When Physics, Economics, and Reality Collide
The Challenge of Cheap Orbital Access

by

John M. Jurist, M.D.
Sam Dinkin, Ph.D
David Livingston, DBA


Contents - Section One

Abstract
Introduction
Basic Concepts
Air Launch
Horizontal Ground Launch
Hydrogen Propellant
Methodology
Expendable Launch Vehicles
Reusable Launch Vehicles


Abstract

Engineering problems are only part of the difficulty of achieving a price per pound of less than $1,000 to low earth orbit (LEO). Insurance and range costs can each cost more than $1,000 per pound if no effort is put into reducing them. Achieving low cost to LEO also requires solving problems associated with the economic limitations of chemical rockets, lack of business planning, and failure to identify a workable path that will take us from an immature to a mature launch industry. A mature launch industry would exhibit low cost to LEO and significant flight rates by reusable vehicles with long lifetimes. When today’s factors, limitations, and reality denials are combined, we believe that they prolong the difficulties of achieving low cost, routine flights to LEO. In other words, we end up inadvertently supporting the status quo.

Introduction

Present costs for putting freight into orbit are high for the same reasons that jet travel on Earth would be expensive if the corresponding rules were followed for the operation:

1. There shall be no more than one flight per month
2. The airplane shall be thrown away after each flight
3. The entire cost of the international airports at both ends of the flights shall be covered by the freight charges.

These comments are as valid today as they were when Theodore Taylor made them in 1966 [Ref. 1]. We would add two more rules to Taylor’s:

4. Jet engines will have narrow safety margins and will not run more than a few hours without major overhaul.
5. Aviation management will consistently avoid high quality business planning and will ignore the technical and financial realities related to their industry.

One of the central tenets of the alternative space access or “alt.space” community is that modern advances in technology and materials will allow cheap access to low Earth orbit (LEO). An assumed consequence is that Homo sapiens will eventually evolve into a space-faring race. Unfortunately, current technological, economic, and regulatory realities combine to forbid payload delivery to LEO for less than $1,000 per pound without changing the rules of the game. Simply creating fleets of reusable launch vehicles (RLVs) is unlikely to solve the problem unless they are large and have lifetimes of many frequent flights. Present technology might permit large, reusable vehicles, but there are many critical missing factors. Nobody has demonstrated the ability to design, fabricate, and fly such vehicles. Nobody has documented a convincing mechanism for financing and then amortizing the necessary research and development to create such vehicles. Nobody has documented a clear, solid business plan to implement the program required to do so. Nobody has demonstrated the market that would support the costs of creating such vehicles. Finally, nobody has proposed a viable strategy to go from our present flight rate of expendables to the high flight rates of RLVs projected for the mature industry which would permit achieving low cost flights to LEO. The nontechnical factors of insurance and range costs are two of many major obstacles to attaining this goal.
There is a scenario leading a potentially successful outcome. This is the methodical evolution from a commercially successful suborbital private-sector industry to private-sector orbital space flight. If a successful suborbital industry develops, it will result from solid and well grounded business planning, streamlined business and management operations, proper use of financial and accounting processes, skilled labor and management, and use of well designed checklists and safety considerations. Evolving successful suborbital companies to orbital operations will require emulating the successful aspects of suborbital development. It will mean no more fantasy business planning and financial proposals. Thus, orbital space access can occur through a step by step process which builds on the foundation of what has been shown to work regarding suborbital commercial space flight. Once the door opens for commercial orbital flight, solid business planning and operational systems improvements will enable lower cost orbital space access. This will produce track records that make sense to the financial world. Eventually, a mature industry with all its benefits can be obtained by steady growth and development.

Basic Concepts

At the Earth’s surface, circular orbital velocity is about 7,905 meters per second [Ref. 2]. This figure declines with orbital altitude and attaining it is eased somewhat by launching to the east. A low latitude easterly launch can gain perhaps 350 to 400 meters per second. However, losses from atmospheric drag and gravity during vehicle acceleration and climb to orbital altitude generally exceed the gain. The net result is that an effective penalty of about 15 to 25 percent is added to the basic orbital velocity requirement for a real-world launch to LEO [Ref. 3]. As shown in Table 1, a practical speed change capability (Delta-V) of about 9 to 10 kilometers per second is required for a launch vehicle to deliver a payload to LEO. This involves expenditure of a lot of energy. Since single-stage-to-orbit (SSTO) capability has yet to be fully demonstrated, our society is effectively dependent on some variant of two stage launch vehicles to attain LEO.


