It's enough atmosphere to be a substantial assist in landing mass on the surface, and actually does provide significant radiation protection while also moderating temperatures. The perchlorate issue is massively overstated: they are not that toxic, and are easy to remove, and there's entire glaciers of water on Mars.
The need for huge energy storage systems or nuclear power from the very start is a significant problem for the moon. The game-breaker though is ISRU propellant production. Getting enough water on the moon to supply return craft will require large scale mining and regolith processing facilities...meaning any return propellant will have to be imported until the colony is well established. On Mars, it should involve little more than drilling into a glacier and lowering a heat source to sublime the ice, which makes it a lot easier to get your spacecraft back so you can use it on another trip. The relative ease of delivering mass to Mars and greater proportion of the delivered mass that can be productive colony hardware can do a lot to compensate for the greater distance and travel time.
Lunar helium-3 mining has always been about as plausible a suggestion as strip-mining the moon for green cheese. Helium-3 is a byproduct of storage of the tritium that 1st generation fusion will breed for fuel, and if you can do He-3 fusion, you can do p-B11 fusion. So: by the time we can make use of it, we'll be able to mass produce it far more easily than we could mine it, and we probably won't even bother with it due to availability of far more abundant fuels.
A "working EmDrive" would be a reversible electromagnetic machine, functioning equally well as a motor or a generator: http://www.emdrive.com/2Gupdat... (page 6, ironically titled Conservation of Energy)
If allowed to accelerate, the microwaves in the cavity would red-shift and lose energy, if accelerated in the other direction, they would blue-shift and gain energy. A "working EmDrive" placed on one end in Earth's surface gravity would thus either continuously create or destroy energy.
The reasonable conclusion is that there is no such thing as a "working EmDrive".
He claims that, but his analysis is based on velocities relative to a fixed universal rest frame, which he seems to believe is the same reference frame as Earth's surface. For example, he says that it produces thrust most efficiently if "stationary", and is best used to counter gravity and allow a craft to hover, with jets and rockets being used for propulsion (he seems unaware that a hovering craft is one that is accelerating upward at a constant 9.8 m/s^2).
If you really take Shawyer's math and vehicle concepts seriously, he's apparently a stationary-Earth geocentrist. More likely, he's just clueless about physics.
The confusion is yours: you can't violate just conservation of energy or conservation of momentum. And it's trivial to show that the claimed behavior of the EmDrive violates conservation of energy: a working EmDrive placed on one end on the ground would turn gravitational acceleration into an infinite source or sink of energy, depending on which end was up.
For operating a vehicle in atmosphere, which occurs at two critical stages of a spacecraft's mission.
That doesn't answer the question. Spacecraft spend only a tiny fraction of their lives in the atmosphere, and sustained aerodynamic flight is not a requirement during their short passages through it during launch and landing. So what do they need wings for?
No. That is specifically the design I am arguing against. Please check my post again and you will see I deliberately *exclude* the mass of the engines.
Engines using diluted low-pressure gaseous ambient oxygen as an oxidizer have poor thrust to weight ratios, and wings are generally used to make up for that, making it possible for a craft with underpowered engines to accelerate early on, though at a cost in aerodynamic drag and sustained heating. If you're *not* using air-breathing engines, you can just fly a near-vertical trajectory that quickly exits the bulk of the atmosphere, without having to deal with aerodynamic drag and heating. As for the return, where are you trying to go between reentry and landing? What do you need wings for?
(Note: "to operate from an airport" is not an answer. Needing a reinforced extra-long runway in addition to all the usual pad infrastructure is a cost, not a benefit.)
Al-Li is ~95% Al. Nobody lists all the components of an alloy every time they refer to the primary material. And the interstage is a tiny fraction of the structure, which originally only served to connect the stages and house separation hardware. It's not at all comparable to Skylon's composite LH2 tanks and airframe.
They've done a good job of optimizing it, but that doesn't change the fact that they chose stir-welded aluminum because it was relatively cheap and easy compared to higher performing alternatives such as carbon fiber. Recent rumors hint that their future projects will make heavy use of carbon fiber, but for staged vehicles it's an optimization for improving performance and SpaceX was able to avoid it for most things until they got established and worked out reuse, while it's virtually a requirement for SSTO craft and spaceplanes just to reach orbit.
