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Could the SuperHeavy booster be SSTO?


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 Running some  numbers for the SuperHeavy+Starship launcher, I was surprised to get that an expendable SuperHeavy alone could be SSTO with quite high payload.  Wikipedia gives the propellant mass of the SuperHeavy as 3,400 tons, but does not give the dry mass. We can do an estimate of that based on information Elon provided in a tweet:

Replying to @Erdayastronaut and @DiscoverMag
Probably no fairing either & just 3 Raptor Vacuum engines. Mass ratio of ~30 (1200 tons full, 40 tons empty) with Isp of 380. Then drop a few dozen modified Starlink satellites from empty engine bays with ~1600 Isp, MR 2. Spread out, see what’s there. Not impossible.

https://twitter.com/elonmusk/status/1111798912141017089?s=20&t=L-xcKvWnRTmbSDa_YI0OyA

  This is for a stripped down Starship, no reusability systems, no passenger quarters, and reduced number of engines.  But this could not lift-off from ground because of the reduced thrust with only 3 engines plus being vacuum optimized these could not operate at sea level. So up the number of engines to 9 using sea level Raptors. According to wiki the Raptors have a mass of 1,500 kg. So adding 6 more brings the dry mass to 49 tons, call it 50 tons, for a mass ratio of 25 to 1.

By the way, there have been many estimates of the capabilities of the Starship for a use other than that with the many passengers, say 50 to 100 , to LEO or as colonists to Mars, for instance, such as the tanker use or only as the lander vehicle transporting a capsule for astronauts for lunar missions.  But surprisingly they all use the ca. 100 ton dry mass of the passenger Starship. But without this large passenger compartment it should be a much smaller dry mass used in the calculations. For instance, the Dragon 2 crew capsule dry mass without the trunk is in the range of 7 to 8 tons for up to 7 astronauts. So imagine a scaled up passenger compartment for 50 passengers or more. That passenger compartment itself could well mass over 60 tons.

 So the dry mass estimate of a stripped down, expendable, reduced engine Starship of 40 tons offered by Elon does make sense. 

Based on this, an expendable Starship with sufficient engines for ground launch could be SSTO:

the ISP of the Raptors for both sea level and vacuum-optimized versions have been given various numbers. I’ll use 358 s as the vacuum ISP of the sea level Raptor. For calculating payload using the rocket equation, the vacuum Isp is commonly used even for the ground stage, since the diminution in Isp at sea level can be regarded as a loss just like air drag and gravity loss for which you compensate by adding additional amount to required delta-v to orbit just like the other losses.

 Then 3580ln(1 +1200/(50 + 50)) = 9,180 m/s sufficient for LEO.      

 But as of now, SpaceX has no plans of making the Starship a ground-launched vehicle. So we’ll look instead at the SuperHeavy. For an expendable version with no reusability systems, we’ll estimate the dry mass using a mass ratio of 25 to 1, same as for a ground-launched expendable Starship. Actually, likely the Superheavy mass ratio will be even better than this since it is known scaling a rocket up improves the mass ratio. So this gives a dry mass of 136 tons. Then the expendable SuperHeavy could get 150 tons to LEO as an expendable SSTO: 3580ln(1 + 3,400/(136 + 150)) = 9,150 m/s, sufficient for LEO.

 But what about a reusable version? Reusability systems added to a stage should add less than 10% to the dry mass:

________________________________________________________________________________________________________________

From: [email protected] (Henry Spencer)
Newsgroups: sci.space.tech
Subject: Re: The cost (in weight) for Reusable SSTO
Date: Sun, 28 Mar 1999 22:37:10 GMT

In article <[email protected]>,
Larry Gales <[email protected]> wrote:
>An SSTO with a useful payload using Kero/LOX is easy to do -- provided that
>it is *expendable*.  All of the difficulty lies in making it reusable...

There are people who are sufficiently anti-SSTO that they will dispute the
feasibility of even expendable SSTOs (apparently not having read the specs
for the Titan II first stage carefully).

>   (1) De-orbit fuel: I understand that it takes about 100 m/s to de-orbit.

That's roughly right.  Of course, in favorable circumstances you could play
tricks like using a tether to simultaneously boost a payload higher and
de-orbit your vehicle.  (As NASA's Ivan Bekey pointed out, this is one case
where the extra dry mass of a reusable vehicle is an *advantage*, because
the heavier the vehicle, the greater the boost given to the payload.)

>   (2) TPS (heat shield): the figures I hear for this are around 15% of the
>orbital mass

Could be... but one should be very suspicious of this sort of parametric
estimate.  It's often possible to beat such numbers, often by quite a large
margin, by being clever and exploiting favorable conditions.  Any single
number for TPS in particular has a *lot* of assumptions in it.

>   (4) Landing gear: about 3%

Gary Hudson pointed out a couple of years ago that, while 3% is common
wisdom, the B-58 landing gear was 1.5%... and that was a very tall and
mechanically complex gear designed in the 1950s.  See comment above
about cleverness.

I would be very suspicious of any parametric number for landing gear which
doesn't at least distinguish between vertical and horizontal landing.

>   (5) Additional structure to meet loads from differnet directions (e.g.,
>vertical
>        takeoff, semi-horizontal re-enttry, horizontal landing).  This is
>purely
>        guesswork on my part, but I assume about 8%

Of course, here the assumptions are up front:  you're assuming a flight
profile that many of us would say is simply inferior -- overly complex,
difficult to test incrementally, and hard on the structure.

>I would appreciate it if anyone could supply more accurate figures.

