Here there be dragons

Being average is great until it’s not. For an engineer or scientist, a predictably average data point means the task is complete. We even count how many data points are a certain distance from what we wanted, our job being to make sure nearly none of the points in the herd stray too far. There was an exercise in college involving marbles and tracks meant to give us students an appreciation of all this. So how does the seemingly random tend to an average? (This also left some of us commiserating about our choice of major. An introduction to statistics and distributions followed the little game of marbles.)

Our launch business commonly frames itself in a graph showing the price of each rocket divided by its payload capability. (Google images of “rocket cost-per-kg” or “per-pound.”) This graph is the rocket science version of the “price per ounce” on the label at the supermarket, helping us decide if we should buy the large jar or the small one. As a rule, there would seem to be some “averageness” to points in this graph; for any size rocket, there is a typical cost per kg. Also, as a rule, you would expect to get a better deal buying the jumbo size. Though perhaps good rules of thumb once upon a time, these no longer seem to hold.

This graph plots dollars of “price” (a “cost” to the buyer/customer) versus the maximum payload capability of the rocket. Some caveats – (1) The rocket may not carry that maximum payload on any particular launch. (2) Prices may be even higher when costs are added for additional launch support (data, access, etc.) after an award but are not advertised at the time. This especially applies to non-US launchers. (3) All payloads have been normalized to the orbit indicated even when the rocket may go higher, so carrying less payload. This is for more of an “apples-to-apples” comparison. Inversely, if orbits are uneven then $/kg might not fairly compare.

Recently, data points are straying far from a predictable line. Yet, in this case, scattering is a good thing. There are times in engineering and technology that we do not want to be average. We want to deviate from the norm; it means something is changing that we want to change. So when the marble keeps falling far from where it usually landed before, something in the underlying setup is different.

Yet deviating from the average on purpose is not always easy, and how to do it is not always obvious. In real life, far removed from data, it’s not hard to find a sense that just the will to change can be enough to step off a trendline. After all, predictability speaks to a sense of fate, a loss of control, and there is a strong temptation to simply oppose anything inevitable as undesirable.

A case in point – it was some time after the loss of Columbia, and there was a meeting about scheduling. It was clear by then the remaining Space Shuttle flights would be to only finish the construction of the International Space Station. Somehow, I got invited even though my duties in the Shuttle program had ended years earlier, mainly as one view on scheduling involved numbers and math and predictions about time and effort, which was still in my field (just for things to come, not the Shuttle). I settled into my chair, wondering if I should have sat this one out, attending to something less predictable. The topic was how long it would take to launch 22 or so Space Shuttles. The first expert wrapped up with the usual – averages, calculations, details I was pretty familiar with right down to the spreadsheets and their rhyme and the reason. The answer was predictable. Give or take a decimal and the usual disclaimers and you could expect no more than five Shuttle launches a year.

Then the meeting went south. The second expert presented, showing a schedule task by task that on paper could finish up the Space Station faster. (I can name that tune in three notes.) First, this meant more than five launches a year. Second, I was awake by now as the meeting I thought I would struggle through in need of coffee suddenly got heated. Third, the tone of our voices had gone up a notch. In the end, if every upcoming Space Shuttle launch was going to clock in better than average, the question was simple – what are you going to do differently? Oh, and why? If you wanted to break away from the crowd and the averages, you should list what was different in your plan. Alternately, you have no case.

The meeting did not end well. Before everyone going up the chain of command with a consensus, there would need to be more meetings. There was some muttering about agreeing to disagree. (Predictably, I sided with the group that had done the math, counting technicians and knowing how many troops you had for battle. Of course, there were statistics too, and an assumption this was not the time for anything new.) In the end, these were merely curious questions and answers, affecting no decisions. This Q&A was situational awareness, nothing more. Eventually, we finished constructing the Space Station with an average launch rate in those last years of about four launches per year. Predictably, the previous average had nowhere to go but down, caution being greater after the loss of Columbia, not less.

Creating a new rocket also inevitably estimates a specific effort, and as time and people are money, you get a cost per launch for the particular payload. Once upon a time, we see Pegasus, ironically one of the first “commercial” rockets. We also know where the NASA Space Launch System will end up more or less (a relatively straightforward calculation for a “no less than” value). These points are way above the trendline, for what that line is worth as the scatter starts below (in statistics, the “fit” is not too good.) We also see that even for reusable Falcons, with less payload as you carry extra propellant and legs to come back, we move far off the predictable line – only now down and in the right direction. LauncherOne and Electron have done this as well, where once the Pegasus resided.

More so, perhaps we should look at dollars-per-kg graphs as if they were vintage maps. There are ocean currents, continents, and islands. We look at small rockets to come or to the territory where large payloads enter the realm of only hundreds of dollars a kg. We should mark these areas as uncharted, and say “Here there be dragons.” One day we may think those old maps so quaint.

Thoughts? Comments below.

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