I'd argue they need to prove that the vehicle weight is lower completely dry (and even that's biased in favor of airbreathing winged vehicles because it ignores the extra complexity and higher cost materials). It's the dry structure that's the expensive part to build and operate, you need the reduction in LOX tank size to make the vehicle smaller and cheaper after adding the wings, air breathing engines, landing gear, etc. If you can make the vehicle cheaper at the cost of pouring in a bit more propellant before launch, it's a win.
As it turns out, LOX is pretty compact and reducing the LOX tank size by airbreathing (again, the only real reason to carry wings) doesn't save much. The trade makes Skylon twice as heavy as the Falcon 9 despite using a super-advanced (and far more expensive per kg) carbon fiber frame instead of the Falcon 9's aluminum.
It's great to see the myths of non-reusable first stage technology being dispelled.
Indeed, SpaceX has thoroughly demolished the claims of SSTO fans that reuse and low cost are somehow incompatible with staging. With an aluminum-bodied, pure-rocket launch system using simple kerosene-burning rocket engines, SpaceX has accomplished the bulk of what Skylon promises to one day achieve with its supertech air-breathing engines, liquid hydrogen fuel, eggshell-thin ceramic heat shielding, etc.
We don't need wings.
They are useful though.
For what? Air breathing launchers need them because of their weaker engines, but staged launchers don't need air breathing. For spacecraft, wings are just dead weight you wish was useful payload while operating in their primary environment, and highly stressed structures subject to catastrophic failure during atmospheric entry. Making spacecraft into poor imitations of aircraft for a brief portion of their flight will not make them as cheap to operate as aircraft.
Spaceplanes are dead. Take Skylon as a representative example: assuming it lived up to expectations, Skylon would have double the dry mass of the Falcon 9, about 10 times the unit cost, its complex engines and other systems would have operating costs that are higher by a similar factor, it'd have the additional headaches of operating with liquid hydrogen (largely unavoidable with spaceplanes), and all for somewhat lower payload than today's mostly-reusable Falcon 9, while competing with the fully reusable successor to the Falcon 9.
Even worse, Skylon would require an expendable upper stage for launches to geostationary orbit, which would likely make it less reusable than whatever SpaceX is operating by the time Skylon can fly. Not to mention that Blue Origin will likely have their orbital launcher up and running and the kinks of reuse worked out by that time as well...
Their earliest recovery attempts involved parachuting stages into the ocean unpowered. All those attempts apparently resulted in the vehicle breaking up during reentry. Large supersonic parachutes are very non-trivial to design and deploy, not terribly reliable at the best of times, and are actually rather heavy, and they needed to do powered reentry and landing anyway to get the vehicle down intact. Since they're already doing that, reserving a bit more propellant is simpler than pretty much any other option, plus it gives them experience they'll need for Mars.
The very first ASDS landing attempt ran out of hydraulic fluid for the grid fins, the engine gimbaling barely managing to get it to the barge...not upright and not at zero velocity.
The next had a sticky valve...my understanding is it was actually for throttle. The control software would command throttle changes, but the valve wouldn't respond until the commanded change was big enough to break it loose, then it'd stick at the new position. The overall effect was that the throttle was lagging behind what the control system expected, which threw things into oscillation with the rocket always overcompensating for its previous errors, always too late to fix things.
The third failure was the Jason-3 launch, which was the last launch of the Falcon 9 v1.1 (non-Full Thrust) with the first version of the legs, and took place in particularly heavy fog. The landing looked perfect, but one leg folded up afterward.
The remaining two failures were on flights 22 and 26, both on ASDS landings from geosynchronous launches with little margin for landing. 22 wasn't expected to make it, 26 came within meters of doing so.
There's probably still things to learn, but they seem out of the "getting it to work" stage and well into "making it work better" stage.
The numbers in the summary are a bit ambiguous/confused: This was the *sixth* rocket they've landed. They've landed four on drone ships and two on land. That's nowhere near half the rockets they've launched (this was the 28th Falcon 9), but means just over half of their landing attempts (11 total) have succeeded.
More importantly, of the last 7 landing attempts, there were only two failures, both due to simple lack of propellant margin due to the demands of those particular launches...there weren't any failures or control problems, they just ran out of propellant. The last actual hardware failure was flight 21, the Jason-3 launch, which actually landed fine, but had an earlier version of the legs which iced up and failed to lock in the extended position. So it's looking like reliability of future landings can be expected to be quite a bit better than 50%.
