August 4, 2006Presented by Clint StallardSupporting data by Dr David Maker

Catapult Launch Assist

Introduction

The purpose of this document is to provide an overview of ground based launch assist using combustion gas driven catapults and the history and status of this proposed technology to date.

The concept for using linear pneumatic catapults for launch assist has been around for many decades. The German V1 rocket used catapult launch assist. The US Navy uses linear pneumatic catapults to launch fully loaded warplanes at 170 MPH using a launch stroke of 300 ft and a 3G launch acceleration. Current UAVs use pneumatic launch.

A Naval funded investigation of an alternative Internal Combustion Catapult Aircraft Launch System catapult technology was made in the late 1990s. An investigation of alternate uses of combustion gas catapult technology such as for launch assist of space vehicles was made. The result showed that it was possible to develop significant thrust and acceleration of heavy launch vehicles.

An inquiry was made of MSFC to determine interest. MSFC recommended contacting the Vehicle Analysis Branch at LARC. Preliminary investigation by the Vehicle Analysis Branch at NASA Langley showed promise. It appeared that a significant reduction of vehicle cost or cost for payload to orbit might be achieved.

A joint proposal with LARC was made to MSFC in support of the Bantam launcher program which showed a 50 % gain in payload with no change to the launch vehicle. The Bantam program was initially funded with $90 million and catapults were assigned a funding line of $5 million over 4 years. Unfortunately the program was then cancelled and the funding line eliminated.

Interest at NASA then shifted to electromagnetic launch and there was no further interest in combustion gas based catapults.

Combustion gas based catapults are low tech, simple and very powerful. The forces that can be generated can exceed 2.5 million pounds per launch tube and the tube can be ganged with other tubes to generate launch force in excess of 10 million pounds (8 tubes = 20 million pounds). Given sufficient track length, speeds in excess of Mach 1 can be achieved. The launch tubes are double wall steel cylinders that are easily fabricated and the combustors are derived from pressure fed liquid fuel rocket engines using LOX/RP1 fuel. There is little developmental technology and the engineering risk is low.

Therefore it is proposed that NASA, given the new missions that it is being given and the replacement of the shuttle being contemplated, undertake or fund an initial investigation of this technology to determine the feasibility and cost effectiveness of incorporating it into current and future launch vehicles.

Index

Section Title

1 Introduction

2 A White Paper

3 Meeting With NASA

4 CBD Steam Catapult Study Procurement

5 Launch Assist Program Plan Slide

6 Dr Talay Notification of Catapult Funding

7 Catapult Launch Assist for Earth to Orbit Launch Vehicles

8 Catapult Acceleration Launch Assist

9 Launch Cylinder Design Cost Study

10 Catapult Requirements for RLV

11 Assisted Launch Speech, Dr. David Maker

Ground Based Catapult Launch Assist For Space Launch Vehicles

Clint Stallard

Executive Summary

Newport News Shipbuilding has been investigating alternative catapult technology as part of the Internal Combustion Catapult Aircraft Launch System (ICCALS) technology. This is in preparation for a proposal in response to the NAVAIR Advanced Technology Launcher (ATL) procurement for CVX 78. Due to reallocation of funding by Congress, start of the ATL procurement has been delayed for at least a year. Alternate uses of catapult technology such as use of catapult technology for launch assist of space vehicles has been investigated. Preliminary investigation, in conjunction with the Vehicle Analysis Branch at NASA Langley, is promising. It appears that a significant reduction of cost for payload to orbit may be achieved.

Synopsis of the status of the NNS-NASA catapult effort to date.

Bob Armstrong of the NASA - Marshall Space Flight Center Program Office issued an RFI to shipbuilders via CBD requesting information for innovative methods of building rocket vehicles for satellite launch. In addition, the RFI requested innovative technologies that might be spun in to NASA from commercial companies in support of satellite launch.

Based upon the RFI, Clint Stallard, technical lead for the ICCALS effort, contacted Bob Armstrong to determine if there was any interest in using catapult technology for launch assist for NASA launch vehicles. The technology proposed by Mr. Stallard was for the use of current aircraft carrier C13 type catapult modules installed in a vertical orientation and attached to NASA launch vehicle. This provides the equivalent of an additional stage for the rocket which is ground based and not attached to the launch vehicle.

Mr. Armstrong was provided a basic package of information that outlined the capacity of the current catapult design and a conceptual installation of catapult modules arranged on a launch pad around a launch vehicle. He had a favorable response to the information and referred me to Bob Porter and Susan Spencer of their Preliminary Vehicle Design Division to whom he provided copies of the information package.

After review, Mr. Porter commented favorably on the concept and offered to fund NNS for a study in the range of $10,000.00. Mr. Stallard pointed out to Mr. Porter that he was fully involved in preparing for a RFP from NAVAIR for an internal combustion catapult and that neither he nor other personnel at NNS had the experience base in launch vehicles to support such a study. Mr. Porter recommended that NNS contact Mr. Larry Rowell, Assistant Branch Head of the Launch Vehicle Analysis Branch at NASA-Langley, to request support in this effort. Mr. Stallard contacted Mr. Rowell which led to a meeting at NASA Langley with Mr. Rowell and Roger Lepsch, one of his engineers. Mr. Stallard provided an information package identical to that provided to Mr. Armstrong, and an explanation of the catapult launch assist concept. Mr. Rowell stated that there appeared to be merit to the concept and agreed for the Launch Vehicle Branch to investigate the concept on an as-possible basis.

Various communications between NASA and Mr. Stallard transmitted information relative to example launch vehicles and the effect of catapult assist on the efficiency of the vehicles and manning, maintenance and life cycle information for an example catapult installation and initial investigations were conducted by NASA.

The favorable indications of these preliminary investigations led NASA to request a follow-on meeting. This was attended by Mr. Stallard, Charles Eldred, Branch Head, Launch Vehicle Analysis, Larry Rowell, Assistant Branch Head, and Ted Talay and Roger Lepsch of the Branch engineering staff. The purpose of the meeting was to review the current NASA investigation results, the NNS catapult manning/maintenance requirements data and to discuss future actions relative to this technology.

As part of the preliminary investigation to date, Dr. Talay of the Launch Vehicle Analysis Branch conducted a preliminary analysis (Enclosure 4) of a single C-13 catapult used with a three stage 6,175 lb. Black Brandt X sounding rocket. The catapult provided a 7.1% payload increase or a 6% altitude increase. Additionally, Dr. Talay analyzed a 3 stage Bantam Launcher weighing 83,000 pounds and capable of placing 220 lb. into low earth orbit if launched conventionally. Use of the catapult for launch assist of the Bantam rocket raised the payload capacity to 329 lb. for the same orbit as an ideal case with no change to the rocket. The equivalent solid rocket booster to provide this performance would cost $100,000 per launch and provides a cost basis for trade study purposes.

An additional study of heavy lift rocket applications was provided by Roger Lepsch of the same group. The vehicle selected for analysis was a Single Stage To Orbit (SSTO) delta wing vehicle weighing 2.4 million pounds and a payload of 45,000 pounds to orbit. A launch end speed of 250 FPS (170 MPH or 150 KTS) was assumed. The preliminary results showed ideally a 40-45% increase in payload to orbit if the launch vehicle can be braced internally to handle the additional acceleration load. Conversely, with no change in payload, the launch vehicle may be as much as a million pounds lighter with catapult launch assist. This information will be provided to NNS at a later date after formalization.

The dramatic difference between the three stage and the SSTO vehicles is accounted for by the ability of the multistage rockets to jettison a significant portion of their launch weight while the SSTO carries to orbit the entire mass (less burned fuel) that it had at launch. Thus the effect of the catapult for the SSTO vehicle is felt for the whole launch event rather than only in the first stage. Additionally, as demonstrated by the result of the multistage rocket study, light high-speed launch vehicles benefit least from catapult launch assist as the benefit appears directly affected by launch vehicle weight.

The rationale for consideration of catapult technology for this application is that heavy loads can be accelerated to high rates of speed quickly by use of the current Naval aircraft carrier catapult technology. Naval aircraft can range from 40 to 70 thousand pounds and are accelerated at 3 to 3.5 G to an end speed of 140 to 160 KTS (161 to 184 MPH). This is using a pair of 21” diameter launch tubes with a launch pressure in the range of 340 PSI which provides a launch force of (10.52 X3.1416)(2)(340)=235,525 pounds of force per foot exerted over a typical distance (height) of 304 ft. As the tubes are rated for 700PSI, a working force of 600PSI would provide a force of (600/340)235,525=415,633 pounds of force per catapult module. By use of multiple modules, very large launch forces can be generated. Wyman-Gordon, the current supplier of launch tubes can provide tubes with an inner diameter of up to 42”. Enlargement of the tubes to, as an example, 40” with external rib bracing and operation at 600 PSI will produce a launch force of (202X3.1416)(2)

(600)=1,507,968 pounds of force per catapult module which almost matches the thrust (1,680,000 Lbs.) provided by the two main engines of the planned Manned Mission to Mars launch vehicle. In considering acceleration, one G of the accelerating force is required to offset earth’s gravity. An installation of 4 catapult modules at this output would provide a gross additional acceleration of 2.5 G or a net acceleration of 1.5G to a 2.4 Million pound vehicle and an additional acceleration of 4 G or a net acceleration of 3 G to a downsized 1.5 Million pound SSTO vehicle. An additional catapult module would add .625 G acceleration to the 2.4 Million pound vehicle and 1 G acceleration to the 1.5 Million pound vehicle. It is assumed that the launch vehicle will be producing at least 1.2 G of acceleration itself.

