Space Transport and Engineering Methods/Phase2B

&emsp;Most of the development in Phases 1 through 3 is aimed at upgrading civilization on Earth, and expanding it to more difficult environments on our planet. But the Earth is finite, and regions in space have vast amounts of available physical space, raw materials, and energy resources to continue that work. So Phases 4 through 6 are aimed at developing those regions and continuing the upgrade and expansion of civilization throughout the Solar System and beyond. In that process we also want meet the program objectives noted in Section 4.1. Several of those objectives benefit Earth, but use space activity to reach them. Conversely, civilization started on Earth, so future development of space has to start here, and will involve continued support and interaction from Earth with the later phases.

&emsp;This section of the book then addresses the meeting point of Earth and Space - that part of Phase 2B on Earth which supports and interacts with Phases 4 through 6 in space, and in turn helps meet the main program goals and objective. However, we are not starting with a clean slate. Space industry is already global, large-scale, and on-going, and most of the activity happens on Earth. Our concepts must therefore account for these existing projects and activities. We also want to address the following questions:


 * What new projects and locations are needed to accomplish our future goals?
 * What parts of existing space projects and locations should remain as they are, in parallel with new ones we add?
 * Do some of the new projects and locations belong in other phases?
 * What industry categories and products are needed in this phase?
 * How will the new projects and locations interact with the rest of our program, existing space programs, and the rest of civilization?
 * In what sequence should the new projects and locations and their products be built?

Concept Exploration
&emsp;Our work here is early concept exploration, the first step among many in a project. It is in no sense finished, but rather a starting point for further work. In later sections of the book we are concerned with developing different regions in space. These are unfamiliar to most people, so we begin those sections by describing the regions in general, their environment parameters, and energy and material resources. We expect most of the new development on Earth will be in moderate environments. These are familiar enough that we do not need to provide a general description in this section. Instead, we will note important features as they come up, and when locations in other environments are needed.

&emsp;Our exploration begins with a survey of the full range of industries on Earth, noting which have current space-related activity, and where there are possible future additions. Since much of the future activity will be based on later needs in space, we have to consider later program phases to determine what will be needed on Earth. We then look at project drivers, including motivations, economics, and technology, to identify which industries can move forward, and when. From past work by others and our own work, we identify specific projects to satisfy the identified needs. We combine all the information into a concept for the phase. This includes a general approach, a list of projects by time and function, how they relate to each other, and to other program phases. In reaching a phase concept we consider different alternatives, develop project details, and make estimates and calculations. They are included as the later parts of this section. Since our work is as yet incomplete, there will be gaps in the discussion. An output from our analysis will be identifying R&D work which will be needed for the respective projects. This is fed back to planning for Phase 0D - R&D for Industrial Locations.

Existing Space Industry
&emsp;According to the Satellite Industry Association, global space industry as of 2016 was US$339 billion/year. These existing projects were previously described in Section 1.9. Most parts of existing space activities are actually carried out on Earth, with a relatively small amount of equipment and people in orbit. For example, just one of NASA's Crawler-Transporters, which carry rockets at the Kennedy Space Center, has a mass of 2700 tons. This is 6.4 times the mass of the entire International Space Station (ISS). NASA's total ground equipment and facilities is much larger, and their ~100,000 government and contractor employees dwarfs the six astronauts who occupy the ISS. This high ratio of ground to space activity will continue until we change how we deliver things to orbit and start to exploit resources already in space. Even then, a significant amount of people and equipment will continue to come from Earth, and space-related industries continue to operate here. Our planet will remain an important part of supporting later program phases in space.

New Project Phasing
&emsp;We will look at changes to existing industries, and new projects that will be needed on Earth, to support later phases of our program in space. To date, production and launch of space equipment has used industrial-scale facilities. Therefore we place the new projects within Phase 2B Industrial Locations. They will make up a subset of all industrial activity in Phase 2B, most of which will be products for use on Earth. The space industry subset strongly interacts with other industries in Phase 2B, and the rest of civilization outside the program. For example, a rocket launch site will typically obtain concrete, steel, and electricity from outside industries, rather than producing them locally. Such locations will mostly be in moderate environments, but some may end up in difficult or extreme ones. When those are identified they will be assigned to Phase 3 as needed. Some of the activity may be small enough in scale to fall into Phase 2A Distributed Locations, and some of the long-term projects have an orbital component. They will be mentioned here as they come up, and assigned to their respective phases later.

