SpaceX progress towards a 100 launch year

[steveleach]

Starship.

Oh, right, thank you.

I've been keeping Starship launches out of the trend analysis, and adding it back in afterwards, purely for the purposes of the "how close to 100 in 2023 do we get?"  Basically treating Starship launch rate as a completely independent variable from F9/FH launch rate.

[steveleach]

There are 18 missions on the manifest, none of them Starlinks.  They need 19 more missions in addition to those to make 100.  They've launched 36 Starlinks this calendar year.

--Not making a point.  Just more data to fit to your curve of choice.

So that means this year there have been 36 Starlinks and 23 others which is 1.56 Starlinks per manifested launch.

If they have 18 more manifested launches that would give 28 more Starlink launches at the same ratio, leading to a total of 59 + 18 + 28 = 105 launches this year, not including Starship.

However, that would be treating Starlink launches as independent from manifested, which clearly isn't the case, so I'm inclined to assume that they just use Starlink launches to consume any available launch capacity after planning the manifested launches.

[meekGee]

If a linear projection in the beginning of the year showed 80-85 launch per year while an exponential fit showed 100-105 and they get 99, the exponential fit is much closer. We’ll find out soon enough.

Except what you call "linear" is actually the silly claim that there will be no growth.

Real linear growth predicted ~100/yr too, as would almost any model based on about a year's worth of data.

You somehow decided that saying "linear" means "no growth" (based on a straight line curve of the cumulative number of launches) but that's wrong. You're looking at the first integral of the quantity we are discussing, which is launch *rate*.

Again, the launch *rate* is not showing exponential growth, and therefore neither does the cumulative number of launches, but the latter does "curve upwards", because the integral of a linear function is a square function (ax^2+bx+c), which you can again go to town fitting to the data, with equal "success" and little additional meaning.

It is much more meaningful to analyze the launch rate.

[eeergo]

If a linear projection in the beginning of the year showed 80-85 launch per year while an exponential fit showed 100-105 and they get 99, the exponential fit is much closer. We’ll find out soon enough.

Yes, but as you've been shown repeatedly in the last few days with actual quotes from yourself, that's counterfactual (and speculatively unrealistic).

The linear projection has estimated 85+ launches for this year. The exponential fit you have been proposing has been predicting up to 110+ launches for the same time period. The linear projection hasn't really changed much, predicting now 89-90 launches (+5%). The *same* exponential fit, even though the launch rate has been increasing lately, for some esoteric reason has decayed to around an average of 103 during the summer (-7%).

However, it is still counterfactual because the most optimistic projection available (Musk's, still current, from just a few days ago) calls for 10 launches/month by the end of this year. This would imply at least a month or two of 8-9 launches and two-three months of 10 launches. Which sums up to 97, tops.

Therefore, if this overoptimistic 97 is the final count, the linear fit will have missed by up to 13 launches, just as the exponential fit. Anything less than the most optimistic result, and the linear fit will have had less error.

[eeergo]

The model that seems to work best for me is a long term exponential trend of about a 35% year-on-year increase since 2012, increasing in the last couple of years due to process improvements at SpaceX to about 55% (3.7% month-on-month).

That fits all the historical data and matches the predicted launch rates coming out of SpaceX.

I can't make a linear fit work at all for the long term trend. It can work for the last couple of years in terms of matching historical data, but then predicts lower numbers than SpaceX are going forward. It's obviously also possible to fit an arbitrary sequence of linear tends to the historical data, but that provides zero predictive power so I'm ignoring it.

Happy to explore other models if anyone can suggest any.

We have gone through this. This thread's discussion doesn't argue a linear fit is better for all historical data or long-term trends. Indeed, the overall fit -computed a while back by AnalogMan- projected around 85-90 launches this year. Instead, it has always been about the annual rate, and whether it could be reliably fit to an exponential that projected 100+ launches this year (which would not be consistent with the overall historical exponential fit thus far).

We are just arguing the actual rate is indistinguishable from a linear approximation, even if it's part of a larger-term exponential, since its exponent in an annual period is so small as to remain in the noise of individual launch dates, and the steeper functional form leads to larger errors. Furthermore, the fact that the linear approximation for yearly periods needs to change slope from year to year (or other periods which may signal discontinuities) is actually not unphysical due to factors that lead to increased rate at a particular moment in time rather than continuously, although this is more speculative. And moreover, the same would need to happen with an exponential fit when applied to several yearly periods separately.

[edzieba]

Since people are now discussing monthly rates rather than annual, here's a rolling 30-day window of monthly launches (blue) along with a rolling 30-day average (orange). Less messy compared to trying to do math per calendar month.
Interestingly, launches appear to be strongly cyclical per quarter.