This technology is attractive to NASA, not only because of the delivered power, but also because this is a mature technology while most of the launch assist technologies being investigated by NASA, such as electromagnetic launch are developmental.

Use of 4 cells of 2 catapult modules each using the larger tubes and 600 PSI pressures would generate a launch force of (4)(1,507,968)=6,785,856 pounds of force which would be appropriate for the concept vehicle for the manned mission to Mars which is projected to weigh 5.7 million pounds and would provide an acceleration of 1.19 G vertical acceleration independent of the launch vehicle engines.

The stroke length of the current catapult design is 307 ft, however longer strokes can possibly be accommodated by adding cylinder sections and changes to the steam supply or use of the NNS ICCALS. This provides gas generation modules replacing the steam accumulator to supply the additional mass flow required by the increased swept volume of the catapult launch tubes. This will allow achieving the required end speed with a more gentle acceleration or attaining a higher end speed with a resultant gain in payload or reduction in launch vehicle size.

Closed loop control of the catapult will allow tailoring of the acceleration curve applied to the launch vehicle to one appropriate to that vehicle so that a wide range of vehicles would be capable of being launched from one catapult launch facility.

Mr. Eldred, the Branch Head agreed that the NASA Launch Vehicle Analysis Branch would do further analysis during the week of 11-24-97 and that we would reconvene during the week of 12-2-97 to determine a course of action. He was very positive about this technology and stated that he had passed information about it to NASA Headquarters in Washington who were also enthusiastic about the potential of the technology. The next logical step, as pointed out by Mr. Eldred is to put together a joint presentation to NASA Huntsville for funding for concept development of this launch assist technology and investigation of its application to other launch platforms.

It is planned that additional investigations will be accomplished by NASA over the next two weeks which look in detail at cost trade-offs and application to other vehicles. Subsequent to this, a meeting will be held to determine the appropriateness of further pursuit of this technology. If a decision is made to pursue this technology, we will work jointly to determine the format and content of a presentation to NASA Marshall Space Flight Center for funding of a task for concept development.

If it is possible for the SSTO vehicle to carry 40% additional payload to orbit using this technology, then 45,000(.4)=18,000 pounds additional payload. The current cost per pound to orbit is $7-10,000 dollars per pound. If the cost per pound were only $1,000, then the additional payload for one launch would support a launch site expenditure of $18 million dollars for one launch. At 20 launches per site and a nonrecurring launch site cost of $20 million dollars, the amortized cost per launch would be $1 million dollars. With a recurring cost of $500,000 cost per launch, the launch cost to NASA of the additional payload would be reduced to $1,500,000/18,000 lb = $83.33 per pound.

The overall launch cost would be $7,000(45,000) + $83.33(18,000) = $315,000,000 + $1,500,000 = $316,500,000. The cost per pound would be $316,500,000/63,000 pounds = $5,023 per pound. This would be a reduction of 1-($5,023/$7000)=28.24% in the launch cost per pound based upon $7,000 launch cost per pound and resulting in a savings of ($7,000-$5023)63,000 lbs = $124,551,000 for this example launch. If the launch cost is $1,000 per pound, then the savings in launch cost is $18,500,00. A significant reduction in launch costs is a current major program within the NASA/Aerospace community. This is the rationale for the NASA emphasis on the SSTO and Advanced Expendable Launcher vehicle programs. The SSTO offers a major cost reduction in launch expenditure as the vehicle is reusable. Thus the cost per pound is reduced as the entire cost of the vehicle is not expended in a single launch. A major reduction in costs could return a large number of launches and aerospace business to the US.

A large number of launches are projected to be accomplished over the next decade. These include the hundreds of civilian satellites for communication networks, the large number of heavy lift launches for the space station , the single stage to orbit vehicles that are projected to be introduced and the space exploration launches to be accomplished such as the manned mission to Mars. The proposed catapult useage could be a facilitating technology.

To: Tom DadeFor: InformationFrom: Clint StallardSubj: Meeting with Larry Rowell, Vehicle Analysis Branch, NASA Langley 12-15-97

I met with Larry Rowell at 2:30 PM in his office by mutual agreement. The purpose of the meeting was to review the catapult launch assist White Paper and review progress toward accomplishment of additional analysis in the last two weeks.

It was agreed that, subject to agreement by NASA and NNS management that this investigation would be continued as the initial effort indicated considerable promise for application of catapult technology to launch assist. In consideration of this, a number of programmatic issues were discussed and further supporting actions were identified to be accomplished. This included:

NASA - Continue system studies and analysis of additional candidate vehicles. NASA - Definition of operational requirements for the launch system as defined by

the launch vehicle and launch site constraints. NNS - Use the operational requirements for the launch system to create a high level

set of requirements for the catapult launch engine.

Mr. Rowell stated that a task statement should be created by NASA- Langley and NNS to seek FY 99 funding from the Space Transportation Programs Office to further develop this technology in support of the NASA effort to reduce the cost per pound of payload to earth orbit. This task statement should be complete and submitted by May 1, 1998. Additionally, it was agreed that funding for an initial effort should be sought from Marshal Space Flight Center which would support the FY99 task proposal.

NASA is currently working a task from NASA Headquarters that develops a launch technology evaluation methodology. This involves using a matrix format to do trade studies and evaluate the impact of new technologies on launch cost and efficiency. Mr. Rowell indicated that this launch assist technology would be an excellent candidate for inclusion in the evaluation matrix as it is based upon a mature technology while most of the proposed launch assist technologies currently being evaluated are simply proposals and do not exist in hardware in any useable or similar form

Mr. Rowell agreed with the conclusions of the White Paper and stated that additional vehicles had been evaluated in the past weeks. He stated that the numbers were different than the 24-28% cost improvement in the white Paper, but no worse. He stated that he saw the future relationship as one where NNS contracted directly with Marshall Space Flight Center (MSFC) with NASA Langley in an advisory role where they provided technical and analytical support to NNS and managed the rocket side of the interface between the rocket and the launch system. NNS would manage the launch system side of the interface and MSFC would function as the program lead.

Clint Stallard

[Commerce Business Daily: Posted in CBDNet on February 4, 1999][Printed Issue Date: February 8, 1999]From the Commerce Business Daily Online via GPO Access[cbdnet.access.gpo.gov]

PART: U.S. GOVERNMENT PROCUREMENTSSUBPART: SERVICESCLASSCOD: B--Special Studies and Analyses - Not R&DOFFADD: NASA/Langley Research Center, Mail Stop 144, Industry Assistance Office, Hampton, VA 23681-0001SUBJECT: B--STEAM CATAPULT LAUNCH ASSIST STUDYSOL 1-050-CB.2081DUE 021999POC Robert B. Gardner, Contracting Officer, Phone (757)-864-2525, Fax (757) 864-7898, Email R.B.GARDNER@larc.nasa.govDESC: NASA/LaRC plans to issue a Request for Quotation (RFQ) for conceptual design, technical trade studies and a cost analysis of a steam-powered catapult lauch assist system to support the NASA Bantam Small Launcher Program headed by the NASA Marshall Space Flight Center. The period of performance for this activity is intended to be 3 months. This procurement is being conducted under the Simplified Acquisition Procedures (SAP). NASA/LaRC intends to purchase the items from the Newport News Shipbuilding under the authority 10 u.s.c. 2304(c)(1). The Government does not intend to acquire a commercial item using FAR Part 12. See Note 26. See Note 22. Any referenced notes can be viewed at the following URL: http://genesis.gsfc.nasa.gov/nasanote.html. Interested firms have 15 days from the publication of this synopsis to submit in writing to the identified point of contact, their qualifications/capabilities. Such qualifications/capabilities will be used solely for the purpose of determining whether or not to conduct this procurement on a competitive basis. Responses received after the 15 days or without the required information will be considered nonresponsive to the synopsis and will not be considered. A determination by the Government to not compete this proposed effort on a full and open competitive basis, based upon responses to this notice is solely within the discretion of the Government. Oral communications are not acceptable in response to this notice. All responsible sources may submit an offer which shall be considered by the agency. An Ombudsman has been appointed. See Internet Note "B".LINKURL: http://nais.nasa.gov/EPS/LaRC/date.html#1-050-CB.2081LINKDESC: Click here for the latest information about this noticeEMAILADD: R.B.GARDNER@larc.nasa.govEMAILDESC: Robert B. GardnerCITE: (D-035 SN295067)

Bantam Program

Dr. Ted Talay of NASA Langley called Clint Stallard, E86, NNS to make him aware of the following. The Bantam program was approved by NASA HQ on 7-8-98 and arrangements are being made at OMB 7-9-98 to fund this program. The approved funding line is over the 1998-2001 time frame with $90+ million obligated.

Dr. Talay is obtaining the documentation used in the NASA HQ presentation and will make it available. The documentation defines the outline of the Bantam program which is to be a technology development effort. The documentation includes a technology road map which defines the technologies that must be developed to support the overall program and indicates funding for each technology development effort.

One of the technology development efforts defined is integration of initial launch assist technology into horizontal launch vehicles. This has an indicated funding line as follows:

1998 $250,0001999 $1,750,0002000 $1,750,0002001 $1,250,000

The follow on program to the Bantam program will be the Pathfinder program and Future X Cycle 2. it is anticipated that these programs will provide the funding for significant hardware procurement such as launch vehicles and launch assist installations. Dr. Talay stated that NASA Langley had been made the lead center for launch assist for the Bantam Program which indicates that launch assist will possibly not be competed, but rather awarded to NNS.