A single-stage formulation of the classic rocket equation dictates that:

where M is the mass ratio of the rocket stage (ratio of fully-fueled stage to empty mass with payload), e is 2.71828… , v is the speed change of the rocket in the absence of aerodynamic and gravitational losses, and c is the propulsive system exhaust velocity [Ref. 4]. The exhaust velocity is largely determined by the choice of propulsive system – especially the propellant characteristics. Assuming that both stages of a two stage vehicle have the same mass ratio and exhaust velocity, the required proportion of a launch system comprised of propellants is roughly 70-80 percent depending on propellant combination as shown in Table 2.

If one allows a 15 percent margin for aerodynamic and gravitational losses, a liquid oxygen and hydrocarbon (LOx/RP-1) two stage launch system must consist of 80.4 percent propellant by weight to attain LEO under the assumption of equal performance and mass ratios for each stage. This means that only 19.6 percent of the launch system is available for motors, propellant tanks, propellant pumps, support structures, guidance and control systems, interstage assemblies, staging mechanisms, recovery systems (if any), and payload. There are some tricks that can ameliorate this situation slightly, such as jettisoning the payload and interstage shrouds before completion of the propellant burn, assigning more of the Delta-V budget to the second stage, and launching to the east for low inclination orbits, but these tricks only affect performance around the margin.

Rocket motor specific impulse varies with ambient pressure and exhaust nozzle expansion ratio. Ideally, the exhaust plume pressure at the nozzle exit is equal to the ambient pressure. If the exhaust stream is over-expanded to lower than ambient pressure, motor efficiency suffers greatly. For example, the Merlin first stage motor for the Space Exploration Technologies Corporation (SpaceX) Falcon-I vehicle demonstrates a sea level specific impulse of 255 seconds and a vacuum specific impulse of 304 seconds. Thus, vacuum performance of the Merlin is roughly 20 percent better than sea level performance. The Falcon-I second stage motor, which is optimized for near vacuum operation (324,000 feet altitude at ignition), has a specific impulse of 327 seconds [Ref. 6].

One way to exploit the improved performance associated with optimizing a motor to near vacuum conditions is the divide the Delta-V budget unevenly between the stages. By lowering the first stage Delta-V, second stage ignition occurs earlier, but still at near vacuum conditions. Thus, the second stage effective exhaust velocity is improved and provides marginal improvement in launch system efficiency.

Air Launch

The speed change capability required for a launch to LEO can be reduced by launching the rocket from an aircraft or, perhaps, a balloon. The ambient air pressure change from launch altitude to vacuum is smaller than it is for a ground launch. By optimizing a propulsion system for an air launch, the average specific impulse over the burn is higher than optimizing the system for ground to vacuum as described above.

As mentioned previously, a low latitude launch to the east reduces the Delta-V requirement by 350 to 400 meters per second. A ground launch adds an additional Delta-V burden of between 100 and 160 meters per second for air drag, and between 1,100 to 1,500 meters per second for gravitational losses. Launching from a balloon at, for example, 80,000 feet reduces the gravitational Delta-V burden by no more than half compared to a ground launch. Even elimination of most of the air drag burden by a high altitude balloon launch at, for example, 80,000 feet leaves a total Delta-V requirement of roughly 8,200 meters per second. Compared to a 15 percent velocity margin for a ground launch, this reduces the propellant fraction from 80.4 percent to 77.1 percent for a LOx/RP-1 or equivalent system.