Industry Survey
&emsp;Phase 2B as a whole covers all types of industrial-scale projects in moderate environments on Earth. In this section we are concerned with the subset which are needed to support later parts of the program in space. Where existing and expected development are already sufficient, we note that, but do not go into much detail. Where additional or unique projects will be needed at some point in time, we try to note what they are. Our list of industry categories is drawn from the latest version of the North American Industry Classification System (NAICS), and we adopt their numbering system. This allows for easier comparison to other data about industry on Earth.

11 - Agriculture: People in space, and those working on space-related projects on Earth, need food to live. Agriculture is already well-developed on Earth, so supply to projects on the ground should be sufficient. For people working and living in space, they will need packaged and storable food to the extent they cannot grow it locally. Once local production is set up in space, there are likely to be food items which are not practical to make locally. There will also likely be a need for modified organisms for the space environment, agricultural equipment, fertilizers, and trace elements which cannot be produced or found locally in space. To the extent they cannot be provided from some region in space, they would need to come from Earth.

21 - Mining: Extraction and processing of raw materials is also well-developed on Earth. Supply of such materials for space projects on Earth is expected to be sufficient. An example is crushed stone and steel to build a new rocket launch site. Hardware to be made on Earth, and delivered to and used in space, sometimes needs specialty materials. Once mining and production is established in space, there are likely to be rare materials and components which are still better supplied from Earth. If those exceed existing Earth industry or need custom design, they may need new projects to support them.

22 - Utilities: Moderate locations on Earth either already have sufficient utilities, or it is straightforward to add them to support new industrial locations.

23 - Construction:

31-33 - Manufacturing:

42 - Wholesale Trade:

44-45 - Retail Trade:

48-49 - Transportation and Warehousing:

51 - Information:

52 - Finance and Insurance:

53 - Real Estate, Rental, and Leasing:

54 - Professional, Scientific, and Technical:

55-56 - Management and Organizational Support:

61 - Education:

62 - Health and Social Services:

71 - Arts, Entertainment, and Recreation:

72 - Accommodations and Food:

81 - Other Services:

92 - Public Administration:

Development Projects
&emsp;We first describe our general approach to Phase 2B projects for space, then organize the ones we have identified by time frame and major function. Since reaching space is necessary to carry out the later phases, a large portion of the projects will fall to the transport function.

General Approach
&emsp;Extensive space industries and projects already exist on Earth, and are likely to continue for the forseeable future. Where these existing projects are useful, we would keep them as they are. As changes and new projects are needed, they would be introduced gradually over time. Current production and operating locations would be re-used to the extent possible to lower costs. We organize projects for this phase by time into four groups. The ones farther in time typically depend on earlier ones to get started, require more R&D to get ready for them, or await markets developing to the point they are needed. Later projects will also benefit from better technology and capabilities from other parts of our program, and from the rest of civilization. The four sets by time are:


 * Current - those already operating, or have started detail design or are in later stages of development.
 * Near-term - those that are planned to reach detailed design within 10 years, and have significant funding sources available.
 * Mid-term - those which can reasonably start detailed design in 10-30 years, and may or may not have funding sources.
 * Long-term - those which will likely need more than 30 years to reach detailed design.

&emsp;Large-scale non-space industry also exists on Earth, unlike space, which starts out undeveloped. For new projects, this make the incentives to bootstrap from starter sets and use local resources less on Earth than later phases in space. The seed factory approach would have been developed in earlier phases, and used in parallel for non-space industry in Phase 2B. So we include it as one of the tools of modern engineering and apply it to space industries when it is useful. The remainder of the industrial-scale projects for space are built and operated conventionally, by importing equipment and materials as-needed from other industries, either within the program or from outside it.

