Falcon 9 expendable performance and re-use penalty estimated from SES-9 mission

[LouScheffer]

Since SES-9 used the full performance of the second stage, we are now in a better position to estimate the expendable performance.

We know the re-entry burn lasted 17 seconds, and the three engine landing an estimated 5 seconds.  That is 66 seconds of extra engine thrust.  At full throttle each engine takes 270 kg/sec, so that's about 18000 kg of fuel.  Assuming an empty first stage masses 30t, and the top stack 126t (one tonne more than Musk said, since we know that in this case the payload is slightly bigger), that's a mass ratio of 1.1154 .  At an ISP of 311 that's an extra delta-V of 332 m/s.

In a previous thread we estimated the delta-V imparted by the second stage at 8314 m/s, with a starting mass of 121t (125 as stated by Musk, minus 4 for the fairing) and a burnout mass of 10,560 kg.   If instead we assume 7983 m/s (332 m/s less), and a starting mass of 122t (since the satellite is about 1t more) we get a burnout mass of 11,742 kg, or 1182 kg more.  Since we know SES massed 5271 kg, that's a 6453 kg payload.

SES-9 represents about the least possible payload penalty, assuming they can get the suicide slam to work.   If they can do 6450 expendable, and 5271 recoverable, that's an 18% penalty for downrange recovery.

These calculations use pretty conservative values (30t first stage empty, 640 m/s gravity loss, 18000 kg fuel).  They are quite insensitive to first stage empty mass (changing empty 1st stage to 25t only changes payload by 36 kg).  They are also insensitive to  assumed gravity loss (which largely cancels out) and second stage empty mass (which cancels entirely).   They are reasonably sensitive to fuel reserved for landing - if they reserved 2000 kg more, then the expendable payload becomes 6600 kg.   If you turn all the knobs to their optimistic setting, and note the SES-9 orbit was slightly super-synchronous, and you can burn the first stage to depletion (a bad idea if you are landing), you MIGHT get up to 6800 kg.

So the expendable version can deliver at least 6450 kg to a (-1800 m/s) GTO, and maybe as much as 6800 kg, if all the stars align.

[cartman]

Lets say they reserved 2 tonnes more propellant for a less extreme landing, how much would that affect the payload?

[AncientU]

Since SES-9 used the full performance of the second stage, we are now in a better position to estimate the expendable performance.

<snip>

So the expendable version can deliver at least 6450 kg to a (-1800 m/s) GTO, and maybe as much as 6800 kg, if all the stars align.

Thanks for the above calculation... 6.4-6.8 tonnes is quite respectable indeed, as is 5+ tonnes reusable.

Using same calculations, what delivery to LEO (pick an orbit) can the expendable handle?

Note: Got trashed a couple days ago stating that F9-FT could do 20 tonnes to LEO expendable (based on 16.6t per NASA listing x 1.3 -- 30% advertised increase for FT).

[nadreck]

Using same calculations, what delivery to LEO (pick an orbit) can the expendable handle?

I get 23t working it from those numbers.

[LouScheffer]

Since SES-9 used the full performance of the second stage, we are now in a better position to estimate the expendable performance.

<snip>

So the expendable version can deliver at least 6450 kg to a (-1800 m/s) GTO, and maybe as much as 6800 kg, if all the stars align.

Using same calculations, what delivery to LEO (pick an orbit) can the expendable handle?

Let's use the parking orbit (28.5 inclination, about 300km average altitude) since that is easiest.  From this parking orbit to GTO takes about 2350 m/s.  At an ISP of 348, that's a mass ratio of 1.99.  Using middle estimates of 5.5t for the stage and 6.5t for the satellite, that's 12t at burnout, hence the stack massed just under 24t when in parking orbit.  However, 5.5t of this is the second stage, so the max payload would be about 18.5t.  As always, there are lots of assumptions baked into this number.

[LouScheffer]

Lets say they reserved 2 tonnes more propellant for a less extreme landing, how much would that affect the payload?

If they substituted a normal one-engine landing burn on SES-9, it would have taken 17 sec x 3 engines, plus 30 sec x 1 engine, for a total of 81 engine-seconds, or 22000 kg.  That means 70 m/s less from the first stage, and about 240 less kg payload.