[steveleach]

The model that seems to work best for me is a long term exponential trend of about a 35% year-on-year increase since 2012, increasing in the last couple of years due to process improvements at SpaceX to about 55% (3.7% month-on-month).

That fits all the historical data and matches the predicted launch rates coming out of SpaceX.

I can't make a linear fit work at all for the long term trend. It can work for the last couple of years in terms of matching historical data, but then predicts lower numbers than SpaceX are going forward. It's obviously also possible to fit an arbitrary sequence of linear tends to the historical data, but that provides zero predictive power so I'm ignoring it.

Happy to explore other models if anyone can suggest any.

We have gone through this. This thread's discussion doesn't argue a linear fit is better for all historical data or long-term trends. Indeed, the overall fit -computed a while back by AnalogMan- projected around 85-90 launches this year. Instead, it has always been about the annual rate, and whether it could be reliably fit to an exponential that projected 100+ launches this year (which would not be consistent with the overall historical exponential fit thus far).

We are just arguing the actual rate is indistinguishable from a linear approximation, even if it's part of a larger-term exponential, since its exponent in an annual period is so small as to remain in the noise of individual launch dates, and the steeper functional form leads to larger errors. Furthermore, the fact that the linear approximation for yearly periods needs to change slope from year to year (or other periods which may signal discontinuities) is actually not unphysical due to factors that lead to increased rate at a particular moment in time rather than continuously, although this is more speculative. And moreover, the same would need to happen with an exponential fit when applied to several yearly periods separately.

I don't think anyone has argued that the short term trends can't be approximated linearly, just that the linear trend might be under-estimating future rates (when used at the start of the year) and an exponential projection might be better.

If everyone was arguing that the linear models were just as effective as the exponential ones while being simpler then I think the debate would have gone differently. But we've had people arguing that the exponential model is incorrect.

I'm not entirely sure how to respond to the point about the year-on-year rates needing to change. That's obviously a drawback of the linear model.

Anyway, my post was responding to a specific point about picking a model and testing it. I responded by describing my model and commenting on it a bit.

[meekGee]

The model that seems to work best for me is a long term exponential trend of about a 35% year-on-year increase since 2012, increasing in the last couple of years due to process improvements at SpaceX to about 55% (3.7% month-on-month).

That fits all the historical data and matches the predicted launch rates coming out of SpaceX.

I can't make a linear fit work at all for the long term trend. It can work for the last couple of years in terms of matching historical data, but then predicts lower numbers than SpaceX are going forward. It's obviously also possible to fit an arbitrary sequence of linear tends to the historical data, but that provides zero predictive power so I'm ignoring it.

Happy to explore other models if anyone can suggest any.

We have gone through this. This thread's discussion doesn't argue a linear fit is better for all historical data or long-term trends. Indeed, the overall fit -computed a while back by AnalogMan- projected around 85-90 launches this year. Instead, it has always been about the annual rate, and whether it could be reliably fit to an exponential that projected 100+ launches this year (which would not be consistent with the overall historical exponential fit thus far).

We are just arguing the actual rate is indistinguishable from a linear approximation, even if it's part of a larger-term exponential, since its exponent in an annual period is so small as to remain in the noise of individual launch dates, and the steeper functional form leads to larger errors. Furthermore, the fact that the linear approximation for yearly periods needs to change slope from year to year (or other periods which may signal discontinuities) is actually not unphysical due to factors that lead to increased rate at a particular moment in time rather than continuously, although this is more speculative. And moreover, the same would need to happen with an exponential fit when applied to several yearly periods separately.

I don't think anyone has argued that the short term trends can't be approximated linearly, just that the linear trend might be under-estimating future rates (when used at the start of the year) and an exponential projection might be better.

If everyone was arguing that the linear models were just as effective as the exponential ones while being simpler then I think the debate would have gone differently. But we've had people arguing that the exponential model is incorrect.

I'm not entirely sure how to respond to the point about the year-on-year rates needing to change. That's obviously a drawback of the linear model.

Anyway, my post was responding to a specific point about picking a model and testing it. I responded by describing my model and commenting on it a bit.

Steve, RB, you guys are not using the term "linear" correctly, not in the sense of "linear growth of the launch rate".

If the launch rate is increasing linearly, i.e. r=r0+kt, then the cumulative launch total would NOT look like a straight line, but would be a parabolic curve, which is why you're getting a fit for the exponential.

The only thing is, you're comparing it to a straight line cumulative curve, which implies a zero growth rate, and is a strawman on your part, even if you did it unintentionally.

