SpaceX 'Star series' simulations

[OneSpeed]

The previous simulation was intended to explore the maximum possible envelope for a 200t dry mass Starship Mk1 with three 170t thrust Raptor engines, and a ceiling of 20kms. At full throttle, and a liftoff T/W of about 1.2, that allowed for about 250t of propellant.

However, the relevant Special Temporary Authority (STA) states:

Station Location

City	State	Latitude	Longitude	Mobile	Radius of Operation
Boca Chica	Texas	North  25  59  50	West  97  9  25	Boca Chica Pad Suborbital Test Veh Max Alt 22.5km	5.00

If the 'Radius of Operation' for communications is 5.00kms, and it is also the 'Radius of Operations' for the flight, then the envelope for the previous simulation would not be allowed. Also, having seen StarHopper fly twice now with throttle never exceeding about 70%, the Starship Mk1 test flight may use less than 100% throttle, and so the propellant load would need to be less than 250t. So, for this simulation, I'm assuming minimal downrange distance, and a maximum of 80% throttle. That allows for a GLOW of about 360t, and therefore 160t of propellant.

Some points of interest:

The simulation now displays both Inertial and Orbital velocities and accelerations (No more step change at the atmosphere height).
Maximum ascent velocity: Mach 1.34
Maximum descent velocity: Mach 0.83
Maximum acceleration: 1.85 gs
Terminal velocity on descent: 102m/s

The physics simulation in the recent Starship presentation has a terminal velocity of 66m/s. The difference could be largely down to the dry mass of Mk1 vs later variants (200t vs 105-120t).

[livingjw]

- Your drag seem low to me. On descent I picked off D=3081kN and q=7.1kPa. From these I calculated D/q=434m^2. This implies that CD is less than 1, since cross sectional area is greater than 434m^2. CD at 90 degrees should track similar to the chart below taken from Hoerner's drag book.

- You can use cross flow theory for obtaining CD and CL at any angles between ~55 degrees and ~125 degrees AoA which I believe is a good assumed range for SS. Use equation 23 to calculate CL and CD where CDbasic is the value from the first chart which is the CD at 90 degrees.

- Has anyone estimated the planform area?  I would guess it is in excess of 500m^2.

John

[OneSpeed]

- Your drag seem low to me. On descent I picked off D=3081kN and q=7.1kPa. From these I calculated D/q=434m^2. This implies that CD is less than 1, since cross sectional area is greater than 434m^2. CD at 90 degrees should track similar to the chart below taken from Hoerner's drag book.

- You can use cross flow theory for obtaining CD and CL at any angles between ~55 degrees and ~125 degrees AoA which I believe is a good assumed range for SS. Use equation 23 to calculate CL and CD where CDbasic is the value from the first chart which is the CD at 90 degrees.

- Has anyone estimated the planform area?  I would guess it is in excess of 500m^2.

John

Yes, my subsonic drag coefficient is closer to a constant 0.8, supersonic looks pretty close though. I'm actually treating the cross sectional shape including the flaps as more like a capsule, rather than a pure cylinder. Perhaps somewhere between the two is a better estimate?

Edit: just re-ran the sim with 105t dry mass, and 20t of landing propellant, and got a terminal velocity of 69m/s. Cd probably is a tad low.

[OneSpeed]

Now that we know that Starship orbital test launches are to be expected from Boca Chica, what would the minimum configuration be for such a test?

In particular, what if there was no payload? After some experimentation, I found that by reducing both the SS and SH propellant loads to about 2/3, it was no longer necessary for the Starship to have 6 engines. Even three is enough if you are prepared to let a 19 engine booster launch the ship into a relatively lofted trajectory.

Also, which stage is more likely to fail? The Super Heavy booster flight envelope is quite close to the Falcon 9 booster RTLS profile, and so not such a stretch goal. Starship orbital re-entry however, although similar in some ways to Shuttle, is new for SpaceX. By minimising the Starship engine count, perhaps the cost of failure can be reduced a little?

Raptor performance appears to be in a rapid state of flux, so it is difficult to say what performance will be available for the first orbital test. Anyway, I had to pick something, and the configuration in this simulation is:

Engine counts: SH 7 x 200t with gimbal, 12 x 250t fixed, SS 3 x 200t with gimbal.
Dry masses: SH 230t, SS 120t
Prop loads: SH 2200t, SS 700t

[envy887]

Thanks for sharing that, and nice work! Can you also do one with booster ASDS landing?