More accurate figures either have to be for a specific vehicle design,
or are so hedged about with assumptions that they are nearly meaningless.
--
The good old days                   |  Henry Spencer   [email protected]
weren't.                            |      (aka [email protected])

https://yarchive.net/space/launchers/landing_gear_weight.html


 The 15% mentioned for thermal protecton(TPS) is for Apollo-era heat shields. But the PICA-X developed by SpaceX is 50% lighter so call it 7.5% for TPS.  And for the landing gear ca. 3%, but with carbon composites say half of that at 1.5%.

  But this would put the reusable payload at ca. 136 tons which is in the range of 100 to 150 tons of the full two stage reusable vehicle!

 How is that possible? A reusable multistage vehicle has a severe disadvantage. The fuel that needs to be kept on reserve for the first stage to slow down and boost back to the launch site subtracts greatly from the payload possible.  But for a reusable SSTO it can remain in orbit until the Earth rotates below until the landing site is once again below the vehicle.

   Robert Clark

 

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4 hours ago, Exoscientist said:

SpaceX has no plans of making the Starship a ground-launched vehicle. So we’ll look instead at the SuperHeavy. For an expendable version with no reusability systems, we’ll estimate the dry mass using a mass ratio of 25 to 1, same as for a ground-launched expendable Starship. Actually, likely the Superheavy mass ratio will be even better than this since it is known scaling a rocket up improves the mass ratio. So this gives a dry mass of 136 tons.

This is wildly, wildly wrong.

I'll take your last point first. Scaling a rocket up improves the mass ratio only if you take advantage of the square-cube law. Simply making a vehicle longer is a linear change, which won't improve the mass ratio at all; in practice, you'll end up needing additional stiffeners when you increase the fineness, so that makes the mass ratio slightly worse.

Also, sanity check. Superheavy has 33 engines on it. Raptor 1 was around 2 tonnes; Raptor 2 is around 1.6 tonnes. A single-stage Superheavy would need fewer engines -- let's say 25 -- but that's still 40 tonnes in engine mass alone. Compare that to the ~13.5 tonnes of engines you were (inaccurately) claiming on the stripped-down expendable starship. Since structural mass is independent of the engines mass, using your own numbers would yield 145.5 tonnes which is already significantly higher than the dry mass you supposed.

And you CAN'T simply scale up the Starship's mass ratio linearly to get here, because Superheavy is MUCH heavier than Starship. It has to be; it is carrying dramatically higher loads. The dry mass of Superheavy is generally believed to be on the order of 200-220 tonnes. Let's take that lower number (since we're not using quite as many engines). So an expendable Superheavy launched without payload, using sea level engine vacuum ISP, has 10.15 km/s of dV. Enough to make orbit empty, sure. Enough to carry meaningful payload, accounting for the added mass of a fairing, etc.? No. Silverbird estimates the payload of this configuration at 232-428 kg.

5 hours ago, Exoscientist said:

I’ll use 358 s as the vacuum ISP of the sea level Raptor.

 Then 3580ln(1 +1200/(50 + 50)) = 9,180 m/s sufficient for LEO.      

Your math here is wrong. 358 s * g = 3511 m/s. Not a huge difference, but a difference. 

5 hours ago, Exoscientist said:

The 15% mentioned for thermal protecton(TPS) is for Apollo-era heat shields. But the PICA-X developed by SpaceX is 50% lighter so call it 7.5% for TPS.

PICA-X is not immediately reusable, so that doesn't even begin to work.

But while we're at it, where is this TPS supposed to go?? Superheavy is a lawn dart.  All of its weight is on the back end. It will plummet back into the atmosphere tail-first and all those Raptor 2s will immediately turn to slag.

And how is it supposed to land? You haven't reserved any propellant for a landing burn. Is it going to land horizontally? If so, you haven't reserved any structural mass for wings (or an explanation of how to get the center of mass forward enough to allow a horizontal landing). None of this makes any sense.

5 hours ago, Exoscientist said:

But this would put the reusable payload at ca. 136 tons which is in the range of 100 to 150 tons of the full two stage reusable vehicle!

How is that possible? A reusable multistage vehicle has a severe disadvantage. The fuel that needs to be kept on reserve for the first stage to slow down and boost back to the launch site subtracts greatly from the payload possible.  But for a reusable SSTO it can remain in orbit until the Earth rotates below until the landing site is once again below the vehicle.

No, your math and your foundational assumptions are wrong.

The reserve propellant for a boostback burn does not even come CLOSE to being significant in comparison to the advantage of staging.

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 Thanks for the response with calculations. The general principle that scaling a rocket up improves mass ratio is coming from the fact that components such as tanks and engines scale approximately linearly with size but things like insulation, wiring, avionics grow at a much lower rate. This was the reason why it was proposed to get lowered launch costs, create a big dumb booster, and to create an SSTO, go large.

 For using the Silverbird Astronautics calculator, you have to be aware of some quirks of the program. First use the vacuum Isp and vacuum  thrust levels in the engine fields since the program takes into account the diminution at sea level. Also, select “No” for the “Restartable upper stage” since otherwise that reduces payload, possibly due to keeping propellant on reserve. Important also is to match the launch angle to the latitude of the launch site. So at Cape Canaveral, set it to 28.5 degrees. 