Dr. Talay stated that he had had conversations with Mr. Monk at MSFC relative to these programs on the morning of the 9th. Mr. Monk recommended that NASA Langley and NNS submit proposals for the Pathfinder and Future X Cycle 2 programs.

Mr. Stallard recommended that a meeting between NASA Langley and NNS be held relatively quickly to develop a mutually agreeable catapult technology development plan and determine if that plan fits the available and projected funding lines prior to continuing any joint effort or submitting any proposals for the mentioned programs. Mr. Stallard pointed out that his management required a commitment to a significant program that a series of small technology development efforts decoupled from a serious program did not meet their needs.

1-28-98Catapult Launch Assist for Earth To Orbit Launch Vehicles

Preliminary Program Description

The purpose of this document is to describe the program that will support the development of a catapult launch assist system. The program is to demonstrate catapult launch technology used as a launch assist for vehicles intended for placing satellites or other hardware into earth orbit. This program will proceed in two phases. The first phase provides the investigations and supporting concept design. The second phase will consist of acquisition of hardware, construction of a demonstration launch assist system at a launch site, modification of a launch vehicle to support catapult launch assist and a demonstration launch. These phases will consist of multiple steps as defined below.

The first step of the first phase is to define the requirements of the launch vehicle selected initially for this application.

Required additional acceleration capability of the catapult launch vehicle. Access requirements to the launch vehicle from the service tower Acceleration input points to the launch vehicle Modifications required to the launch vehicle to withstand the accelerating

force Total weight of the vehicle as modified with payload

The second step is to define the configuration of the interface between the launch vehicle and the catapult launch assist installation. Specifically, what will be the configuration of the attachment points mounted on the vehicle and how will the attaching structure of the launch assist mechanism interface with these points.

The third step is to define the combustion gas based catapult launch assist system. This will include:

Launch tube inner diameter. This will be 48” for the initial demonstration installation.

Launch system working pressure. This will be determined by the weight of the vehicle to be launched and the end speed to be achieved at the end of the launch stroke.

Number of combustors required. This will be determined by the total mass flow required to maintain launch pressure behind the catapult pistons throughout the catapult stroke.

Combustor inlet control valve design. This will be a quick acting shutter which will reroute the combustor output from the atmosphere to the launch cylinder inner diameter

Delivery system from the fuel storage to the launch engine combustor. This will be sized to assure minimum pressure drop.

Piston capture assembly. This captures the piston assembly at the end of the catapult stroke and brings it to a stop. The design is open as there are numerous viable methods for accomplishing this and the site configuration may dictate the method.

The fourth step is to define a concept design for the mounting and supporting structure for the launch engine. This structure will be the full height of the launch engine plus structure to allow capture and arrestment of the shuttle and interface assembly. The structure must meet the following requirements:

Mount and support the launch engine. Maintain the launch engine tubes in alignment prior to and during launch. Withstand full launch loads at the base of the launch engine without

deflecting. For an example launch vehicle of 3,000,000 pounds at an acceleration force of 3.3G, the base load will be the dynamic load of 9,900,000 pounds applied over a 3-4 second period.

Withstand wind loads with the launch vehicle attached. This must be done without excessive deflection of the launch engine.

Provide required access to the launch vehicle for maintenance and check-out. Provide full access to the launch engine over the length of the engine for

maintenance and check-out.

The second phase of the program will consist of three steps.

The first step will be to develop a detail design of the catapult launch assist installation and component parts. This will include: The mounting and supporting structure for the launch engine which includes:

the launch tower with supporting structures launch engine support and alignment structures shuttle support and guide system vehicle access vehicle and catapult support systems

The internal combustion catapult system which includes: the launch engine the combustors the launch engine control system the shuttle/piston arresting gear the shuttle assembly the vehicle interface unit

The second step will consist of procurement of hardware and services to construct the catapult launch assist system. The estimated costs are listed below:

Launch engine cylinders $1,109,900 ROM cost for each 300 ft stack, including piston

The launch control system, $160,000 ROM cost for system including all sensors The combustor systems including combustors, fuel pumps and fuel storage

$200,000 ROM cost The shuttle assembly is indeterminate until vehicle is selected, ROM cost of

$70,000 The shuttle/piston arrestor mechanism, ROM cost of $22,000

The third step will consist of construction of the catapult launch system including the launch tower with supporting structures and the launch assist system at a site designated by NASA.

The launch tower will potentially use an existing launch tower which will be modified to suit this use. No ROM cost is assigned due to uncertainty of existing tower availability.

The launch engine tubes will be assembled into the launch tower by a steel erection contractor under program supervision.

The launch tower support services and support hardware will be as specified by NASA and will be priced accordingly.

The fourth step will be to accomplish a thorough series of tests of the launch assist system which will include the launch of dead-weights that simulate the vehicle to be launched. The purpose of the tests will be to demonstrate the reliability and capability of the catapult launch assist system to generate the required launch energy over the length of the catapult stroke and to accelerate the launch vehicle to the required end speed repeatably.

A Look At Catapult Launch Assist

A vertically oriented catapult, ground based launch assist can be provided which allows fuel not used in the initial part of the launch event to allow heavier loads to orbit or reduced vehicle size for the same payload.

The catapult is a combustion gas based piston and slotted cylinder engine, somewhat similar to the catapult used aboard Naval aircraft carriers. These catapults provide 3G acceleration to 70,000 pound planes using a pair of 21 inch diameter cylinders.

A vertically oriented catapult can be augmented in capability both in size of cylinders and number of cylinders. As an example, a ground based launch assist facility might operate at 800 PSI and consist of 6 launch cylinders with a diameter of 60 inches. This will provide a total vertical thrust of:

6*302 *3.1416*800 = 13,560,000 pounds of thrust or an acceleration of 4.52 G for a 3,000,000 pound launch vehicle. Assuming that an initial acceleration of 1G is required to offset earth’s gravity, this leaves a net 3.52 G of acceleration available at the first part of the launch. The total benefit will be determined by the vertical height of the ground based launch assist engine.

The basic equation for determining this benefit is:

d = vt + 1/2at2

where d is distance traveled in a certain amount of time (t), v is starting velocity, a is acceleration (must be constant), and t is time. This is rearranged as follows. d - vt = 1/2at2

Initial velocity (V) for a launch event = 0 ft per second

a = 113 ft per second ( 2.86 G acceleration)

t = 1 D = 56.6 Total distance = 56.6 FT

t = 2 D = 226 Total distance = 282.6 FT

t = 3 D = 509.3 Total distance = 719.9 FT (509 ft/sec = 4.6 Miles/Minute = 347 mph) .455 Mach

Catapult offers initial vertical guidance of the launch vehicle during the first part of the launch which removes the requirement for vectoring of the launch engine nozzles to maintain vertical stability during the low speed portion of the launch.

Given the above numbers transposed to a horizontal (angled) launch, the following demonstrates the capability of the system for a 3G launch. The advantage of an angled system is that it can be installed on the side of a mountain to minimize the energy required to turn the vehicle to the

vertical compared to a horizontal launch. Additionally, the thrust required to offset gravity is partially applied to acceleration. For example, for a 450 track, an additional .5 G would be available for acceleration. For a 600 track, an additional .66G would be available for acceleration.

t = 4 D = 728 Total distance = 1365 FT ( 728 ft/sec = 8.2 Miles/Minute = 496 mph) .64 Macht = 5 D = 1137.5 Total distance = 2502 FT (1137 ft/sec = 12.9 Miles/Minute = 774 mph) .99 Macht = 6 D = 1638 Total distance = 4140 FT (1638 ft/sec = 18.6 Miles/Minute = 1168mph) 1.44 Mach t = 7 D = 2229 Total distance = 6369 FT (2229 ft/sec = 25.3 Miles/Minute = 1519 mph) 1.98 Mach

Above these speeds, gas inertia starts to play a role which may limit the top speed that can be reached due to the time required to establish gas flow into the cylinders from the in-line combustors located along the length of the launch engine.

Given the two cases above, what are the fuel savings from the catapult that may be applied to additional payload or vehicle size reduction?

Case 1, vertical launch. Terminal speed at the end of 3 seconds is 509 ft per second. Fix the rest of this Vehicle weight is 3 million pounds and acceleration is 3.86 G. Total thrust is 11,581,194 for 3 seconds.Given an ISP of 285 for RP1/LOX, 11,581,194/285 = 40,635 pounds per second times 3 seconds = 121,905 pounds of RP1/LOX that is not required to achieve the initial velocity of 409 ft per second and is available for more payload to orbit or reduction in vehicle weight of 146,286 pounds given structure weight is 20% of fuel weight.

Case 2, angled launch. Terminal speed is 2,229 feet per second at the end of 7 seconds. Vehicle weight is 3 million pounds and acceleration is 3.86 G. Total thrust is 11,581,194 for 7 seconds.Given an ISP of 285 for RP1/LOX, 11,581,194/285 = 40,635 pounds per second times 7 seconds = 284,445 pounds of RP1/LOX that is not required to achieve the initial velocity of 2,229 ft per second and is available for more payload to orbit or reduction in vehicle weight of 341,334 pounds given structure weight is 20% of fuel weight.