All without any nets/cables/tubes/funnels/magnets/giant catcher's mitts.
Basalt fiber (more or less "mystery glass" in fiber form) turns out to have surprisingly good mechanical properties, and a composite hull would be much tougher than a blown bubble, plus you would have more flexibility in the shapes achievable. Additional layers of basalt fiber fabric and "sandbags" filled with waste rock wrapped around the outside could provide radiation and micrometeorite shielding and thermal mass. Nothing you'd want to haul around the solar system, but for setting up habitable volume near an asteroid, you'd just need to import some spinning/weaving machinery and resin and a pile of silicate-rich rock.
2.5 degrees is about 245 km. Without the boostback, the stage ends up coming down about twice that distance to the east of the launch site despite that motion. But that's missing the point, particularly for RTLS: the directions considered horizontal and vertical are basically identical at launch and landing, and adding to vertical velocity after staging will only send the stage further downrange (unless you posit spending utterly unrealistic amounts of delta-v on the maneuver). RTLS is not an orbital maneuver, and the reasons for those rules of thumb you quoted do not apply. And yes, of course SpaceX accounts for Earth's rotation and so on, they need to actually hit a precise landing target. However, they are irrelevant to understanding the basic maneuvers, and simply do not require the maneuvers you describe.
Another factor is that if things were done as you say, the RTLS would take far, far longer than the ASDS landings, because the stage would have to be thrown on a high enough trajectory that the landing site could come into position under it, which would take much more of a rotation. The fact that CRS-9 did the entry burn just 4 minutes after the boostback burn should be another hint that something's wrong with your analysis.
Since you apparently trust Flight Club, just look at their CRS-9 model: https://flightclub.io/results/... The boostback burn happens from 162 to 211 s. For the first 7 seconds of that, it is completing a maneuver to a pitch angle of -2 degrees, where it remains for the remainder of the burn.
If you truly found someone at Reddit who told you that the stage went west by thrusting up, you found someone who doesn't have a damn clue what they're talking about, and you should find someone else. Ignoring the issues of inadequate propellant and far more severe reentry conditions, the stage would have to go far higher than a couple hundred of km, and fly for far longer to allow the launch site to catch up and pass beneath it, and then it'd end up far to the south of the actual launch and landing sites due to the non-equatorial launch site. Earth only rotates about 2.5 degrees between launch and landing, the stage has the same initial velocity as Cape Canaveral and only travels a few hundred km in any direction, none of the factors that make orbital mechanics counterintuitive are significant here. None of the people who are doing simulations (you're talking to one of them here) will tell you otherwise.
And no, those diagrams are mostly correct, and nothing I've said conflicts with them...they show a horizontal boostback burn, contrary to the rule of thumb you quoted. Your mis-application of an approximate rule only appropriate for objects in the nearly-circular coplanar orbits of Niven's smoke ring (or in a very limited sense unrelated to landing, for maneuvers around geostationary orbit), on the other hand, does. It's not even internally consistent, by that reasoning the stage should fly off to the east as it descends, and the final burn should be done horizontally, like a capsule docking with the space station from above or below. SpaceX certainly needs to take factors like the rotating reference frame into account in order to hit their landing spots, but for just understanding the maneuvers it is entirely appropriate to treat them as basically parabolic trajectories over flat ground.
It's not that orbital mechanics knows if you're in orbit or not, it's that it simply isn't involved if you aren't. The rules of thumb you quoted work between objects in reasonably circular orbits because objects in lower circular orbits travel faster than those in higher orbits. The launch/landing site is not in any kind of orbit and is moving at only a few percent of what orbital velocity at sea level would be, and the first stage is in an extremely eccentric orbit that intersects the ground just a hundred km or so below apogee and which can accurately be analyzed as a parabolic trajectory over flat ground.
Even worse: canceling out your eastbound velocity, burning westward, and then canceling out your now-westward velocity so you can land. You can manage some of that with aerodynamics rather than rocket power, fortunately.
The propellant requirements of returning to land are considerably higher, roughly doubling the payload penalty. However, it means you don't have to run a barge and its support boat for a couple weeks and can immediately get started on preparing the stage for reuse, and the propellant is dirt cheap, so it's very worth doing when they can manage it.
