Section 4.6 - Low-G Transport
Not every type of cargo can withstand the high acceleration of the Hypervelocity Launcher. In particular, humans are limited to about 3-6 gravities. So until this step of the combined system, we used whatever existing launchers were available for people and delicate cargo. With the availability of the Skyhook we now consider the alternatives for this task and how to choose among them.
Choosing among Alternatives
There are already existing rockets for launching cargo and people into space, and new ones are under development. We assume this will continue to be true in the future. In engineering design, parts are subjected to a Make or Buy Analysis to determine whether to make a part internally, or buy it from someone else. This method also applies to the human transport job. If building our own launcher is sufficiently better on cost, technical risk, and other parameters, then we do so. If better alternatives are available from others, then simply buy the launch services. Comparing all the alternatives is called a Trade Study. First you choose the parameters to use to compare with, and a scoring system to convert diverse parameters into a common scale. You then make the best estimates for each alternative, and choose the one that scores best. When doing a trade study, it is important to use the same assumptions, such as material strengths, for all the alternatives.
Technology and what alternate systems are available changes over time. There is also uncertainty in the engineering estimates before design and construction is completed. Input assumptions like tons of cargo per year can vary over time. Thus for a complex system, a single point comparison is not sufficient. A Sensitivity Analysis looks at variations of parameters and assumptions ahead of time to see how it affects the final choice. This can be done efficiently with a mathematical or computer model of the system. Later on, when one of the conditions just mentioned changes, the trade study should be repeated to see if the previous answer is still valid.
Existing and In-Development Launchers
As of 2012, the following launchers are specifically designed to transport humans, which requires a pressurized environment and other design features. Other existing and under-development launchers can deliver cargo, and some of those could be adapted to carrying humans.
Crew Transportation System
This is a NASA funded project with multiple private sector contracts to develop components and ultimately a functioning transport system. As of April 2012, proposals for the next stage of development were being reviewed by NASA.
Space Launch System
A project from Reaction Engines Limited (REL) with Alan Bond directing the efforts. The Skylon spaceplane is designed as a single-stage-to-orbit craft, that can take off and land like a normal airplane. The engine is built around a hybrid approach, it functions both as a normal air-breathing engine (jet) and a rocket (in the high atmosphere). This setup is intended to reduce the amount of oxidizer propellant required to send cargo into space as to cut costs.
An European Space Agency (ESA) design evaluation commissioned by the UK Space Agency (UKSA) and concluded in May 2011 stating that "ESA has not identified any critical topics that would prevent a successful development of the engine,".
As of April 2012 the funding of the project was mostly from private investors 85%, and funding is still being sought to complete the project. The Reaction Engines Ltd Skylon Users' Manual (Rev 1, Sep 2009) gives extensive detail about the vehicle and it's engine.
These are potential launchers to add to our combined system. They are not in any particular order. A considerable amount of design work will be needed before reliable estimates can be made, and then comparison among them and existing launchers. So for now this is merely a list with some rough estimates.
The Stratolaunch system currently in development uses a subsonic carrier aircraft. The Jet boost launcher uses military fighter engines to reach supersonic speeds and higher altitudes. Both systems share the idea of using air-breathing engines for the early part of the flight, which are 4-20 times as efficient as rocket engines. They also avoid using rocket engines in the least efficient part of their operating range: going vertically, which causes gravity loss, and through dense air where you have drag and engine pressure loss. Jet boost dispenses with most of the carrier aircraft by using vertical launch and landing. Using wings allows getting more mass off the ground, but they also limit operating altitude. Less hardware to develop should lower the development cost. The engines are mounted to a Booster Ring, which in turn carries the rocket stage. The booster ring lifts the rocket to around 15 km altitude and 480 m/s (Mach 1.6) velocity. The rocket ignites and continues it's flight from there, while the booster ring returns to a vertical landing at the launch site.
For human transport, the minimum capacity is 1 person. Extrapolating from the SpaceX Dragon capsule mass, which carries up to 7 people, we estimate total mass to orbit as 1,500 kg, of which 750 kg is passenger and life support, or uncrewed low g cargo. In an early version the Skyhook would not be present and the launcher is used to deliver the first components for orbital assembly. Air-breathing boosters function better with more air, so unlike an all-rocket system, they prefer to launch at low altitude. We assume a sea-level equatorial launch site. For a 200 km altitude circular orbit a delta V of 7,900 m/s is required from 15 km, including potential and kinetic energy. The Earth's rotation contributes 465 m/s, and gravity, drag, and pressure losses are assumed to be 200 m/s from that starting altitude. Therefore the net velocity for the rocket stages is 7635 m/s.
