Now we come to the interesting part: propulsion.
We have a lot of options here. Unfortunately, the rules are ambiguous about certain key facts which effect what our best choice is going to be, so we're going to have to get hands-on to determine the best option.
We use a fabricate spell to make a disc of mithral three inches thick and two feet in diameter. (I do not include the cost of the mithral here because we will reuse it later.) We build a one-use spell trap of burning hands at the center of the disk (costing 50 gp x 0.75 x 0.75 x 0.9 x 0.95 = 24.05 gp), and strap a thermometer and barometer to the piece next to the trap, outside of the spell's area of effect. (Somehow, the authors of D&D forgot to put scientific instruments in any of the price lists, so call it 50 gp each.) Then we use a second fabricate spell to make a hollow, airtight mithral sphere three feet in diameter and with two inch thick walls around the disc. We fire the spell trap and use clairaudience/clairvoyance to read the instruments. We then allow the chamber to cool to room temperature, and read the instruments again. Combining these two data points with the ideal gas law will determine if the burning hands spell produces real matter and, if it does, how much and how hot it is.
Let's assume that burning hands does not make matter, because, like I said, I think this is a more plausible interpretation of the rules. The logical next step is to use conjuration (creation) spells instead - these explicitly do make real stuff. BUT! According to the SRD, while evocation spells "make something out of nothing", conjuration (creation) spells "manipulate matter to create an object or creature". This implies that our conjuration traps will have to be "fed" matter to turn into exhaust. The logical source for this matter is a decanter of endless water. (Decanters of endless sand from Sandstorm have a better mass flow/cost ratio, but might clog up our exhaust nozzle.) Now, you could argue that the decanter is replicating the conjuration (creation) create water spell, but that's not explicit anywhere in the rules. Still, let's test it.
Break open our mithral sphere and put a decanter of endless water inside, set to stream mode, which produces 1 gallon per round. Use fabricate again to seal the sphere back up, and watch what happens inside with clairaudience/clairvoyance. If the decanter is actually making matter, the pressure inside the sphere should build, fast, so be ready to pop the sphere again in a hurry.
Let's assume the decanter does make matter, because frankly I don't want to worry about the rocket equation. Now, once you bring up the decanter of endless water, one possibility is to make a steam rocket by combining it with permanent walls of fire, matter agitation, or heat metal. Unfortunately, the temperature produced by these effects is not specified, so we don't know how many of these effects we need to vaporize our exhaust. The other possibility, already mentioned, is to use the matter produced by the decanter in a conjuration (creation) spell such as blast of flame (from Complete Arcane). We'll test both possibilities to see which offers better thrust/cost.
Refabricate the mithral into a giant funnel. Cast wall of fire on the end of the funnel, pour water through it, and use the thermometer to measure the temperature of the water after it passes through the wall. If the water flashes into steam, drop iron ingots through the wall instead (1 pound of iron costs 0.1 gp). There are two possibilities here: the wall might change the temperature of anything that passes through it to the temperature of "fire", or it might generate pseudoreal "fire" that imparts heat to anything that passes through it, and that heat might be pseudoreal or actually real. We can use this experiment to evaluate all three possibilities. If the water is room temperature on the other side of the wall, the heat is pseudoreal and this is not a viable propulsion method. If it is hot on the other side, try varying the speed of water falling through the wall; if the temperature remains constant, then it's setting the temperature of the water to some number. If it doesn't, we can work out how much heat is being added to the water per second in the wall by dividing the temperature change by the time it takes to pass through. All fairly straight-forward. We can then repeat for matter agitation and heat metal - we'll assume that we have a Psion-1 and a Druid-3 among our followers so we don't need to pay for these.
Once we have these results, we also want to test using a decanter to feed a blast of flame spell instead. Build a one-use blast of flame spell trap (costing 1400 x 0.75 x 0.75 x 0.9 x 0.95 = 673.31 gp) and fix it to the mithral disk with the thermometer and barometer next to it, refabricate the mithral into a sphere around the disk, and set it off. From the ideal gas law we can determine how much material, and at what temperature, the spell is producing, and from that we can determine the thrust/cost ratio.