Air launch from a balloon has severe limitations on allowed vehicle mass. For example, a recent large balloon launch involved a 40,000,000 cubic foot volume of helium to carry a total liftoff weight (balloon, controls, and payload) of about 9,300 pounds [Ref. 7]. A 40,000,000 cubic foot sphere has a diameter of about 420 feet. Launching a balloon of this volume involves many problems related to its size and wind conditions. Yet, a liftoff weight of 9,300 pounds implies a rocket with a fuelled mass that is no more than perhaps 9,000 pounds. The payload to LEO of a two stage rocket with a fully fuelled mass of 9,000 pounds is minimal.
Launching a vehicle like the Orbital Sciences Corporation Pegasus horizontally from an air breathing “mother ship” at perhaps 40,000 feet and 500 miles per hour potentially reduces the required Delta-V by roughly 750 meters per second. The required propellant fraction is potentially reduced by an amount similar to the reduction obtained by a balloon launch at 80,000 feet. Other potential advantages of air launch include low energy abort modes, more flexible launch windows, and the ability to ferry the launch vehicle to a remote location to provide convenient access to the desired orbit and partially abate launch fees. However, if the launch vehicle track intrudes on a national range, range and tracking fees will still apply [Ref. 8]. Transporting the launch system to a remote, foreign location may involve export regulations for launchers originating in the United States. Insurance fees may also be reduced by ferrying to an uninhabited area.

Technical limitations also apply for air launch. Henry’s thesis [Ref. 9] reports that the Pegasus is limited to a payload of 976 pounds into LEO with a vehicle dry weight of 5,395 pounds. The “mother ship” for this vehicle is a modified Lockheed L-1011 wide-bodied jet. Reportedly, development costs for the Pegasus approximated $150 million or about $30,000 per pound. Using a modified Boeing 747 as a “mother ship” might allow a maximum vehicle launch weight of up to about 180,000 pounds [Ref. 9]. The largest aircraft in the world, the Antonov An-225, is limited to a maximum payload of 605,000 pounds [Ref. 10]. That limits the maximum fully fuelled weight of an air launched rocket to perhaps 600,000 pounds. When the launch vehicle is dropped horizontally from the “mother ship,” it accelerates out and then pitches up into a climb to get above effective atmosphere. This maneuver adds to the Delta-V budget because of turning or steering losses and the increased drag associated with the non-zero angle of attack during the pitch maneuver. In addition, wings add a significant mass penalty for a system used only during the initial pitch maneuver and potentially during landing for an RLV. The Pegasus has an overall propellant fraction of 90 percent compared to 91 percent for an Atlas-II. Another approach is to drop the launch vehicle from an aircraft flying horizontally and then rotate it until it is vertical before igniting the rocket motors. The required robustness of the vehicle is increased because it must withstand the rotation and maintain some cross wind capability until its translational speed is mostly lost before ignition. If there is a motor failure, the fuelled launch vehicle may well be lost. A safety advantage results from the launch vehicle climbing out behind the “mother ship” rather than dropping behind and below and then accelerating and climbing ahead of the “mother ship.” The latter entails some potential collision hazard between the launch vehicle and the “mother ship.”

Horizontal Ground Launch

A winged vehicle launching horizontally from ground level experiences a 200 to 300 meters per second penalty relative to a vertical takeoff vehicle [Ref. 11]. In addition, it must carry a landing gear designed to accommodate launch weight. This latter factor is one basis for some of the proposals for taking on fuel and oxidizer after takeoff for some horizontal takeoff concepts.

The stresses on a vertical launch vehicle are primarily longitudinal or axial. The stresses on a horizontal take off vehicle are initially transverse and bending and then transition to axial during climb out. Designing a structure to accommodate these stresses imposes an additional weight penalty for horizontal takeoff vehicles compared to vertical takeoff concepts.
Because of the limitations of the various horizontal takeoff and air launched concepts, we confined our analysis to vertical takeoff two stage vehicles launched from ground level.