Industrial Production for Space
&emsp;Transport to space requires supplying cargo containers at a minimum, but usually more complex vehicles. Making these falls to the production function. Transport also requires some type of ground facilities. At a minimum the ground facilities support vehicle operations, but in some cases do much of the work of accelerating payloads to orbit. Building the ground facilities is also assigned to the production function. Operating the vehicles and ground facilities falls to the transport function. Whatever type of cargo is going to space must also be produced, or at least acquired. When produced internally they are also assigned to this function.

Industrial Habitation for Space
&emsp;This function in general includes large scale construction which is intended to be occupied by people. Examples include large office buildings, hotels, residential towers, retail complexes, and entertainment venues. Space for people to live, outside of their work for the program, is generally well-developed on Earth. So our program does not have to provide it, except to note where significant additions are needed. Office, laboratory, and other space to accommodate people working within the program are included in this function. In the case where people are living in a remote location, such as a floating ocean launch site, their living space would be provided by the program, and therefore included.

Industrial Transport for Space
&emsp;Phases 4-6 include future Orbital, Planetary System, and Interstellar Development. For any of that to happen, we first have to deliver people and equipment to space. The lowest stable orbits at 160 km altitude require 30.48 MJ/kg kinetic and 1.53 MJ/kg potential energy to reach. Those are ideal values, with current rockets consuming about 285 MJ/kg. This is because chemical rocket propellants don't contain enough energy relative to what is needed to reach Earth orbit. So existing rockets need a very large ratio of propellant to payload mass, yielding about 11% overall efficiency. Useful low-orbit payloads average 1,500 kg in mass, therefore needing 427.5 GJ per launch. A minimum reasonable launch rate is 6 times a year, so the total energy use is over 50 times annual average US electric consumption/capita. Beyond energy needs, transport systems need hardware and operations support, making such projects industrial scale activity, and therefore part of Phase 2B.

&emsp;Before 2015, the vehicle hardware was mostly used once and thrown away. To enable a useful payload mass while carrying so much propellant, the hardware had to be high performance and light weight. It was also produced in fairly small numbers. This made the hardware expensive, and throwing it away led to very high costs to reach space. Some post-2015 programs are developing reusable rockets. This will partly solve the cost problem, but the underlying inefficiency of chemical rockets remains. Our approach for the mid- and long-term is to replace part or all of the transport to Earth orbit with methods that are inherently more efficient. Alternately or in addition to this they would use equipment produced in larger quantities, or with less extreme performance needs, leading to lower costs.

&emsp;The transport function in general includes large scale delivery of energy, discrete and bulk cargo, fluids and gases, people, and data. Current transport to orbit uses the same vehicle for cheap bulk items, like propellants, as for people and high-value equipment. Safety, reliability, and other features are driven by the needs of the latter payload types. Those features are applied to the bulk payloads too, even if they don't need them. On Earth, we use different kinds of transportation depending on what is being carried. So another part of our approach is to use different transport methods suited to their respective payloads, when that makes sense.

Industrial Transport Alternatives
&emsp;Phases 4-6 cover a long period of time, and have a wide range of potential needs for transport from Earth. So the space transport portion of Phase 2B will also have to cover the same range times and needs. Our analysis will therefore look at a wide range of potential alternatives. The baseline option is to stay with currently existing launch systems, and those already under development or planned. One alternative is to keep the baseline systems, but add items like more launch pads and vehicles to increase capacity. Another is to explore new transport systems to be developed within our program. For current systems, we include ones already operating, and those which have entered detailed design and production. For planned we include those expected to start detailed design in the near-term (within 10 years), and have significant funding sources available.

&emsp;For new systems, one alternative is another conventional launch system, of the types already operating, but sized to meet our Phase 4-6 needs. Such a launch system may or may not have outside funding, but we assume using advanced production, of the type developed for our program, to lower costs. More advanced alternatives can be grouped into those that augment or supplement chemical rockets, but still use rockets as the primary method to reach orbit, and those which substantially or completely replace chemical rockets. The latter may depend partly on orbital systems which would be part of Phase 4A.