It goes up because it's already going up at stage separation. Gravity will take care of reversing the vertical component of its motion, so there's no point in burning fuel to halt the upward motion: the boostback burn only has to reverse the horizontal motion. If allowed to continue on a parabolic arc to an ASDS landing, its peak altitude would be similar, it'd just be reached much further downrange.
"Out takes you west", etc. only works for objects in orbit, relative to other objects in orbit. Objects in lower orbit move faster and travel east relative to objects in higher orbits. Earth's surface isn't moving at orbital velocity and will continue to trail behind to the west until you get up past geosynchronous orbit. The RTLS trajectory is more like a ball bouncing off a vertical wall than anything to do with orbital dynamics.
We've dropped the Shuttles and are building launch systems capable of putting mass into orbit at a small fraction of the cost, along with spacecraft capable of going beyond Earth orbit. How is this not progress?
Their intent is to "gas and go": replenish fluids and fly again. They've discussed future plans of refueling at sea and flying the stages back to land, which gets them back in a few minutes and avoids a long and costly trip with a support vessel towing an ASDS which is unavailable for landings until it gets towed back out to sea.
They've not relaunched, but they refueled and fired up the first stage they brought back. Something broke loose and was ingested by one of the turbopumps, shutting one engine down, but the stage was otherwise in full working order. Their plans are to run the second recovered stage through ten test fires and fly it again, and SES is interested in having one of their satellites be the payload.
It's also not the only aneutronic fuel. If you can build aneutronic He-3 reactors that produce useful power, you can probably do the same with p-B11 or p-Li7, with the advantage of not having to scoop up continent-scale areas of lunar surface to find fuel.
Surely you can cite some of these "early attempts at production of fusion power", right? ITER is the first experimental reactor intended to produce power. Most of the research devices don't even use real fusion fuel...they know fusion works, it's the plasma physics they are researching, and building a big power-producing reactor, handling tritium, and dealing with fusion neutrons is unnecessary for that and far beyond the budgets typically allocated to fusion experiments.
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It's enough atmosphere to be a substantial assist in landing mass on the surface, and actually does provide significant radiation protection while also moderating temperatures. The perchlorate issue is massively overstated: they are not that toxic, and are easy to remove, and there's entire glaciers of water on Mars.
The need for huge energy storage systems or nuclear power from the very start is a significant problem for the moon. The game-breaker though is ISRU propellant production. Getting enough water on the moon to supply return craft will require large scale mining and regolith processing facilities...meaning any return propellant will have to be imported until the colony is well established. On Mars, it should involve little more than drilling into a glacier and lowering a heat source to sublime the ice, which makes it a lot easier to get your spacecraft back so you can use it on another trip. The relative ease of delivering mass to Mars and greater proportion of the delivered mass that can be productive colony hardware can do a lot to compensate for the greater distance and travel time.
Lunar helium-3 mining has always been about as plausible a suggestion as strip-mining the moon for green cheese. Helium-3 is a byproduct of storage of the tritium that 1st generation fusion will breed for fuel, and if you can do He-3 fusion, you can do p-B11 fusion. So: by the time we can make use of it, we'll be able to mass produce it far more easily than we could mine it, and we probably won't even bother with it due to availability of far more abundant fuels.
A "working EmDrive" would be a reversible electromagnetic machine, functioning equally well as a motor or a generator:
http://www.emdrive.com/2Gupdat... (page 6, ironically titled Conservation of Energy)
If allowed to accelerate, the microwaves in the cavity would red-shift and lose energy, if accelerated in the other direction, they would blue-shift and gain energy. A "working EmDrive" placed on one end in Earth's surface gravity would thus either continuously create or destroy energy.
The reasonable conclusion is that there is no such thing as a "working EmDrive".
He claims that, but his analysis is based on velocities relative to a fixed universal rest frame, which he seems to believe is the same reference frame as Earth's surface. For example, he says that it produces thrust most efficiently if "stationary", and is best used to counter gravity and allow a craft to hover, with jets and rockets being used for propulsion (he seems unaware that a hovering craft is one that is accelerating upward at a constant 9.8 m/s^2).
If you really take Shawyer's math and vehicle concepts seriously, he's apparently a stationary-Earth geocentrist. More likely, he's just clueless about physics.