Hydrogen Propellant

Using liquid hydrogen (LH2) as a fuel reduces the propellant fraction, but the density of liquid hydrogen is only 12.3 percent that of RP-1 [Ref. 5]. The required tank volume and associated mass is increased markedly as a consequence and offsets the roughly 40 percent performance gain of hydrogen compared to hydrocarbon fuel without introducing undue program risk. Besides, the stuff is comparatively expensive and difficult to handle. With a liquid hydrogen cost of about $10 per pound [Ref. 12], overall propellant costs of a LOx/LH2 system will run roughly $2.50 per pound. As will be shown below, this is more than 8 times the cost per pound of RP-1 and LOx. Yet, Table 2 shows that the required propellant fraction of a two stage vehicle is only reduced from roughly 80 percent to about 70 percent by replacing RP-1 with LH2. The net savings in vehicle weight to achieve the same payload is offset by the more difficult engineering of a hydrogen system and the increased propellant cost. This makes hydrogen propellant inconsistent with low cost routine operation at this time. As a consequence, the following analysis will be confined to RP-1 and LOx as a propellant combination.

Methodology

We examined programmatic costs of baseline expendable (ELV) and reusable (RLV) vehicles capable of delivering 1,000 pounds to low earth orbit (LEO). These costs were separated into direct and indirect costs for total flight programs of 500 launches. Then, to examine the effects of some of the more sensitive variables on the model, we tested the effects of payload size on costs by analyzing ELVs and RLVs capable of delivering as much as 100,000 pounds to LEO. We also analyzed the effects of flight lifetime per vehicle and fleet size for the RLVs.
As part of the analysis, we attempted to counteract the effects of our biases by typically understating the actual costs of the various elements by making optimistic assumptions whenever hard figures were not available. This understatment was substantial in the case of research and development (R&D) and fabrication costs. The costs of R&D and fabrication are compared to similar costs for aircraft after correction for vehicle mass. The various cost and mass relationships were scaled between extremes by the logarithm of vehicle mass or payload.
As an example of our optimistic assumptions, we can compare our payload to vehicle mass relationships to the SpaceX Falcon series [Ref. 6]. The design payload capability to LEO for the Falcon-I and Falcon-V is 1,474 and 13,244 pounds, respectively. Gross launch weights are published as 60,000 and 400,000 pounds, respectively. Using an average exhaust velocity of 2,798 meters per second (specific impulse of 286 seconds versus 255 seconds at sea level and 304 seconds in vacuum for the Merlin motor used in the Falcon-I), a mission Delta-V of 9,091 meters per second, and equal Delta-V for each stage results in vehicle dry weights (including payload) of 11,820 and 78,553 pounds for vehicles with the published Falcon payload capabilities. This yields payload to vehicle dry weight ratios of 12.5 and 16.9 percent. The assumptions we used in our analysis for the 1,000 and 100,000 pound payload ELVs correspond to 14.8 and 27.9 percent, respectively, when interpolated for the Falcon-I and Falcon-V payloads.

Expendable Launch Vehicles

With this basic information, some hypothetical launch systems can be characterized. Expendable launch vehicles (ELVs) will be considered first and compared to RLVs. The baseline ELV will be assumed to carry a payload of 1,000 pounds to LEO and have an optimistic payload to dry vehicular mass ratio of 12.5 percent. Then, the total vehicular dry mass, exclusive of payload, is 7,000 pounds and the total propellant load for RP-1 and LOx is 32,607 pounds for a total take-off mass of 40,607 pounds. This is considered optimistic in that the 7,000 pounds dry structural mass consists of a two stage vehicle with total tankage holding 32,607 pounds of propellant, motors and pumps for both stages, guidance and control systems, an abort system (typically required for launches on national ranges), payload shroud, etc. with sufficient structural integrity to withstand all launch loads with an acceptable safety factor.

Fuel costs are $0.31 per pound and LOx costs about $0.30 per pound [Ref. 12]. An oxidizer to fuel mixture ratio of 2.24 by weight is also assumed. This results in a propellant cost of $9,853 per flight exclusive of losses. Rounding to $10,000 for reserve adds 18 cents per pound of payload to the propellant cost of $9.82 per pound of payload. If a sufficient flight rate is assumed, a LOx plant can be fabricated on site for a considerable capital investment to reduce these direct costs.