 For the Raptor engine ,  several different Isp and thrust levels have been given. I’ll use the vacuum Isp of 358 s for the sea level Raptor. For estimating the vacuum thrust, I’ll use the 650 kg/s flow rate of the Raptor in the Wiki page, then at a 358 s vacuum Isp, using (thrust) = (exhaust speed)x(flow rate), we get a vacuum thrust of 358*9.81*650 = 2,280,000 N. So for 33 engines, 75,300,000 N, ~75,000 kN. Inputting this data into the Silverbird calculator looks like this:

CF5-AD8-FF-E087-425-A-99-D9-67-FB0-C9-F3

 

 And the results is:

976-C6-D4-A-5-E91-45-D0-B87-D-653-B975-A

 

 So a 160 ton payload to LEO as an expendable. I’ve found the Silverbird calculator to be approximately 10% accurate plus or minus. For the fairing, I’ve found inputting it reduces the payload ~10%. But there are various ways of reducing the fairing weight to reduce this lost payload even further.

 For the PICA-X thermal protection it has reusability for dozens of uses.

 Even if the dry mass of the SuperHeavy is 200 tons, that still leaves an LEO payload of ~100 tons.

 

    Robert Clark

 

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I wrote the following yesterday, but didn't finish it, so didn't post:

At 4mm thickness, the 69.5m tube of steel is ~160t, not counting tank domes, plumbing, or engines. That drops to 120t for 3mm steel. Again, just the cylinder part.

Pic, just because pics are cool:

FNZ3phcXIAAdfpt?format=png

 

TWR doesn't need to be as high for expendable (not optimized to save props), and it doesn't need 33 engines because it doesn't need to lift 1300+t of Starship.

Might only need low 20s on engine number (TWR ~1.3 for 20 engines) . 20 is ~30t, so we're still at at least 200t dry for a 4mm steel SH. Might be more like 160t for 3mm.

 

 

Still not finished, but some useful numbers.

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1 hour ago, Exoscientist said:

So a 160 ton payload to LEO as an expendable. I’ve found the Silverbird calculator to be approximately 10% accurate plus or minus. For the fairing, I’ve found inputting it reduces the payload ~10%. But there are various ways of reducing the fairing weight to reduce this lost payload even further.

 Even if the dry mass of the SuperHeavy is 200 tons, that still leaves an LEO payload of ~100 tons.

Plugging in realistic numbers for the mass of Superheavy and adding a payload fairing no longer than the one on Falcon 9, Silverbird gives me an 88.6 tonne payload with 33 engines and an 84.4 tonne payload with 27 engines.

And this is all extremely silly because why would you expend an entire booster for an 80-90 tonne payload when you could recover the booster and expend only an upper stage to get 3x as much payload into LEO??

Anything an SSTO can do, a TSTO can do better. 

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9 minutes ago, sevenperforce said:

Anything an SSTO can do, a TSTO can do better. 

Except for making spaceflight enthusiasts of a certain mindset squeeee.  

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Posted (edited)

 The military is considering using the Starship for troop transport:

TECH & SCIENCE

Pentagon Mulls Using Elon Musk's Rockets to Deploy Troops From Space

BY ED BROWNE ON 6/24/22 AT 12:33 PM EDT

https://www.newsweek.com/pentagon-military-elon-musk-starship-deploy-troops-space-1718969

 Clearly for such a use it would be better to have this capability as a single stage. Considering that the military, like NASA, overpays for everything SpaceX could probably get a billion dollar deal for developing this capability.

 Having a SSTO capability would be a great selling point for this purpose.

   Robert Clark

Edited by Exoscientist
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Posted (edited)
5 hours ago, sevenperforce said:

Plugging in realistic numbers for the mass of Superheavy and adding a payload fairing no longer than the one on Falcon 9, Silverbird gives me an 88.6 tonne payload with 33 engines and an 84.4 tonne payload with 27 engines.

And this is all extremely silly because why would you expend an entire booster for an 80-90 tonne payload when you could recover the booster and expend only an upper stage to get 3x as much payload into LEO??

Anything an SSTO can do, a TSTO can do better. 

It's actually quite remarkable that the SSTO performance could even be as good as 1/3 the TSTO performance.

43 minutes ago, Exoscientist said:

 The military is considering using the Starship for troop transport:

TECH & SCIENCE

Pentagon Mulls Using Elon Musk's Rockets to Deploy Troops From Space

BY ED BROWNE ON 6/24/22 AT 12:33 PM EDT

https://www.newsweek.com/pentagon-military-elon-musk-starship-deploy-troops-space-1718969

 Clearly for such a use it would be better to have this capability as a single stage. Considering that the military, like NASA, overpays for everything SpaceX could probably get a billion dollar deal for developing this capability.

 Having a SSTO capability would be a great selling point for this purpose.

   Robert Clark

Rockets are not remotely combat hardenable. It's akin to trying to land a very large and very delicate bomb near your own positions. Not remotely recommended anywhere even remotely unsecured. Add in that opponents are liable to view it as an incoming ICBM (and react to it as such) and this is probably not an idea that will reach widespread implementation.

Edited by RCgothic
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1 hour ago, Exoscientist said:

 The military is considering using the Starship for troop transport:

TECH & SCIENCE

Pentagon Mulls Using Elon Musk's Rockets to Deploy Troops From Space

BY ED BROWNE ON 6/24/22 AT 12:33 PM EDT

https://www.newsweek.com/pentagon-military-elon-musk-starship-deploy-troops-space-1718969

 Clearly for such a use it would be better to have this capability as a single stage. Considering that the military, like NASA, overpays for everything SpaceX could probably get a billion dollar deal for developing this capability.

 Having a SSTO capability would be a great selling point for this purpose.

 By the way, an irritation of mine is that SpaceX is so completely focused on the idea the SuperHeavy/Starship has to be the be all, end all for all launchers. SpaceX is being insightful in recognizing reusability has been the name of the game for any transportation system. But an aspect they are not recognizing is that transports always come in various sizes, going all the way back to the horse-drawn era. 