The confusion is yours: you can't violate just conservation of energy or conservation of momentum. And it's trivial to show that the claimed behavior of the EmDrive violates conservation of energy: a working EmDrive placed on one end on the ground would turn gravitational acceleration into an infinite source or sink of energy, depending on which end was up.
Did you miss the part about Skylon having double the dry mass of the Falcon 9?
For what?
For operating a vehicle in atmosphere, which occurs at two critical stages of a spacecraft's mission.
That doesn't answer the question. Spacecraft spend only a tiny fraction of their lives in the atmosphere, and sustained aerodynamic flight is not a requirement during their short passages through it during launch and landing. So what do they need wings for?
No. That is specifically the design I am arguing against. Please check my post again and you will see I deliberately *exclude* the mass of the engines.
Engines using diluted low-pressure gaseous ambient oxygen as an oxidizer have poor thrust to weight ratios, and wings are generally used to make up for that, making it possible for a craft with underpowered engines to accelerate early on, though at a cost in aerodynamic drag and sustained heating. If you're *not* using air-breathing engines, you can just fly a near-vertical trajectory that quickly exits the bulk of the atmosphere, without having to deal with aerodynamic drag and heating. As for the return, where are you trying to go between reentry and landing? What do you need wings for?
(Note: "to operate from an airport" is not an answer. Needing a reinforced extra-long runway in addition to all the usual pad infrastructure is a cost, not a benefit.)
Al-Li is ~95% Al. Nobody lists all the components of an alloy every time they refer to the primary material. And the interstage is a tiny fraction of the structure, which originally only served to connect the stages and house separation hardware. It's not at all comparable to Skylon's composite LH2 tanks and airframe.
They've done a good job of optimizing it, but that doesn't change the fact that they chose stir-welded aluminum because it was relatively cheap and easy compared to higher performing alternatives such as carbon fiber. Recent rumors hint that their future projects will make heavy use of carbon fiber, but for staged vehicles it's an optimization for improving performance and SpaceX was able to avoid it for most things until they got established and worked out reuse, while it's virtually a requirement for SSTO craft and spaceplanes just to reach orbit.
I'd argue they need to prove that the vehicle weight is lower completely dry (and even that's biased in favor of airbreathing winged vehicles because it ignores the extra complexity and higher cost materials). It's the dry structure that's the expensive part to build and operate, you need the reduction in LOX tank size to make the vehicle smaller and cheaper after adding the wings, air breathing engines, landing gear, etc. If you can make the vehicle cheaper at the cost of pouring in a bit more propellant before launch, it's a win.
As it turns out, LOX is pretty compact and reducing the LOX tank size by airbreathing (again, the only real reason to carry wings) doesn't save much. The trade makes Skylon twice as heavy as the Falcon 9 despite using a super-advanced (and far more expensive per kg) carbon fiber frame instead of the Falcon 9's aluminum.
It's great to see the myths of non-reusable first stage technology being dispelled.
Indeed, SpaceX has thoroughly demolished the claims of SSTO fans that reuse and low cost are somehow incompatible with staging. With an aluminum-bodied, pure-rocket launch system using simple kerosene-burning rocket engines, SpaceX has accomplished the bulk of what Skylon promises to one day achieve with its supertech air-breathing engines, liquid hydrogen fuel, eggshell-thin ceramic heat shielding, etc.
We don't need wings.
They are useful though.
For what? Air breathing launchers need them because of their weaker engines, but staged launchers don't need air breathing. For spacecraft, wings are just dead weight you wish was useful payload while operating in their primary environment, and highly stressed structures subject to catastrophic failure during atmospheric entry. Making spacecraft into poor imitations of aircraft for a brief portion of their flight will not make them as cheap to operate as aircraft.
Spaceplanes are dead. Take Skylon as a representative example: assuming it lived up to expectations, Skylon would have double the dry mass of the Falcon 9, about 10 times the unit cost, its complex engines and other systems would have operating costs that are higher by a similar factor, it'd have the additional headaches of operating with liquid hydrogen (largely unavoidable with spaceplanes), and all for somewhat lower payload than today's mostly-reusable Falcon 9, while competing with the fully reusable successor to the Falcon 9.