A direct incremental vehicle fabrication cost of $75 per pound exclusive of research, development, and design costs results in a vehicular structural cost about $525,000 per unit. For comparison, an upscale automobile costs on the close order of $20 per pound.
Commercial aircraft costs run in the neighborhood of $100 to 300 per pound. The new Airbus A380 costs approximately $230 per pound ($280 million retail sales price less 50 percent for fixed costs and an empty weight of 608,000 pounds) [Ref. 13]. However, commercial aircraft are designed and fabricated for lifetimes of perhaps 30,000 flights. This tends to boost both R&D and fabrication costs. An offsetting factor is that vehicles such as the A380 are evolutionary end products that can use tooling and facilities amortized on previous model production runs. Airbus also enjoys significant government subsidies that may not be reflected in their stated R&D and production costs.

Assuming a preflight preparation cost of $5,000 (100 man hours at $50 per hour) results in a direct launch cost per flight of $540,000. This preparation labor estimate approximates twice the maintenance man hours consumed per flight hour of high performance military aircraft. As will be seen below, the preflight preparation cost estimate adds $5 per pound of payload to the direct flight costs.

However, this does not represent total flyaway costs. Program research and development must be amortized over the launch program lifetime. With a total program of 500 flights, a $50 million R&D program is amortized at $100,000 per flight exclusive of interest. That comes to $100 per pound of payload. In addition, launch facilities (launch pads, checkout structures and facilities, telemetry, etc.) must be amortized over the program lifetime. Assuming a very favorable cost of about $2 million for these facilities results in a per flight cost of $4,000 exclusive of interest.

In addition, range costs are quite significant. Currently, they are estimated at between $1 million and $1.3 million for flight day on a national range [Ref. 14]. These costs are governmentally controlled and usually passed on to the user. If not, the costs are absorbed by the taxpayer in one fashion or another. They could be reduced somewhat by performing more than one flight daily or by using strong political negotiation for discounted costs, but the underlying activities resulting in the costs are unlikely to be reduced in the current risk adverse culture. In essence, range costs are a political problem and have the effect of stifling demand. Insurance, including launch, delivery, and liability coverage is another expensive component of launch costs. These costs currently run about 15 percent of vehicle, payload, service, and ground facility costs [Ref. 15]. Of course, insurance costs will trend downward as vehicle reliability increases and purchasing methodology improves. The current estimate of insurance cost is based on historical failure rates of ELVs and traditional brokered transactions.

Table 3 [below] summarizes these costs over a program lifetime of 500 flights. The table does not include payload insurance costs. The direct costs are $540 per pound to LEO, indirect costs are $961 per pound to LEO, and total fly-away costs are $1,501 per pound for a total cost of more than $750 million to deliver 500,000 pounds to LEO. In this table, range costs are based on negotiated figures provided by SpaceX as a function of payload weight. These costs are lower than the range costs as outlined above and reflect taxpayer subsidies of unknown magnitude.

Reusable Launch Vehicles

An obvious thought is to drive launch costs down by reusing the launch vehicles. This does nothing to reduce the range costs.

Other costs creep into the system with RLVs. Assume that a program of 500 flights using a fleet of 5 vehicles is created. This assumes a lifetime of 100 flights per vehicle. From an historical standpoint, the only partial RLV capable of payload delivery to LEO, the Shuttle Transportation System (STS), has a higher loss rate that this. From a business standpoint, vehicle lifetimes of more than 100 flights are to be desired because vehicle fabrication costs and program R&D costs can be amortized over many more flights. If more flights per vehicle proves feasible, it would drive indirect launch costs down and make spacecraft operations more like aircraft operations. Because RLVs must be more robust than ELVs in order to withstand recovery and multiple uses, the payload fraction is lower than in ELVs. The longer the projected vehicle lifetime in terms of number of flights, the more robust the vehicle must be. A reduction in payload fraction from 0.125 to 0.09 is assumed. In addition, a recovery system must be incorporated into the vehicle. This could be wings and landing gears or parachutes. Also, de-orbit systems must be built into the second stage, and thermal protection systems must be incorporated into both stages. If the RLV is manned, a life support system and, hopefully, a non-destructive abort system must be added. This not only drives up costs secondary to system weight gain, but crew salaries and training costs are incurred. The entire recovery system is assumed to comprise 25 percent of the dry vehicle mass.