Clint Stallard851-3475

Cost Study For Combustion Catapult

60” ID 73.5 OD double walled launch cylinder

.75” plate for inner cylinder, 61.5” outer diameter, 16.1’ circumference, and 20 ft long. Make from 4 pieces of plate 8’ by 10’ 9,792 lbs

.75” plate for outer cylinder, 73.5” outer diameter, 19.24’circumference, and 20 ft long. Make from 5 pieces of plate 8’ by 10 12,240 lbs

11 pieces of C shaped stiffeners, .5” thick, 61.5 ID X 72” OD Make from 4’ X 7’ plate 572 lbs

2 pieces connector .75” thick, 72” long, 8” wide, roll to 73.5 IDMake from 8’ X 1.5’ plate 122 lbs

60 pieces longitudinal stiffeners .5” thick, 5.25 wide, 23.5” longMake from 5 pieces of 4’ X 12’ 2,448 lbs

2 pieces slot liner, .75” thick, 6” X 20’Make from 2’ X 10 ft plate 1,224 lbs

1 Slot seal .4375” thick X 6” X 20’Make from .45375 Cres 316, 12” X 10’ 356 lb

1 hinge, 20 ft longMake from schedule 40 Cres Pipe, 1.5” X 20’ 100 lbMake hinge pin from K Monel rod .75 X 20 ft 34 lbMake hinge plate from .75” X 4” X 20’ 204 lb

1 piece connector hardware 1.25” X 12” X 76”Make from plate, roll to 76” ID 357 lb

1 piece Seal ring 61.5 OD 1.5” thick X 4” X 61.5”Make from 1.5” plate, 4” X 8’ roll to 60” ID 217 lb

Weld metal 5890” at .25 lb per inch 1,472lb

20 Bolts, 3/4-10 UNC 2” long

Total weight 29,138 lbs plus 200 lbs for misc hardware = 29,338 lbs

Must add foundation every 6 foot (3 foundations)2 pieces .75” thick, 20” long X 6” 50 lb2 pieces .75” thick, 18” wide X 6” 46 lb 1 piece 1” thick, 24” X 22” 38 lb 134 lb total per foundation = 402 lb

Total weight = 29,740 lbs or 1,487 lbs per foot.

Steel cost at $1.25/ft = $1,858Welding at $10.00/ linft = $245 Machining per foot = $1,350Painting and preservation = $80Total per foot = $3,533Total per 20’ tube = $70,660

Piston @ 800 PSI, length = 20 ft, Moment 2,200,000lb X 1ft = 246,000 lb X 9 ftTow point located at center of piston. Estimated cost = $50,000

Rear Disk, 1” thick X 58” ODRear seal carrier .5” X 58” OD X 4’4 pieces rear wear strips 1” X 24” X 4’ Bearium B8 impregnated bronze(Bearing pressure on bottom two = 106 PSI) 3 pc metallic seal u-cup gas operated 60” OD, 59” IDFront Disk .25” thick X 58” ODFront wear strip carrier .75” thick X 58” OD X 4’4 pieces front wear strip 1” X 60” OD X 4’ Bearium B8 impregnated bronze(Bearing pressure on top two = 106 PSI) Top flange 1” thick X 36” X 19’ 10.5”Bottom flange 1” X 36” X 19’ 10.5”Piston I beam web .5” X 58 X 19’ 10.5”Piston to vehicle interface 2” X 30” X 12”

Total per 300 foot assembly with piston = $1,109,900 ROM cost At 800 PSI, tube generates 2.2 million pounds of thrust. Therefore launch tube cost per pound of thrust delivered is $0.5045Amortized over 20 launches, cost per pound of thrust is $0.02523

Amortized cost per launch for 12 million pound thrust 6 tube launcher over 20 launches is $302,700(Pressure selected is for costing, can go higher and generate greater thrust)

The above numbers do not include combustors, upgrading of launch tower, instrumentation, fuel storage and piston recovery equipment.

Clint Stallard757-851-3475

Combustion Gas Powered Pneumatic Catapult ProposalFor RLV Launch

Introduction

Mankind has been unable to find an inexpensive method of launching large objects into space. For the past 40 years, the only method has been multi-stage rockets. There has always been great interest in a single stage Reusable Launched Vehicle (RLV). In fact, today’s “Space Shuttle” was envisioned as a single stage vehicle, but that proved impractical. NASA canceled a more recent attempt at a single-stage design, the X-33, in January 2001 when problems proved insurmountable. The solution is an “assisted launch” to propel the RLV to supersonic speeds before it fires its engines. However, the technology for current single-stage proposals does not allow attainment of orbit. Numerous discussions by the authors led us to realize that current technology will allow a inclined pneumatic catapult launch system to solve this problem.

Brief Summary

No one has seriously considered using proven pneumatic launch systems, although there is an extensive history of usage of this technology by the US Navy. Our figures prove that large RLVs can be propelled to supersonic speeds using pneumatic launch and an inclined launch ramp. The major challenge is identifying large mountains with lengthy inclined slopes on which to build the rail system. The system may begin on an inclined track directly from a launch pad, or it may begin horizontally and ramp up to the desired inclined launch angle. A review of each element of the title is helpful:

Reusable Pneumatically-powered and Pneumatically Levitated Sled System for Launching Spacecraft and Airborne Test Vehicles at Supersonic speeds

Reusable - keeps launch costs reasonable compared to the traditional method of disposable rocket stages. Pneumatically powered-this is a scale-up and simplification of existing Naval catapult launch technology with combustors rather than steam providing the motive force

Pneumatically Levitated–uses an on-sled combustor to provide gas pressure to levitate the launch sled above parallel concrete guideways which will form a lengthy inclined track. This removes the requirement for wheels which become problematic above Mach 1 due to centripetal forces generated within the wheels

Sled – the object which couples the catapult thrust to the launch vehicle and levitates the vehicle to be launched by the catapult at high speeds. Given two parallel concrete guideways 10’ wide and two forward and two aft levitating pads 20 ft long each, 2.88 million pounds can be levitated by a levitating pressure of 25 PSI. Spring loaded consumable seals are used on all four sides of each levitating pad. It is expected that the seals will be replaced for each launch.

Spacecraft – this system provides an assisted launch to increase the payload capacity or reduce the size and weight of spacecra ft.

Test Vehicles – this system is useful for launching a variety of test aircraft and missiles, or to test their aerodynamic properties at high speeds. (do we want to say this? Or modify it to say self-powered or gliding test vehicles?

Supersonic speeds – launch speeds in excess of Mach 1 are possible.

Integrated Impulse Equation Mass Ratio Requirements

Newton’s second law implies that F=dp/dt=d(mv)/dt. d(mv) is composed of the incremental propellant mass dm going out the back at propellant velocity V (impulse =Vdm) and rocket mass m forward at small velocity dv due to the motion backwards of propellant mass dm (impulse =mdv) . There are no external forces in this scenario so the net momentum change of the center of mass is zero so that <-Vdm= -mdv-> Rearrange this equation to read dv=V(dm/m) and integrate (dm/m) =ln(mf/mo) so that:v=Vln(mf/mo)=Vln(1/r) where r is the mass ratio, see graph below.The mf is the deadweight plus payload and deadweight is a function of the surface to volume ratio (how much surface vs. volume there is) the engine weight, payload,... The surface to volume is smallest for a large near radius spherical object and a small surface to volume ratio is what is required here. A Titan II is known to have the sufficiently low surface to volume ratio given its ISP. Here is a graph (From the NASA space data handbook) of velocity vs mass ratio r for various ISP s (specific impulse) which are related to fuel exhaust velocity V. Here we reason out how to obtain a RLV single stage to orbit for maglev launch. For 24,000 ft/second orbital velocity, Nitrogen tetroxide isp of 340 we see from the graph that the mass ratio r is about 9. In step one of this thought experiment we exchange the nitrogen tetroxide fuel for a higher ISP fuel H2-O2 increasing the isp to about 490 (step 1) but decreasing the fuel weight causing us to lengthen the fuel tank if we are to have the same fuel weight. At the same time we put wings on the TitanII and thermal insulation (that doubles as reentry tile) because of the cryogenic fuels (H2O2) which effectively halves the mass ratio to 5 (step 1 still). But because of the assisted launch it will go about the equivalent of 1/10 of orbital velocity faster (step 2). Add payload (step 3) and that brings it back to 24000 ft/sec orbital velocity. Thus instead of the Titan II mass ratio of 9, where it is able to carry its huge rocket, we have here 4 parts fuel to 1 part structure for a mass ratio of 5, doable.

Combustion Gas Pneumatic Catapult Launch –Combustion gas driven pistons within cylinders are the primary source of power for the internal combustion engine that powers most of the world automotive fleet. This is an extremely well known technology. Pneumatic launch is well characterized by Naval aircraft carrier catapults which have a phenomenal performance and safety record.. The current catapults operating in the fleet have a capability of delivering more than ½ million pounds of thrust. Scaling up the size of the cylinders and pistons provides a huge increase in delivered thrust. Simplification of the design provides a significant reduction in cost per pound of thrust delivered.

