Author Topic: Estimating second stage empty mass from new performance data  (Read 4676 times)

Offline LouScheffer

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With the new performance data, we can try again to estimate the empty mass of the second stage.

My first thought was this - use the delta-V from a parking orbit to a minimal GTO orbit to estimate the empty mass.   The SpaceX web site says the GTO numbers are with a 175 km perigee, and from a 175x175 to a 175x35786 orbit is 2463 m/s.  So you can ask what the empty mass must be such that an 8.3t payload gives 2463 more m/s than a 22.8t payload.

But this is not quite right.  The first stage will have higher performance with the lighter load.  Assuming the first stage has 394t of fuel, an empty mass of 29t, and the second stage minus the payload is 120t (fuel + empty stage + fairing) then the booster will get an extra 189 m/s with the lighter load.  So now the difference is 2274 m/s. 

Next, the web site does not quote the exact LEO orbit.   It's surely higher than 175x175 km, though, since this orbit would decay in a few days.  About 300x300 km seems the minimum reasonable, with month-ish lifetimes.  This requires about 73 m/s more than the 175x175, again reducing the difference, now to 2200 m/s .

Now we can do the calculation.  At an ISP of 348, fuel of 111t, what empty mass do you need to get a 2200 m/s difference between an 8.3mt and a 22.8 mt payload?  Turns out it's 4.54t, giving 5530 m/s in one case and 7730 m/s in the other.  As a double check, this ISP and empty mass, and a 2463 m/s burn, gives a fuel mass of 13.6t and a total mass, in parking orbit, of 26.3t.  This seems plausible for on-orbit mass, and the LEO velocity in the 22.8t case is likewise plausible.

Re-doing these same calculations with a plus-or-minus 50 m/s range (2150 to 2250 m/s difference) gives second stage empty masses ranging from 4.18t to 4.91t.  So it seems likely the empty mass is in this range, with a best guess of 4.54t.


Offline sewebster

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The LEO and GTO inclinations are a bit different too on the page...

Offline LouScheffer

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The LEO and GTO inclinations are a bit different too on the page...
Yes, it always pays to reduce the inclination at least some on every burn.  This is because (for small angles) you can get a significant sideways components (sin(theta)) for a very small reduction in your main burn (cos(theta)).  But the effect on the main direction is small.

Here we have a 1.5 degree course change in a 7800 m/s burn.  To first order, this will  pick up 7800*sin(1.5 degrees) = 204 meters of sideways velocity, and still increase speed by 7800*cos(1.5 degree) = 7797 m/s.  So you lose only 3 m/s of orbital velocity, way down in the noise for the accuracy of the calculations here.

This calculation is for the ideal case of a single impulse burn directly over the equator.  The real calculation will be more complex and somewhat less efficient, but the difference should still be small.


Offline edkyle99

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Here is a quickie spreadsheet guess for an 8.3 tonne GTO mission, with the first stage boosting 120 tonnes to staging per Elon Musk's press conference statement.  That 0.96 PMF seems necessary, which is remarkable when comparing these stages to others from the past.  I've assumed identical mass ratios for both stages, which of course is a hand waving estimate.  The first stage PMF is likely higher than the second stage PMF. 

 - Ed Kyle


        Falcon 9 v1.2+ 2016 est         5/2/2016
        Masses and Forces in Metric Tons (Tonnes), Velocity in Meters/Second         
PMF             GLOW            Mpusuable       Mfinal          Thrust   Isp
0.96    Stage 1 424.6237338     407.6387844     16.98494935     775      302
0.96    Stage 2 111.7           107.232         4.468            95      348
        Fairing 2.0               
        Payload 8.3               
                     
                        Mi              Mf              Delta-v         Burn Time       T/W             GLOW-PL
        Flight Stg 1    546.6237338     138.9849494     4054.929359     158.8476295     1.417794274     536.3237338
        Flight Stg 2    120              12.768         7645.06926      392.8077474     0.791666667   
        Total                                          11699.99862      
« Last Edit: 05/02/2016 02:29 pm by edkyle99 »

Offline cambrianera

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For reference, Falcon91.0 second stage was 2957 kg
http://forum.nasaspaceflight.com/index.php?topic=28882.msg915790#msg915790
Assuming:
!450 kg domes (Al-Li 12 mm thick)
600  kg side skin (Al-Li 5 mm thick)
700  kg engine
200   kg others

Falcon9 1.1 second stage could be
1450 kg domes (same as v1.0)
1300 kg side skin (more than double)
700  kg engine (same as v1.0)
350  kg others (some more helium)
3800 kg

For Falcon FT lenght is 20% more (and helium must be more) therefore something like 4100-4200 kg
Oh to be young again. . .

Offline S.Paulissen

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For reference, Falcon91.0 second stage was 2957 kg
http://forum.nasaspaceflight.com/index.php?topic=28882.msg915790#msg915790
Assuming:
!450 kg domes (Al-Li 12 mm thick)
600  kg side skin (Al-Li 5 mm thick)
700  kg engine
200   kg others

Falcon9 1.1 second stage could be
1450 kg domes (same as v1.0)
1300 kg side skin (more than double)
700  kg engine (same as v1.0)
350  kg others (some more helium)
3800 kg

For Falcon FT lenght is 20% more (and helium must be more) therefore something like 4100-4200 kg

This is a small difference but Merlin 1D (470kg) is significantly lower mass than Merlin 1C (520kg back calculated from data from the same wiki article).  I only mention it because for stage 2 mass-payload is 1:1.

Quote from: wikipedia
In June 2015 Tom Mueller answered a question about the Merlin 1D thrust-weight ratios on Quora. He specified that the Merlin 1D has a weight of 1,030 lb (470 kg) including thrust actuators, a current vacuum thrust of 162,500 pounds-force (723 kN), and an uprated vacuum thrust of 185,500 pounds-force (825 kN), which still weighs the same.

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Offline jrasor

Anybody have a firmer figure for mass of Merlin 1D FT vacuum? Cambrianera estimates 700 kg for that. 1D FT regular version masses 470 kg.

Offline Dante80

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Anybody have a firmer figure for mass of Merlin 1D FT vacuum? Cambrianera estimates 700 kg for that. 1D FT regular version masses 470 kg.


Welcome to the forums, jrasor.

We don't really have much info on the MVac mass. It is definitely a lot more than the M9, since the engine bell is enormous. 700kg should be inside the ballpark for that.

Offline cambrianera

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As Dante80 said not so much info.
The value I gave is a guess (like the other estimates in my previous post).
Please consider that Merlin 1C was at 600 kg (wiki says 630)
M1D is lighter mainly due to the loss of the thrust structure (heritage of Falcon1) thanks to the adoption of the octaweb.
But thrust structure of M1C VAC and M1D VAC should be fairly similar.
All in all, I think 700 kg is a good approx for both, on minus side for M1C VAC, on plus side for M1D VAC.
In the pic you can compare M1C with M1C VAC.

(and here M1C VAC is shown without the niobium bell)
 
« Last Edit: 06/20/2016 07:14 pm by cambrianera »
Oh to be young again. . .

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