We assume a re-used two stage chemical rocket with exhaust velocity of 3350 m/s, similar to the SpaceX Merlin 1C extended nozzle engine. Since ignition of the rocket is at altitude, we optimize it for vacuum thrust, which is effectively the operating condition after the first 20 seconds of operation. We increase the Falcon inert mass from 6.5% of stage mass to 11% of stage mass to account for heat shield and other stage recovery hardware so it can be used again. Each stage is assigned 50% of the required velocity, so the calculations are as follows:
- Stage 2 delta-V = 3817 m/s. Mass ratio = 3.125, so final mass = 32% of start mass. Stage inert = 11% x 68% of start mass fuel consumed = 7.5% of start mass. Thus payload = 24.5% of start mass, and also equal to 1500 kg from above. Therefore Stage 2 start mass = 6,122 kg.
- Stage 1 delta-V = 3818 m/s. Mass ratio = 3.126, so final mass = 32% of start mass. Stage inert = 11% x 68% of start mass = 7.5% of start mass. Thus Stage 2 + Payload (what the first stage has to carry) = 24.5% of start mass, and also = 6,122 kg, thus Start mass = 24,989 kg, which we round up to 25,000 kg.
- A modern fighter engine such as the PW F-135 generates 191 kN thrust on full afterburner at sea level. For performance reasons, we want to take off at 2.0 gravities, thus the allowed mass is 9.74 tons per engine. The engine itself (1700 kg) , fuel (450 kg), and booster ring hardware (590 kg) has an estimated mass of 2.74 tons . Thus each engine can lift 7 tons of rocket stages and payload, and we need 4 engines for the 25 ton rocket with some margin.
The net payload to orbit of 3% of the rocket initial mass is not remarkable, but the ability to recover and use all the stages repeatedly is. Liftoff mass of the booster ring + rocket is 36 tons, about an order of magnitude smaller than the Falcon 9 vehicle + Dragon capsule, and it should therefore be proportionally less expensive to develop. If not too much low-g cargo needs to be delivered to orbit, or if other launch systems reach comparable operating costs, then this system may not be justified. Buying launch capacity from someone else would be less total cost.
For an advanced version, we assume the Skyhook is in place and reduces the required velocity rocket to 4,810 m/s. For this version we assume a single rocket stage, and keep other values as above. The mass ratio is then 4.2, leaving 23.8% of start mass after rocket burn. Net cargo mass is 12.8% of rocket initial mass. With a 20 ton rocket stage, that provides 2.5 tons cargo to the Skyhook, or about 3 human passengers. If larger payloads are desired, then the booster ring would need more than 3 jet engines. A reasonable limit would be 8 jet engines, which can lift up to 56 tons of rocket stage, and deliver 7.15 tons of cargo.
Gun Boosted Ramjet
Ramjets are mechanically simple compared to turbine type jet engines, so potentially low cost. The drawback is they do not function at low velocity, so for this alternative we assume a low acceleration gun is used to reach sufficient velocity for the ramjet to operate. At higher velocity, ramjets lose performance, so the vehicle will use rocket power to finish the mission.
The gun location is assumed to be on a mountain slope with a barrel length of 6 km, and the ends at 3200 and 4200 m elevation, such as the SW slope of Cayambe, Ecuador. Acceleration is limited to 6 g's (60 m/s2) for human passengers, so the muzzle velocity is 850 m/s (Mach 2.8). An uncomplicated ramjet will operate roughly over a 2:1 velocity range. Beyond that requires more compensation in inlet shape and combustion conditions, so we assume the maximum velocity will be 1700 m/s. Average equivalent exhaust velocity is about 14 km/s over this range, using hydrocarbon fuel. We will assume single stage to orbit and do calculations purely on theoretical performance for now.
Single Passenger Scaling
For a single passenger minimal system, we again assume a 1500 kg capsule with 750 kg of delivered human + life support, or low g cargo. Calculations are as follows:
- Rocket mass: 12,500 kg - The rocket stage needs to supply 5,900 m/s net, which implies a mass ratio of 5.88, or 17% final mass. With 11% harware mass, we end up with 6% payload. Our initial rocket mass is therefore payload in kg/payload in percent = 12,500 kg, or about 1/3 lighter than the Jet Boost concept.