&emsp;Reasons to explore alternatives include not enough capacity in mass to orbit, or costs too high to make projects in later phases feasible. Additional reasons include improving system efficiency and lowering cost for business reasons. The development cost and complexity for new systems have to be weighed against the performance and payload gains they generate. Where new or more advanced methods are used they typically add substantial R&D time and cost. There is also a technical risk of the methods not working as intended, or less well than desired. The extra time, costs, and risks must then be weighed against the limitations of current and near-term systems to determine a preferred set of concepts. Our exploration of these alternatives begins with identifying what they are. In the concept details section below we compile later phase needs in terms of time and traffic. Finally, for each alternative, we attempt to estimate performance, costs, and risks.

Identifying the Alternatives

 *  Conventional Alternatives: 

&emsp;Current and near-term launch systems include a large variety of Multi-Stage Rockets and a few Air-Launched ones, where a carrier airplane takes the rocket above most of the atmosphere before ignition. Information about these systems can generally be found in their User's Manuals when they are in operation or later stages of development. For those in earlier stages, information can be found in public sources or by contacting the projects directly. For our current purpose, general information is sufficient. For new conventional systems we can design another pure rocket or subsonic air-launch system similar to existing ones, but sized to meet the expected traffic.


 *  Augmented Rocket Alternatives: 

&emsp;Augmented rockets use technology beyond what is currently used for launch to orbit. They still use chemical rockets for over 80% of the velocity needed. Since payload is non-linear with rocket velocity, a 20% reduction in the rocket portion can result in 50-80% increase in payload. Examples in this group include ejector rockets, high Mach carrier aircraft, aerostats, vertical jet boosters, and low-G gas accelerators. A combination of methods may be used to reach the 20% level.


 *  Rocket Replacement Alternatives: 

&emsp;Part 2 of this book provides an extensive list of space transport methods. We consider the subset which can replace 20-100% of the velocity from the Earth's surface to low orbit from conventional rocket stages. To do this they must overcome the Earth's gravity while contributing to orbital altitude and velocity. They must also operate safely in the atmosphere, and be feasible in the time frame of the later phases, both in technology readiness and cost. Multiple transport methods may be used to replace a higher percentage of the total velocity, including some of the augmented group. Examples include high Mach combined cycle air/rocket engines, hypervelocity gas or electromagnetic accelerators, and orbital spaceports with an elevator system. The last of these would be in low orbit and belong to Phase 4A, but can supply part of the velocity needed.

Traffic and Schedules
Which systems are suitable for later phases will depend on Traffic Models for the phases. These are launch needs in terms of payload sizes, mass, and quantity by year. Our models would be drawn from the needs of later program phases in space, and necessarily become more uncertain in later years. The long-term portion will mainly identify what early transport R&D should be invested in, so that they will be ready when the need arises. In developing a traffic model, larger payloads will need dedicated launches to their desired destinations. Smaller ones can fly as secondary cargo on an "as available" basis, when the main payload leaves some unused capacity. Transport capacity to fill the model's needs, for both existing and new systems, can be tabulated in terms of payload and number of launches per year.

Performance, Cost, and Risk Estimates
&emsp;Full-scale design of any large-scale system has to consider many factors. At the concept exploration stage, the most important are performance, cost, and risk. For transport to orbit, performance includes physical size, mass, destination orbit, and launch schedule. The schedule includes necessary time for R&D, design, and production for facilities and vehicles. Cost includes R&D, design, and production costs, plus ongoing operations costs. Technical risks are the uncertainties that the system will work at all, less well than desired, or suffer failures. Cost risks include availability of funding, uncertainties in development and operations costs, and market needs for the system. The more advanced and farther in the future a given alternative is, the less accurate our estimates become. That includes technology improvements that will happen outside our program. Even uncertain estimates are useful to identify R&D investments that have high potential gains. Some high-risk/high-payoff investments will not work out. This is acceptable if enough of them do to justify the overall R&D effort.