I'd expect initial SuperHeavy landings on orbital attempts to be at sea, as indicated in the EA for launching Starship from KSC. ASDS landings have lower environmental impact, lower risk to on-shore infrastructure, which means less insurance cost and better chance of getting a launch license, and also higher performance, which means less liftoff mass and fewer engines, or higher margins.

[OneSpeed]

Thanks for sharing that, and nice work!

Thanks for the feedback!

Can you also do one with booster ASDS landing?

I'd expect initial SuperHeavy landings on orbital attempts to be at sea, as indicated in the EA for launching Starship from KSC. ASDS landings have lower environmental impact, lower risk to on-shore infrastructure, which means less insurance cost and better chance of getting a launch license, and also higher performance, which means less liftoff mass and fewer engines, or higher margins.

All good points, but would the offshore platform at KSC necessarily be an ASDS? A fixed or floating platform say 20km offshore would cover most of the environmental concerns, but would make little difference to performance to orbit. Nevertheless, let's say they had a spare drone ship. Current F9 landings are certainly accurate enough, and the extra mass of the Super Heavy would not be noticed by an ASDS which can displace 20,000t+ of seawater.

So, again, after some experimentation, and with some slightly tighter margins, here's what the sim suggested:

Engine counts: SH 7 x 200t with gimbal, 6 x 250t fixed, SS 3 x 200t with gimbal.
Dry masses: SH 230t, SS 120t
Prop loads: SH 1600t, SS 600t

So, a saving of 6 Raptor engines, and about 700t of propellant.

[sdsds]

Attached is a visualization of the possible downrange landing location.

Recent comments from Musk suggest the production version of SH might have a center cluster of 8 engines. So a plausible SH prototype might have only those 8, and none on the outer ring. Is it right to think that would change the propellant loading only a little? Would it lead to any significant changes in the flight profile, e.g. conditions at stage sep or downrange distance to the landing location?

[OneSpeed]

Recent comments from Musk suggest the production version of SH might have a center cluster of 8 engines. So a plausible SH prototype might have only those 8, and none on the outer ring. Is it right to think that would change the propellant loading only a little? Would it lead to any significant changes in the flight profile, e.g. conditions at stage sep or downrange distance to the landing location?

It might be helpful to consider the conditions at liftoff. A rocket's thrust needs to exceed the mass of the vehicle to fly, in Starship's case by a factor of 1.5 or so. So, eight 210t thrust engines, giving 1,680t of thrust might be suitable for a gross lift of weight (GLOW) of around 1,120t. Adding another 20 300t engines would increase the thrust to 7,680t, for a GLOW of perhaps 5,000t. If the dry mass plus payload of the rocket is say 350t, then the difference in propellant loading is from 1,120 - 350 = 770t to 5,000 - 350 = 4,650t, six times greater.

Mainly because of the resultant differences in percentage mass fraction, the differences in flight profile would also be very significant. Hope this helps

[sdsds]

Good point: it certainly helps if the rocket can get off the ground!

A lift-off T/W ratio of 1.5 seems quite conservative though. 1.15 isn't outside the realm of possibility.

[envy887]

Good point: it certainly helps if the rocket can get off the ground!

A lift-off T/W ratio of 1.5 seems quite conservative though. 1.15 isn't outside the realm of possibility.

The reason for the high acceleration is to minimize the distance traveled during the first stage burn, reducing the fuel needed for booster RTLS. RTLS is a big deal for refueling launch turnaround time.

[abaddon]

For a point of comparison, based on Wiki I calculated the following thrust-to-weight ratios here: https://forum.nasaspaceflight.com/index.php?topic=46338.msg2081947#msg2081947:

Delta IV Heavy: 1.32
F9 Block 5: 1.42
Falcon Heavy: 1.65

[OneSpeed]

Here is a simulation of the upcoming Starship SN8 flight to 20kms altitude and return, assuming a 120t dry mass, significantly less than the 200t of Starship Mk1. We know SN8 will have three SL Raptor engines, but the sim showed that these would provide much more thrust than necessary to complete the mission. However, by running the engines at roughly 2/3 of full thrust, this mitigates the risk of a single engine failure. If the SN8 dry mass is as low as estimated, then a propellant load of as little as 100t would be sufficient.

[livingjw]

Here is a simulation of the upcoming Starship SN8 flight to 20kms altitude and return, assuming a 120t dry mass, significantly less than the 200t of Starship Mk1. We know SN8 will have three SL Raptor engines, but the sim showed that these would provide much more thrust than necessary to complete the mission. However, by running the engines at roughly 2/3 of full thrust, this mitigates the risk of a single engine failure. If the SN8 dry mass is as low as estimated, then a propellant load of as little as 100t would be sufficient.

What was your subsonic 90 deg drag coefficient?

