Although this occurred at Bell Aircraft several years prior to this point in my employment at Space Technology Labs, I still carried the feelings of disappointment and frustration I experienced when I learned how expensive it would be to launch the boost-glide (BOMI) vehicle we had worked on for several or more years. Unless a better way was found, I too was convinced that space operations would be limited by excessively high costs.
I was given one idea to start: recover the Titan first stage by having a helicopter snatch it before it crashes into the sea. At that time helicopter snatching of jettisoned reconnaissance satellite capsules was a successful technique; and Sikorsky was developing a very high-load capacity crane, large enough to carry the spent Titan stage. I also asked several of the staff for ideas. Almost everyone suggested recovery of part or all the hardware as the most promising concept to pursue. At first glance it seemed that the goal might be met by successfully recovering all the hardware perhaps only 20 or 30 times. "Fly-backs," or winged recoverable stages, were considered to be the promising concept for total hardware recovery.
In studying the snatching of the Titan first stage, I found that adding minor-weighing frills to the stage in order to make it flat-spin in, would make the concept feasible. The stage would then be subjected to low dynamic pressures and negligible aerodynamic heating, and arrive at the snatchable altitude at a low-enough speed. A rough cost estimate, however, showed that the concept fell far short of the goal. Various concepts for retrieving the second stage, protected against the thermal and aerodynamic loadings of reentry, were briefly studied and found not at all promising on a cost basis.
I then examined recoverable, winged stages. Those were the days of the slide rule, and only rough calculations of the back-of-the-envelop variety were possible. The concepts, of which there were many variations, turned out to be sure losers when total life-cycle costs were considered, that is, the sum of the nonrecurring and recurring costs for the life of the program.
I recall having only one concept left that warranted study. I can trace the origin of the concept to my training and experiences, particularly my experience on the Minuteman program. We often used the "exchange ratios" for the missile as design guidelines in minimizing weight and maximizing performance. These ratios related the burnout (essentially hardware) weight and the engine specific impulse of each stage to the weight and velocity (or, range) of the payload.
Since maximizing the weight of the payload and increasing its range were desired objectives, it had the effect of stimulating the need for decreasing weight and increasing engine efficiency almost regardless of the added cost. Although the burnout weight and the engine efficiency of the first stage had the least influence on the payload weight and its velocity, all stages were designed to have the same level of high sophistication. Every pound of structural weight removed and every point in specific impulse gained in any stage were considered rewarding.
I subscribed to this design approach. I seriously thought that perhaps we were spending too little funds advancing technology. More specifically, I felt that if we learned how to further minimize hardware weight and increase propulsion efficiency to some higher levels of sophistication, the sought after cost reduction might be achievable. I thought I might be able to devise an exploratory analysis that would show that advancements in technology are needed. The analysis I subsequently prepared gave surprising results; it lead to the minimum cost design criteria.
To conduct an exploratory analysis of this nature it was necessary to make rather sweeping, yet reasonable assumptions. The major assumption was a definition of the relationship between hardware cost and weight. In formulating this relationship I assumed that all weight was designed by pressure loads since the tanks and engine represent almost all of the inert weight. Additional, minor assumptions were made, and these may be found in The Aerospace Corporation report, "Proposed Minimum Cost Space Launch Vehicle System," by A. Schnitt and Col F.W. Kniss, July 1968.
I used only two points to define the cost-weight relationship that I intuitively felt was exponential-that pressure vessel cost increases exponentially with decreasing weight. I learned that the basic Atlas and Titan propellant tanks cost about $100/lb. I knew from my experience at Bell Aircraft, in deriving design and testing criteria for high-pressure airborne pressure vessels, that commercial tanks built to ASME codes have a factor of safety of 4.3, can be pressurized an infinite number of times, are fabricated from very ductile materials, operate at relatively low stress levels, and cost $1/lb in steel and $3/lb in aluminum.
A graphical presentation of the relationship is shown in the figure below. Hardware cost on linear and log scales are related to the operating stress level given in thousands of pounds per square inch (ksi) in steel. Note that the operating or working stress level is the inverse of hardware weight. The expected optimum regime is shown to be somewhere beyond the current, minimum weight state-of-the-art.
The hardware cost-weight relationship was introduced into the ideal rocket equation: V = Isp g ln (Wi/Wbo), where
The inceptive analysis considered only a first stage. The initial vehicle weight was the takeoff weight of the total vehicle. The burnout weight was the weight of the stage before being jettisoned plus the weight above it, or, the takeoff weight less the weight of the fuels consumed by the first stage. In treating a first stage, the payload weight is the weight above the first stage.
The first stage of a typical three-stage, expendable, liquid-fueled vehicle designed to reach low earth orbit (LEO) was studied. Losses due to gravity and aerodynamic drag were accounted for in estimating the ideal velocity of the stage at burnout. An average Isp was assumed, as well as the hardware weight as a fraction of the stage weight. The optimum cost of the hardware was calculated at about $4/lb. Correspondingly, the reduction in stage cost was huge although it grew somewhat in size. This unexpected, incredulous answer led me to conduct a parametric analysis from which it might be possible to understand and rationalize the validity of the result. A range of values of each variable in the ideal rocket equation was considered.
I had the support of a team of people filling out table after table-work
that now can be done in relatively little time by a programmable hand calculator.
The thought that if the analysis is correct and we have indeed been designing
space vehicles "to play in the wrong ballpark" was indeed stimulating.
Had I hit the jackpot in finding the solution to the cost problem?
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much of total launch cost is dictated by hardware? What do you
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Next Column: Results of the parametric analysis.