I'm going to assume that the blast of flame trap is the better option going forward, and that it fills its area of effect with "flame", which is isomorphic to air heated to the temperature of a propane torch.
One further thing we need to test is whether a lyre of building can protect a decanter of endless water and magic traps built into a wall, because - as we'll discuss below - we're going to use the lyre to keep our combustion chamber from evaporating from the energy we're putting through it. The lyre "negates any attacks made against all inanimate construction (walls, roof, floor, and so on)". I think that it's reasonable to interpret the decanter and traps as part of the construction, but there's insufficient information in the rules-as-written to determine the answer. So: build a cheap magic trap (another 24.05 gp) and attach a decanter to our disk of mithril, play the lyre, cast burning hands at the objects, and see if they're damaged. In what follows, I will assume the lyre does protect them.
Finally, we also want to test the range at which we can control the decanters of endless water - if they're twenty feet away and on the other side of a mithral wall, will they still respond to the command word? In what follows, I will assume they will not.
Research Program, Phase II: 821.51 gp
Ideas That Won't Work
A few notes on possibilities that won't actually work:
- Using many, many spell traps of telekinesis. Given the weight limits on telekinesis, this would require either pumping our caster level into the thousands, or stripping our "spaceship" down to basically a chair for the astronaut to sit in. Even more problematic, though, is that telekinesis appears to generate pseudovelocity rather then real velocity: it shifts the target from place to place but is not described as producing lasting motion. So we would have no practical way to match velocities with any planet we wanted to visit.
- Using either permanent gust of wind or gust of wind spell traps. First, this requires interpreting "creates a severe blast of air" to mean it creates air in the form of a blast, rather then creating a blast by moving air that already exists. Second, this requires an enormous frontage to get any real thrust. If that isn't enough, it also runs into the whole real/pseudoreal issue that confronts burning hands spell traps.
- Use shrink item on alchemist's fire to reduce its size by a factor of 4,096, then store it in a portable hole so its mass doesn't count. Then, pump it into a permanent antimagic field to return it to its original size before burning it in a regular old rocket engine. Now, first of all, alchemist's fire is really freaking expensive, so it's cost-prohibitive just on the face of it. Second, you'd need to find a good way to store air for combustion, unless the permanent gust of wind trick works. And third, I don't want the book-keeping on keeping track of fuel.
- Using a decanter of endless water in geyser mode as a water rocket. If we assume the mouth of a decanter is 1 inch wide, then 30 gallons per round works out to an exhaust velocity of 37.4 m/sec, which translates to a thrust of 706.86 N per decanter. To give our 30 ton cockpit module a 1.5 G acceleration - enough to get off the ground - we would need a thrust of 450,000 N, or 637 decanters. At a price of 4500 x 0.75 x 0.75 x 0.9 x 0.95 = 2164.22 gp per decanter, that's 1,378,608.14 gp, a bit outside our price range.
Our "combustion chamber" is going to be a hollow cone we use to capture the exhaust produced by our blasts of flame so we can direct it through a nozzle. That means it's going to need to be able to withstand extreme temperature and pressure.
In theory, we could just use make whole traps firing once per round, but in practice we are going to be doing so much damage to the chamber walls that it would probably melt before the trap fired. We could apply permanent animate objects, followed by awaken construct (from Savage Species), followed by mantle of the fiery spirit (from Sandstorm), which would turn our engine into a sapient creature that's immune to fire. That would be both really cool and help with steering, but while that would protect us against fire it wouldn't keep the chamber from bursting from the pressure. We could make the chamber out of permanent walls of force or riverine (from Stormwrack) but this is expensive and geometrically awkward, and we need a workable surface to mount our spell traps on.
