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Some start-up launch companies have pursued air launch in order to avoid the expense associated with high chamber pressure rocket engines needed for ground launch, to improve the performance of rocket stages (by starting in near vacuum), reduce aerodynamic constraints on the vehicle and avoid the need for launch pads. Some disadvantages to this approach are the size limitations it imposes upon the launch vehicle, the difficulty of attempting to integrate the vehicle into the airframe of the launcher aircraft without resulting load imbalance or deterioration of aerodynamics and the fact that most jet aircraft would be limited to ~30,000 feet.
An alternative could be provided by the liquid nitrogen rocket. This would produce thrust by spraying liquid nitrogen and super-heated water into a thrust chamber. The nitrogen droplets would boil explosively by absorbing the internal energy of the water droplets. The exhaust would consist of a mixture of high pressure nitrogen gas and water ice crystals.
I have made a few calculations on performance. Water stored at a temperature of 510K (237C) has a vapour pressure of 31.66 bars and can therefore function as a self-pressurising propellant. The total thermal energy released by 1kg of water cooled from 237C to 0C is 1060KJ. The latent heat of melting of water is 334KJ/Kg, so total heat released is 1393.4KJ/Kg. The latent heat of evaporation of liquid nitrogen is 199KJ/kg and the specific heat of nitrogen vapour averages at 1.05KJ/kgK between -178C and 0C. The total energy needed to evaporate 1kg of nitrogen and heat it to 273K (0C) is therefore 385.9KJ/Kg. Therefore, some 21.7% of the injected propellant should be saturated water, with the remainder being liquid nitrogen. The exhaust velocity of the engine can be calculated using the ideal rocket equation.
For a chamber pressure of 2.5MPa, this gives a Ve of 753m/s in vacuum and 584m/s at sea level. However, 21.7% of the exhaust is water ice, which contributes nothing to ISP. On this basis, the effective Ve is 516.8m/s at sea level and 666.3m/s in vacuum. Under lower stage launch conditions, I am going to take an average and say ~600m/s for Ve, or an ISP of 61.2 seconds.
The proposed feed mechanism is pressure-feed for both propellants. Pressurisation of both propellants can be maintained by injecting small amounts of liquid nitrogen into the hot water tank and allowing the ullage gas to pressurise both containers through interconnecting tubes. Tank material is proposed to be Vectran or Kevlar for the liquid nitrogen tank and maraging steel for the water tank. The chamber and engine nozzle can both be constructed from high strength polymer. Neither will require cooling, although the chamber throat may require abrasion resistance due to high-speed shot blasting from ice particles in the exhaust.
The dry (non-payload) mass fraction of the vehicle is expected to be ~10%. Assuming that the nitrogen tank is Vectran and a design factor of 4 is applied, the mass fraction of the tank is ~4% of full weight. Maraging steel has a similar tensile strength to Vectran, but is 5 times denser, so the water tank weighs as much as the nitrogen tank despite having one fifth of the volume. An alternative to maraging may be a Kevlar tank with some sort of internal lining providing thermal insulation from the hot water. The engine components work at lower pressure than the tanks and are constructed from Vectran. Manoeuvring and stability are expected to be achieved using aerodynamic means, as the vehicle will achieve the entire booster phase within the Earth’s atmosphere.
Payload mass (i.e. upper stages) are expected to account for 10% of take-off weight, so total dry weight is 20% and total mass ratio is therefore 5. For an average exhaust velocity of 600m/s, the total delta-V of the rocket is therefore 966m/s. The plan is for the vehicle to fly straight up, as its function is to deploy the upper stages above the Earth’s atmosphere. If aerodynamic and gravity losses account for some 30% of launch energy, the vehicle will reach a height of 100,000 feet (30,770m) with a residual speed of 244m/s.
At this height, atmospheric pressure is <1KPa and drag effects are small. On this basis, if the upper stages can be housed within an internal bay during the booster phase and deployed at 100,000’ the upper stages need not account for aerodynamic effects or thermal gradients from the atmosphere. Engines can be optimised for vacuum (low chamber pressure) and the payload will require minimal housing. Total delta-V required reaching orbit from this height and speed is still ~8km/s. However, the vehicle is accelerating under vacuum conditions, which makes the propulsion job much easier. A LOX/H2 fuelled rocket could achieve this with a mass ratio of ~6 and would not need the thermal management system associated with a ground launch SSTO. A nitrous oxide / propane vehicle could achieve a delta-V of 8km/s with a mass ratio of 30 if some 50% of the N2O were housed within a drop tank. This is because some 90% of propellant mass is N2O. A tank containing chilled N2O need only be lightly pressurised and it could be constructed from low-cost carbon manganese steel, with the remainder of the upper stage being reusable.
