Because of my interest in reusable launch systems, I have followed the activities of SpaceX closely for a number of years. By the same token, I also follow Blue Origin... although I'll be much more interested in them once they make the move beyond sub-orbital boosters. When ULA announced that their proposed Vulcan launch vehicle would be partially reusable, I was (briefly) interested in it -- although one look at their proposal damped much of my enthusiasm. The convoluted plan that ULA devised in order to reuse just the engines of the Vulcan first stage seems to involve a significant design effort for a minimal return. At best it is an evolutionary step in reusable launch technology when both SpaceX and Blue Origin are working towards revolutionary steps.
A few days ago, an article I read reminded me of the Vulcan and prompted me to check if there was any recent news about it. While searching, I ran across a white paper from ULA: Launch Vehicle Recovery and Reuse. The paper is an interesting read -- in particular the analysis used to sell the notion that the Vulcan Sensible Modular Autonomous Return Technology (SMART) plan makes economic sense. The chart to the left comes from section 7 of that document: Economics of Reuse. In this section, the authors explain why SMART would be more effective at reducing launch costs than the booster flyback concept of SpaceX. According to the paper, the chart demonstrates that SMART will reach break even when compared to a comparable expendable booster at the second launch and subsequent reuses would drop costs to about 90% of an equivalent expendable booster. By contrast, it purports to show that the Falcon 9 flyback concept does not break even until the tenth use and never matches the cost reduction of the SMART concept.
The formula that ULA used to generate the graph is shown in the image below. Unfortunately, while the white paper notes that the accuracy of the information generated by the formula is highly dependent on the values used in it, the paper does not actually provide the specific numbers used to generate the chart. The readers are presumably intended to accept that the authors chose reasonable values.
One thing soon became apparent as I was tweaking the equation inputs. The variable which far and away made the most difference in how rapidly the break even point was achieved as well as the overall economic viability of the two concepts was p. This is the ratio of the performance of the expendable system to the performance of the reusable system. To see the true elegance of this coefficient (from ULA's point of view), it is necessary to understand the effect it has in the equation. If the rated mass-to-orbit of a fully expendable launch vehicle is 30% greater than the rated mass-to-orbit of an equivalent launch vehicle with reusable features, then the function increases the reusable mission cost by 30%. The paper even states that this is the primary reason for the 'cost difference' in the two concepts: 'The difference is mainly because of the 30 per cent performance loss to land the booster downrange on a barge.'
While I'm certain that viewpoint is an attractive one to the ULA team behind the SMART concept, it does not mesh with reality. The Falcon 9 missions seldom make use of 100% of their rated capacity. If an expendable booster only uses 70% of its rated capacity to launch a given payload into its designated orbit, the costs for the launch are not reduced by 30%. By the same token, launch costs would not increase by 30% if an equivalent reusable launch vehicle required its full rated capacity for the same payload. It is true that there are additional performance-related mission costs for a flyback mission when compared to one with an expendable first stage -- notably additional propellant. However, Elon Musk has indicated that propellant costs are less than half a percent of the total mission costs. In any event, the cost of that additional propellant should be included in the C(RR) variable of the equation. Arbitrarily increasing the mission cost because the reusable tech decreases the maximum potential mass-to-orbit is madness. For that matter -- it makes no more sense when applied to SMART than it does for the flyback option of SpaceX. However, it favors the SMART concept because the additional mass required for the parachutes, inflatable decelerator, and engine separation mechanism has a lower impact on the total mass-to-orbit than the flyback option.
I can accept the reduced mass-to-orbit capacity caused by adding reusability features to a launch system having a tangible cost impact if it were to put a payload outside the rated capacity of the launch vehicle. This could require the payload to be launched on a larger (and more expensive) booster. Of course this would require mission planners to blindly decide that since the Falcon 9 cannot launch the payload to the required orbit and accept the performance penalty of the first stage flyback -- that the mission would simply have to be launched using the F9-heavy at a higher cost. The logical flaw in this thinking is obvious. Nothing says that SpaceX cannot simply launch such a payload without recovering the first stage. A mission like this might well make use of a first stage that has been used on several previous flights and is approaching the point where it is not feasible to refurbish.
I may well be maligning the authors of the ULA white paper. However, it strikes me that someone who was putting together an equation like this might well have initially developed one that did not contain the performance ratio. After populating the equation, it would have quickly become obvious that even using unfavorable assumptions for SpaceX production and refurbishment costs, there was no way for the formula to make SMART look like a competitive solution. A person in this situation might well have decided that the formula needed a coefficient which would heavily favor SMART. For maximum effectiveness, such a coefficient would need to be a single value that acted as a multiplier on the rest of the equation. The p variable is exactly what was needed in exactly the right place. That seems overly convenient to me.
Anyone who is interested in playing around with the analysis is welcome to the spreadsheet I created. The first tab contains the analysis using my best guess at the ULA numbers. In the second tab, I changed the SpaceX numbers to match values I believe are closer to reality.