 In point of fact Starship itself can form an independent launcher without the SuperHeavy and it would have been advantageous to develop a Starhopper-sized stage as well. If they had, then we already would have had a launcher capable of single launch lunar and Mars missions, using the Starhopper-sized  stage used as the 3rd stage for the SuperHeavy/Starship.

 However, the military wanting an orbital troop transport may encourage SpaceX to develop such smaller stages for independent orbital flight.

  Robert Clark

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1 hour ago, RCgothic said:

It's actually quite remarkable that the SSTO performance could even be as good as 1/3 the TSTO performance.

Rockets are not remotely combat hardenable. It's akin to trying to land a very large and very delicate bomb near your own positions. Not remotely recommended anywhere even remotely unsecured. Add in that opponents are liable to view it as an incoming ICBM (and react to it as such) and this is probably not an idea that will reach widespread implementation.

 

True... but remember that.... when has the last time the USA fought a peer power?

 

When you already have air superiority because you have taken over a weaker country and their air fields, the only real fear of a counter attack you face is an RPG by a local who would have to get past drone patrols and soldier patrols to do so.

 

Worst case scenario would be if a more powerful rival sold or gave more advanced surface to air handheld weapons to locals, then the spacex troop transport would be in grave dangerm

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26 minutes ago, Exoscientist said:

By the way, an irritation of mine is that SpaceX is so completely focused on the idea the SuperHeavy/Starship has to be the be all, end all for all launchers. SpaceX is being insightful in recognizing reusability has been the name of the game for any transportation system. But an aspect they are not recognizing is that transports always come in various sizes, going all the way back to the horse-drawn era. 

This is a fundamental misunderstanding about SpaceX. I'm not in the "colonize Mars" camp, myself—but SpaceX is. It is their raison d'être. Everything else they do is incidental. Making money was at first to survive/exist, the global launch market is chump change, it's not about that.

They are making the smallest vehicle they can to colonize Mars. Yeah, kooky, but that;s what they are doing. They are optimizing for making lots of them, and reducing cost to LEO—since they need to refill in LEO to go to Mars.

 

26 minutes ago, Exoscientist said:

 In point of fact Starship itself can form an independent launcher without the SuperHeavy and it would have been advantageous to develop a Starhopper-sized stage as well. If they had, then we already would have had a launcher capable of single launch lunar and Mars missions, using the Starhopper-sized  stage used as the 3rd stage for the SuperHeavy/Starship.

Musk has said they are open to expendable "starships" which in this case means "normal" upper stages based on the same 9m pattern. If someone had a use case for splitting that into stage 2 and stage 3, and wanted to write a check, they'd probably do it.

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Posted (edited)
10 hours ago, tater said:

I wrote the following yesterday, but didn't finish it, so didn't post:

At 4mm thickness, the 69.5m tube of steel is ~160t, not counting tank domes, plumbing, or engines. That drops to 120t for 3mm steel. Again, just the cylinder part.

Pic, just because pics are cool:

FNZ3phcXIAAdfpt?format=png

TWR doesn't need to be as high for expendable (not optimized to save props), and it doesn't need 33 engines because it doesn't need to lift 1300+t of Starship.

Might only need low 20s on engine number (TWR ~1.3 for 20 engines) . 20 is ~30t, so we're still at at least 200t dry for a 4mm steel SH. Might be more like 160t for 3mm.

Still not finished, but some useful numbers.

  The ~70 m stage length contains the top and bottom domes and the engine length as well as a forward skirt at the top above the tank. Estimating the top and bottom tank domes as hemispheres, the two together would be a single sphere of 9 m diameter. So subtract that off the 70 m to get the vertical side length of the tanks. The Raptor engines at the bottom are 3.1 meters long so subtract that off as well. Commonly, the engine nozzles of the upper stage extend into the forward skirt of the first stage. However, it appears the Starship upper stage engines are recessed into the upper stage, so the nozzles do not extend  down below the stage.  Still the forward skirt has some length. I’ll estimate it as 2 m. Then the actual length of the vertical part of the first stage tanks might be 70 - 9 -3 -2 = 56 m.  

The volume of the  vertical tank walls, i.e., not counting the domes is Pi*(diameter)*(thickness)*(length) = 3.14*9*.004*56 = 6.3 m.  The density of stainless steel is in the range of 7,850 kg/m3. The vertical tank walls would mass 6.3*7850 = 49,500 kg. To this we would also have to add the mass of the two domes but these usually are a fraction of the vertical tank wall mass.  If the wall thickness can be shaved down to 0.003 m then we can cut perhaps 12,000 kg off the tank mass.

   Robert Clark

Edited by Exoscientist
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12 hours ago, sevenperforce said:

Plugging in realistic numbers for the mass of Superheavy and adding a payload fairing no longer than the one on Falcon 9, Silverbird gives me an 88.6 tonne payload with 33 engines and an 84.4 tonne payload with 27 engines.

And this is all extremely silly because why would you expend an entire booster for an 80-90 tonne payload when you could recover the booster and expend only an upper stage to get 3x as much payload into LEO??

Anything an SSTO can do, a TSTO can do better. 

 As I said, in actuality the reusable SSTO gets at or above the payload of the reusable TSTO because of the severe payload loss from the reusable TSTO having to keep a large amount of propellant on reserve in the first stage to cancel out the forward motion then boost back to the landing site.

