*Copyright 2022 Robert Clark*

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:

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: henry@spsystems.net (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 <kemJ2.876$Vc2.18603@news-west.eli.net>,

Larry Gales <larryg@u.washington.edu> 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 henry@spsystems.net

weren't. | (aka henry@zoo.toronto.edu)

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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