- Ramjet thrust: 400 kN - At an average climb rate of 210 m/s, we want the ramjet to gain 850 m/s velocity over 40 seconds, or a little over 20 m/s2. Therefore the ramjet thrust needs to be 250 kN for acceleration. Drag is roughly estimated at 150 kN, so total engine thrust is estimated at 400 kN (90,000 lb) A very rough estimate of engine size would be 1.0 m2 in area. Since this is less than human passenger capsule size (1.6 m seated), the passenger size will govern barrel diameter.
- Ramjet mass: 3950 kg - Ramjet Thrust to engine mass ratio averages about 20:1, thus the engine will have a mass of around 2000 kg. Fuel required is about 1150 kg, and remaining ramjet related parts about 800 kg. So total ramjet stage would be 3,950 kg.
- Total mass: 16,500 kg - By adding the rocket and ramjet stages, or about 40% less than the jet boost. It should be emphasized that these are preliminary calculations.
- Gun pressure: 500 kPa - A 1.6 m barrel accelerating 16,500 kg at 60 m/s2 requires a total force of 990 kN. Dividing by the barrel area gives a pressure of 492 kPa ( 71 psi ). This is not expected to be a difficult challenge from a technical standpoint. More of a challenge will be installing 6 km of pipe on a mountain.
Small Prototype Scaling
To build a small scale demonstrator for this concept, let us assume a payload of 20 kg to orbit, with a higher allowed acceleration of 10 g's, and a two stage rocket. The higher acceleration allows us to reach 900 m/s over a shorter barrel length of 4 km, and the ramjet function up to 900 m/s. The net velocity for the rocket stages is then 5,835 m/s, or 2918 m/s each. For a smaller size we assume slightly lower exhaust velocity (3300 m/s) and higher hardware fraction (15%). Mass ratio for each stage is 2.42. Weights are calculated as follows:
- Stage 2 final mass = 1/mass fraction = 41.3%
- Stage 2 payload mass = final mass - hardware = 41.3% - 15% = 26.3% = 20 kg (by assumption)
- Stage 2 initial mass = 20 kg / 26.3% = 75 kg
- Stage 1 final mass = 41.3% (same velocity as 2nd stage)
- Stage 1 fuel used = 1 - final mass = 58.7 %
- Stage 1 hardware weight = 15% x fuel used = 8.8%
- Total Stage 1 = fuel + hardware = 67.5%
- Stage 2 then = 32.5% of launch weight.
- Total mass = Stage 2 / 32.5% = 231 kg
At 20 m/s2 acceleration, the ramjet needs to provide about 5000 N thrust ( 1100 lb ), which only requires roughly 1/80 square meters engine area. The rocket stages can be represented by a cone 0.5 meters in diameter and 3.5 meters tall with a density of 1, so the engine is small relative to the rocket stage diameter. Ramjet mass would be around 25 kg, and fuel used about 15 kg. Total launch mass would then be 271 kg. Allow 29 kg for carrier/sabot to fit the barrel, and we have an accelerated mass of 300 kg. At 100 m/s2, the acceleration force then is 30 kN, and the required pressure is 152 kPa ( 22 psi ).
Low Acceleration Guns
You can launch people and delicate cargo with a gas pressure type accelerator if you lower the g forces sufficiently. That forces the barrel length to be as long as possible, so we need to look at geography to select a location. Two good locations present themselves, although others may be possible.
- Island of Hawaii
Hawaii is the best location on Earth as far as a large constant slope mountain, requiring minimal grading and support for the barrel, and so lower construction cost. An equatorial site would be preferred to meet up with the Skyhook, but let us first look at Hawaii. It is a shield volcano and cooling lava flows at a constant slope. Therefore you have a nearly perfect ramp on the west side of the island pointing up to the east to build on about 22 km long. You could get as much as 100 km if you extend down into the ocean or add support towers on the eastern slope, but that would be more expensive than building at ground level. For a 100 km long version at 6 g's the muzzle velocity could be as high as 3,460 m/s, but we will use 20 km for this example.