  Robert Clark

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8 hours ago, Exoscientist said:

However, the military wanting an orbital troop transport may encourage SpaceX to develop such smaller stages for independent orbital flight.

The military likely isn’t interested in an orbital troop transport, it wants speedy rear area supply which would be well defended. In modern combat getting more air-to-air missiles to an airbase in 20 minutes instead of 15 hours could make all the difference in a battle.

”Troop transport” is likely a random concept tacked on to help gain support in other areas of the bureaucracy. You won’t only have Transport Command advocating for it, you will have the whole Army and Marines too. Once the product is finished no one will care whether it actually fulfilled those extra goals. An example of this elsewhere in the US government is how NASA sold the Space Shuttle as a military platform only for it to do little military work and get replaced in military service by Delta, Atlas and Titan after Challenger, but did go onto to do a ton of civilian stuff NASA actually wanted.

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Posted (edited)

 I forgot that SpaceX does want to add 3 more engines to the Starship to bring it to 9 engines:

 

  We’ll replace the vacuum Raptors with all sea level engines. Again using the equation, (thrust) = (exhaust velocity)*(flow rate), a sea level Isp of 330s and propellant flow rate of 650 kg/s gives a  sea level thrust of 330*9.81*650 = 2,104,245 N, so 9 would be 18,938,205 N, or 1,900 tons of thrust. Then depending on how much the propellant is increased this might be enough thrust to lift off from ground.

 But I wanted to check the results using the current propellant load of 1,200 tons using the Silverbird Astronautics calculator. For 9 sea level engines with a vacuum Isp of 358 s, the vacuum thrust would be 358*9.81*650*9 = 20,545,000 N. Using again the 50 ton dry mass estimate and 1,200 ton propellant load for the 9-engined Starship with no passenger quarters the Silverbird calculator gives:

9833-E3-D2-FC22-4466-A3-B3-15847-E2-E91-

 

 Again you have to select the “No” option for “Restartable Upper Stage”, and enter launch inclination of 28.5 degrees to match the Cape Canaveral latitude, so as not to reduce the calculated payload. Then the results are:

 

F671-E89-E-8-E1-E-4-A65-A15-C-5633-D379-

 

 Quite close to the estimate we got using the rocket equation of 50 tons. This is the expendable payload, but again the reusability systems should subtract less than 10% of the dry mass from this payload.

   Robert Clark

 

 

 

 

Edited by Exoscientist
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39 minutes ago, Exoscientist said:

 Quite close to the estimate we got using the rocket equation of 50 tons. This is the expendable payload, but again the reusability systems should subtract less than 10% of the dry mass from this payload.

Not for the Ship in orbit. Ship right now is more like 100t dry (tiles, flaps, etc), possibly more. I think I have seen others do the math showing that Starship could maybe be an SSTO with functionally no payload.

I just don't see the point in SSTOs for most use cases, and for SpaceX, it doesn't get them to Mars anyway. Point to point is another optimization, and the safety/regulatory issues are nontrivial (to put it mildly).

Stage 1 recovery is pretty much a given. They can certainly achieve that, it's just a matter of how crazy they can be in terms of stage recovery—landing on/with the pad/tower, or having to stick legs on it like F9.

 

As @sevenperforce said, TSTO is always better than SSTO, and in this case it's TSTO with booster recovery/reuse.

More useful alternative SH uses/calculations would be expendable upper stages, or an upper stage designed for reuse in space, IMO (my fave being a 9m dia tug).

 

 

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It will *never* make sense to throw away a 20+ engine booster to put 50t payload into orbit SSTO when you are aspiring to put 3x that into orbit TSTO completely reusable, or 5x that by only throwing away the 9-engine upper stage.

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15 minutes ago, RCgothic said:

It will *never* make sense to throw away a 20+ engine booster to put 50t payload into orbit SSTO when you are aspiring to put 3x that into orbit TSTO completely reusable, or 5x that by only throwing away the 9-engine upper stage.

What matters is cost to LEO per ton.

That will play out different ways, obviously. For SpaceX, that is their actual cost, all-in. For customers, it's what you can go on the market and buy a launch for. In the short term, that cost is whatever SpaceX feels like charging given market constraints. The constraints is that in certain payload size/mass ranges, there are other providers, and they have to be competitive, or no one uses them. For the huge payloads we are talking about there are not really other options until New Glenn is around except SLS—and SpaceX could charge a few billion for 1 launch and still be cheap compared to SLS.

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10 hours ago, Exoscientist said:
23 hours ago, sevenperforce said:

Anything an SSTO can do, a TSTO can do better. 

 As I said, in actuality the reusable SSTO gets at or above the payload of the reusable TSTO because of the severe payload loss from the reusable TSTO having to keep a large amount of propellant on reserve in the first stage to cancel out the forward motion then boost back to the landing site.

You've said this several times before.

It is false. Absolutely, categorically, wholly wrong. This is not how the math works.

Consider a putative vehicle with a launch mass of 2000 tonnes. For the sake of simplicity, let's say it is launching methalox propellant as payload to an orbital prop depot so we don't have to worry about fairings or payload mass. Let's make all the assumptions in favor of SSTO over TSTO: equal structural mass ratio on both stages, same engines, same specific impulse, same recovery mass penalty, same T/W ratio. Let's set the structural mass ratio at ~30:1 and use enough sea level Raptor 2 engines to give a T/W ratio of 1.5 (or as close to it as we can come). Let's set the recovery mass penalty at 10% of total dry mass even though that's wildly unrealistic (it will be much lower for a first stage and much higher for a second stage or SSTO). Finally, because we'll be using vacuum thrust and isp, let's set the required dV for LEO at 9.6 km/s. Then we can just figure out how much propellant we have remaining when we reach 9.6 km/s of dV, which gives us our total payload.