The return mode of the booster is dependent upon its size. To launch small payloads of ~1 tonne using N20-propane upper stages, total take-off weight would be 300 tonnes, about 30 tonnes of which is the dry weight of the lower stage. Such a stage could be slowed to terminal velocity using a parachute and dropped into the ocean or could even conceivably glide back to Earth using extendable wings. Larger heavy lift payloads of up to 100tonnes would require a take-off mass of 30,000 tonnes, some 3,000 tonnes of which would be the dry weight of the lower stage. This would require a drag chute to slow their terminal velocity for ocean impact. Work carried out for Sea Dragon suggests that impact decelerations would have been survivable for the structure and components.
The economics of the concept depend upon the low cost of both propellants and the simplicity and reusability of the vehicle. The propellant cost in the large volumes under consideration is a function of the cost of energy. Liquid nitrogen can be manufactured at an energy cost of 0.4kWh/kg. This energy tends to be electrical energy. From a big nuclear reactor, electric power costs about $0.05/kWh. So 1kg of N2 has an energy cost of about 2 cents. The hot water will probably be provided using a coal boiler local to the refuelling point. At a coal price of $50/tonne, the hot water would cost about 0.5Cent/MJ (assuming total plant cost 3 times fuel cost). For an 80/20 mix of N2 and H2O, lower stage propellant would cost about 1.7Cent/kg. So lower stage propellant cost would be $4.2 per kg delivered to LEO. The preferred mode of operation would appear to be a sea launch, with the stage rapidly refilled and turned around between launches. To prevent stress-cycling of the propellant tanks, it would be preferable to keep them pressurised at all times.
Last edited by Antius (2016-08-19 11:11:20)
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That's an interesting variation on the steam rocket idea that Bob Truax built for Evel Kneivel and his Snake River Canyon jump. I think the plain steam rocket had Isp = 83 sec as built, but didn't go anywhere near as high as you are talking about. There was no ice and only a little condensed water in its exhaust. Having condensed phases in your exhaust does sharply reduce Isp. The more, the worse the effect.
With a 10% inert fraction in your booster stage, would you not be better off (and a smaller booster stage) if you just built a plain solid propellant rocket booster? Those are typically 10-15% inert, depending upon size and pressure level, but feature a much better Isp, around 240-260 sec at sea level with a limited expansion area ratio and AP-oxidized composite propellants.
Chamber pressures are limited in large sizes because steel is only so strong: around 900 psia operating pressure in the 120 inch diameter shuttle SRB's. Smaller is higher pressure and can use larger expansion ratios, even at sea level. Your typical tactical missile motor is 4 to 10 inches diameter, operates around 2000+ psia (a few as high as 4000), and will have Isp pretty near 255 sec with AP composite propellant. Double base and AN-oxidized stuff has lower Isp, by around 10% or so.
We occasionally used T-250 maraging steel for motor cases, but our favorite materials were 4130 and D6ac stainless steels. We would cold flow-form thin-wall cases to dimension and properties simultaneously with those materials, very reliably and very affordably. Tensile strengths achieved by cold-working typically fell between 250,000 and 280,000 psi. We achieved this at still-acceptable elongation capability, which was the real limiting factor. Too little elongation, and the steel shatters like cheap glass.
We also did this with aluminum for some Sidewinder variants, but steel really is the better choice. Experimentally, we did this with beta-phase titanium, but that experiment failed, because of room temperature aging (properties completely lost within a few months at 77 F).
With a flow-formed case tube, there's no no roll-and-weld joint to discount strength because of weld inefficiencies. You can weld fittings to thickenings built into the case during flow-forming. That way, weld inefficiency strength degradations do not affect the overall product. It is truly a good way to build stuff, although sizes are inherently limited, maybe to something like 30 inch diameters.
Roll-and-weld can be done in any size desired, but you must roll annealed, and heat treat after welding (which adds expense). Electron beam welding in vacuum offers the least strength degradation, but costs some extra effort to do.
Part of the expense of reusing shuttle SRB's had to do with the segmented motor and case design. Ocean impact often messed up the joint geometry. You can get away from that by using a non-segmented design, and get around the size limitations for casting such a motor by clustering several small ones to make what is effectively one big one.
Such one-piece motor cases are like the old JATO bottles: cheap enough to throw away, but rather easy to refurbish if you want to, and small and simple enough not to be damaged by ocean impact. About the only component damaged by ocean impact and immersion is the nozzle, which being ablative, is thrown away anyway.
Just food for thought, based on industry experiences. Some of this might apply to your high-pressure propellant tanks in your liquid nitrogen rocket.
GW
Last edited by GW Johnson (2016-08-19 11:42:21)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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Thankyou GW for an excellent and informative response.
My back of the envelope calcs indicate that a solid propellant booster with Ve of 2500m/s would be about 10% of the mass of the liquid nitrogen rocket doing the same job. So capital cost would be a lot lower. Operational costs, I am not sure.