Design Scaling - Assume a 20 km long pipe x 10 m diameter, pushing a 500 ton single stage multiple use rocket. The vehicle will not fill the whole pipe, it is shaped for aerodynamics, and rides on a sled and pusher plate that fits the pipe. It works out the pressure in the barrel needs to be 2 atmospheres (200kPa, 30 psi) to give you 3 g's acceleration, safe for most humans (general public) and satellite parts. Muzzle velocity is 1100 m/s (Mach 3.6), which is not a huge fraction of orbit velocity, but a nice running start before you light up your on-board rocket. Given those starting conditions, a non-cryogenic rocket should have a payload of around 35 tons, which along with a 10 meter maximum diameter should be plenty for any cargo or people you want to launch. This is the upper end of what you might want to build in terms of barrel diameter. For higher mass vehicles, you just need higher operating pressure in the barrel. A first low-g cargo launcher can be a lot smaller than 10 meters, and increased in performance by adding length or going to larger barrels over time. Hawaii is about 20 degrees N latitude, so a launch from there would not be able to reach an equatorial Skyhook, but it would deliver more passengers and cargo than an unaided rocket.
- Cayembe, Ecuador
Cayembe is the name of both a city and large mountain about 50 km north-east of Quito, Ecuador. We previously discussed a hypervelocity launcher on the side of the mountain. For transporting people, the barrel will need to be much longer for lower acceleration, and extend west somewhat past the town. For this version we assume a trained crew rather than general public. With pressure suits, conforming seats, +x acceleration (forward facing seats), and crew in good condition you can safely use 6 g's, and thus get a muzzle velocity of 1560 m/s. That's Mach 5.2, or 20% of orbit velocity. The Skyhook has been available since the previous step in the combined system example, which subtracts another 2400 m/s from the rocket stage requirement.
The geography of Ecuador is not a smooth slope like Hawaii. We assume the barrel is 20.25 km long, but curved upward with a segmented radius that keeps centrifugal acceleration at or below 12 m/s^2. That will be felt by passengers as a vertical acceleration (head to toe). The barrel will need to be supported on towers or use tunnels as needed to fit the terrain, and the curvature roughly fits the geography, which is flat initially, rising to a mountain at the end. The ends are at 2778 m elevation south west of the town, and 5731 m at the top of the mountain, with initial and final slopes of 1.4 and 12.4 degrees caused by the curved barrel The gentle curvature keeps the vertical acceleration low relative to the forward acceleration. The higher slope at the muzzle end also allows faster climb through the atmosphere and less drag loss. These assumptions may be changed with more detailed analysis. We assume the rocket stage is 4 x 32 meters in size, and closely fits the barrel, with a mass of 400 tons at launch.
Drag - With a drag coefficient of 0.2, the rocket stage will see 1.93 MN of drag at the muzzle, producing -4.82 m/s^2 deceleration if the rocket does not ignite immediately. The climb rate of sin(12 deg) x 1560 m/s = 335 m/s. The equivalent thickness of the atmosphere is called the scale height (8640 m vertically) over which the pressure drops by a factor of e (2.718...). An exponential pressure decay per scale height over many km is how the real atmospheric pressure changes, but it can be approximated as the muzzle pressure for one vertical scale height and then dropping to zero. 8640 m scale height / 335 m/s vertical velocity = 25.76 sec. Multiplied by the deceleration the total drag loss can be estimated at 124 m/s. This value will change depending when the rocket is started, since drag is a function of velocity.
Rocket Performance - The net velocity required for the rocket is found from the Skyhook tip velocity relative to the Earth's center (5074 m/s), less the Earth's rotation at the equator (-465 m/s) and gun velocity (-1560 m/s) plus drag loss (+124 m/s) and other losses and maneuvering which we make an estimate for (+200 m/s). This comes to 3,373 m/s net. The SpaceX Merlin engine has an exhaust velocity of 2980 m/s. 4-6 engines will probably be required for sufficient thrust. The rocket equation gives the rocket mass after reaching the Skyhook as 32.2% of initial mass. Allowing 10% for the vehicle itself gives 22.2% payload, or 89 tons. This is a large passenger and cargo capacity, with a correspondingly large Skyhook to support the arrival mass. A first version would likely be smaller.