Raptor 2 masses 1.6 tonnes and produces 230 tonnes thrust at sea level. Using your 358 seconds of vacuum specific impulse and 330 seconds of specific impulse at sea level, that's 358/330 or 8.5% greater vacuum thrust, for a total of 2448 kN of vacuum thrust. However, for liftoff thrust considerations, we need to use sea-level thrust. Since the launch mass of 2000 tonnes is going to be the same whether it is an SSTO or a TSTO, the liftoff thrust needs to be 3000 tonnes, which will require thirteen Raptor 2 engines off the pad.

First we do the math for the SSTO case. Thirteen Raptor 2 engines mass 21 tonnes, leaving 1,979 tonnes to play with. Using our structural mass ratio of 30:1, that gives us 64 tonnes of structural mass which means 75 tonnes of dry mass. But as you'll recall we have a 10% payload penalty for recovery which we will pretend is enough for deorbit props, TPS, landing gear, and landing props, so that adds 8 tonnes, bringing dry mass to 83 tonnes with 1917 tonnes of propellant. By the rocket equation, mf = m0 / eΔV/ve, and ve is 9.81 m/s2 * 358 s or 3512 m/s. e9600/3512 = 15.39 and m0 is 2000 tonnes so mf = 130. 130 tonnes minus 83 tonnes of dry mass means this SSTO reaches LEO with 47 tonnes of propellant as payload for the propellant depot.

Now let's try doing the same math, but for a TSTO. We assume that the first stage provides impulse up to a total ΔV of v1, where it stages at a velocity of vs. Note that vs is significantly less than v1 because v1 includes gravity drag, aerodynamic drag, and pressure drag. To return to the launch site, the first stage executes a boostback burn vb which is equal to the horizontal component of vs plus whatever additional impulse is needed to get a ballistic trajectory back to the pad. In order to make this as generous as possible to the SSTO case and as punishing as possible to the TSTO case, we will set vb = (vs + v1)/2 even though it would never be that high in reality.

Gravity drag is negligible for the second stage, so the second stage needs only provide ΔV equal to 7.8 km/s - vs. This means all of the drag is concentrated in the first stage, making v1 = vs + (9.6 km/s - 7.8 km/s). 

The question then becomes, where do we put vs? Well, we can balance the first and second stage however we want. General wisdom says to make the total calculable ΔV on both stages approximately equal, but since reuse changes the calculation, we don't necessarily have to follow that advice. We know the total mass of the vehicle is 2000 tonnes so let's look at what happens when we vary the total wet mass of the second stage.

TSTO.png

As you can see, as long as the second stage wet mass is greater than ~10% of the total launch mass, TSTO is going to beat out SSTO every time. This is precisely what we would expect. The efficiency of staging is vast; losses due to boostback propellant reserves are not going to cut into that unless your upper stage is comically small.

Changing the math won't help you because any changes to one stage will be translated to the other stage. And this was with ALL the most generous assumptions. A TSTO first stage will NOT need as much recovery mass and an SSTO will need significantly more. A second stage can use a vacuum engine and a better structural mass ratio.

Anything an SSTO can do, a TSTO can do better. There are certain advantages to SSTO architectures, but the math does not support your notion that the TSTO boostback penalty is significant enough to overcome the efficiencies of staging.

16 hours ago, Exoscientist said:

The ~70 m stage length contains the top and bottom domes and the engine length as well as a forward skirt at the top above the tank.

There is no forward skirt that extends beyond the tank.

e6kOZ.jpg

The top dome of the tank is 3.7 meters so that's the most you can subtract off the top.

16 hours ago, Exoscientist said:

Estimating the top and bottom tank domes as hemispheres, the two together would be a single sphere of 9 m diameter. So subtract that off the 70 m to get the vertical side length of the tanks.

No, you can't subtract off the height of the bottom tank dome, because the thrust structure transfers the engine thrust directly to the tank walls, so you need the walls to extend down to the bottom.

w6q28i4iz9g81.jpg?width=960&crop=smart&a

16 hours ago, Exoscientist said:

The Raptor engines at the bottom are 3.1 meters long so subtract that off as well.

Sure. You also need the shielding around the engines but that can be thinner steel so we'll set it aside for now.

So the actual first stage tank wall height is 70 - 3.7 - 3.1 = 63.2 meters. 

16 hours ago, Exoscientist said:

To this we would also have to add the mass of the two domes but these usually are a fraction of the vertical tank wall mass.

A fraction, yes; negligible, no. You can't just ignore the mass of parts of the vehicle. Plus, there are actually three domes since Superheavy uses a common bulkhead. So the total area of the steel required is going to be 63.2 meters * pi * 9 meters + 1.5 * 4 * pi * 4.5^2 or 2,169 square meters.

With 4mm walls that's a volume of 8.676 cubic meters; with 3mm walls that's a volume of 6.507 cubic meters.

16 hours ago, Exoscientist said:

The density of stainless steel is in the range of 7,850 kg/m3. The vertical tank walls would mass 6.3*7850 = 49,500 kg.

The density of low-carbon 304L stainless is 8 tonnes per cubic meter.

So the actual structural mass of Superheavy tanks alone is going to be 52-69 tonnes depending on whether 4mm or 3mm steel is used.