Industrial Services for Space
[TBD]

Program Integration
[TBD]

&emsp; -

Transport Details
&emsp;

Current & Near-Term Systems
&emsp;
 *  Current Conventional Rockets: 

The following is a subset of significant conventional rockets which have flown recently as of 2017, and multiple times previously, which we consider current. Payload masses are to Low Earth Orbit unless otherwise noted. Variant rocket configurations yield different payload masses.

&emsp;* Antares (US, Orbital ATK) - 6,500 kg

&emsp;* Ariane 5 (ESA, Arianespace/Airbus) - 16-20,000 kg

&emsp;* Atlas V (US, United Launch Alliance) - 9-20,500 kg

&emsp;* Delta IV (US, United Launch Alliance) - 13-28,899 kg


 *  Near-Term Conventional Rockets: 

This includes rockets expected to reach detailed design by 2027.

&emsp;* BFR (US, SpaceX) - 150,000 kg


 *  Current Air-Launched Rockets: 


 *  Near-Term Air-Launched Rockets: 

[To Merge]
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.

Soyuz

Shenzhou

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

Stratolaunch

Skylon

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 its engine.

New Conventional Rocket
&emsp;Conventional rocket design has been done many times in the past, and is well understood. We refer you to any of a number of texts and references on the subject, such as Rocket Propulsion Elements (9th ed., Sutton & Biblarz, 2017), for more detail. We give an example of a small multi-stage rocket to provide a general overview of the design process. That process starts with some initial assumptions, from which we can make an estimate of the vehicle size. We then progressively add more detail and do more accurate estimates. This will replace our initial estimate with a series of better ones, and possibly force revising the assumptions. A complete preliminary design considers all the major components and is at the point where you would start the detailed design and final drawings. We will not carry it that far, but want to show enough of the process to show how it is started.


 *  Design Assumptions 


 * Payload: 20 kg to 250 km circular orbit - This is very small for a practical system, but the same formulas work at any size. We need to specify an orbit to calculate the mission velocities.
 * G-Limit: 10 gravities or 100 m/s2 - This limits accelerations and structural loads on the payload. Larger payloads are typically limited to 6 g's, but ones this small can withstand higher acceleration without much penalty.
 * Exhaust Velocity: 3300 m/s in vacuum - This is typical of a moderate performance engine using Methane/Oxygen propellant mix.
 * All stages are re-used for cost reasons. Hardware mass fractions are assumed to be 14, 15, and 18% for the first to third stages. The upper stages would have higher fractions due to smaller size and increasing heat shielding.
 * Launch Site: Equator at 4600 m altitude - This is at Cayambe, Ecuador to take the most advantage of the Earth's rotation and highest starting altitude to reduce drag and mission velocity.


 *  Preliminary Estimate 

&emsp;Conventional rockets are sized by the Rocket Equation, which determines propellant mass ratios. A preliminary estimate of the velocity required can be made from experience. A second estimate will use a trajectory simulation that calculates fuel use, thrust, drag, and acceleration in small time steps.

&emsp;The ideal velocity to reach a 250 km orbit, neglecting losses, is found from the total energy of that orbit, which is the sum of kinetic and potential energy. Velocity is 7756 m/s, with an energy of 30.08 MJ/kg, and potential energy is 2.375 MJ/kg. The sum implies a velocity of 8,056 m/s. The various real losses may be estimated at 900 m/s based on experience, giving a total ideal velocity of 8956 m/s. Rotation of the Earth at the Equator is 465 m/s, thus the rocket has to produce a net velocity of 8,491 m/s. If we divide it equally into 3 stages, this gives 2830 m/s per stage. Mass estimates are calculated from top to bottom as follows:


