# What are the Odds?

I wanted to expand on one thought from last night. If you have a launch vehicle that you want a reasonably good chance of reusing 1000x, it actually needs a lot better than a 1:1000 Loss of Vehicle probability for any given mission. With a 1 in 1000 chance of losing the vehicle on any given flight, you actually have a very high chance of losing it long before the 1000th flight. The odds of not losing a vehicle in x consecutive flights with a given reliability rating (probability of a non-LOV flight) is:

Psurvive_all = PnoLOV ^ x

Or solving for the required probability of not losing a vehicle on any given flight (assuming an equal probability on any flight):

PnoLOV = Psurvive_all^(1/x)

So, if you want a 75% chance of surviving 1000 flights in a row, you get:

PnoLOV = 0.75^.001 = .9997 or about 1 in 3500 probability of losing the vehicle on any given mission.

If you’re ok with a 50% chance of surviving 1000 flights in a row, you need more like a 1 in 1500 probability of losing the vehicle on any given flight, and if you want a 90% chance, you’re up to almost one in 10,000.

Long story short, if you want a high probability of amortizing the vehicle over 1000 flights, you’ll need to do much, much, much better than the historical best reliability levels of liquid fueled rockets (98% or so at a 95% confidence interval). This suggests that design for survivability is likely going to be just as important as design for performance or design for cost if you want a lot of flights on an airframe.

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#### Jonathan Goff

President/CEO at Altius Space Machines
Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and is the founder and CEO of Altius Space Machines, a space robotics startup in Broomfield, CO. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.

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Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and is the founder and CEO of Altius Space Machines, a space robotics startup in Broomfield, CO. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.
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### 17 Responses to What are the Odds?

1. Bob Steinke says:

It might not be that bad. For amortizing fixed costs what you care about is the average number of flights per vehicle, some will have more, some less. Even for a startup the question is more likely to be can our first three vehicles get at least 3000 flights total, not necessarily 1000 each.

2. Bob Steinke says:

Granted, you still need .999 reliability to average 1000 flights per vehicle so your conclusion about needing a lot better than historical reliability is still valid.

3. Peterh says:

What you need is survivability, more than reliability. If you have an intact abort on average every 100 launches that reduces your reliability, but not your survivability. Airliners have mechanical trouble far more often than you hear about, but usually it doesn’t cause loss of mission, and loss of aircraft or payload is very rare.

4. Jonathan Goff says:

Peter,
I totally agree. My point is that to get to a vehicle that can survive its way through 1000 flights, you’re going to need something that is dramatically safer than anything that has ever flown. And a big part of that will be designing the vehicle from the start to make failure modes not just unlikely, but survivable. So far, it seems like SpaceX’s approach has focused more on high-performance even if it creates scary failure modes than a survivability/reusability-driven design. They may eventually get there, but my guess is it will require a design dramatically different from BFR. And learning how to build such a vehicle is likely a lot easier to do if you start small than if you keep skipping to bigger and bigger vehicles.

~Jon

5. Dave Salt says:

Hi Jon,

The point you make doesn’t just ‘suggest’ that design for survivability is going to be important; it screams out to anyone with the least bit of common sense that it’s going to be absolutely fundamental!

The history of aviation shows that high reliability/survivability requires not only good design but also significant testing, especially at the complete system level (e.g. a thorough flight test program involving many hundreds of flight cycles). Moreover, modern aircraft design and operations have improved by learning from failures of past designs and, in doing so, have evolved towards what are essentially generic solutions that enable the extremely high level of reliability and economy we have now come to expect in modern aviation.

What this means is that any ‘true’ RLV (i.e. a launcher capable of hundreds of flights between major overhauls) will require a significant test program and, ideally, have been evolved from the accumulated knowledge and experience of at least one previous generation (e.g. an X-vehicle). History also shows that the key element that will need the most amount of development and testing will be the propulsion system, which favours designs that are both simple and offer larger margins for error (e.g. expander cycles, rather than staged-combustion/topping cycles).

Given the fact that the costs also tend to scale with vehicle size, this also suggests that a anyone aiming to develop a ‘true’ RLV should start with as small a vehicle as possible… unless, of course, you’ve got incredibly really deep pockets!

6. Dave,

I agree on all points. Even Falcon 9 is probably way too big to learn the lessons on of how to do a 1000-flight-lifetime RLV. I can see getting to a 20 or 50 reuse vehicle the path SpaceX is going, but I’m skeptical they’ll ever get something to even 100 reflights, let alone 1000 without a major change in approach.

~Jon

7. Dave Salt says:

I really do applaud both Musk and Bezos because they’re actually building machines that will fly into orbit while moving the art forward significantly – arguably for the first time in almost half a century. Unfortunately, they both seem to have chosen the route that has little prospect of delivering a ‘true’ RLV for reasons already mentioned, which is another reason why I was deeply saddened by the demise of XCOR’s Lynx.

Although XS-1 may well be the only ray of light in this regard, I’m still hoping that there’s another billionaire space cadet out there that has sufficient vision and enthusiasm to appreciate that “small is beautiful“ when it comes to developing a ‘true’ RLV.

8. mike shupp says:

I’ve no (or little) clue as how this ultra-liability is going to be achieved. Lots of electronics, lots of tiny sensors. I’ve got notions of a technician waving some kind of wand over a vehicle structure and an excited voice shouting out “I’m too loose, boss. I’m the third screw from the left on the top of this panel and I need turning another 38 degrees right now!” Maybe we can build adjustment mechanisms into some machine components so they automatically reposition themselves to maintain proper tensions or angular positions.