A middle ground such as you suggest means 35 m/s less from the first stage, and about 120 kg less payload.

[Remes]

Using same calculations, what delivery to LEO (pick an orbit) can the expendable handle?

I get 23t working it from those numbers.

Am I missing something or is that more than an Ariane 5 or an Atlas 5 with 5 solids could lift?

so the max payload would be about 18.5t.

That would be about 10% less then an Ariane 5 or A552 could lift.

[nadreck]

Using same calculations, what delivery to LEO (pick an orbit) can the expendable handle?

I get 23t working it from those numbers.

Am I missing something or is that more than an Ariane 5 or an Atlas 5 with 5 solids could lift?

In the case of an Atlas 5 the upper stage is much smaller but has a higher ISP. So as you increase the payload you are decreasing the fuel mass fraction much faster. Shaving 2,500m/s Δ-V off a H₂ and LOX stage with and ISP of 450 where the prop mass is 20t, structure is 2.5t and the payload is 8t  means going from a ΔV of 4700m/s at a mass ratio of 2.905 to 2200m/s which implies a mass ratio of 1.65 which means that 20t is .65 * payload plus structure or 27t payload.  However that does not account for the lower performance of the boosters and first stage with the heavier upper stage and as the amount their mass ratios change as you increase payload is much greater than the change on a Falcon with a so much more massive 2nd stage.  Which is how you end up with the Atlas 5 being quoted at about 19t.  The Ariane 5 using the H₂ and LOX upper stage would have a simillar performance hit and using the hypergolic upper stage would would equal the F9 GTO performance (ok just slightly exceed the F9) but be over 20t to LEO.

so the max payload would be about 18.5t.

That would be about 10% less then an Ariane 5 or A552 could lift.

I think that is equal to the 551 capability, but note that Lou's calculation was based on how much mass made it to LEO when a GTO bird was launched and added that as payload. In reality the extra fuel that made it to LEO would be burned on the way to LEO and it would allow for a slightly larger payload to LEO, which is where I got my 23t.

[Robotbeat]

Atlas V 551 only gets 18305kg to 200km, 28.5degrees LEO according to elvperf.ksc.nasa.gov . Most likely F9 full thrust is more capable than that in fully expendable mode (Atlas V pulls ahead again at higher energy orbits).

[John Alan]

Note... I asked Chris B. before bring this thread back from the dead... 

Question...
Now that SpaceX has flown 7 more times and we are 10 months later... since this was discussed in some detail...
And now that it's confirmed that expendable missions like EchoStar 23 and Inmarsat 5 F4 are coming up...

Are the numbers posted above as to expendable performance... still the consensus of all???
In other words... will the hardware about to be flown meet or exceed these numbers posted 10 months ago??

[LouScheffer]

The numbers don't change much with our most recent data.  The SES-9 mission had a 5.27t payload, about 66 sec of remaining burn (3 x 17sec + 3 x 5sec), which would mean 18000kg of fuel for landing.  On one of the landing flights, Hans quoted a 27t landing weight, which we were guessing at before.

So we start by figuring the basic performance for the SES flight, using our best assumptions (436t fuel, 311 ISP, first stage at burnout = 45t (27t structure + 18t fuel)).  Second stage fuel 111.5, empty 4.5, fairing 4t (carried only by first stage), ISP 348.  In this case first stage delta-V = 3868 m/s and second stage is 8590 m/s.

Now for fully expendable, max payload, the second stage performance will go down (since the payload is more), but the first stage performance will go up.   The mass of the first stage at burnout leaves no fuel for descent (which reduces empty mass to 27t).  In addition there are no legs (known to be about 2t) and no grid fins & thrusters (maybe 1t, better guesses welcome).  So the burnout mass should be about 24t.

Using these numbers, I get about 6200 kg expendable.  At this mass, the second stage supplies 280 m/s less, and the first stage 280 m/s more, for the same final orbit as SES-9.

I can't see any way to make this consistent with the SpaceX web site claim of 8.3t for expendable.  If Falcon-9 can do 8.3t expendable, then SES-9 should have been a piece of cake, with plenty of reserves for recovery.  Alternatively, if 5.3t SES-9 was right on the edge of recovery, them I can't see 8.3t getting to GTO at all (I get almost a 600 m/s deficit compared to SES-9).   Maybe the 8.3t is for the fabled Block 5, even fuller thrust, no kidding this time, version.