In order to deliver the same 1,000 pound payload to LEO, the required RLV is larger than an ELV. The RLV dry mass is 7,333 pounds exclusive of payload and 45,288 pounds of propellant are required to boost the payload to LEO. Total take off mass is 56,399 pounds (a gain almost 16,000 pounds compared to the ELV).

Because the launch system is reusable, fabrication costs are assumed to increase from $75 per pound in the case of ELVs to $400 per pound for RLVs because of additional labor and more expensive materials used in the RLVs. As discussed previously, aircraft fabrication costs typically run between $100 and $300 per pound. Given the relative energies involved in space flight and aviation, we believe the fabrication costs used in the model to be optimistic. In addition, prelaunch checkout costs are assumed to increase by 25 percent because of the increased complexity of the RLVs compared to ELVs. The increased complexity comes from the addition of recovery systems for both stages. By designing for simplicity of checkout, checkout costs can be reduced at the expense of increasing R&D. This would increase R&D costs by an estimated 50 percent (to $75 million). The magnitude of the increase in R&D costs is almost certainly optimistic.

Using RLVs adds an additional dimension to the cost analysis. That is recovery and refurbishing. Vehicle recovery cost is assumed to be $50,000 per flight. Refurbishing cost is assumed to average two percent of the vehicular structural cost per flight (we include the last flight because the vehicle is likely to be retired due to a failed inspection or incur an expensive post mortem). The refurbishing cost includes labor and spare part or component replacement costs. Table 4 summarizes the RLV costs.

This scenario projects an increase in flyaway costs of 22.9 percent by switching from ELVs to RLVs with comparable payload capacity. The hypothetical program delivers a total of 500,000 pounds to LEO for a program cost of $923 million. The simulated RLV program uses the same assumptions as the ELV program except as noted.

As is the case with ELVs, the dominant factors in this analysis prove to be range and insurance costs, which result from political, regulatory, and economic factors. For RLVs, the cost of insurance per flight creeps ahead of vehicular structural costs in ELVs, but insurance is also a major component of ELV flyaway costs. In the case of ELVs, range costs plus insurance runs about $856 per pound of payload, and increases to $1,500 per pound of payload for RLVs because of increased insurance costs. Insurance costs are higher because replacement of the vehicle is insured and the maximum probable loss (MPL) is higher because the RLV is heavier than an ELV. In the long run, launch operations with a proven highly reliable system would reduce insurance costs, but in the near term those high costs are a fact of business life unless the launch company is willing to self-insure for a large share of the liability or invest in studies to demonstrate safety. Self-insuring the vehicle makes sense when vehicle replacement cost is cheap. Self-insuring the vehicle in our model is a much cheaper option. Self-insuring the first party property (almost all of the $540,000 difference between ELV and RLV insurance costs) pays for a new vehicle every eight flights. For bulk cargo like water where payload does not need to be insured, that gets the price down to $345 per pound plus $620 per pound in range and insurance costs (including $40 per pound in self-insurance for a 0.99 reliability vehicle). Self-insuring first party property frees us from Ted Taylor’s second law: “The airplane will be thrown away after each flight.” By self-insuring the vehicle, RLVs become cheaper than ELVs according to our assumptions, but may make the vehicle program more expensive to finance. Since self-insuring lowers the insurance to nearly the same cost as for ELVs, we recommend self-insuring the RLV structure. Investing in a design reliability study is another option to lower projected failure rates [Ref. 16].

Until a launcher has proven its safety, insurers will still charge large fees for insuring expensive payloads and third party liability. Holding an auction for commercial insurance instead of having a negotiation could potentially reduce insurance costs by 20 percent since 35 percent of commercial insurance premium costs are transactional costs [Ref. 17]. Going direct to insurers instead of using a broker may reduce insurance costs an additional five to 10 percent. Old fashioned telephone and fax bookmaking leave money on the table as oversubscribed insurance purchases get reduced pro-rata rather than via a premium reduction.

Go to Section 2 >>