Last updated 5/25/02
Iím experimenting a bit with nozzle fabrication. Rather than weld or machine a nozzle for my prototype, Iím trying to use castable ceramic thatís good to 1700C. This picture is my ďlatheĒ, a drill press with a bolt and a washer holding up a clay spindle, which will ultimately provide the mold for the high-temperature ceramic nozzle. Well, itís progress. Aremco makes the ceramic.
Length; 20 meters. Scoop diameter is 2 meters. Est. design weight is 1000kg. Include man-pod. Buoyancy is based on the volume, which is roughly 63 cubic meters.
Parabola; y2=4fx (f = distance focus to vertex) Linear cross section of parabola = approx. 2.30 Area of reflector; 2.3 x 20 = 46 m2 Solar incidence area normal to reflector; 2m x 20 = 40m2 Est. Solar Incidence on reflector at 700W/m2 (1400 in free space) = 700 x 40 = 28KW Guestimate of losses; 50%, yield to transfer tube 14KW. Actual tests.Material; 2 mil Mylar, reflective lower half, clear upper half. Good to 150C. Seam-sealed with mylar glue, maybe tape, maybe a mechanical seam of some sort. Experimenting with heat-sealing, makes a pretty good seam, but thereís no ďsewing machineĒ type heat sealer available. Volume will be pressurized. Makeup air and cooling air will be provided by forward air scoops and vent flaps on rear. I bought the clear mylar from Conservatorís Emporium. They sell document protection plastics, and book repair glues. The reflective mylar came from AHL Hydroponics. They sell plant growing stuff. Thereís probably some central place I could buy all this stuff, but these popped up on the web search, so they got my business.
THERMAL TRANSFER TUBE STATS
Transfer tube; 20 meters, 1 cm diameter. Wall thickness TBD Tube pressure; 10 Atm (using TBD technique for pressure; ram/pump/pulsed) Nozzle diam; 2 cm Nozzle throat; 0.5 cm Scoop throat; TBD Scoop diameter; 2 meters Scoop area; 3.14 m2 Mass throughput; .024 kg/s at 2000KOperating temperature; copper melts at around 1000C. Iron at 1500C. Molybdenum at 2600C. Moly-Ti at 2900C. Iron/steel is easy to work and cheap. Initial test bed will be done with copper tube and a nozzle made from Aremco castable ceramic 575-N, good to about 1700C. Subsequent testing will require more exotic materials.
Scoop area, calc as flat plane perp to flight path. Call drag "N", actual is TBD.
Lifting surface; aspect ratio 2, flat plane, L/D approx. 6:1 tilted at 6 degrees incline to flight path. Drag set to 0.3N, Lift then is 1.8. L/D is 1.8/1.3 = 1.38
Surface drag; TBD
BUOYANCY Buoyancy per cubic meter is roughly .3kg per cubic meter with 100C internal temp, so the total is around 20kg buoyancy. Doubling the length and width of the balloon would give us 8 times as much buoyancy, or 160kg, and 4 times the solar collection area.
AVAILABLE THERMAL ENERGY
Collected solar is based on about 800 W/m2 at Earth's surface (1400 in free space). We're taking a WAG that we can get 500W/m2 out of reflectors, which might be optimistic, since the thermal transfer tube will be radiating, too. Based on this, our prototype design of 40m2 will only yield 20KW. Assuming we want to heat gas up from 300K to 2000K, then based on the formula for the internal random kinetic energy of gas, 3/2*RT=Joules=Watt seconds, where R = 8.31 Joules per mole Kelvin, we find that the internal kinetic energy of 1 mole of gas at 300K is 3750J. Calculating for the max number of moles that I can heat in 1 second to 2000K, I get 20/21.2, a bit less than 1 mole, or 21 liters of gas at STP, or about .021 m3 of gas per second. That's not much. Restricting the airflow would guarantee I can reach the high temperature, but as we will see, I won't get as much thrust out of this as I would like. A collection area 45 times as large would let me process 1 cubic meter of gas per second to 2000K, but would require 900 m2 of solar collector area and a subsequently larger frontal drag area/scoop. I suppose using a giant "snake" concept might work, like a flying train, but it sounds almost too silly, and the longer it is, the more the heat-tube weighs, and it's potentially the biggest mass in the vehicle. Anyway, based on the 40m2 model, I can have a mass through-put of about 26 grams of gas per second, heated to a chamber temperature of 2000K.
NOZZLE EXIT VELOCITY AND THRUST
Given that the exit velocity, v2, can be calculated from SQRT(2kRT/(k-1)), and that k equals about 1.3, and R in this case is in its kilogram form (based on average .024kg/m3 atmospheric gas); 345.7 J/kg-K, then v2(max) equals SQRT(2*345.7*2000*1.3/0.3) = 2448m/s. Not too bad. Without yet calculating chamber pressure or nozzle throat diameter, we can use F=m' * v2 for our little thruster to get 2448m/s*.026kg/s = 63 Newtons, just enough to vertically lift a bit over 6 kilograms, and plenty of force to drive the ship forward.
Oddly, and counterintuitively, we notice that if we double the mass throughput to two moles, the output temperature drops to 1102 K, and v2 drops to 1817m/s. Plugging the new v2 and mass flow into the Force formula, we get 1817m/s*0.052kg/s= 94 Newtons. So, by pushing more, cooler gas through, we get a better thrust. Unfortunately, the form F=mív2 is an approximation anyway. Thereís obviously a lower limit to this conjecture, though it isnít evident from the formula. If I pump through so much gas that my output temperature is 460K (10 moles), then my thrust would supposedly be 281N. Because of the lower temperature, the chamber pressure doesnít actually change much between the two situations, despite having ten times as much mass flow. This will be very interesting to test in practice.
The obvious reason for this phenomenon is that no matter how much gas we pump through, we are always adding 20000 Joules per second to it (Watts). Weíll get an added bonus from the pressure differential at the nozzle exit (p2-p3)*Area, based on the big mass flow. However, at the cooler temperatures, we wonít reach supersonic flow on the nozzle, so that might be detrimental. The test mock-up will resolve a lot of these issues. The actual limit on mass-flow will probably be based on the drag on the ship once it gets going.
NOZZLE THROAT DIAMETER
We will try a number of nozzle throat diameters and a variety of restricted inlet flow throats. I suspect I might need a smaller throat on the inlet than on the thruster, but Iím not sure yet. Calcs on the throat area are TBD.
MAXIMUM ALTITUDE AND VELOCITY USING ATMOSPHERE AS PROPELLANT
MASS/TEMPERATURE OF H2O TO REACH ORBIT.
Naturally, thereís some question whether I can carry enough H2O to get to orbit. So, this will remain TBD until my thrust tests are done.