I never said long term growth of the launch rate was zero. In fact I argued for the opposite.

This is not semantics - it's exactly the important stuff.

SpaceX's launch RATE, not total launches, has been increasing, but by a smaller fraction each year.  It is increasing by a similar AMOUNT each year.

You're plotting not the rate, but its first integral, so you're thrown off. It took me a while to understand that you're unaware and not mentally compensating for it.

But the derivative of an exponent is still an exponent, and that of a quadradic is linear - and that entirely unambiguous.

So be precise.  The title of the thread, and how the conversation started, was about *rates*.  Stick with that.

Now consider the trend of that quantity, again.

Look maybe at the even longer term, going back to 2019... You'll see the rate actually decreasing, and yet the cumulative graph keeps increasing, since again, it's an integral.

Makes sense now?

[spacenut]

Who cares whether they get 85 launches or 100 launches.  It still breaks records and SpaceX is launching more than anyone else.  Sure I would like to see them get 100. 

They increase launch rate and get 100. 

Weather can play a huge roll if there are more hurricanes or thunderstorms in the area. 

Then there is Starship.  When and how many this year? 

So we are back to guessing. 

[steveleach]

Makes sense now?

Yep. You're trying to redefine what you've been saying to what we've been saying, and what we've been saying to something else entirely, which would make you correct.

[meekGee]

Makes sense now?

Yep. You're trying to redefine what you've been saying to what we've been saying, and what we've been saying to something else entirely, which would make you correct.

Ok now we're in kindergarten country.

This is math. Words have meaning, and what I'm saying now is what I've been saying before.

I just understand now why the word "linear" triggered y'all into thinking that I meant no growth, no matter how much I explained this was not the case.

There's not much to argue about. There's nothing exponential about any of the growth trends, and the reason you think you had a better fit is because you were comparing it to something you pretty much made up.

[steveleach]

Makes sense now?

Yep. You're trying to redefine what you've been saying to what we've been saying, and what we've been saying to something else entirely, which would make you correct.

Ok now we're in kindergarten country.

This is math. Words have meaning, and what I'm saying now is what I've been saying before.

I just understand now why the word "linear" triggered y'all into thinking that I meant no growth, no matter how much I explained this was not the case.

There's not much to argue about. There's nothing exponential about any of the growth trends, and the reason you think you had a better fit is because you were comparing it to something you pretty much made up.

The only thing triggering me is you telling me what I'm thinking.

[meekGee]

Makes sense now?

Yep. You're trying to redefine what you've been saying to what we've been saying, and what we've been saying to something else entirely, which would make you correct.

Ok now we're in kindergarten country.

This is math. Words have meaning, and what I'm saying now is what I've been saying before.

I just understand now why the word "linear" triggered y'all into thinking that I meant no growth, no matter how much I explained this was not the case.

There's not much to argue about. There's nothing exponential about any of the growth trends, and the reason you think you had a better fit is because you were comparing it to something you pretty much made up.

The only thing triggering me is you telling me what I'm thinking.

Shrug.  I only know what you're writing.

[eeergo]

Who cares whether they get 85 launches or 100 launches.  It still breaks records and SpaceX is launching more than anyone else.  Sure I would like to see them get 100. 

They increase launch rate and get 100. 

Weather can play a huge roll if there are more hurricanes or thunderstorms in the area. 

Then there is Starship.  When and how many this year? 

So we are back to guessing. 

Who cares = literally anyone reading and commenting on this thread titled "Progress towards 100 launches in 2023".

And the specifics are important to avoid stating blatantly incorrect assertions, or worse, send messages that make projections wildly conflicting with reality. Same as if SpaceX suddenly decided to stop launching today for the rest of the year. They would still have performed an extraordinary feat, launched more payloads with more launches more often than anybody else - but the details would be extremely important. Weather also affects the rest of providers, and other uncontrollable random effects also affect everyone's rates. I have no doubt SpaceX's rates would climb visibly exponentially every year if everything was ideal and were powered by Musk's interests alone, but the analysis is relevant because indeed not everything is ideal.

Starship in 2023 is a 1-to-3 launch correction to the analysis - barely significant. Regarding when, there are plenty of threads (and hypes) for that.

[rockets4life97]

meekGee wants to use linear in regard to the slope or derivative of the function
Everyone else is using linear to reference a linear function
That is my two cents

[meekGee]

meekGee wants to use linear in regard to the slope or derivative of the function
Everyone else is using linear to reference a linear function
That is my two cents

Well the argument (and thread title) was whether the RATE was growing exponentially.

