Is it true, strictly speaking, that you may use less propellant in the expendable stage due to air-drop? Sure. Although to be clear when talking about engine efficiency, it's really about being able to run a larger area ratio nozzle and getting a higher mission-averaged Isp. But ultimately when you consider all the "puts and takes" in launch system economics, those considerations are small potatoes (price out bulk LO2, and your choice of fuel). People (even university professors make this mistake) get so focused on minimizing propellant use that they fail to realize that complexity and dry weight are orders of magnitude more important.
The only serious advantages to air-launch are the logistical ones you noted. Also note that for U.S.-based systems, the idea that you will be able to fly down to equatorial latitudes requires you have the range to carry the laden launch system (and top-off to contend with LOX boil-off) pretty far. Strato certainly doesn't have these kinds of legs. Virgin will probably be able to get more out of their system, but it's not going to scale significantly higher.
I agree that for traditional launch systems it doesn't make that much sense -- particularly in light of the recent development of reusable (or at least, partially reusable) rockets.
That being said, I think the math changes somewhat for smaller launchers. The smaller the rocket, the worse the losses to the atmosphere get, and the more advantageous it is to escape atmospheric resistance in the soupy low atmosphere. So I think where air-launch systems could really shine, is by enabling low-cost launch of very small payloads.
I am, however, not entirely convinced that a sufficient market for those kinds of dedicated launch services will emerge (as opposed to hitching a ride in spare fairing space of a separate launch). I could see this going either way; as much as I'd like to see easier space access for eg. university-funded nanosats, I'm not sure the timing will be right for something like Stratolaunch, because the new private aerospace (SpaceX, Blue Origin, etc) is focused so intensely on pushing down the cost of larger-scale rocketry, to a point where that same market would be better served by bulk launches using some kind of standardized dispenser.
> That being said, I think the math changes somewhat for smaller launchers.
Do you have any analysis you can point to to substantiate this? I suspect any such analysis is heavily predicated on assumptions, such as whether or not the small launcher is designed around existing engines/motors.
I don't think there is a compelling case to be made that operating an air-launch carrier aircraft in addition to the costs associated with the remaining rocket stages works out economically^.
Orbital was not able to get compelling economics out of Pegasus. To be fair, they were doubly-hamstrung by their use of a carrier aircraft airframe operated by vanishingly few (L-1011) as well as the Pegasus using expensive solid rocket motors (here's another non-intuitive reality of rockets - solid motors are very expensive unless you buy in bulk).
^The most compelling test of economic viability of air-launch for small systems will come with Virgin Orbit/VOX space that is using a carrier aircraft airframe which is still in significant commercial use (quite a few 747 air freighters) as well as modern-yet-relatively low complexity LOX/RP liquid rocket propulsion. And if they want to say double their payload capability, they will not be able to do that with the 747. Maybe at the extremely low-end, GOLauncher will also be similar.
> Do you have any analysis you can point to to substantiate this?
Unfortunately I don't, no. I thought about running such an analysis as part of my grad studies (this was quite a while ago; I've switched careers since then) but I didn't get much farther than filling up a napkin before I decided I was already stretched too thin in my coursework.
Ultimately the premise is based on cubed-vs-squared relationships in rocketry (both in terms of aerodynamic forces and structural ones, though through a neat trick of math the mass of your fuel tanks actually scales linearly with their volume [1]). Like most other things in engineering, there are also economies of scale at play (for example, avionics mass consumes a smaller mass fraction of larger rockets), but my hunch -- and this is, as you say, fairly unsubstantiated -- is that the aerodynamic effects alone are sufficient. Cubed-vs-squared in aerodynamics is really just incredibly punishing. At 35kft (Stratolaunch's altitude) it's not as good as at 100kft or so (like you might expect with a weather balloon), but it's still a pretty big difference [2] -- basically allowing you to halve the radius of your rocket compared to an equivalent aero loss at sea level.
To take this to a really absurd level, I can imagine a 100kg rocket -- large by amateur model rocket standards, but beyond tiny compared to consumer rocketry -- with sufficient mass ratio to make it to orbit in a vacuum, but I can't possibly imagine the same rocket making it from the earth's surface.