John

[Twark_Main]

Here is a simulation of the upcoming Starship SN8 flight to 20kms altitude and return, assuming a 120t dry mass, significantly less than the 200t of Starship Mk1. We know SN8 will have three SL Raptor engines, but the sim showed that these would provide much more thrust than necessary to complete the mission. However, by running the engines at roughly 2/3 of full thrust, this mitigates the risk of a single engine failure. If the SN8 dry mass is as low as estimated, then a propellant load of as little as 100t would be sufficient.

What was your subsonic 90 deg drag coefficient?

John

Working backwards from drag force and dynamic pressure, it looks like the drag area at 90.1 degree AoA and M = 0.62 is about 432 m². Just plug in your estimate of frontal projected area to work out the drag coefficient.

[OneSpeed]

What was your subsonic 90 deg drag coefficient?

At 500m altitude in the sky diver orientation it is 0.965 form drag plus 0.002 for skin drag. This gives a velocity of 81m/s before rotation commences, somewhat higher than the 66m/s reached in the 2019 SpaceX simulation. However, my ship dry mass estimate is 120t, and the long term goal for Starship is more like 105t. As well, I'm carrying about 34t of propellant as ullage, and most of this is for ballast. To avoid landing off vertical like SN5 and 6, I'm running the three SL Raptors at 50% throttle for landing (apparently lower than that there is chugging). Even with 34t of ballast, that is a 1.7g hoverslam, quite a bit higher than for the Falcon 9 booster.

So, in short, I realise my terminal velocity seems high, but if the upcoming test confirms it, I'll certainly update the model to match.

[Twark_Main]

What was your subsonic 90 deg drag coefficient?

At 500m altitude in the sky diver orientation it is 0.965 form drag plus 0.002 for skin drag. This gives a velocity of 81m/s before rotation commences, somewhat higher than the 66m/s reached in the 2019 SpaceX simulation. However, my ship dry mass estimate is 120t, and the long term goal for Starship is more like 105t. As well, I'm carrying about 34t of propellant as ullage, and most of this is for ballast. To avoid landing off vertical like SN5 and 6, I'm running the three SL Raptors at 50% throttle for landing (apparently lower than that there is chugging). Even with 34t of ballast, that is a 1.7g hoverslam, quite a bit higher than for the Falcon 9 booster.

So, in short, I realise my terminal velocity seems high, but if the upcoming test confirms it, I'll certainly update the model to match.

This suggests you're assuming a frontal cross section of 447 m², correct?

[Okie_Steve]

Attached is a visualization of the possible downrange landing location.

The Gulf of Mexico get deep fairly quickly along the Texas coast but there is a shelf that continues from the Yucatan peninsula and reaches further North than Cuba. Also the West Florida Shelf is about the size of the peninsula. Depending on your definition of shallow/deep there are lots of places in the gulf for a platform, but there in the middle it is 4000+ meters deep. Definite ASDS territory there.

[OneSpeed]

This suggests you're assuming a frontal cross section of 447 m², correct?

At that altitude and velocity, yes. The drag coefficients and cross sectional areas are constantly being re-calculated by SpaceSim, based on local velocity, density and viscosity, as well as the shape and orientation of the components. The program has been tweaked over time by comparing it to as many real rocket launches as possible, and so the calculated cross sectional area may be slightly different from the planform area at any point in time. Further tweaking may well be required for the Starship model. If you are interested, an earlier version of the C# program source code is available at: https://github.com/zlynn1990/SpaceSim

[vaporcobra]

Given the knowledge that Raptor is currently limited to ~90 seconds of continuous operation at 300 bar, it would be interesting to see what the absolute ceiling of performance is if you assume that neither Super Heavy or Starship can burn for longer than that uninterrupted. Or, say, if current longevity permitted several more minutes of operation but only at ~80% throttle or ~250 bar. Basically, what's possible within those known or estimable constraints

[steveleach]

Given the knowledge that Raptor is currently limited to ~90 seconds of continuous operation at 300 bar, it would be interesting to see what the absolute ceiling of performance is if you assume that neither Super Heavy or Starship can burn for longer than that uninterrupted. Or, say, if current longevity permitted several more minutes of operation but only at ~80% throttle or ~250 bar. Basically, what's possible within those known or estimable constraints

It would be more accurate to say that the Raptor they tested was limited to ~90 seconds of operation at 300 bar.

The design is evolving all the time though. That test will have told them what failed, and they will now be working on ways to make that component survive longer. Then they will retest, and see what component to work on next. Rinse and repeat.

Only when they can't economically improve things significantly will we be able to say what the actual limitations are.