[gongora]

The numbers on the SpaceX site are not for the current vehicle, they should be the initial estimate for block 5.

[John Alan]

So how does block 5 get them to 8.3t expendable?
Based on where we seem to be at now with block 3 at ~6.2t expendable...

Does cranking S1 thrust to nearly 2,000,000 lbs gain that much getting out of the gravity well?
Are the new legs rumored that much lighter? (like zero?)... That can't be all of it!...
They take weight out of S2 somehow?... where did they find 2t?
Weight out of S1... what 6+t?

The one thing that keeps bugging me is this "helps with S1 recovery and reuse"
How... How do you do that... I asked myself...
Slow down your staging speed... I said to myself...

<lightbulb> 

Would SpaceX be so bold as to shorten S1 and lengthen S2 to rebalance the fuel load?
Stage sooner and slower... Have S2 do more of the delta V to orbit?
Same overall length... just move the joint and middle umbilical hookup at S2?
Same Fuel and LOX load... just rebalanced... 8.3t expendable quoted...
Maybe 6t GTO w/barge landing?

It that the real fix called block 5?
NAH... that can't be... that can't be it... can it??   

[Robotbeat]

Increasing the thrust of the first stage lowers gravity losses which lowers the delta-v needed to get to orbit. Instead of 9.3km/s, maybe 9.2 or 9.1. And it may also increase Isp due to higher chamber pressure.

Another thing: they reduced the hold-down time, which should increase performance.

[Sohl]

<lightbulb> 

Would SpaceX be so bold as to shorten S1 and lengthen S2 to rebalance the fuel load?
Stage sooner and slower... Have S2 do more of the delta V to orbit?
Same overall length... just move the joint and middle umbilical hookup at S2?
Same Fuel and LOX load... just rebalanced... 8.3t expendable quoted...
Maybe 6t GTO w/barge landing?

It that the real fix called block 5?
NAH... that can't be... that can't be it... can it??   

I dunno, but I've also wondered why the current S1 vs. S2 ratio is set the way it is, especially considering the frequency of GTO versus LEO missions.  If recoverability is a goal, why not make the staging lower and slower?  It seems there would be enough ISP and fuel mass fraction in a longer S2 to get to GTO pretty well, but I haven't done the math. It would make S2 a bit more expensive, and that is being thrown away, but I think it would pay back in terms of having easier barge recoveries or more RTLS flights.

[Lar]

Interesting trade, is it worth throwing away a larger S2 if it makes recovery of a now somewhat less valuable S1 easier on average? I'd opine if that was the only reason, no. But if it also increases the payload to GEO or GTO then maybe. 

Balance that against the fact that they are probably going to be doing a LOT of LEO launches soon as CommsX ramps up and maybe it's not such a good trade? Larger value fraction in the recoverable part seems more important?

[John Alan]

The cost of say 10ft worth of tankage wall moved from S1 to S2 (and then expended) can't be that much...
Can it...??
 

[Stan-1967]

Very interesting trade.  It's not just moving 10 ft ( or whatever amount) of tankage between S1 & S2 to get better mass staging ratios, I think the advantage of the M1-Vac burning at 348s ISP vs. 311 ISP would be the big kick additional performance. 

So a good question to figure out would be the altitude at which you can have a clean staging event, and ignition of S2 can take place without increasing too much gravity loss from the lower T/W of S2?

[cambrianera]

Already done guys.
Moving from v1.0 to v1.1 staging speed changed from 3000 m/s to 2000 m/s.
Less than this?

[MP99]

Increasing the thrust of the first stage lowers gravity losses which lowers the delta-v needed to get to orbit. Instead of 9.3km/s, maybe 9.2 or 9.1. And it may also increase Isp due to higher chamber pressure.

Another thing: they reduced the hold-down time, which should increase performance.

Alternatively, could they be thinking of leaving the first stage length unchanged, and extending the length of the second stage so as to "use up" the additional thrust of the M1 SL, IE keep the liftoff T/W unchanged? (Or, a 5m S2 which could be shorter while carrying a greater kerolox prop mass?)

A larger S2 would also be great for FH performance. Maybe even a longer 5m S2 for FH Mars missions?

Cheers, Martin