Fuel is almost irrelevant from a money perspective. However, two rockets both cost the same to build and one needs less fuel to orbit that directly translates into more payload to orbit. It’s a question of mass not money.
Alternatively, you can spend that budget on something else like a ‘single stage’ to orbit system which more directly lowers costs. This is more useful for tiny cargo like an anti satilite weapon system where getting even a few pounds into the right orbit works.
As to long term costs, having already built the aircraft that becomes a sunk cost. It might have been a poor choice, but it represents actually value before you can get satilite stock orbit. Which then allows a company to raise more money on better terms.
> However, two rockets both cost the same to build and one needs less fuel to orbit that directly translates into more payload to orbit. It’s a question of mass not money.
The way you state this is insufficiently constrained as to make the comparison I think you are trying to make. I think what you are trying to suggest that is that if two launch systems have the same per-launch recurring costs and the same gross mass the one that has higher payload mass fraction is better. Well, I can't disagree with the rocket equation.
If you are trying to relate this back to air-launch, my point is that for equivalent technology levels (meaning the same propulsion system other than nozzle area ratio, tankage with similar structural efficiency, etc.), the benefits you get in terms of recurring cost per unit mass from air-launch (by reducing rocket propellant consumed and dry mass of expended hardware) pale in comparison to the operating economics of having to additionally operate the air-launch platform. In other words, the recurring cost per unit mass to orbit, for the equivalent mass class, will be higher for air-launch than ground launch. And that doesn't even take into account the non-recurring costs associated with the air platform and need to amortize them.
> Alternatively, you can spend that budget on something else like a ‘single stage’ to orbit system which more directly lowers costs.
I'm not even sure where "directly lowers costs" applies in the SSTO case. I'm guessing you mean the case of a fully-reusable SSTO vehicle? At the end of the day, your per-fligt costs will reflect the need to amortize the non-recurring costs you've incurred. SSTO systems will tend to very high non-recurring costs, and the extreme sensitivity to dry mass means you will pay more per pound of dry mass for an SSTO vehicle than a multistage vehicle. The only people that think SSTO with today's technology will lower costs are the ones still hoping for the VentureStar to become operational.
> As to long term costs, having already built the aircraft that becomes a sunk cost. It might have been a poor choice, but it represents actually value before you can get satilite stock orbit. Which then allows a company to raise more money on better terms.
I'm not sure what you're trying to say here. If Strato can find a net cashflow-positive way to use their carrier aircraft, great. I think it's unlikely their launch economics will beat other systems in the marketplace so it won't win on pure cost short of Strato taking a loss on launches. However, in terms of launch, they may get some business if a customer really needs the logistical flexibility mentioned in the root post of this thread.
> pale in comparison to the operating economics of having to additionally operate the air-launch platform.
That’s likely true, but depends on how many launches you do. An air launch platform could likely handle multiple launches per day, but finding customers for thousands of launches per year is not going to happen.
> I'm not even sure where "directly lowers costs" applies in the SSTO case.
I am very specifically talking about a non reusable, anti satilite weapon. You can find several such weapons launched from aircraft. In that specific case using far more fuel and a larger rocket is potentially worth it to have dramatically fewer moving parts. Actual designs may be multi staged to increase capabilities to reach geostationary satilites etc, but it’s far less nessisary for LEO.
Is it true, strictly speaking, that you may use less propellant in the expendable stage due to air-drop? Sure. Although to be clear when talking about engine efficiency, it's really about being able to run a larger area ratio nozzle and getting a higher mission-averaged Isp. But ultimately when you consider all the "puts and takes" in launch system economics, those considerations are small potatoes (price out bulk LO2, and your choice of fuel). People (even university professors make this mistake) get so focused on minimizing propellant use that they fail to realize that complexity and dry weight are orders of magnitude more important.
The only serious advantages to air-launch are the logistical ones you noted. Also note that for U.S.-based systems, the idea that you will be able to fly down to equatorial latitudes requires you have the range to carry the laden launch system (and top-off to contend with LOX boil-off) pretty far. Strato certainly doesn't have these kinds of legs. Virgin will probably be able to get more out of their system, but it's not going to scale significantly higher.