 * Payload = 20 kg
 * Stage 3 final mass /initial mass = 42.4% - From rocket equation
 * Stage 3 hardware fraction = 18% - of entire stage including payload
 * Stage 3 initial mass = 20 kg / payload fraction = 20 kg / (final mass - hardware) = 81.9 kg
 * Stage 2 m(f)/m(i) = 42.4%
 * Stage 2 hardware = 15% x (100-42.4%) = 8.64% - of 2nd stage fuel only
 * Stage 2 initial mass = 81.9 kg / (42.4% - 8.64%) = 242.5 kg
 * Stage 1 m(f)/m(i) = 42.4%
 * Stage 1 hardware = 14% x (100-42.4%) = 8.06% - of 1st stage fuel only
 * Stage 1 initial mass = 242.5 kg / (42.4% - 8.06%) = 706 kg


 *  Second Size Estimate 

&emsp;To make a second estimate we need some details of the rocket thrust and drag, and therefore it's size and shape. We assume Oxygen/Methane fuel at 3.6:1 mixture ratio by mass. The chemistry of CH4 + 2O2 = CO2 + 2H2O has a theoretical mass ratio of 4 Oxygen : 1 Methane. By using slightly less Oxygen some of the Methane is left unburned, leaving CO or H2 in the exhaust. This lowers the average molecular weight and increases the exhaust velocity. It also ensures the combustion is not Oxygen rich, which would tend to react with surrounding materials.


 * Tank Sizing:

&emsp;From our preliminary masses above, we can determine tank sizes from the density of the respective fuels: Oxygen = 1140 kg/m3 and Methane = 423 kg/m3:


 * From above, all stages have a final mass of 42.4% of initial mass, therefore burn 57.6% of initial mass in fuel. Therefore fuel masses are 406.7, 139.7, and 47.2 kg.
 * With a mixture ratio of 3.6:1, the Methane component is 1/4.6 = 21.74% by mass, and Oxygen is the remainder. Thus the Methane mass by stage is 88.4, 30.4, and 10.25 kg, and the Oxygen mass by stage is 318.3, 109.3, and 36.95 kg.
 * From the densities we can calculate the respective tank volumes. Allowing 3% extra volume so that there is some pressurizing gas at the top of the tank and fuel margin, we obtain first stage tank volumes of 215 and 288 liters, second stage of 74 and 98.75 liters, and third stage of 24.95 and 33.35 liters for Methane and Oxygen respectively.
 * Rocket stage tanks can share a common wall between fuel and oxidizer if they are fully sealed, and usually use an ellipsoidal dome with a 70% height ratio to minimize structural mass. We assume the payload has a density of 1 kg/liter, and thus requires 20 liters volume.  For aerodynamic and structural reasons we want to keep the total vehicle height at 10 times the base diameter or less.  Each combined stage tank can be modeled as two ellipsoidal domes plus a cylinder.  Applying some geometry results in tank diameters of 60, 42, and 30 cm.


 * Drag Coefficient:



&emsp;From the tank sizes we can do a preliminary layout of the vehicle. We have to include a forward payload fairing and aft engine sections for each stage to get the total height of the vehicle. For this design we assume an aerospike type engine with platelet injectors for each stage, which gives a total vehicle height of about 6 meters. The layout shown here is not intended as a design drawing. It is a schematic sketch to estimate size and shape of the cylinder and cone sections, from which the drag can be estimated. The layout grid lines are at 25 cm spacing.

&emsp;At our assumed launch altitude of 4600 m, air density is 0.769 kg/m3, velocity averages 120 m/s in the subsonic region, the rocket length is 6 meters, and the reference viscosity of air is 18.27 x 10 -6 Pa-s. Therefore the Reynolds number, Re, averages 30.3 million, but it will change with altitude and velocity. From reference data as a function of velocity and Re, the skin friction coefficient, Csf, will vary from about 0.0032 at low velocity, to 0.00245 at 120 m/s, to 0.00215 at 240 m/s. This is adjusted by a correction factor based on the shape of the rocket, which in this case is 1.085, and the wetted area to cross section ratio, which is ~8.3/0.283 = 29.3. So the total drag coefficient will vary from 0.102 to 0.078 to 0.068 at the given speeds, based on cross section area. Drag coefficients at transonic and supersonic velocities are different, but found through similar steps.