Fuel Tank Statics and Dynamics

A full cryogenic fuel tank sitting horizontal has to be supported by many points but yet has to be allowed to (thermally) contract when the cryogenic fuel is added. This support is provided by an interface support panel that sits on a slipway on the sled and is captured at the back of sled The interface panel is disposable and will be configured to suit the vehicle being launched. Secondly there is the question of how to use a minimum amount of interior structural reinforcement for a huge fuel tank sitting horizontal. It appears to me that very little reinforcement is required at all! That interface support panel supports the fuel weight when stationary and at 3-4 gs acceleration from the sled pushing on the bottom of the

tank along the track direction the "dynamics" is that of a nearly vertical fuel tank as in ordinary rocketry!!!! It's as if that tank reinforcement problem doesn't really exist at all, with light weight cables offering the best hope of reinforcing the interior if that should still be necessary. Replacing that heavy aerospike engine with conventional rocket engines may compensate for this small weight increase as well.RLV Release The RLV rocket engine has to be ignited before leaving the sled and yet these rollers must not tear off the thermal tiling when release occurs. Thus the sled must decelerate (but not the RLV) and jerk downward on RLV release, allowing inertia and the ignited rocket engines to carry the RLV. The interface panel will fall away after deceleration of the sled. The point is to make it so there is little added internal structural reinforcement needed for a X-33 type vehicle on the launch sled. Otherwise the added weight defeats our purpose.Track Length and Location The next issue is that of track length and location. The most ideal design I know of is a parabola on its side with the release point at 45deg pitch. This saves a huge amount on vertical mountain requirements. The 'small' track radius of curvature only exists on the section of the track where the speed is smallest so that centrifugal force (mv2/r) torques are smallest. For mach 2 release, instead of 2.5 miles vertical, you need only about 3/4 of a mile vertical which could be found in many places in the continental US, including in southern Texas, and at White Sands NM, especially on west side of that mountain range near Alamogordo NM. For political reasons the pneumatic launch system facility probably cannot be situated on the equator so the track must made longer to compensate for the lower initial velocity of higher latitudes. Note the initial velocity due to the earth's rotation goes approximately as 1000cos(lat) so for lat=25 deg (southern US) this is 1000(.91); you need an additional 93mph from the track. Because the release velocity goes as the square root of the length (times 2g) the track length must then be increased by about a third. Thus a vertical mile should be allowed (instead of 3/4 mile) for mach 2 launch which is still achievable at many places in the southern USA.

Need Launch Pitch Angle

Why not horizontal launch you ask? If you release a RLV moving at mach 2 ~700m/sec and demand lets say that it be moving near 60 deg pitch after 1000 meters, what centripetal acceleration necessary? It is 50 g s. The structural integrity is gone. So how many kilometers radius of curvature do you need for about a 1 g centripetal acceleration given this type of release? At least 50km. So for at least 30 miles the RLV is moving in the lower densest part of the atmosphere doing work against the air as it goes. =1kg/m3, take C=1, A=10m2, v=700m/sec. Approximate work=FD=½CAv250000 ~10^11 joules, more than the assisted launch energy itself ½mv2 = ½12400X7002 =3X1010 joules . Thus, the closer the launch release to vertical, the less work must be expended against the atmosphere to achieve orbit.

The X-33 failed without assisted a launch

NASA hoped to build the X-33 RLV as the world’s first single-stage to orbit spacecraft. This would allow safer and inexpensive space launches, compared to the “Space Shuttle” which requires an expensive first-stage booster rocket. However, after many years of research design incorporating the latest technologies, NASA was unable to develop a design that would allow the X-33 to reach orbit under its own power. As a result, the X-33 project was canceled in January of 2001. It was clear that the X-33 could make orbit with assisted launch. It should be considered that the heavy aerospike engines must be replaced by conventional rocket engines. The X-33 must be situated in a carriage on the sled that supports the fuel tank structure so that additional structural support is not necessary when the fuel tank is full of fuel. A number of methods for braking and capturing the sled are available and the most appropriate method will be selected for a given catapult installation. This carriage must allow for the contraction of the tank on fueling with these cold liquids.

The value of Initial Velocity which assisted launch provides

The core of the problem is that given the choice between a large initial mass m0 launch system and a large initial velocity v0 system. Let me make the case for the large v0 option. Let m0 be the total initial fully loaded mass of the rocket, ‘m’ the mass after the fuel is expended, V=exhaust velocity =4500 m/s, (calculated from H2+O Isp) v=8km/sec orbital velocity, t =8min time to orbit without having the initial velocity v0.

“R” the usual value of m0/m for the case v0 =0. The t 0v term is the decrease in time

(term) to orbit due to the fact of having an initial velocity. So this time is subtracted from the real time to get an effective time.

t(v0 )=60X1.5sec (saves ~1.5 minutes in flight , maxQ from 50-85sec), V=4500(m/s)=isp for H2+O. t=8min., v0=700 m/s=Mach2 with maglev. Thus in the rocket equation (resulting from integration of the impulse equation):

v gt Vmv m

00ln so dividing by V and taking the exponential and solving for

mo/m:

=1.42R again with R being the exponential term without assisted launch.

Thus the booster can be .7 times smaller for unmanned payloads, nearly half the size! This would make it so that even the large X-33 RLV could make it into orbit! The original X-33 design launched vertically from a dead-start could reach only about Mach 15, needing Mach 24 to make orbit. An assisted launch could close the gap. The ability to add this much extra mass in the form of reentry tiles (with a modification to X-33 like lifting body shape) would clearly still have orbital possibilities.

They key is to consider the pre maxQ vertical component of gt(vo) term in the impulse equation. This represents the work that would have had to have been done against gravity had the larger fuel load been carried up. This term is two to three times larger than the vo itself. It represents essentially a large “amplification” of the effect of assisted launch.

For an example of a pneumatic launch installation, we will use two five ft ID launch tubes operating at 464 PSI (design pressure of 1000 PSI) generating 2,624,000 pounds of thrust to launch an X-33 size RLV with sufficient speed to make orbit.

Parameters For ExampleLaunch weight of an X-33 = 273,000 lbs

Catapult Thrust = 2X1.4 million lbs each

Newton’s Second Law used to Calculate Required ThrustNewtons’s 2nd law F=maSum of Forces =Air Resistance+Thrust+gravity+Friction=ma2X1,312,000 lbs=2,624,000 lbs Thrust

Air Resistance: V=m , V=Ax so dm/dt=dV/dt=A(dx/dt)=Av inD(½)CAv2 Given typical vehicle drag coefficient D=.5, 1kg/m3 at v2X340m/sec, 10X30 m2 cross section, then:

D(½)CAv2 = =.5(.5)(1kg/m3)(10mX3m)(2*340m/s)2 =3,468,000N=778,000 lbs.

Friction to contributes little here. Gravity ForceTake sled plus rocket motors to be about 100,000 lbs weight at top of track since all the fuel has been used in the rocket motors. SoFg =mgsin=(273,000+100,000)sin45=263,711 lbs

Total Force Required for 6 gsTotal Force=air resistance+Thrust+gravity+Friction=ma=m6*9.8Total Force=D+Thrust+Fg=m6*9.8Thrust-778,000-263,711=ma=(263,000/32)6*32=1,578,000= lbs

So required Thrust =2,624,000 lbs provided by the pneumatic catapult. The track mounted on a pair of raised concrete,guideways like an expressway ramp, each 10 feet wide.

A spoiler can be used at the top of the track along with other brakes to help keep the sled moving on a downward moving track while the RLV leaves according to Newton's First Law. Large decelerations of the sled are possible because the RLV containing the people will be airborne. The 6G thrust requirement is provided by the pneumatic launch system..

Track Length For 6g Acceleration and Mach 2 Final Velocity so

4km2.5miles

So the inclined track must be on the order of 2 ½ miles (13,200 feet) long. Since the Earth has dozens of mountains over 20,000 feet tall, building rail ramp up a mountain at a 45-degree slope is certainly feasible; using the same construction techniques used to build interstate highways and rail lines through large mountain ranges. Variables for Inclined Pneumatic Launch Systems

Each launch site must be custom designed based on a variety of factors:

Location of launch site – a location closer to the earth’s equator is greatly advantageous for spacecraft launches, ideally pointing east. A large steep mountainside in needed to support the inclined rail. A rural area is best because of the launch noise and sonic booms.

Size of potential vehicles – the weight of the objects to be launched and their aerodynamic characteristics determine the length of track and thrust required.

Desired Speed of Launch – faster is usually better, but the thrust needed, angle of launch, and length of track are constraints.

Desired Angle of Launch – spacecraft going for orbit are best at near vertical take-off from the end of the rail. Of course the higher the angle the more thrust needed to achieve the desired speed, and rail/track construction becomes more difficult.

Maintenance and Support Choice – a system may use a dead start in which the object to be launched is mounted on the inclined rail in front of the thrust-powered sled and launched directly with a large “blast off”. A second option is for a horizontal support area in which the launch begins on a horizontal rail and ramps up to the desired angle on the track. At some locations, it is impractical to locate the support areas near the mountain base, so the track may begin with several miles of horizontal rails where a locomotive pushes the sled up to the inclined area before the thrust engines ignite. Ideally, a large airfield will exist nearby to allow spacecraft to land for easy reuse.

Braking System – Unless the sled is designed to go airborne and fly to an airbase for reuse after launching the RLV, some induction braking mechanism is needed rail. There are a dozen possible methods using simple existing technology.

Abstract

This method will allow a reusable guideway-mounted pneumatic launch system sled to launch spacecraft or airborne vehicles from earth at supersonic speeds using existing technology properly integrated into an inclined sled system. This system is much safer than the traditional method of launching rockets vertically since the launch can be aborted if problems develop. Moreover, it is far less costly since the sled can be reused within hours after a launch and the guideway system can accommodate a variety of sleds to launch objects of many different sizes.

1) Basic System Elements & Design & Configuration Catapult tubes are double wall steel tubes fastened end to end Combustors derived from LOX-RP1 rocket engines. Well understood. Ramp formed from concrete guideways with pneumatically levitated

sled. Somewhat like air hockey

Vertical launch or angled launch. Angled launch Ramp at or near 45 degrees, Concrete & Steel

Construction. Civil engineering is major component.

