft. Note that this does not mean that the Sao Martinho can actually climb to 14,000 ft in normal operations (because there should always be some disposable load on board).
Something else to consider is the reduction in engine efficiency when the air density reduces with altitude. For example, when air density is at 50% of sea level density, engine performance is also down 50%, so to maintain the same delivered HP you had at sea level will take something like twice the fuel.
The normal operating altitude of the Sao Martinho will be about in the range 100-200 m, as this offers significant fuel economies over higher altitudes. The Hindenburg was usually operated at about 650 ft (198.25 m), so "we are not alone". However, the Sao Martinho has an "altitude and air temperature" allowance of 10% of gross lift. That means the Sao Martinho can fly, fully laden, in conditions at sea level of 15 degrees C, 76mmHg, to an altitude with an air density of 0.90-about 915 m (3,000 ft)-without having to vent hydrogen. For every hour of flight at cruise power the Sao Martinho will gain about 40 m^3 of buoyancy due to fuel being consumed, and if nothing is done to prevent it, she will naturally gain altitude. At about 915 m the gas bags will reach 100% inflation, and as more fuel is burned, the Sao Martinho will want to climb higher. To prevent the gas bags rupturing, safety valves will automatically vent hydrogen. At the static ceiling, gas volume will be 100%, but we will have vented almost 40% of the hydrogen we started with.
Ground operations
You don't absolutely HAVE to have a hangar to store an ai
rship. However, it is nice to have somewhere safe to put your airship, especially in bad weather. This is especially so for timber-framed rigid airships. Wood is naturally hydroscopic (will absorb water). Irrespective of what water might do to the glue holding the airship together, there is the added weight of absorbed water. That is one reason why all wood surfaces have to be waterproofed with paint or varnish. However, paint scratches-enough said.
For short periods (days), there is no real problem in leaving an airship outdoors attached to a mooring mast. Just as long as it is a low one, as the airship virtually needs to be flown (trim etc maintained) at all times while moored to a high mast [Brooks, p.146]. Certainly, on the South America run, the Zeppelins didn't have a hangar in South America until the Brazilians built one at Rio de Janeiro in late 1935, and they never built one at the Recife stopover, where they just used a low mooring mast.
However, you do HAVE to have a hangar to build your airship. These are enormous, and thus expensive structures, as witnessed by the willingness of the Germans to limit the size of the Graf Zeppelin (LZ-127) to the dimensions of the available hangar, rather than build a larger hangar. Even though they knew the resulting airship would be a sub-optimal design.
The Sao Martinho is based on the maximum diameter of the Schutte-Lanz S.L.20 class, and they were built in hangars between 26 m – 38 m wide, and 25 m – 35 m high, and up to 240 m long. The larger hangar was in Berlin (was 38 m wide, 35 m high, and 240 m long), and it took 6 months during war-time to build.
It'd be a tight fit putting a 22.96 m diameter airship into something 26 m wide and 25 m high, but a 30 m by 30m opening might be a more comfortable fit. It also has to be over 170 m long. To give an example of how big this is, St. Paul's Cathedral in London has a nave 37m wide and 30m high, and the cathedral is about 175 m long. The airship hangar for the Sao Martinho is about the volume of the main building (excluding the dome and the transepts).
The United States built two, mostly timber construction, airship hangars at Tustin, in California [RDF Consulting]. Each hangar was about twice as long and three times as wide as what is predicted necessary for the Sao Martinho and took about six months to build under wartime urgency. Each hangar required about three million board feet of wood, of which 750,000 board feet was needed for the 51 roof arches, 79 tons of bolts and washers, and 30 tons of ring connectors. It sounds a lot, but each hangar only used about 33 tons of structural steel, whereas a regular design would have required 4,000 tons of structural steel. The airship base, with two hangars and other buildings, cost about US$10 million Y1943 dollars, that's about US$100 million in Y2000, suggesting a price for the Sao Martinho, purely on a per square meter basis, of around 80,000 thaler, which is probably an under estimate of what the hangar might cost down-time. And yes, it could be possible to build a hangar for the Sao Martinho down-time in six months, although a year to eighteen months would be a more reasonable schedule.
Ground handling is where a lot of accidents happen, and trying to thread 170 m of airship through a small opening-into or out of the hangar-is "difficult". The Germans "tied" their airships to ground vehicles on rails to run them in and out of their hangars. This is what I'd like to see for the Sao Martinho.
Outside the hangar, ground handling is still mostly done by humans. The purpose of a ground party is partly to move the airship, and partly to provide ballast to hold down a buoyant airship. With all disposable load removed the Sao Martinho has excess buoyancy of forty percent of gross lift, or 20,532 kg. At 75 kg per man, that is a minimum of 274 men.
Costs:
There are two basic airship designs. Either you have a cylinder with curves at each end, or you have a modified "teardrop" shape. The cylinder design has the advantage that most of your ring frames are exactly the same size and shape. This provides savings in time and money, as you can use jigs. The down-side is that the aerodynamics of the cylinder design is less than optimal.
The teardrop design has a better drag coefficient (being a more aerodynamic design). However, this is at the cost of ease of manufacture. In the teardrop design, nearly every ring frame is a different size, so you can't just use a standard jig to build every ring frame. That adds costs in construction, but the lower drag coefficient means that for a given size airship (gas capacity) you need less power for a given cruising speed, which means you use less fuel. Meaning you can carry more payload. For these reasons the Sao Martinho will be a modified teardrop design.