Knowing the area of the barrel and the rocket vehicle mass and acceleration, we can calculate the required pressure as 1.91 MPa ( 277 psi ) for the 4 meter gun and 1.22 MPa ( 177 psi ) for a 2.5 meter gun. The challenge will not be barrel pressure, but filling it fast enough when the projectile is moving rapidly. The length will likely require tanks and valves space out along the barrel. The muzzle velocity will likely require a heated gas to fill the pipe, but exactly which gas will be left for detailed analysis. Large gas accelerators have reached above twice the muzzle velocity, so it is more a matter of lowest cost than feasibility.
Spaceport Growth - We had previously built an operational Hypervelocity Gun on the mountain with a muzzle velocity of 5000 m/s and an unaided payload to orbit of 180 kg. With the Skyhook in place, we can calculate the new payload as follows:
- The Skyhook's tip velocity relative to Earth's center is 5074 m/s. Earth's rotation deducts 465 m/s. Drag loss is 1000 m/s from the initial 5000 m/s. Trajectory elevation of 23 degrees means the horizontal component, which is all that counts for getting to orbit, is cos(23 deg) = 0.9205 x 4000 m/s after drag = 3682 m/s. We allow an extra 200 m/s for maneuvering and other unaccounted losses. So the net delta-V of the rocket becomes 1127 m/s.
- Using the same exhaust velocity as the SpaceX Merlin engine (2980 m/s) but at 1/60th the thrust level, we get a final mass of 68.5% x 1200 kg start mass = 822 kg. With the same empty vehicle mass of 180 kg as the version before the Skyhook, we now have 642 kg payload, or about 3.5 times as much.
Going from 642 kg payload with a 60 cm caliber (barrel diameter) gun to 89 tons with the 4 meter caliber human accelerator is a factor of 139 times larger. Since the Skyhook has to be enlarged for the larger delivery mass, a program of gradual improvement will be needed. The launchers will add barrel length and move to larger diameters in steps, and use part of their cargo to deliver Skyhook cable and other materials, so that later deliveries with more payload can be handled. If orbital mining can supply sufficiently strong materials, they can be used, but otherwise they can come from Earth. A smaller version of the human accelerator than the one above could use a 2.5 x 20 m size rocket vehicle with a mass of 100 tons. Using similar calculations, we end up with 20 tons net cargo for it. At some point the low-g accelerator would be too small for seated human passengers, probably around 1.6 meter diameter, but they can still be used for sensitive cargo. Bulk non-sensitive cargo will always have a cost advantage because the higher muzzle velocity lets you deliver 3 times more payload as a percentage of rocket vehicle weight, so it makes sense to keep both types of launchers.
Depending on traffic needs, you may want to keep smaller launchers operating in parallel with their larger replacements. In theory you could launch every time the Skyhook passes over in its orbit, which is every 100 minutes, but barrel cool down or other needs may prevent firing a given gun that often, so having several may be useful. At the upper bound, delivering 89 tons per launch x 14.4 orbits per day x 300 days per year (allowing some maintenance time) yields an astounding 384,480 tons/year to orbit. This compares to the ~1,000 ton/year capacity of current and near-term launchers worldwide.
Cost - At this point, cost has not been estimated to any degree of accuracy. The Falcon 9 rocket has a total mass of 333.4 tons and a payload to low orbit of 10.45 tons. So the ratio of rocket mass besides payload to payload is 30.9 to 1. The bulk cargo launcher has a non payload mass of 558 kg vs 642 kg payload, or a ratio of 0.87 to 1. This 35.5 to 1 advantage should lower costs significantly, but not in that exact ratio. The gun and Skyhook are large installations relative to the rocket stage, and their cost per use will depend on how many times they are used. The Falcon 9 hardware is not currently reused, while the rocket stage is intended to be used multiple times. De-orbiting from the Skyhook is 63% of the unaided velocity from orbit, and thus (0.63)^2 = 39.5% of the kinetic energy to dissipate. This makes the heat shield easier to design, and the stage is pretty rugged in design, since it needs to be fired out of a gun at high acceleration. So in principle it should be able to be recovered and used again.
In the absence of more detailed estimates, for now we will adopt the 35.5 times reduction in rocket size per payload and apply it to the $54 million/10,450 kg = 5,167 $/kg Falcon 9 cost, to get a first estimate of 146 $/kg. To compare to some popular consumer items, the iPad 3 64 GB costs 583 $/kg including packaging, and a Toyota Camry is about 15 $/kg, although neither is designed to survive high-g launch.