Ramp, parabola on its side with release point at 45 degrees. Pneumatic launch cylinder actuator. Track would be 2.5 miles long but with a net vertical displacement of less than a mile. It would be capable of launching RLV at mach 2 with 6g acceleration. The v=vo+Vln(m/mo) mass ratio considerations then allow a X-33 capable to orbit with payload.

2) Best or Proposed Locations for System / Facility( Mountain Location On or Near Earths Equator )

Put on the side of a mountain in the southern United States, <25degN lat., facing east The track needs to be about 1/3 longer because it won’t be at the equator. There are such mountains at White Sands, near Alamogordo, NM and in Texas.

3) Potential Program Participants and Scale (International Scope)( National Governments & Private Sector Interests Globally )( Development Costs, Operation Costs, and Funding Strategies =ie: Taxes/Government, Profits/Commercial, Grants/Academic, andDonations/Private )

Rick Dobson, David Maker

4) Potential Uses of Program, System, and Facility( ie: Government, Commercial, Scientific, Academic, and Private )

I would be a real space port. If working the way we envision it would mean cheap access to space, complete reusability. With the assisted launch capability of maglev there would also be substantial payload capability. Passengers could travel to this location using commercial air travel and then go directly to the part of the terminal that would take them into space. It would make moon and mars missions finally mean something: we could stay in these places because we could then afford to, not have these decade long hiatuses between trips.

5) Types & Purposes of RLV's & SSTO's as Launch Vehicle Candidates( ie: Large, Medium, Small & Mission Specific, Cargo, Passenger )( ie: Venture Star & AVATAR )

This would be for the X-33 without those heavy aerospike engines. At first it could be used to launch 3 people into space, with more payload capability to follow later. This would be useful for space station work and moon mission transfers.

6) What Infrastructure Other Than Pneumatic Launch System Facility & Vehicles Is Needed?The pneumatic launch system would need access roads, power line connections to the power grid and facilities for receiving and making vehicles ready for launch

A) Orbital Refueling Capability of RLV/SSTO Vehicles

The RLV could be used as a space tanker for ventures beyond earth orbit. This could be done if the crew quarters were modular, replacable with unmanned fuel tank launch capability.B) Large Scale Transport of Non-G Sensitive Fuel, Cargo, Raw Materials to Orbit Using Other Supporting Systems (ie: Space Cannon/Rail Gun)Electricity could be used at off peak use hours for operations. The hydrogen and oxygen fuel for the RLV could be separated from water on site by electrolysis using the electricity that at other times would be needed for maglev operation. Additionally, the oxygen for the catapult combustors can be generated on site. Thus only kerosene would have to transported to the site to support the catapult. C) Use of present Systems & Resources already in use to Support and Enhance Launcher Facility & Program & Services.

Combustor design, both for rockets and jet engines is a mature technology and knowledge bases and companies exist to support combustor design for this application.

Large cylinder pneumatic launch technology is also mature and support is available from the US Navy where required.

D) Training, Education, and Research & DevelopmentTraining would be available to operate the vehicleE) Society Supports & Outreach It would give children a reason to hope, make space accessible all people. The dream would finally come true. It might lead also to a resurgence in interest in pursuing science once again.

Dr. David Maker

Clint Stallard

ASSISTED LAUNCH David Maker

Abstract Congress has given space launch "experts" many opportunities to create a better launch system than the space shuttle. There was the national space plane in the 1980s, the X-33 in the 1990s along with SLI more recently. These are all failed programs and yet the trend still continues. So what really is the problem here? How do we escape from this cycle of failure? The source of this problem is that the mass ratio of .91 for the optimum available isps (given the fuel densities) cannot be exceeded at least by means of chemical propulsion. In this talk I explain the mass ratio problem, rules of thumb for determining whether a given space launch system will violate it thus providing a simple solution to this problem.An example of one way to obtain single stage RLV to orbit is provided by heated gas pneumatic launch. Some interesting nonequilibrium thermodynamics mathematics can be used to justify this method.But the main theme of this talk is a wakeup call to +30 years of repeating the same mass ratio mistakes on space launch. My primary motivation for giving this talk is try to help us break out of this cycle of decade after decade of making the same fatal mass ratio mistakes in space launch, thereby wasting our future away.

The talk will be in five parts:1) Discussion of why there has been 30+ years of repeating the same mistakes in

space launch over and over again. And it continues, with our future going down the tubes because of it. Explain this in terms of the mass ratio problem for RLV single stage to orbit.

2) Connect this discussion to the many ways of (wrongly) violating the delta V (integrated impulse) equation

3) Thus write down some rules of thumb that avoid repeating these many errors, this being the most important part of this presentation.

4) Mention one possibility of using pneumatic launch for overcoming this problem. Give the parameters required for pneumatic launch.

5) The nonequilibrium thermodynamics of overcoming the STP mach 1 with non detonation heated air. Specifically the second law of thermodynamics implications allowing for higher velocities (in heated gas) in the tube needed for single stage RLV to orbit.

 

Outline Of Problem and Ways of Solving It

The problem is that single stage to orbit for a completely Reusable Launch Vehicle (RLV) is not possible with present chemical propellants because the mass ratio of .91 has never been exceeded for these types of vehicles. The X-33 was the closest to the goal of single stage to orbit and in fact only needed assisted launch to be successful. One intuitive way of understanding the consequences of the integrated impulse (or deltaV) equation, when assisted launch is put in, is that it takes a lot of fuel to lift a lot of fuel. If you have a high velocity launch then the fuel that was otherwise required to get to that high velocity (say mach 2) is not needed and so the launch system requires even less fuel since that unneeded fuel doesn't have to be lifted anymore. Also there is less time in doing work against gravity because of the high initial velocity so less fuel is required for that reason as well. So given these two advantages, if even a modest fraction of the orbital mach 24 orbital velocity can be reached, you still have great gains provided by assisted launch. In that regard it is often stated that mach 1 assisted launch "saves a stage". >Mach 2 assisted launch, if properly done, saves two stages and allows single stage RLV to orbit especially for a X-33 type vehicle which was closer than any other method to being able to achieve orbit all by itself. Note that the space shuttle uses up approximately ½ of its fuel in reaching a mere 1000mph, about 1/24 orbital velocity.

If care is taken that you don't increase the weight of your vehicle because you are

doing assisted launch, then assisted launch becomes the only way to ever have single

stage totally reusable RLV to orbit. Single stage totally reusable small RLV to orbit

would be one of the greatest achievements of rocketry, allowing eventually cheap to orbit

and so the large scale development of space.

Integrated Impulse (DeltaV) Equation and The Mass Ratio ProblemLet m0 be the total initial fully loaded mass of the rocket, ‘m’ the mass after the fuel is expended, V=exhaust velocity =4500 m/s, (calculated from H2+O Isp) v=7.7km/sec orbital velocity, t =8.5min time to orbit without having the initial velocity v0. “R” the usual value of m0/m for the case v0 =0. The t(vo) term is the decrease in time (term) to orbit due to the fact of having an initial velocity. So this time is subtracted from the real time to get an effective time.

D= ½ at2 if the initial velocity is zero. Thus to get out of the atmosphere and headed in a nearly horizontal direction at about 70 miles or 100km for 3g climb we have 100X103 = ½ 3(9.8(.707))t2. So t =98.1 sec.Given initial assisted launch velocity vo orbital height D, 3g near constant acceleration ‘a’, D= ½ at2 +vot 100X103 = ½ 3(9.8(.707))t2..Solve for t to find time So t =98.1 secSubtract this time ts from time required without assisted launch t in the integrated impulse equation:Plug into the integrated impulse equation (deltaV equation):(Integration of the impulse equation): v=vo+g(t-ts)-gt+Vln(mo/m). The gt term represents the loss in velocity due to work against gravityThe mass ratio =deadweight mass plus fuel on ground mo divided by deadweight mass of rocket after fuel exhausted “m”. The “mass ratio” of .91 is here (mo-m)/mo. The logarithm (of mo/m) term is the most critical of course. This (logarithmic) insensitivity to that mo/m ratio makes it very hard to make mo/m big enough given what we have available for V, the exhaust velocity (a function of isp).

Also note from the delta V equation the two sources of gain in final velocity v achieved by assisted launch:

1) the first being in the decreased time in doing work against gravity (t-ts)2) and the other and most important given by vo, the initial velocity of assisted launch.

Note the mass ratio is a function of the surface to volume ratio (plus engine and payload mass). The ratio of surface to volume is small for nearly spherical (fat) objects. For spheres the surface to volume ratio is proportional to the 1/radius =1/r, Thus large r means small surface to volume ratio. Thus big round objects have a small surface to volume ratio. For a near linear thin projectile (with constant width) the surface to volume ratio is proportion to a constant, stays big! Thus the surface to volume ratio is large for streamlined narrow objects. Thus the mass ratio is optimum for “fat” round objects.

This deltaV equation (integrated impulse equation) provides a way to do back of the envelope calculations to check on the viability of a given space launch method (it’s a ‘reality’ check).

RULES OF THUMB (from DeltaV equation)How do we obtain some clarity about what is possible in space launch, what our options are so that we are not to continue decade after decade of this folly?

1) First of all check your launch method against these kinds of back of the envelope calculation techniques (the goal of this talk!). Don’t just rely on the computer spread sheets. Try to get a intuitive sense of what can be a single stage to orbit RLV and what can’t. Note that to have low surface to volume ratio these RLVs need to be essentially fat fuel cans. Sleekness means a high surface to volume ratio and so a low mass ratio. Since RLVs have to be fat it is best to have high altitude near vertical launch so that the effects of air friction are minimized. Thus one of the intuitive ways to identify whether a launch system is a viable RLV single stage to orbit is whether it is fat. In terms of viable RLVs Think FAT!