I will take some time to redefine the concept based on your feedback. It would appear from a brief review of your feedback that smaller engines and tanks are much easier to fabricate than larger items. It suggests to me that it may be much easier to achieve cheap access to space using very large numbers of small mass produced two-stage vehicles that are air launched. Maybe it would be possible to fit out a 747 to carry these within the fuselage.
Could a Mars mission be assembled in orbit more cheaply using 200 x 1te payloads?
Last edited by Antius (2016-08-19 14:13:10)
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Re. small payloads, considering that most of the mission mass is going to be fuel, then it depends on how expensive it is to ship the fuel in 1 tonne packages vs. a single 50 tonne tanker launched on a Falcon Heavy. If you can ship small payloads economically (perhaps an orbital tug to collect them?), then you can ship fuel, water, food, interior furnishings etc on such a rocket.
I would suggest using a Falcon Heavy to launch the hull, though, and outfit it on orbit with the 1 tonne packages. That would give you quite a large spacecraft I would think, especially if you launched two and docked them together.
Another thing that could be launched with small payloads is a lightweight frame and lots and lots of aluminised mylar...
"I'm gonna die surrounded by the biggest idiots in the galaxy." - If this forum was a Mars Colony
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I have carried out some additional research that may help refine this concept.
The lower stage consists of three pressure containing items, the largest and most technically challenging of which is the liquid nitrogen tank.
The LN2 tank is likely to be too large to be flow formed using the techniques suggested by GW as a single entity. The flow forming technique would however appear to be useful for the upper stage propellant tanks and engine. The lower stage could potentially be constructed from multiple smaller units clustered together. However, this would appear to introduce additional complexity into the device which would need to mechanically couple these smaller units together. The design would also appear to make the stage vulnerable to single point failure.
I investigated the possibility of using austenitic stainless steels. In its annealed state, 316SS has yield strength of 540MPa. For a tank filled with liquid air, this would result in a tank mass fraction of 20.1% for a spherical tank with a safety factor of 4 on room temperature strength. For the hot water tank, the most economical choice appears to be Improved Formability HLSA, which has an ultimate tensile strength of 620MPa, is only 24% more expensive than A36 steel and is easily weldable on thickened sections. Mass fraction for this tank is 18% based on cold strength and SF of 4. The expansion chamber and nozzle are assumed to be constructed from 316SS also. I have assumed that these weigh half as much as the combined mass of the tanks. Adding additional mass for steering and assuming a 5% payload fraction, takes the overall dry mass fraction of the first stage to 35%. On this basis, total delta-V would be about 550m/s. I have really made an educated guess that air resistance and ceiling will consume one third of the total propulsive delta-V of the stage, because it is extremely difficult to work out precisely. Peak air resistance deceleration for Sea Dragon was 0.2g, gravity losses are obviously 1g, so for a vehicle that accelerates at 4g, 30% would appear about right. This would put the maximum ceiling of the stage at 10.3km (33,500’). This largely fails the design criteria, as air density is ~25% sea level at this height, meaning the upper stage engines would not be firing in vacuum and air resistance is considerable.
My attentions turned to cold working austenitic stainless steel. According to the AK Steel 304SS data sheet, 304SS has annealed room temperature UTS of ~600MPa and 0.2% YS of 241MPa. With 25% cold working, UTS increases 920MPa and YS = 750MPa. Elongation is ~20%.
For a stage with take-off weight 300tonnes, 20% dry fraction (including payload), some 192 tonnes of liquid air/N2 must be stored. This has a density of 870kg/m3 close to boiling point. A spherical pressure vessel must be 7.16m in diameter to contain it, assuming zero ullage space. If the tank has a pressure of 30 bar, the wall thickness would be 2.33cm (0.92”) assuming safety factor of 4. The dry mass fraction of the tank is 13.2% for a tank weighing just under 30 metric tonnes. The water tank made from IF HSLA would weigh 8800kg. The water propellant contained within the tank weighs 48 tonnes. Again, I will assume that the engine chamber and nozzle weighs half as much as the combined empty weight of the tanks, say 19,000kg. For plumbing, outer skin, attitude control, and drag chute, I will add another 10 tonnes. Total vehicle dry weight would be 67.3 tonnes. Assuming that the upper stages and payload weigh 15 tonnes, the total dry weight would be 82.3 tonnes, versus a total propellant weight of 240 tonnes. This gives an overall mass ratio of 25.5%. Assuming a Ve of 600m/s, gives a total delta-V of 819m/s. Again, air resistance and gravity losses are taken to account for one third of total energy expenditure. On this basis, maximum ceiling works out to be 23,054m (74,900’). The atmospheric pressure at this height is about 2KPa. Would that be enough to achieve the design objects? Maybe just.