Even worse, Skylon would require an expendable upper stage for launches to geostationary orbit, which would likely make it less reusable than whatever SpaceX is operating by the time Skylon can fly. Not to mention that Blue Origin will likely have their orbital launcher up and running and the kinks of reuse worked out by that time as well...
Their earliest recovery attempts involved parachuting stages into the ocean unpowered. All those attempts apparently resulted in the vehicle breaking up during reentry. Large supersonic parachutes are very non-trivial to design and deploy, not terribly reliable at the best of times, and are actually rather heavy, and they needed to do powered reentry and landing anyway to get the vehicle down intact. Since they're already doing that, reserving a bit more propellant is simpler than pretty much any other option, plus it gives them experience they'll need for Mars.
The very first ASDS landing attempt ran out of hydraulic fluid for the grid fins, the engine gimbaling barely managing to get it to the barge...not upright and not at zero velocity.
The next had a sticky valve...my understanding is it was actually for throttle. The control software would command throttle changes, but the valve wouldn't respond until the commanded change was big enough to break it loose, then it'd stick at the new position. The overall effect was that the throttle was lagging behind what the control system expected, which threw things into oscillation with the rocket always overcompensating for its previous errors, always too late to fix things.
The third failure was the Jason-3 launch, which was the last launch of the Falcon 9 v1.1 (non-Full Thrust) with the first version of the legs, and took place in particularly heavy fog. The landing looked perfect, but one leg folded up afterward.
The remaining two failures were on flights 22 and 26, both on ASDS landings from geosynchronous launches with little margin for landing. 22 wasn't expected to make it, 26 came within meters of doing so.
There's probably still things to learn, but they seem out of the "getting it to work" stage and well into "making it work better" stage.
The numbers in the summary are a bit ambiguous/confused:
This was the *sixth* rocket they've landed. They've landed four on drone ships and two on land. That's nowhere near half the rockets they've launched (this was the 28th Falcon 9), but means just over half of their landing attempts (11 total) have succeeded.
More importantly, of the last 7 landing attempts, there were only two failures, both due to simple lack of propellant margin due to the demands of those particular launches...there weren't any failures or control problems, they just ran out of propellant. The last actual hardware failure was flight 21, the Jason-3 launch, which actually landed fine, but had an earlier version of the legs which iced up and failed to lock in the extended position. So it's looking like reliability of future landings can be expected to be quite a bit better than 50%.
All without any nets/cables/tubes/funnels/magnets/giant catcher's mitts.
Basalt fiber (more or less "mystery glass" in fiber form) turns out to have surprisingly good mechanical properties, and a composite hull would be much tougher than a blown bubble, plus you would have more flexibility in the shapes achievable. Additional layers of basalt fiber fabric and "sandbags" filled with waste rock wrapped around the outside could provide radiation and micrometeorite shielding and thermal mass. Nothing you'd want to haul around the solar system, but for setting up habitable volume near an asteroid, you'd just need to import some spinning/weaving machinery and resin and a pile of silicate-rich rock.
2.5 degrees is about 245 km. Without the boostback, the stage ends up coming down about twice that distance to the east of the launch site despite that motion. But that's missing the point, particularly for RTLS: the directions considered horizontal and vertical are basically identical at launch and landing, and adding to vertical velocity after staging will only send the stage further downrange (unless you posit spending utterly unrealistic amounts of delta-v on the maneuver). RTLS is not an orbital maneuver, and the reasons for those rules of thumb you quoted do not apply. And yes, of course SpaceX accounts for Earth's rotation and so on, they need to actually hit a precise landing target. However, they are irrelevant to understanding the basic maneuvers, and simply do not require the maneuvers you describe.
Another factor is that if things were done as you say, the RTLS would take far, far longer than the ASDS landings, because the stage would have to be thrown on a high enough trajectory that the landing site could come into position under it, which would take much more of a rotation. The fact that CRS-9 did the entry burn just 4 minutes after the boostback burn should be another hint that something's wrong with your analysis.
Since you apparently trust Flight Club, just look at their CRS-9 model: https://flightclub.io/results/...
The boostback burn happens from 162 to 211 s. For the first 7 seconds of that, it is completing a maneuver to a pitch angle of -2 degrees, where it remains for the remainder of the burn.
