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.
The "weight empty" or "deadweight" is the weight of the airship after removing everything that can and is normally removed between voyages (Things like water, crew, food, payload, fuel and oil for the engines, and ballast-usually water or sandbags.)
Table 2. Percentage of Gross lift given to Weight Empty for the last of the rigid airships (using numbers from Brooks). Gross lift is calculated at 1.09 kg/m^3 of gas capacity The ratio is calculated by dividing Weight empty by Gross lift
Yes, some of the WW1 Zeppelins had ratios below fifty percent, but that was achieved by seriously weakening the structure-essentially, removing a third of the ring frames-and halving the number of layers of goldbeater's skin used on the gas bags. That might be acceptable for war time expedients, but we don't want what happened to LZ-114 to happen to our airship. (LZ-114, a war prize, being operated by the French as Dixmude, suffered a structural failure in flight and fell, burning, into the Mediterranean, with the loss of all fifty aboard. [Brooks, p.108].).
The Hindenburg was the last rigid airship design, and we can assume she was designed using all of the available knowledge built up over the years, making her suitable for commercial operations. Therefore, for this exercise, we will allocate the same sixty percent of gross lift to "weight Empty."
Appendix 2: The route, based on Iver's Route 2.
Iver's article assumes that the power delivered by the propeller (i.e., the propulsive power implicit in airship motion) is 71% of the power output from the engine [Cooper]. I used this setting in his spreadsheet when calculating this route.
Depart Cadiz,
1) Head south through Variables for 5 hours at an engine setting of 211.26 HP, at an altitude of 100m
2) Continue south to Trades for 12 hours at 101.81 HP, at 200m.
3) Follow Trades westward for 157 hours at 20.64 HP, at 200m.
Arrive in Havana after 174 hours, with reserves of 2,620 kg fuel.
Depart Havana,
4) Head north to Variables for 24 hours at 207.74 HP, at 100m.
5) Head north to Westerlies for 12 hours at 101.81 HP, at 200 m.
6) Follow Westerlies for 66 hours at 9.86 HP, at 915 m.
Arrive in Cadiz after 102 hours, with reserves of 2,664 kg fuel.
You will have noticed that the reserves of fuel are about 45%. However, those flight times and power requirements are based on average winds. It is hoped that this reserve will be sufficient to ensure safe transit under most conditions.
Appendix 3: Calculating the Deadweight
Appendix 3i: Formula from Crocco [p.10].
Deadweight (kg) = (0.1759 + 0.00002275 x velocity^2) x Envelope volume +
(0.09994 x Number gas cells + 3.075) x Envelope volume^(2/3) +
(0.0019725 x Envelope volume^(4/3) + (Gross HP x 2.150)
Where Envelope is the volume of the envelope, and one gas cell per 9 m of length.
Inserting numbers = (0.1759 + 0.00002275 x 15^2) x 49,114 +
(0.09994 x 17 + 3.075) x 49,114^(2/3) +
(0.0019725 x 49,114^(4/3) + (240 x 2.150)
= 8890.644 + 6402.561 + 3547.834 + 516
= 19,357
Note that this value doesn't include trim ballast, and it uses lighter engines, and Duralumin rather than plywood for structure
Appendix 3ii
Appendix 3ii-a) The basic frame. 16,876 kg
The British R.31 class airships (Which are of a similar gross lift and gas capacity to the Sao Martinho.)were built using spruce plywood using three panels 10' long and 10" wide formed into equilateral triangles[Airship Heritage Trust: R31]. Assuming 28 lbs per cubic foot for air dried spruce, plywood half an inch thick, and that the holes cut into the panels leave 30% of the panels, each 10' girder is 0.03125 ft^3 or 8.75 lbs.
However, wood is hydroscopic (absorbs water) so we need to seal the plywood. We'll want to apply at least two coats of varnish, at 9 lbs per 450 ft^2. Each girder has a basic surface area of about 15ft^2, so that’s an extra 0.60 pounds for 9.35 pounds per girder (4.25kg). Note that I'm ignoring nails, glue, and any internal framing.
As everything else is metric, we'll convert these to 3m girders weighing 4.18 kg. How many do we need? Let's approximate. The envelope volume is 49,114 m^3. The radius of our structure is 22.96m. We could call our airship a cylinder with a cross section area of 414m^2 and ~117 m long (rounding down the actual value of 118.63 to give a value divisible by 3 and 9).
If we put a major ring frame every 9m, and minor rings every 3m, and we have a lateral every 3 meters, then:
a) each ring is ~72 m circumference, needing about 24 girders
b) each lateral is 117 m, or 39 girders
c) there are 39 ring frames (13 being major frames)
d) there are 24 laterals.
e) double frames for major rings 13 frames at 24 girders
a x c + b x d + e = (24 x 39) + (39 x 24) + (13 x 24) = 2,184 girders = 9,129 kg (1).
Admittedly there is another (170-117 =) 53 meters of hull to frame. A wild guess would be ad an extra 25% (53 m is ~31% of the cylinder, but it is made up of two curved shapes)-2,282 kg (2).
Next we add the fin surfaces. Based on the Hindenburg fins [Brooks, p.180], these are aerofoil shapes, having two layers of girders. Laying out the girders I estimate there are 80 x 3m girders per fin. With four fins, that is 320 girders, or 1,338 kg (3).
There are Keel and central walkways on the Hindenburg. Each running the full length of the airship, if we just call that one girder wide for ~170 m or 57 girders per walkway (114 girders), 477 kg (4)
Then we have to add the lattice that actually stops the gas bags pushing against the outer envelope. This is made of cable strung between the girders, and in a photograph of R29 under construction (Brooks, p.117) they look quite thick. If we call it 3/8" manila at 23 ft to the pound (0.065kg/m), and make a 0.3m lattice on our cylinder (72/ .3 = 240 circumference runs (240 x 117 = 28,080), plus 117/0.3 laterals (390 x 72m = 20,080), we need about 56,160 m of "rope", or about 3,650 kg. (5)
Total structure (Sum(1:5)) = 16,876 kg
Appendix 3ii-b) The gas bags 3,745 kg.
The surface area of the gas bags can be estimated based on a cylinder based on the gas volume of 48,103 m^3. It is ~116 m long, with a circumference of 72m. Each end (two per bag) is 414m^2.
Each gas bag is 9m, we have 13 gas bags, so area of gas bags is:
116 x 72 + 13 x 2 x 414 = 19,116 m^2. Using the Hindenburg standard latex-Gelatin formulation to produce gas tight fabric at 180 gsm gives a total gas bag weight of 3,441 kg (1). To which we have to add the actual (170/9=) 19 bleed valves etc at 16 kg each =304 kg (2).
(1) + (2) = 3,745 kg.
Appendix 3ii-c) The Envelope 4,071 kg.
Woodhouse [p.211] talks about an envelope being made of rubberized fabric with protective coatings of heavy spar varnish, "Valspar" or its equivalent. Actually, he says the fabric should have at least five applications of nitrocellulose, and final coat of "Valspar". The protective coating should be at least 70 grams per m^2, and no piece of fabric should weigh more than 440 gsm.