In the end, I think our best option is to make the chamber out of mithral and use a lyre of building. Once per day, the lyre "negates any attacks made against all inanimate construction (walls, roof, floor, and so on) within 300 feet." This requires us to interpret the heat and pressure of our exhaust gas as an attack, and to interpret our decanters and spell traps as construction, but I think that's reasonable if we build the decanters into the wall. The lyre's effects last for only 30 minutes per day, but we'll have thrust to compensate, and we'll carry two lyres so we can fire our engine more then once a day.
Blast of flame produces a 60-foot-long cone of fire. Now, in D&D, a "cone" is defined as a quarter-circle on a 2-dimensional map. I'll assume that it's axially symmetric, so that its three-dimensional shape is a rotated quarter-circle, which I will regard as a section of a solid sphere of radius 60 feet = 18.29 m:
That shape will have a surface area of:
Where r is the radius, equal to 18.29 m. The surface area of this shape will be 1,043.06 square meters.
But, we need more than just the cone. In addition to the cone, we need a flat surface to mount the cone to our cockpit, and - as I'll discuss in the next section - to mount the decanters to. We'll do this by attaching a 1-meter-diameter, 1-meter-long open cylinder to the top of the cone, so that the base of the cylinder is 0.5 meters from the tip of the cone, as shown below:
We'll have holes in the cone in the area covered by the cylinder, as shown, to allow the water from the decanters to flow into the combustion chamber. The cylinder will have a surface area of 3.93 square meters, making a total of 1,046.99 square meters.
We want our walls to be as thin as we can make them without having the chamber collapse under its own weight while on the launch pad, but D&D somehow doesn't have rules for that kind of architectural calculation (a gross oversight, I know). Let's call it one centimeter thick - if anyone has suggestions for a more accurate approach, or a good way to reinforce it so we can make it thinner, let me know in the comments. We can get a very good approximation of the volume of the chamber walls by multiplying the thickness by the surface area, giving us 10.47 cubic meters. Mithral is described as weighing half as much as iron, and iron has a density of 7874 kg per cubic meter, so that works out to 41,221 kg, or about 90,877 pounds. Assuming we're using the "structural" mithral of Stronghold Builder's Guide, that costs 29,989.41 gp. We'll use fabricate to turn it into a combustion chamber, and sovereign glue (2,400 gp) to attach it to our cockpit.
Combustion Chamber: 32,389.41 gp (charged to general budget)
Once the combustion chamber is done, we install the engine. Instead of using blast of flame traps directly, we use an energy transformation field (from Magic of Faerun) loaded with blast of flame. That spell absorbs any magic cast in its area of effect, then, once its absorbed as many levels of spells as the level of the spell it's loaded with, it casts the spell. It costs 5,000 gp in material components, plus 13 x 70 gp = 910 gp in subcontracting fees, but a transformation field powered by spell traps of first level spells is still more cost efficient then using a blast of flame trap by itself.
Now, our spaceship so far masses about 75 tons. The volume of our combustion chamber is given by:
So the chamber volume is 3,753.26 cubic meters. Every time the blast fires, it will fill that volume with "flame", which we are assuming is isomorphic to air at the temperature and density of a propane blowtorch, about 1,720 degrees Kelvin. The density of air is given by the ideal gas law:
Where d is the density, P is the air pressure, R is the specific gas constant for air, and T is the temperature. Room air pressure is about 100,000 Pascals, while R is about 287.1 J/(kgK), giving us a density of 0.203 kg per cubic meter. Multiplying density by volume, we get 761.9 kg of exhaust per blast.
The exhaust velocity of a thermal rocket with an ideal nozzle is:
Where k is the specific heat ratio, R' = 8,314 J/(kMol K) is the universal gas constant, T is the exhaust temperature, and M is the exhaust average molecular weight. The average molecular weight of air is 29 kg/kMol. For air at these kinds of temperatures, k is about 1.3. Overall, that gives us an exhaust velocity of 2,067 meters per second.