If you truly found someone at Reddit who told you that the stage went west by thrusting up, you found someone who doesn't have a damn clue what they're talking about, and you should find someone else. Ignoring the issues of inadequate propellant and far more severe reentry conditions, the stage would have to go far higher than a couple hundred of km, and fly for far longer to allow the launch site to catch up and pass beneath it, and then it'd end up far to the south of the actual launch and landing sites due to the non-equatorial launch site. Earth only rotates about 2.5 degrees between launch and landing, the stage has the same initial velocity as Cape Canaveral and only travels a few hundred km in any direction, none of the factors that make orbital mechanics counterintuitive are significant here. None of the people who are doing simulations (you're talking to one of them here) will tell you otherwise.
And no, those diagrams are mostly correct, and nothing I've said conflicts with them...they show a horizontal boostback burn, contrary to the rule of thumb you quoted. Your mis-application of an approximate rule only appropriate for objects in the nearly-circular coplanar orbits of Niven's smoke ring (or in a very limited sense unrelated to landing, for maneuvers around geostationary orbit), on the other hand, does. It's not even internally consistent, by that reasoning the stage should fly off to the east as it descends, and the final burn should be done horizontally, like a capsule docking with the space station from above or below. SpaceX certainly needs to take factors like the rotating reference frame into account in order to hit their landing spots, but for just understanding the maneuvers it is entirely appropriate to treat them as basically parabolic trajectories over flat ground.
It's not that orbital mechanics knows if you're in orbit or not, it's that it simply isn't involved if you aren't. The rules of thumb you quoted work between objects in reasonably circular orbits because objects in lower circular orbits travel faster than those in higher orbits. The launch/landing site is not in any kind of orbit and is moving at only a few percent of what orbital velocity at sea level would be, and the first stage is in an extremely eccentric orbit that intersects the ground just a hundred km or so below apogee and which can accurately be analyzed as a parabolic trajectory over flat ground.
Even worse: canceling out your eastbound velocity, burning westward, and then canceling out your now-westward velocity so you can land. You can manage some of that with aerodynamics rather than rocket power, fortunately.
The propellant requirements of returning to land are considerably higher, roughly doubling the payload penalty. However, it means you don't have to run a barge and its support boat for a couple weeks and can immediately get started on preparing the stage for reuse, and the propellant is dirt cheap, so it's very worth doing when they can manage it.
It goes up because it's already going up at stage separation. Gravity will take care of reversing the vertical component of its motion, so there's no point in burning fuel to halt the upward motion: the boostback burn only has to reverse the horizontal motion. If allowed to continue on a parabolic arc to an ASDS landing, its peak altitude would be similar, it'd just be reached much further downrange.
"Out takes you west", etc. only works for objects in orbit, relative to other objects in orbit. Objects in lower orbit move faster and travel east relative to objects in higher orbits. Earth's surface isn't moving at orbital velocity and will continue to trail behind to the west until you get up past geosynchronous orbit. The RTLS trajectory is more like a ball bouncing off a vertical wall than anything to do with orbital dynamics.
And that math and arithmetic are the same thing, which is just as wrong.
We've dropped the Shuttles and are building launch systems capable of putting mass into orbit at a small fraction of the cost, along with spacecraft capable of going beyond Earth orbit. How is this not progress?
Their intent is to "gas and go": replenish fluids and fly again. They've discussed future plans of refueling at sea and flying the stages back to land, which gets them back in a few minutes and avoids a long and costly trip with a support vessel towing an ASDS which is unavailable for landings until it gets towed back out to sea.
They've not relaunched, but they refueled and fired up the first stage they brought back. Something broke loose and was ingested by one of the turbopumps, shutting one engine down, but the stage was otherwise in full working order. Their plans are to run the second recovered stage through ten test fires and fly it again, and SES is interested in having one of their satellites be the payload.
It's also not the only aneutronic fuel. If you can build aneutronic He-3 reactors that produce useful power, you can probably do the same with p-B11 or p-Li7, with the advantage of not having to scoop up continent-scale areas of lunar surface to find fuel.
Surely you can cite some of these "early attempts at production of fusion power", right?
ITER is the first experimental reactor intended to produce power. Most of the research devices don't even use real fusion fuel...they know fusion works, it's the plasma physics they are researching, and building a big power-producing reactor, handling tritium, and dealing with fusion neutrons is unnecessary for that and far beyond the budgets typically allocated to fusion experiments.