A) For example these sleek X prize entries are not viable single stage to orbit RLV s because they violate the mass ratio by having too high of surface to volume ratio, hence too large of deadweight ‘m’ in the deltaV equation. Also that sleek National Space Plane of the 1980s, X-33-Venturestar concept with its deadweight scaling problem and heavy engine. These are dead enders for the same reason. In any case trying this is all essentially duplication of what the X-15 program accomplished in the 1950s

B) For Towing a large fat RLV full of fuel with poor aerodynamics would not even get off the ground.

C) For horizontal assisted launch the distance (arc) required to gain near vertical velocity is too large because of the necessity of minimizing the bending torques caused by the need of too high centripetal force mv2/r. Thus the work done Fdx pushing air this large distance of distance in the lower atmosphere by a fat RLV (thus with large air friction cross section) is nearly the same as that gained from the assisted launch. Also horizontal full fuel tank launch means added structural reinforcement for the fuel tank against bending torques further limiting the advantages of assisted launch. Thus horizontal plane launched (Pegasus) and horizontal maglev are not viable single stage to orbit RLV concepts.

D) Don’t even consider RLV single stage to orbit for northern latitudes. Sacrificing that 0 latitude (equatorial) earth rotation 1000mph(times the cosine of that latitude) speed is not viable. Even the 100mph gain in going from Cape Canaveral Florida latitude to the equator gives ocean launch a substantial payload advantage over Florida launch. Recall X-33-Venturstar spaceports were even being advertised for Montana, brother.

E) High g launches (>6g) imply substantial structural reinforcement requirements for the RLV (given bending force F=ma), further limiting the advantages of assisted launch.

F) Note from deltaV equation that high velocity vo (and so not necessarily height) is needed for single stage to orbit. Some schemes such as balloon launch don’t give that necessary initial velocity.

G) Be aware of large long heavy engines that solve one problem (exhaust plume expansion with altitude) but create another more serious one (e.g., overweight engine). The aerospike solved the plume expansion problem but was a very wide heavy engine. Too heavy. Might need ceramics or a conventional smaller engine.

H) Of course carbon fiber fuel tanks are an advantage that lowers the ‘m’ in the deltaV equation.

You have got to admit that a balloon launch engineer might need to know that what is really critical in getting to orbit is velocity (that vo), not height. The person contemplating putting these assisted launch facilities in Alaska might want to know that defeats the purpose of assisted launch. The person trying to build a sleek concord type RLV single stage to orbit might want to know that it can never carry enough fuel to reach orbit. Anyway all these issues stem from a basic misunderstanding of that mass ratio problem in the deltaV equation.  If all this information was well known to everybody then perhaps we will stop making mistakes in space launch (that have plagued us decade after decade) and finally start progressing again.  

2) Thus single stage to orbit looks hard. But all is not lost. There is another interesting rule of thumb that the Titan II first stage provides for predicting single stage To orbit viability

The Titan II Length 89.9 feet (2.7m) used in Gemini program for example.Diameter 9.8 feet (3m).Weight 330,800 lbs (1,472,000 N)

Thrust 430,000 lbs or 1,900,000 NewtonsPropellant nitrogen tetroxide N204 and aerozine 50 Aerojet General Corp (propulsion) and Martin Company (first and second stage)

Note that the Titan II first stage could make it into orbit. But as single stage to orbit it couldn’t reenter (without burning up) let alone carry significant payload. ADD surface insulation which doubles as thermal reentry tile!! Nifty since then high isp and low density H2 can then be used as a fuel!

Liquid hydrogen has a higher isp 456 vac than N204 (250 vac) and also has less than 1/3 the density of N204 giving it far greater lift capability and thus allowing single stage orbit with cryogenic insulation. But this cryogenic insulation could do double duty as reentry tile as well. In addition the aluminum fuel tanks could be replaced with carbon fiber as is now feasible giving equal strength but with less weight.. Thus there is a very good possibility of single stage to orbit albeit with small or no payload but nonetheless with RLV capability. Note that the space shuttle uses about ½ of its fuel in reaching about 1000 mph. Thus if one could get this modified titan II up to ~1000mph not only would there be substantial payload capability but allowance for shrinking the size of the RLV from that of a titan II size. Launch could be done in a vertical tube without sabots.Ice accumulation limited by dehumidification of surrounding air, vertical so that little structural reinforcement is required. Only ~12 atmosphere over pressure needed on bottom Air heated to higher temperature to allowing for higher velocity launch. Tube put near equator, perhaps at a high altitude somewhere South America so that earth’s orbital speed also used.

Pneumatic Launch IntroductionBut to get a large payload and/or be able to shorten the vehicle so that it would be easier to manufacture you could do pneumatic assisted launch from a long nearly straight vertical tube. The hydrogen and oxygen could be obtained from electrolysis from locally available

water, thus there would be no fuel transportation costs. For this purpose build your own power station or reopen one of these mothballed nuclear reactors that are scattered around the country, sell the power when not using the air compressors. Anyway the costs here go down and down since this whole process could be automated, wouldn't even need the people that haul the fuel, could even get cheaper than airline flight with this kind of cost reduction!!!!!. Imagine going into space for LESS than it costs for a airline ticket! If that wouldn't lead to the large scale development of space I don't know what would. Money would be made all around, humanity would be served by more than just spectacular stunts like going to the moon or inventions like tang and velcro (NASA as a Disney show).. It would actually help ordinary people lead their lives. RLV with deep slits in the wall of the tube for the wings to fit in so no sabots are required. You don't have to worry about mountain contours and such here, just need the vertical height, could even come out of a mine shaft on a high HORIZONTAL plateau if you wanted. No worry about iced track, etc.. There is no humongous, dangerous rocket sled attached here either, no braking problems. You could reload in the case of the horizontal plateau option by simply dropping it back down the tube and use the compression of the air near the bottom to stop it (close the lower air outlets). Anyway pneumatic assisted launch has got to be the best option. So you solve the sled size problem, the sled size is zero!! You solve every problem frankly. In the mountain you could even install the facilities for making the hydrogen and LOX

The principle objection to pneumatic assisted launch is that it only gives mach 1 launch due to shock waves created if above that speed. But non detonation heating the gas below the projectile to about 600K increases the velocity for which shock waves will be created. This can be shown from nonequilibrium thermodynamic considerations.

Definition of the Max Payload and The Vehicle to Carry it.

Example Parameters :

propellant for the launch gasses hydrogen-oxygen

-combustor design and fuel consumption

-vehicle to tube interface and sealant method

The Bernoulli effect makes it so that air is the tube interface.

273,000 lb launch weight

In a 3 X 6 meter tube this ~12 atmospheres pressure from below.

Newton’s Second Law used to Calculate Required Thrust

Newtons’s 2nd law F=ma

Sum of Forces =Air Resistance+Thrust+gravity+Friction=ma

Air Resistance:

The drag coefficient is indeed a mess. In fact for some Reynolds numbers it even drops. For example in some cases you can make it drop using a rough surface! (e.g., golfballs and baseballs). In any case here we use: V=m , V=Ax so dm/dt=dV/dt=A(dx/dt)=Av in

D(½)CdAv2

To get close to that m/mo~ .9 the RLV must be somewhat BLUNT and fat so the drag coefficient adjusted for transonic and supersonic effects and adding lift drag, Cd>1 (we will conservatively take Cd=1). Also because of the bluntness A~r2~3X22~10 for mac truck crossectional area (X-33 area also?), near sea level air density r»1kg/m3 for average up to about 6miles high, v~mach2~2X340m/sec, so v2~4X105. So Fd~ (1/2)(1/2)(1)4X10X105~2X105,

People have also done calculations of pneumatic launch using the numerical Navier Stokes method. On the average the size of the launch system(given by these calculations) is about twice as big as that of conventional fanno flow calculations would predict, still not prohibitively large.

Gravity Force

Take the RVL plus air pushed to be about 100,000 lbs weight at top of tube since all the fuel has been used in the rocket motors. SoFg =mgsinq=(273,000+100,000)sin80°=367,333 lbs

Total Force Required for 6 gs

Total Force=air resistance+Thrust+gravity+Friction=ma=m6*9.8

Total Force=D+Thrust+Fg=m6*9.8

Thrust-367,333=ma=(263,000/32)6*32=1,945,333= lbs

So the required Thrust =1,945,333 pds. Note this represents the maximum thrust needed.

Tube Length For 6g Acceleration and Mach 2 Final Velocity

so =2X340m/sec so s=4km2.5miles

So the inclined tube must be on the order of 2.5 miles (13,200 feet) long. A single large cylindrical fuel tank has a low surface to volume ratio and so has advantageous mass ratio. . But splitting the tank in half along its axis means adding a great deal of structure to hold the two halves together and also adds tank wall surface for this inside wing storage region. For example the F111 wing container assembly essentially divides the fuselage in half, (in this case it would divide the fuel tank in half) adding a lot of structural reinforcment weight and internal tank surface area, thus even more added weight.   In that regard that biplane idea is useful in keeping wings out of the center of the cylindrical fuel tank when folded in and also having a strong structure for wing support, that rod connecting the two wings.. .In fact this folded wing biplane idea seems to be the best for doing pneumatic launch. Putting a space shuttle shaped structure into that tube would make for a very large diameter tube(and a huge sabot)  to contain the wings(fifty feet wide?) making it even more impossible to find the funds to build the tube which needn't be much more than 12 feet in diameter with this fold out biplane wing structure.