All the numbers discussed by everyone (7/month, 60/year) were rates.

Only a graph by RB or SL was made to show the cumulative number instead of the rate, and then the term "linear" applied to it, instead of to the quantity being discussed

And still, even so, there was nothing exponential about the graph...  but since it does (naturally) curve upwards, it made people argue for "exponential"...

Just an entire salad: Talk about one quantity, graph another quantity (its integral), see that the integral is not linear (probably closer to parabolic) and claim that the original quantity was exponential.

Words have meanings, and consistently really matters.

[Barley]

Well the argument (and thread title) was whether the RATE was growing exponentially.

All the differentials and integrals of an exponential are exponential.  The same cannot be said about linear function.

[DanClemmensen]

It’s not linear, either. Linear would imply negative launch rates in the past. Parabolic/quadratic would imply in the far past, huge launch rates. Exponential is a simple model that while not perfect, has the advantage of being well behaved when extrapolated forward or backward in time.

I expect the Falcon launch family to have a sigmoid shaped cumulative launch number function. But as an approximation to a sigmoid, exponential is a better approximation than linear and has no more free variables than linear.

Why should it be any function?  This is like econonmics therory "...first assume a spherical frictionless horse with perfect information interacting with it's own best interests in mind..." etc. Gravity has an underlying function that is near perfect at moderate levels but why assume something as chaotic and rare like a lauch (compared with say the common exhange of money and goods) will fit some simple function like a straight line or exponential or anything that basic?

The field of operations research is devoted to this sort of analysis. You are supposed to start by creating the best model you can for the phenomenon you are analyzing. I think that both the linear growth model and the exponential growth model are far too simplistic to yield any useful analysis.

The model that seems to work best for me is a long term exponential trend of about a 35% year-on-year increase since 2012, increasing in the last couple of years due to process improvements at SpaceX to about 55% (3.7% month-on-month).

That fits all the historical data and matches the predicted launch rates coming out of SpaceX.

I can't make a linear fit work at all for the long term trend. It can work for the last couple of years in terms of matching historical data, but then predicts lower numbers than SpaceX are going forward. It's obviously also possible to fit an arbitrary sequence of linear tends to the historical data, but that provides zero predictive power so I'm ignoring it.

Happy to explore other models if anyone can suggest any.

You are modelling historical launches, reasonably enough. I think these have been constrained by demand and by LV production. An operations researcher would be trying to model additional constraints that have not yet had much effect. These include range availability, weather, FAA holiday constraints, and pad reconfiguration, among other things. Up until now, if a launch is scrubbed it just slips a day or two with no other effect. but as the schedule fills up a slip becomes increasingly likely to affect the next launch. There may also be a seasonal demand cycle at least for non-Starlink launches.

There is not enough data to accurately evaluate all of these quantitatively, but this more detailed model might allow for a prediction about when we may see any of these begin to have a discernible affect.

[meekGee]

Well the argument (and thread title) was whether the RATE was growing exponentially.

All the differentials and integrals of an exponential are exponential.  The same cannot be said about linear function.

Exactly.  I was assuming people understood that.

The actual rate (+100%, +50%, +20%...) clearly isn't exponential, so the cumulative graph can't be either.

But if the rate increases linearly, the cumulative looks like a parabola, and if someone isn't paying attention, they fit an exponential to it, and then they again don't pay attention and call the flight rate itself exponential...  and that's how we got here.

[eeergo]

That's an interesting detail actually, which some of us touched upon a while back - but since there was such a strong reaction it was dropped in the interest of more fundamental points.

The historic launch graph is visibly non linear when studied since 2010. It can be fitted by an exponential with a certain goodness of fit value, but because of the arguments meekGee mentions, it can probably also be fitted to other functional forms with similar success as trend model - such as a quadratic equation.

This is actually motivated by the fact that the launch rate is seen to increase linearly over certain time period, rather than also exponentially (as in the above remarks: the derivative of a quadratic function is a linear one [ d(ax^2+b)/dx = 2ax ] but the derivative of an exponential is another exponential [ d(e^ax)/dx = a·e^ax ]). On the other hand, this rate has stronger deviations from an ideal function over the last decade than the cumulative launch tally, so it may have limited value as a predictive model.

The point about all this is which model can give a greater predictive power with the fewest assumptions, leading to lower errors - not whether there's an true, underlying absolutely analytical model, which is clearly not the case.

Moreover, it's apparent a linear approximation is pertinent when analyzing smaller (up to yearly) periods of time, because the overall function -be it exponential or quadratic- is too flat to generate deviations over the noise in such a short period of time.