Stuff that’ll look like magic, from a 20th century mechanic’s viewpoint. But widespread magic, because cheap ultra-reliable parts aren’t going to be useful just for spaceships. You’ll see them in automobiles and trucks — particular self-driving autos — and aircraft and subway trains and for all I know, childrens’ toys and household appliances.

It’s actually something it would make sense for the US government to push. There’s potential for a lot of exports, and probably a decent amount of employment.

9. DougSpace says:

I think that 1,000 reuse is a concept that we can sort of pit in the back shelf. For one, the first people to go won’t demand that level of safety and there won’t be that level of safety for a very long time, maybe never. But when you amortize the cost of the construction of the vehicle over its use, the greatest benefit comes with the earliest reuse. In practice, the high level of reliability is really for the benefit of the traveling public — that is to say their willingness to purchase the ticket given news reports of people having died with previous missions. I think that the traveling public will always know that trips to Mars will always be more dangerous than trips to Paris.

10. I’m kinda with Bob Steinke, above. Assuming that you’re not killing a lot of people, the real question is how much new hardware you’re having to toss into your operating fleet to maintain capacity at a profitable level. That implies more of an average component lifetime with some standard deviation than an exact survivability number.

Presumably, ITS maintenance and lifecycle practices will look a lot more like the airline industry than the current launch industry. In other words, you’ll work out some maintenance schedule, assuming average life for various components, and you’ll plan to inspect/replace components on some variation around that average. Then you build out your fleet to achieve some particular operational tempo.

Loss of an entire launcher is then sort of an outlier event in the maintenance schedule, but it’s not necessarily an extreme outlier. It definitely changes the rate at which you have to throw new components into the pipeline, but it’s entirely likely that the loss of a vehicle then just becomes a fairly modest blip in your component production schedule.

Note that none of this applies if you’re killing lots of people, which is certainly possible with what is now a fairly unquantified EDL profile. But otherwise, you’re just running a particularly expensive airline.

I’ll bet the airlines have a bunch of queuing theory wonks that eat this kind of problem for breakfast.

11. Chris Stelter says:

I don’t think .999 reliability is unreasonable. .99 reliability (or close to it) is already possible with expendable vehicles, and reuse should allow another order of magnitude improvement.

But the first ones won’t be anywhere near that reliable.

12. Chris Stelter says:

Also, it seems like SpaceX is going to be doing Grasshopper-like development tests and envelop expansion for /both/ the spaceship and the booster separately. They’ll probably lose a vehicle or three doing this, but they could have significant experience launching and landing and generally flying the vehicles even before the first orbital flight.

And they could save money and time by not fully populating the engines, just like they did with Grasshopper and F9R-dev1.

13. WhySpace says:

I largely agree with Chris. Once a launch vehicle has been flight proven, it probably has an order of magnitude less chance of failing in a given launch. Pfailure(launch#) will follow a bathtub curve. https://en.wikipedia.org/wiki/Bathtub_curve

However, this implies lots of failures on the first flights, and then lots more after thousands of flights as things wear out. There isn’t really a way to simulate things like g-loading and atmospheric conditions on such large parts during component testing, so early LOVs seem likely. This is great for passengers, since you can use vehicles for cargo launches only during their first couple launches, and then have a much saver crew vehicle. However, it kills the average number of flights, which is what matters if you want to amortize the production cost over lots of missions.

The only hope I see is that recovering vehicles will allow SpaceX to tear them apart and find flaws and unexpected wear that allows them to build much more reliable vehicles. Disassemble everything, and test each component to failure, and see what parts fail earlier than unused parts. Examine how flight wears things differently from parts only used during ground simulations like the static fire.

If such information does exist though, it would be an extremely valuable trade secret, and not the sort of thing we would know the details of.

14. Michael Egorov says:

In 60’s, Soviet Vostok with RD-107 engine showed 99.73% reliability [http://www.dunnspace.com/leo_on_the_cheap.htm]. That gives you ability for 100 launches with 75% reliability already

15. Peterh says:

Another way of looking at the probability, negative binomial distribution: if each launch has a 1:1000 chance of an accident losing or forcing retirement of a vehicle (assuming regardless of vehicle age), a vehicle has an expected life of 1000 additional launches. Some will be lost/retired before 1000 flights, some will (under the assumption above) last much longer. Of course this all neglects cumulative wear.

16. DougSpace says:

Also, how many of the 2% of launches lost were due to problems that would have happened on the rocket’s first launch. Well, 100% of those. But with a reusable system, most of the flights are not a rocket’s first flight. So, for example, that rocket in Russia which went haywire because someone installed a sensor backward, that defective rocket would only get one (failed flight). But if that type of rocket was reusable then those rockets that had the sensor installed correctly would have been reused a 2nd, 3rd, 4th, etc times. So, the more reliable rockets would make up a larger percent of the overall flights.

17. Jonathan Goff says:

WhySpace,

I agree that a bathtub curve is likely a realistic model for vehicle system reliability. One important question though is what do the bathtub curves look like for various subsystems, how detectable is it when your systems are starting to get to the far side of the curve, and how survivable is your vehicle in the case of a failure. A vehicle that is built with fault tolerance and survivability in mind is a lot more likely to hit high overall reliability than one that is fragile. With a fragile vehicle, you’re likely going to see a shorter bathtub curve that’s closer to the curve of the least reliable component. With a more survivable/fault-tolerant vehicle, you’re likely going to see a much wider curve that is driven more by the overall system wearing out.

My concern is that Elon’s performance uber alles approach pushes you more toward the brittle/non-survivable scenario.

~Jon