&emsp;If the vehicle had a base area exclusive of the nozzle, we would need to add base drag. In the case of a functioning rocket, the exhaust fills the base and there is no low pressure area to create a net force by pressure difference relative to the front. If the vehicle flies other than directly pointing in the direction of motion, there will be an additional component of drag due to lift, but for this estimate we assume a zero-lift trajectory for simplicity.


 * Trajectory:

&emsp;The launch trajectory cannot be determined by a simple formula or graph, because the thrust, drag, and mass of the vehicle are all varying continuously. Therefore a simulation must be done in small time steps so that the above parameters are nearly constant within each step. If the average values within each step are close to correct, then the total trajectory will be nearly correct. This is too many calculations to do by hand, so a computer program or spreadsheet is used. The simulation takes as inputs variable vehicle masses and a Trajectory Profile, which is how the vehicle tilts vs time and varies thrust or does staging. The inputs are varied until the desired payload mass and orbit is reached. Modern trajectory simulations will vary the inputs automatically to find an optimal trajectory profile.


 * Reference Concept:

&emsp;With a known trajectory profile and propellant masses, the major dimensions of the stages can be determined, and a reference concept for the overall vehicle prepared. Preliminary design can proceed from this point to include layout of the engines and other major components, and their masses. From the vehicle design, preliminary work on the supporting ground systems (launch pad, handling equipment, storage tanks, etc.) can be started. Since we assumed a specific launch site, a site plan can be developed using the actual geography.

Augmented Rocket Alternatives
&emsp;The augmented rocket category still uses chemical rocket stages for at least 80% of the velocity change to reach orbit, but different or higher performance methods than sub-sonic air-launch used currently or in the near-term. These alternatives are not in any particular order. A considerable amount of work will be needed before we have reliable estimates for these systems. So we cannot yet choose among these and the other alternatives. For now we provide whatever details and calculations we have available.

Ejector Rocket
&emsp;This is a low grade augmentation by entraining air flow with the rocket exhaust. It increases thrust in the first stage by increasing mass flow.

Carrier Aircraft
&emsp;Current carriers are limited to subsonic speeds. More advanced ones can potentially reach about Mach 5 using ramjets.

Aerostats
&emsp;Lighter-than-air platforms can reach higher altitudes than winged aircraft, providing a better starting point for launch.

Jet Boost
Rather than using a carrier aircraft, this approach uses high thrust/weight jet engines as a first stage for vertical launch and landing.

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.

Early Version

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.

Advanced Version

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.

Low-G Gas Accelerator
Low pressure gas in a pipe, typically on a mountain, provides the initial velocity for a rocket. For people and complex equipment the acceleration is limited, allowing up to about Mach 5 at the end of the pipe, after which rocket stages take over.

Gas Accelerated 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% hardware 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 ).

Gas-Accelerated Rocket
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.


 * Cayambe, Ecuador

Cayambe 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.

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Section Header 4
For the self-build options we do preliminary designs, then compare to the existing launcher choices. We need to make some design assumptions to start with:


 * Payload Mass - We will assume that 20 kg is sufficient mass for a functional hardware item using modern technology. That might need to be changed with a better understanding of payload needs, but we will use it as a starting point.  Larger devices can be assembled from several items in orbit, but keeping the item size small lets you use a smaller launch vehicle, and thus lower development cost to start.  There is also the possibility to use this as an "express package delivery" service between larger launches on other vehicles, and bring in some revenue.
 * Launch Rate - We assume an initial rate of about 1 launch per month, and continuing on a steady basis.
 * Production - We assume one or more Advanced Manufacturing type factories, as described on the previous page, are used to build the launcher. This imposes production capabilities on the factory and links the systems. Any materials or components that are not reasonable to make within the factory are bought.  The cost of the factory has to be included when deciding which launcher to use.

There are multiple possible ways to launch a small payload to orbit. The conventional approach would be to design a small rocket with two or three stages. Any alternative ideas can be compared to that to see if it has a lower expected development and operating cost.

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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.