Brooks [p.199] suggests that the late WW1 airships needed something of the order of 800,000 – 1,000,000 hours of "direct shop-labor" to build the first airship of a new type, while the post WW1 airships took two million, or three, or even more direct shop-labor hours to build. The Sao Martinho is probably big enough to require at least one million hours of shop-labor. That equates to something like 100,000 man days. At the standard rate for skilled tradesmen (carpenters and blacksmiths) of 0.3 thaler per day (USE$30), that is 30,000 thaler. We know the Vasa (lost 1628) cost about 40,000 thaler [wiki: Vasa], but that was for a completed warship. The Sao Martinho's labor cost alone is three-quarters what the completed Vasa cost. As you can see, airships are going to be very expensive down-time.
As we can't find period prices for most of the components, any pricing beyond the base labor content would be just be guessing. However, we know labor is usually a fraction of any construction cost, so the materials aren't going to be cheap.
There is some good news. From the German experience, it has been shown that airship construction follows the "learning effect" [Brooks, p.199]. For every doubling of production of a design, man hours required drops by twenty-percent.
Cost in operations. These include fuel to propel the Sao Martinho, and to produce the hydrogen gas, the labor cost of flight and ground crews, depreciation to reflect repairs and maintenance, and then there are "opportunity costs". For now, we'll just look at the cost of fuel and hydrogen generation.
Fuel for each inbound or outbound flight is budgeted at 5,897 kg (~6,700 liters). That's about 1,770 US gallons, and if we cost it as Greenland Whale oil (0.35 thalers/gal) we get close enough to 620 thaler (USE$62,000) each way.
Hydrogen, made by blowing steam on to red hot iron filings (See Appendix 5 for calculations) to replace the vented hydrogen (5,897kg fuel at 1.09 kg/m^3 = 5,410 m^3), will need about two thaler worth of firewood to generate the steam. Keeping the iron filings red hot will use a bit more fuel, but probably not enough to bring the cost of hydrogen generation much above two thaler (about five cents per cubic meter of hydrogen). However, at 1.870 kg/ m^3 of iron filings, that's 10,117 kg of iron filings. Maybe they can be reused, but that's about 602 thaler (USE$50,500) worth of iron, based on period wholesale prices (5.95 thaler/ 100 kg of Swedish bar iron). There are also manpower costs to consider, even if we have a good Lane Hydrogen producer, and it only takes 48 hours, that's likely to add another 20 thaler (USE$2,000) per fill. For a rough estimate of 625 thaler (USE$52,700) per fill.
Then we have to pay for crew and maintenance personnel. But how much do you pay an airship crewman? We have nothing to compare the skill sets with, so any number would just be guessing. However, twenty-five men at an average of, say, 0.4 thaler (USE$40) a day (About 150 thaler pa) is a total of about 3,750 thaler pa. If they make one return flight per month, that's 156.25 thaler per crossing. On any trip carrying first-class passengers, there will be a need for passenger service crew. They'll add a further 25 thaler per trip. Then there are airship and hangar maintenance personnel. We don't really know how many are needed, nor how much they should be paid.
We can make a reasonable guess at the cost of the massive ground crew needed for launching and landing the airship. The job is mostly low skill. A handful of men who know what to do can control several hundred unskilled laborers. Still, ground parties will cost around 50 thaler any time you want to "ground handle" the airship (Assuming standard European pay rates), or 100 thaler for each trip (launch and landing parties).
A rough guess w
ould suggest, ignoring wages of the maintenance staff, the direct labor and consumables cost of a one-way crossing of the Atlantic would be about 1,526.25 thaler (USE$152,625) per trip.
Conclusion
With an allowance per passenger of 150 kg [Crocco], the Sao could carry thirty-three passengers. Make eight of those passenger service crew, and we have space for maybe twenty-five paying customers. At 100 thaler per head (about a year's wages for a tradesman, or a month's pay for a military captain/ lieutenant-colonel) there is a gross income per flight of 2,500 thaler. With one return trip per month, that is a revenue stream of 60,000 thaler, which we hope would cover expenses.
Alternatively, the Sao Martinho can carry high value freight (like the gold, silver, pearls, and jewels of the fabled treasure fleets). The 1628 treasure fleet captured by Piet Heyn carried about 80,300 kg of silver and 30 kg of gold. The Sao Martinho might not be able to carry that all at once, but she could carry it all if she could manage 17 return trips a year (About one return trip every 21 days.). The savings in ship days, provisions, and wages for ships to carry the treasure across the Atlantic should easily justify using an airship for the task. It'll also provide a more regular revenue stream, which will make balancing the books easier, and keep the bankers happier.
This analysis suggests that a rigid airship large enough to service the Cadiz-Havana trade could plausibly, and profitably, be built by the Spanish using down-time resources. It won't be easy, and it will take time. A suitable hangar needs to be built. The plywood framing has to be developed by trial and error (before it goes into the first airship). Gas bags need to be made, engines need to be produced, and there is a need for suitably skilled workers to build the airship. If we assume the Spanish started working with airships in 1632, and start building a hangar in 1634, it is possible that work on the Sao Martinho could start as early as 1636-37.
Appendix 1.
Grantville Gazette 36 gg-36 Page 21