4 hours ago, Exoscientist said:

I wanted to check the results using the current propellant load of 1,200 tons using the Silverbird Astronautics calculator. For 9 sea level engines with a vacuum Isp of 358 s, the vacuum thrust would be 358*9.81*650*9 = 20,545,000 N. Using again the 50 ton dry mass estimate and 1,200 ton propellant load for the 9-engined Starship with no passenger quarters. . . .

By the way, you don't have to worry about mass flow rate in calculating the vacuum thrust. Just multiply sea level thrust by the ratio of vacuum isp to sea level isp. Sea level isp for the raptor is 330 seconds. I think you're underestimating thrust a little.

Anyway, Elon's BOE estimate at 40 tonnes was with no fairing. If you want to get a payload to orbit you need some kind of fairing. And if you want to add "reusability systems" then the fairing can't be jettisoned.

5 hours ago, Exoscientist said:

Quite close to the estimate we got using the rocket equation of 50 tons. This is the expendable payload, but again the reusability systems should subtract less than 10% of the dry mass from this payload.

So you think that you can make a stripped-down expendable Starship fully reusable by adding only 5 tonnes of dry mass?

That doesn't make sense. There IS a fully-reusable Starship, and it has a mass of 85 tonnes. That's just the fairing and the flaps and the flap drive motors and the heat shield, no crew quarters. And if you added three more engines to it then it would be 90 tonnes. And it needs to reserve 30 tonnes of propellant for re-entry and landing. So "dry mass" in this scenario is 120 tonnes and the actual useable propellant is 1,170 tonnes.

Plugging that into Silverbird:

TSTO.png

Doesn't close.

On 6/30/2022 at 9:44 AM, Exoscientist said:

there have been many estimates of the capabilities of the Starship for a use other than that with the many passengers . . . such as the tanker use or only as the lander vehicle transporting a capsule for astronauts for lunar missions.  But surprisingly they all use the ca. 100 ton dry mass of the passenger Starship. But without this large passenger compartment it should be a much smaller dry mass used in the calculations. For instance, the Dragon 2 crew capsule dry mass without the trunk is in the range of 7 to 8 tons for up to 7 astronauts. So imagine a scaled up passenger compartment for 50 passengers or more. That passenger compartment itself could well mass over 60 tons.

 So the dry mass estimate of a stripped down, expendable, reduced engine Starship of 40 tons offered by Elon does make sense. 

The Dragon 2 crew capsule dry mass without the trunk includes aeroshell, heat shield, and parachutes. The square-cube law is going to help if you're scaling up, since there are a lot of things that don't scale linearly when you increase passenger capacity. So no, you cannot simply multiply out and subtract 60 tonnes. The 40-tonne mass Elon quoted, again, is without flaps or heat shield or recovery propellant or anything else. 

I don't see how you're claiming you can make a stripped-down 50-tonne Starship recoverable using only 5 tonnes of recovery mass. You talk about PICA-X being lightweight and everything, which is great, but let's do the math. The Apollo CM heat shield was 1400 kg and covered a surface area of 11.95 square meters. The tank section and skirt of Starship, with no fairing at all, is 28 meters high, so covering one-half of it with TPS would mean 28 meters * pi * 4.5 meters = 396 square meters. Let's suppose PICA-X is half the weight of Apollo-era ablative TPS. 0.5 * 1400 kg * 396 m2 / 11.95 m2 = 23.2 tonnes. Let's be generous and say you can cut that in half again, both because Starship is fluffier than a crew capsule and because you only need to deal with LEO re-entry and not cislunar re-entry; that's still 11.6 tonnes, which is more than twice your estimate for total recovery mass.

But let's go with that. You've launched your stripped-down 9-engine Starship to LEO, and your 48.6-tonne payload capacity has been cut back to 37 tonnes due to TPS weight. How are you going to get it back down to Earth? You'll need deorbit propellant, about 100 m/s worth. That's about 3 tonnes. With 9 engines in the back and nothing in the front, Starship is a tail-first lawn dart, so you're going to need wings or flaps of some sort to keep the heat shield oriented properly. But let's pretend you don't need wings at all for attitude control (perhaps you have four mini-Raptor thrusters mounted dorsally?), and you're going to just land the whole thing with parachutes in order to avoid needing any more reserve propellant. You'll need a lot of parachutes. Total dry mass is now nearly as much as the Shuttle SRBs, which each required 3.5 tonnes worth of drogue and main parachutes in order to reduce splashdown speed to 23 m/s. Let's imagine those mini-Raptor thrusters you used for attitude control (using no propellant to do so) are going to provide your soft landing. If they're mounted dorsally, then you're looking at cosine losses of at least 30%. To get the 2+ gees required for an efficient landing, they'll need to produce a total of 123 tonnes of thrust plus another 43% to make up for cosine losses, so that's a total of 176 tonnes of thrust; if you can scale down the Raptors perfectly then you're looking at a total of 1.2 tonnes of engines.

Even though a smaller engine won't be as efficient as Raptor, let's pretend it will. Your isp of 330 s is cut back to 231 seconds due to cosine losses. Factoring in gravity drag and the need to cancel out residual horizontal velocity from the chutes, you'll need about three tonnes of propellant. You're also going to need some sort of landing gear, which is going to be around 2-3% of landed mass. Let's be friendly and call it 2%, so that's 1.3 tonnes. 

So your actual payload to orbit has been reduced from 48.6 tonnes to 25 tonnes. That's still something, right? Yes...but you have no fairing, no RCS, no propellant reserves for controlling re-entry attitude...nothing. And that's making all the assumptions in favor of the SSTO.