If our blast fires once per second, we have a total thrust of 1,574,873.09 Newtons. Our ship masses about 75 metric tons, so that works out to an acceleration of 2.1 G.
For each firing we need to supply 761.9 kg of water from decanters to the chamber. On its maximal setting a decanter of endless water produces 30 gallons per round. A D&D round is six seconds, so that's equal to 18.9 kilograms per second. That works out to 41 decanters. Each decanter costs us 4,500 gp x 0.75 x 0.75 x 0.9 x 0.95 = 2,164.22 gp, for a total price of 88,733.02 gp.
If we want our blast to fire once per second, that's six times per round, meaning we'll need 24 spell traps powering our energy transformation field. At a cost of 500 x 0.75 x 0.75 x 0.9 x 0.95 = 240.47 gp each, that works out to 5,771.27 gp.
We also want to be able to turn our decanters off when not in use, to avoid clogging the engine with ice. We'll do this with a second energy transformation field, this one loaded with antimagic field. This adds another 5,910 gp in subcontracting fees, plus another spell trap costing 240.47 gp.
We can choose the origin point of the spell cast by energy transformation field, provided it lies somewhere inside the field itself. Now, we want to ensure that the energy transformation fields do not cover the decanters, because if they did they would absorb the decanters energy and prevent them from working. But, we want the antimagic field to cover the decanters, so it can turn them off. An energy transformation field's area of effect is a 40'-radius spread, 40 feet being equal to 12.192 meters. An antimagic field is a 10'-radius emanation, 10 feet being equal to 3.048 m.
In D&D, an emanation is a sphere that is blocked by anything that blocks line of sight. In other words, if I can draw a straight line from a point to the origin of the antimagic field that does not pass through any physical objects, and which is 10' long or less, then that point is within the antimagic field. A spread is like an emanation, except it can turn corners. In other words, if I can draw a path that curves and bends from a point to the origin of the antimagic field that does not pass through any physical objects, and which is 40' long or less, then that point is within the energy transformation field
We can easily position the blast of flame-generating energy transformation field so that it does not cover the decanters. We then set the origin of the antimagic field-generating energy transformation field inside a box, closed except for an opening leading to a pipe which curls around itself for 39'. The spread of the energy transformation field will follow the pipe, ultimately emerging at the end in a 1'-radius sphere. We place the spell trap powering the field inside the box. We set the origin of the antimagic field at the end of the pipe. Since the antimagic field has a radius of 10', we can position the box and the pipe at the tip of the cone so that the antimagic field covers the decanters but the energy transformation field does not.
So, to sum up:
5,910 gp (energy transformation field for blast of flame)5,771.28 gp (24x spell traps powering blast of flame)
88,733.02 gp (41x decanters of endless water)
6,252.19 gp (2x lyres of building)
5,910 gp (energy transformation field for antimagic field)
240.47 gp (spell trap powering antimagic field)
Engine: 112,816.96 gp (charged to general budget)
Putting It All Together
So let's add this up. For the Landlord budget, we have:
Research Program, Phase I: 1,442.81 gp
Vehicle Assembly Building: 9,289.77 gp
Cockpit: 20,183.29 gp
Environmental Support and EVA: 1,803.52 gp
Navigation and Sensing: 240.47 gp
For the general budget, we have:
Environmental Support and EVA: 4,664.22 gp
Navigation and Sensing: 8,310 gp
Research Program, Phase II: 821.51 gp
Combustion Chamber: 32,389.41 gp
Engine: 112,816.96 gp
Total, Landlord Budget: 32,959.86
Total, General Budget: 159,002.1 gp
By the books, an 11th-level character has 66,000 gp to spend, plus 75,000 gp from the Landlord feat. Between our astronaut and three financial backers, that works works out to 264,000 gp in general budget. So this should fit comfortably inside the budget.
To Be Continued
Next Time: Mission Planning