I have made a lot of hunches and guesses that might turn out to be erroneous. I have assumed that 25% cold worked 304SS is acceptable material for a pressure vessel at -196C. If it isn’t, then dry weight could be heavier still. I have assumed a safety factor of 4, as per ASME pressure vessel regulations. Non-destructive testing might bring that down a bit, but would add cost to the vessel and complexity to build operations. I have probably under-estimated the weight of ancillary equipment, such as plumbing, attitude control surfaces, exterior housing and the drag chute (which is essential to reusability). I have made no account for the need for insulation on both tanks.
Other ways of getting the weight down would be the use of fibre-composite tanks. These would cut dry weight by half or more, but appear to be difficult (therefore expensive) to make and I do not know how well they would stand up to repeated ocean impacts, which would result in acceleration loading of several g’s and probably numerous point loadings onto the fibre-epoxy casing of the tank. The added expense and complication would appear to violate a design principle of the idea, which is supposed to be a cheap and simple way of clearing the Earth’s atmosphere. The stage could use lower pressure tanks and gas jet pumps to increase the pressure of fluid delivered to the engine chamber. But again, this introduces complexity into something that needs to be simple. Without a detailed cost-benefit analysis it is difficult to be sure. Are there any other stainless steels that can be manufactured in 1” gauge that are both stronger and sufficiently ductile at -196C? My guess is that the viability of the liquid nitrogen lower stage rests on the answer.
If the LN2 lower stage proves too heavy, the alternatives are some sort of easily reusable solid booster, as per GWs recommendation or a very simple pressure fed, liquid fuelled lower stage. The first option would work best if propellant costs were no more than a few dollars per kg and the devices could be rapidly and cheaply refurbished between flights. The second option could work well if the same conditions apply. A nitrous oxide (laughing gas) / propane propellant combination is room temperature storable, does not need cryogenic steels and self-igniting if a portion of the N2O is put through a catalyst bed. Both stage ideas could make use of clustered flow-formed propellant tanks, which are limited to about 70cm in diameter.
Last edited by Antius (2016-08-23 05:58:53)
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I have carried out some additional calculations. By reducing thrust chamber pressure to 10 bars, tank pressure is reduced to 20 bars. This reduces exhaust velocity by 9% to an average of 549.3m/s. However, total tank weight drops by 1/3rd. To provide sufficient thrust to accelerate a rocket vehicle of mass 300 tonnes at a chamber pressure of 1MPa, the thrust chamber must have diameter of 4.05m. This is 57% the diameter of the nitrogen tank and operates at half the pressure, so the thrust chamber itself will actually have 9% of the mass of the LN2 tank. I am going to assume that the nozzle has similar mass.
Working at only 2/3rds the pressure, the LN2 tank would weigh 13,000kg, the hot water tank would weigh 5,867kg and the thrust chamber and nozzle would weigh 2,340kg. Additional items were previously assumed to add 10,000kg to dry empty weight. This gives a total dry stage weight (minus payload) of 31,207kg. The propellant inventory would weigh 240,000kg. Assuming that upper stage and payload weigh 15,000kg, the mass ratio of the stage is 6.194 giving a total delta-V of 1001.7m/s. Assuming again, 33% drag and gravity losses, the stage would exhaust its forward momentum at a height of 34.48km (112,000’).
The concept therefore meets its design objectives, although this is largely accomplished at the expense of mass ratio. Assuming the upper stages have a mass ratio of 30, then a ground take-off weight of 300,000kg will deliver just 500kg to orbit – using the N2 lower stage therefore results in a very large take-off mass for each kg delivered to orbit. This may be acceptable due to the very low cost of liquid nitrogen hot water bipropellant, which was previously calculated to be $0.017/kg. On this basis, the fuel cost of operating the lower stage is $8.16/kg delivered to low Earth orbit.
A LOX/RP-1 stage operating under the same conditions would have a mass ratio of 1.4 for a 3000m/s average exhaust velocity. Assuming a total dry stage weight, excluding payload of 20%, some 50% of take-off mass would be payload (i.e. upper stages). This means that to launch 500kg into orbit would require 12,000kg of LOX/RP-1. Liquid oxygen costs about $0.1/kg, RP-1 costs about $0.5/kg. A mix of 2.3 to 1 would cost $0.22/kg. Total fuel cost would be $2640 or $5.28/kg payload lifted to orbit.
So LOX/RP-1 fuel costs would be lower than LN2/H2O costs and the stage takeoff weight (excluding payload) would be almost 20 times less massive. Unless the liquid nitrogen stage has cheaper capital and operating costs, it will not compete favourably against a pressure-fed RP1/LOX lower stage. It is hard to see how it could, given that it is 20 times larger.
Last edited by Antius (2016-08-23 11:15:41)
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