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With the Stratolaunch flying this week I was interested in seeing how good it was compared to a Falcon9. I figured comparing energy contribution would make sense. The stats as best I can find:

  • Stratolaunch: 250t to 11km at 220m/s. 6.2GJ (KE) + 26.2GJ (PE) is 32.4GJ
  • Falcon9 first stage to MECO: 90t to 70km at 1800m/s. 180GJ (KE) + 61GJ (PE) is 240GJ

[78t(2nd stage)+13t(payload)]

So it looks like Stratolaunch as a first stage provides less than a seventh as much energy as a Falcon9 first stage. Does this look reasonable or is there a better way to look at this?

How much of the Falcon9's first stage fuel is used to get to a Stratolaunch energy level? It is a lot more than a seventh but I don't know how to figure this.

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    $\begingroup$ they're really not comparable in any meaningful sense. $\endgroup$ – user20636 Apr 14 '19 at 23:42
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    $\begingroup$ All your Stratolaunch numbers should be in megajoules, not gigajoules. The difference is more like 1/7000th as much. The carrier aircraft for air launch is really an aerial launch platform, not a first stage. $\endgroup$ – Christopher James Huff Apr 15 '19 at 2:38
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    $\begingroup$ @ChristopherJamesHuff In every technical sense, it’s a first stage; it’s just that “first stage” doesn’t say anything about relative performance. $\endgroup$ – Russell Borogove Apr 15 '19 at 3:17
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    $\begingroup$ 250 tonnes being the 'correct' way of writing 250k kg $\endgroup$ – user20636 Apr 15 '19 at 7:47
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    $\begingroup$ Those 500 mph of Stratolaunch are horizontal speed, but the 6600 kph of Falcon 9 are speed in the desired direction of the choosen trajectory. Not to compare easily. But what a nasty mix of different units. Please use only metric units, speed in km/s and height in km, mass only in tonnes. $\endgroup$ – Uwe Apr 15 '19 at 8:22
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Comparing the performance of one component of a launch system with a different component of another launch system is questionable. In the end, the overall performance of a system is its ability to deliver mass to LEO.

Breaking down the cost of a space journey is typically not done with what energy is required, but by the Delta-v (change is velocity) required. In the case of an orbital launch, that's 8 km/s to get orbital velocity + some extra costs. In the case of Earth, that some extra costs part is a bit troublesome since the rocket has to fight against strong gravity for quite a while, and gain sufficient altitude to avoid the thick atmosphere.

  • Stratolaunch: 220 m/s, 2.8% of orbital velocity (but the rocket still needs to climb a bit, so not necessarily all of this horizontal speed is useful)
  • Falcon 9: 1800 m/s, 23% of orbital velocity.

The altitude numbers are also relevant, but the main observation to be made there is that the Falcon first stage deals with most of the atmosphere, while Stratolaunch is still low enough that the air can still lift a plane.

The above should show that the Falcon 9 first stage is a much larger part of the launch configuration than the aircraft is for Stratolaunch. In a sense, this is "higher performance".

Applying the inverse rocket equation to that 1600 m/s velocity gap gives a mass ratio of about 1.5 (about 170t to the same velocity that the Falcon stage delivers to), which makes the Stratolaunch aircraft a slightly heavier lifter than what Falcon 9 is. In a another sense, this is also "higher performance".

A third way to measure performance is the cost of a launch. Since no actual Stratolaunch missions have been flown yet, a plausible cost comparison is not yet possible.

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  • $\begingroup$ I realize this is apples to oranges and as you state the cost of a launch to orbit is probably the only thing that makes complete sense, but given that is not possible I thought energy might work as a substitute. Isn't delta v the same as change in kinetic energy and altitude change in potential energy? One thing that became apparent is that the kinetic requirement dominates and Stratolaunch doesn't contribute much that way. $\endgroup$ – Pilothead Apr 15 '19 at 15:15
  • $\begingroup$ And of course the far smaller payload supported by Stratolaunch ensures it's aimed at a vastly different market. Basically anything much larger than a microsatellite isn't going to even fit in its payload fairing. $\endgroup$ – jwenting Apr 17 '19 at 4:09
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As pointed out the ranking of best to worst really doesn't make sense here. There are a lot of issues that come into play. (Even if we ignore things like reliability and cost...).

The main reason is that it hugely depends on what options you have for the next stages. If you have very good rocket technology (high TWR and ISP) then high mass to low speed is more helpful than low mass to high speed, compared with poorer tech.

This is because it takes exponentially more mass to change a rocket's velocity by a fixed amount. Another way to interpret that is it takes a fixed fraction of the mass to change velocity by a fixed amount. However what mass fraction is needed, for a given change in dV, is dependent on the rocket.

So the question "how much faster to you have to go to make it worth having half the mass?" doesn't have a natural answer. It depends on the final goal and what stages you have left.

Though in this case it's probably safe to say the Falcon 9 booster 'wins': Falcon-9 block-5 gets 22,800 Kg to LEO and from 549,000 Kg at launch. About 4% which is pretty good. Stratolaunch's 250,000 Kg 'first stage' payload would not get as much to orbit using Falcon-9 tech scaled down as an actual Falcon-9.

There are also some other things that make this question really hard to give a meaningful answer to, for example:

  • Gravity losses: The Saturn V famously 'oozed' off the pad, instead of blasting off. That because the TWR was very low when fully fueled. I this case gaining a small dV required a large theoretical dV. For the if there had been a first stage that had given it 100 m/s off the pad it would have gained around 400m/s in orbit if there was not atmosphere*.

  • Atmospheric losses: In exactly the converse, the faster you are going in the lower atmosphere, the more losses you have. Hence extra velocity, while you are still in the atmosphere but with enough velocity to not be experiencing much by way of gravity losses, will not all be retained.

  • Putting your low ISP stages first: Earlier on in the launch the craft is less susceptible to low ISP fuel sources (this is why rockets use SRBs as the first stage), so the rocket equations's constant mass ratio to velocity change doesn't hold in practice which makes it even harder to compare things.

[*] Imagine the TWR was 1.001 but somehow had 1000 time the dV, it would gain height and speed, but would be using almost all of the thrust to fight gravity with very little gain however once in space this is all gets used to add energy to the orbit.

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Keeping with the energy criterion as a measure of "goodness" in spite of its limitations, I found this Falcon 9 altitude/velocity graph and the spreadsheet from which it was built.

enter image description here

falcon 9

Taking 90t of 2nd stage and payload from the 250t total mass of a Falcon 9, I used 160t as a rubber 1st stage. MECO is at 147 sec so I subtracted 1/147th of this mass for each second of flight, figuring that useful weight was everything that was left. Then calculating KE and PE for useful weight on the Falcon 9 flight profile, I found the point where total energy matched that of Stratolaunch.

This point turned out to be 70 seconds into the flight. Useful weight was 174t, altitude was 10,700m and velocity was 406m/s. So Stratolaunch is about half a Falcon 9 first stage as measured by energy. At roughly the same altitude, Stratolaunch carries half again as much weight at half the speed of a Falcon 9.

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