 

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 The key point is the large amount of payload lost for a TSTO due to unused propellant in the first stage during the ascent to orbit, since it has to be used for return to launch site. Elon has acknowledged this cuts full reusability payload by 50%. When you consider the lost payload for a SSTO due to reusability can be less than 10%, the reusable SSTO beats the reusable TSTO.

 The estimates of the dry mass of the Starship always is for the passenger version with the passenger quarters for ~50 colonists to Mars. That would not be the mass for the tanker version with just a big empty space where the passenger quarters would have been.

 SpaceX acknowledged this for the prior version the Interplanetary Transport System:

CE62-F1-EC-039-C-44-DF-9-D00-8-C38-E85-A

 

 Note the first stage already has a mass ratio of 25 to 1, sufficient for SSTO with significant payload. And the upper stage tanker version has mass ratio of 30 to 1, and would also be at 25 to 1 mass ratio when given further engines for ground launch.

    Robert Clark

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4 hours ago, Exoscientist said:

The key point is the large amount of payload lost for a TSTO due to unused propellant in the first stage during the ascent to orbit. . . .

A reusable first stage which uses a boostback and landing burn will have a lower total payload than one which is expended, yes.

4 hours ago, Exoscientist said:

Elon has acknowledged this cuts full reusability payload by 50%.

Reusing the first stage cuts into the payload of an existing TSTO architecture. And since an optimized TSTO architecture will have VASTLY higher payload than an SSTO of equivalent launch mass, losing 50% of your payload still beats out even an expendable SSTO.

4 hours ago, Exoscientist said:

When you consider the lost payload for a SSTO due to reusability can be less than 10%

It cannot.

And that's not even what your own numbers said. You said that the payload penalty would be 10% of the total vehicle dry mass, not 10% of the payload. If you have an SSTO that masses 70 tonnes dry and delivers 30 tonnes to LEO, and you want to claim that you can make that 70-tonne SSTO reusable by adding 10% of its dry mass, then you need 7 tonnes, which cuts your payload by 23%. Much more than 10%.

4 hours ago, Exoscientist said:

the reusable SSTO beats the reusable TSTO.

No, because even if your numbers were right (which they aren't), you're comparing apples and oranges. Even if it was true that an SSTO can be reused with only a 10% payload penalty and a TSTO requires a 50% payload penalty, which it isn't, that STILL doesn't mean the SSTO beats the TSTO, because the payload of the TSTO was already 3-4X greater than what the SSTO could manage. If your TSTO already delivers 3-4X more payload than an SSTO of equivalent size, then losing half of your payload mass STILL beats out the SSTO even before you apply the SSTO reuse penalty.

4 hours ago, Exoscientist said:

The estimates of the dry mass of the Starship always is for the passenger version with the passenger quarters for ~50 colonists to Mars. That would not be the mass for the tanker version with just a big empty space where the passenger quarters would have been.

The mass for the expendable version is 40 tonnes.

The mass for the tanker/cargo version is 85 tonnes.

The mass for the Mars transport passenger version is ~100 tonnes.

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Posted (edited)

Yes, the TSTO fully reusable payload of Starship Superheavy is ~150t. This is *already* with the reuse penalty applied.

Total mass to orbit is ~265t (150t payload plus 30t landing propellant + 85t ship). Assuming a 40% mass to LEO penalty from booster reuse, the total mass to LEO expendably would be 475t. With an expendable 40t ship with no landing fuel, fins, heat shield etc, that's an expendable TSTO payload of 435t.

That's your apple for comparison with the SSTO.

And now we go back and see that even expendably an SSTO Superheavy would put up *maybe* 50t expendably. Then we note that making Starship reusable (an equivalent task to reusing Superheavy SSTO)  more than doubles the structural weight, plus requires over 30t of reserved landing propellant and oh look we're all out of payload. Superheavy SSTO reusable doesn't close.

SSTO *never* wins against TSTO

Edited by RCgothic
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 I’ve acknowledged the expendable TSTO gets more payload to orbit than the expendable SSTO. The point I’m making is the reusable SSTO meets or exceeds the reusable TSTO payload. The reason is the fully reusable TSTO loses 50% of its payload due to the large amount of propellant that has to remain unused on ascent to orbit in order to cancel out the first stage forward motion and to boost it back to the launch site. Note this unused propellant is doubly disadvantage as far as orbital payload is concerned. First, it adds deadweight on ascent to orbit, and secondly it reduces the propellant load that can be used for that ascent.

 Elon has stated this reduction in payload on full reusability numerous times:

Replying to @PPathole and @SpaceX
Optimized, fully-reusable Starship is ~150t to same reference orbit as Saturn V. In expendable mode, Starship payload would be 250t to 300t.

 

  In contrast, the SSTO loses less than 10% of the dry mass on adding reusability systems, allowing it to meet or exceed the payload to orbit of the reusable TSTO. 

  Robert Clark

 

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5 minutes ago, Exoscientist said:

The point I’m making is the reusable SSTO meets or exceeds the reusable TSTO payload.

No. Not ever. This is honestly incoherent.

Any assumptions you make about the mass requirements for SSTO recovery also apply exactly to the TSTO version (except the booster would actually require less mass, as it is not doing EDL from orbit).

 

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21 minutes ago, Exoscientist said:

In contrast, the SSTO loses less than 10% of the dry mass on adding reusability systems, allowing it to meet or exceed the payload to orbit of the reusable TSTO. 

Correct me if I got the basic math wrong, but how can even an expendable Superheavy SSTO (with a payload capacity of around 50t, as mentioned before in this thread) exceed the 150t of the fully reusable Superheavy/Starship TSTO?

I won't even mention the 250 to 300 t of the expendable TSTO here...

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