EXAMPLE OF A PNEUMATIC LAUNCH TUNNEL

The world has several railway tunnels over 30 miles long. A near vertical 2.5 mile tunnel would not make the list of the worlds 250 longest railway tunnels. This makes the site selection easy since angle of launch can be chosen, weather is rarely a factor, tunnel reduces noise and environmental concerns.

TUNNEL CONSTRUCTION

Source The Traylor Corporation

Costs based on hard rock tunneling

Maximum bore size 26 feet

Cost per mile of tunnels finished to transportation standards on the order of $15M

VACUUM PUMPS

Source Ingersol Rand Company

Off-the shelf “Stokes pump with following characteristics

Pumping capacity:50,000 CFM

Pump power:approximately 7MW

Approximately $1.25M installation

COMPRESSORS

Source Ingersol Rand Company

Pressure 600 psi

Capacity 25,000CFM@600psi

Compressor power 3.7 MW

Cost:approximately $1.5-2 M w/installation

RLV MODEL

The titan is a paradigm for where to start in single stage to orbit. Titan II template: Length 89.9ft, Diameter 9.8ft, Weight 330,000 lbs, Thrust 430,000 lbs Propellant orbit non return Nitrogen Tetroxide, Aerozone 50~5400F , Isp =253 SL, 340VAC,1.20 g/cc

But for O2, H2,density= .31g/cc, isp 5500, 345 atm. , 456 VAC. Note that because of the far lower density of H2,O2 and higher isp the payload and deadweight lifting capability are far higher with O2, H2 than with the nitrogen tetroxide, aerozine. Thus the thermal reentry heat shield structure can do double duty also as thermal insulation to allow high isp, cryogenics O2 (note the higher isp and lower density) storage thus providing the extra thrust needed for also lifting this heat shield.

Also hydrogen can be used in pneumatic launch tube to stop condensation on the rocket (ice impacts on the side could destroy the vehicle given that it is in a tube) and also increase the allowed speed of launch far beyond the STP speed of sound so that launch could be supersonic. Recall that the space shuttle uses half its fuel to get to 1000mph. Thus wing weight could easily be added given a supersonic assisted launch because so

much fuel would be saved for 1000mph assisted launch. Thus it is easy to argue viability for this launch method.

Vibration ReductionFor the first couple of launches vibration (of the projectile in the tube) reduction can be achieved by means of Sabots. Later when the modes of vibration of the RLV as it moves up the tube are known and damping is implemented than the SABOTs need not be used.

Here is more on CELT.

http://technology.ksc.nasa.gov/WWWaccess/techreports/2002report/400%20Spaceport%20Struct/406.html

APPENDIXNon Fanno, Non Rayleigh Flow, Non lagrangian Ballistics Approach The principle objection to pneumatic assisted launch is that it only gives mach 1 launch due to shock waves created if above that speed. In that case the velocity here would no higher than airplane launch making the construction of a giant pneumatic launch facility meaningless

But non detonation heating of the gas below the projectile to about 600K (620F) increases the velocity for which shock waves will be created. This is because the velocity of sound is larger in this heated air.

As an alternative it is possible to use pure hydrogen gas with a sound speed of v=1284 m/s at STP and so no heating to obtain a velocity several times the mach number of air. In any case it is possible to use heated air to get a higher launch speed than mach at stp. In the pneumatic launch facility the temperature can be made gradually larger in the bore but not by detonation. Thus the speed of sound in room temperature air can be greatly exceeded in this case. We show how this can be done by doing non Fanno, non equilibrium thermodynamics. Here we derive the T-S diagram for NONFannoi, Non Rayleigh flow. We will then be able to find the effects of the second law of thermodynamics on the flow history.

The usual result you get from Fanno flow is that the second law of thermodynamics leads to a flow at M=1 (Mach 1) given a long enough tube. But Fanno flow is steady flow so that no net positive external work is being done on the system. In this derivation we will have nonzero positive outside work. The result is that the long tube Mach 1 result is no

longer a limitation imposed by the second law of thermodynamics. The result we are trying to find here is for nonsteady flow in which the equation for continuity doesn’t in general hold since, there is more rate of flow into one side of a given volume than the other side due the nonzero inertia of the material. This is not the usual Lagrange ballistic theory and is not treated in such standard texts as John and Stanyukovich and Shapiro. Rose uses an aerodynamic piston drag iteration approach and here we try for a closed form for the flow rate. In the second part of this paper we will propose a specific example with NonFanno flow and show how to calculate the important parameters (such as pressures, Mach number, tube lengths, accelerations). We start out with a number of free parameters in an exponential which are determined in the lagrange ballistic theory limit. We take our channel to be constant area and our gas behavior in a specific region to be adiabatic-isentropic. The energy equation can be written:

hvg

h h tc

T 2

2

1) where here the enthalpy h t is a function of time so that work is being done on the system. v is the velocity, gc is the acceleration of gravity and:

h uP

, dh du d

Pdu

dP

PdP

2 2)

Recall for the enthalpy h that h=cpT , Note that v g h h tc f 2 3) Also

c T Tvgp

c1

2

2 and

T Tvc gp c

1

2

2

4) In Fanno flow h(t) would be a constant. But for non Fanno flow the flow is not steady and h(t) is not a constant. Here we take the flow rate v to be exponentially increasing (recall nonzero inertia) with time due to a exponentially increasing pressure at the base. So: v kect 5)

ke

v

ct

6) In Fanno flow c=0 in equations 5 and 6 because of continuity. Using the conservation of energy dQ du PdV , and definitions of entropy change ds=dQ/T, enthalpy h (equation 2) we have that:

du PdV dQ Tds dhdPP

pdV duP

d PdV

2 7)

And for an ideal gas: P RT . Here is mole density. We assume constant specific heats and work being done on the system. Now we can plug in for P the ideal gas result and plug into equation 7 for from equation 5:

s s cTT

R cTT

R

kev

kev

Wv v

ct

ct

1

1 1 1

2

1

2

1ln ln ln ln

= s s cTT

Rvv

Rc t t Wv 11

2

12 1ln ln

8)We also assume that a state 1 is a reference state for our flow.Plugging into equation 8 the respective v s from equation 3 we get:

s sc

TT

T TT T

Rcc

t t Wv t v

1

1

1

12 1

12

ln ln

s sc

TT

T TRcc

t t T T Wv v

t

1

11 2 1 1

12

12

ln ln ln

9)

Here the terms in the square brackets are assumed to be time varying whereas in Fanno flow the square bracket terms would be a constant. Now we can plot T vs s from equation 9 and obtain the behavior of the point of highest entropy on this diagram which we will call point 0.

T o

S Figure 1

The Fanno line for this equation is graphed in figure 1. Recall that ds>0 for a system with friction. Thus the system will tend to the point 0 if there is a long enough tube. To find the behavior at point 0 we take the derivative of equation 9 with respect to T. The last term is not specifically a function of T so it drops out. So:

ds

c dT T T TRcc

dtdT

dWdTv v

1 12

01

10)

Multiplying both sides by cp and using c ccc

ccc

c c Rp pp

vv

p

vp v

1 we have

v g RTTRc

dtdT

dWdT

c2 1

1

so the Mach number M equals:

MTRc

dtdT

dWdT

2 1

1

11)at point 0 in figure 1. Note that c=0 and dW/dT are zero for Fanno flow. Since the kelvin temperature T is on the order of 300 and R are of order 1 then even

small values of dt/dT and c can yield nearly a unit value for TRcdtdT

dWdT

.

This is our most important result. So there doesn’t need to be an explosion to get supersonic motion here as in a gun, steady external positive work does the job just as well. The flow is irreversible due to friction. Thus ds>0 and so the entropy increases in the flow direction. The entropy is at its highest were equation 11 holds. What if a given flow starts out at Mach 1. Due the increasing entropy the state of the system will be to tend to the Mach number after a long enough time in a long enough tube. In Fanno flow this has effect of slowing down a supersonic flow since the Mach number there is 1.

This is because of the second law of thermodynamics says that the entropy cannot go down for a isolated system and here must go up since this is an irreversible process. Here though the Mach number is large due to the work being done so there is no longer a limitation on the final velocity due to the second law of thermodynamics.

Finally there is that curious singularity in M when TRcdtdT

dWdT

=1. In this case small

dt/dT caused by adiabatic compression and large W can make for large increases in the mach number M. Thus it is possible to have a large Mach number even with a long tube.

i James John, Gas Dynamics, Allyn and Bacon,, 1969, P.158

The second law of thermodynamics does not prohibit getting a large Mach number if the flow is exponentially increasing due to external flow and pressure increase.

I have detailed numerical examples of an application of the last theorem that unfortunately take up too many kilobytes to include in this paper. But one important result that I must mention is that the air flow are requirements are extremely diminished by the slow preheating we are discussing above.This non Fanno flow analysis demonstrates that slow heat input (as opposed todetonation) can give a much higher temperature and higher speed of sound in thepeashooter barrel.Summary1) If the exponential terms in the theory are incorrect by just a small amount the time squared dependence in the exponential causes enormous changes (uncertainties) in flow rate.2) This problem can be solved by introducing a small ammount of hydrogen gas and combusting it. This also solves the problem of the Fanno flow mach 1 dependence caused by the second law of thermodynamics.3) Have to take into account time delay due to gas propagation in tube. Leads to nonFanno flow dynamics. Can’t use the constant flow equations here.