Author Topic: Calculating second stage performance and mass from Inmarsat mission  (Read 11171 times)

Offline OneSpeed

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What's the duration of the burn?

About a minute. For what it's worth, here is the output from my Inmarsat-5 sim. The orbit at SECO1 is about 160 x 590 kms, and mass is 25.5mT. At SECO2, mass is 11.6mT. A 4° plane change from 28.5 to 24.5° would require an additional 540m/s, for a burn to depletion S2 total of 9.9mT. Subtracting 6.1mT for the satellite, gives 3.8mT S2 dry mass, a touch lower than I would have expected.

Offline LouScheffer

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The stage final mass may be quite sensitive to the throttle setting, but then so is the corresponding initial propellant load -- and you have some better constraints on the initial propellant load, right? 
Unfortunately, the initial propellant load is not well constrained either.  We have three factoids, none very accurate.

(a) An environmental impact statement for the original Falcon 9 specified 80,000 kg fuel+lox.  However, since then they have stretched the stage and densified the fuel and LOX, with neither of these quantified.

(b) Elon stated that the first stage is pushing 125 tonnes to MECO.   This includes the fairing, the second stage, the payload, and the fuel.  The fairing is unknown, the particular payload was not specified, and 125 is a round-ish number.   One set of guesses is fairing = 4t, payload 5t, second stage 4.5t, fuel 111.5t.  This adds up to 125t, but the sum was not really specified to this precision.

(c) The SpaceX web site quotes a second stage ISP of 348 and a thrust of 934,000 N, and a burn time of 397 seconds (accurate from the webcast).  The ISP and thrust gives a flow of 273.8 kg/sec, which times 397 gives 108.7t.  But this seems too low..  If the second burn is really conducted at roughly 80% throttle, it's even worse, giving 105t total fuel.  Furthermore, the first stage is spec'ed at 8,227,000 N, 9 engines, ISP=311.  This gives a flow of 299 kg/sec/engine.  The two engines are thought to use the same turbopump and thrust chamber, so the flow could be higher, but maybe the throttle range is less.

So overall the fuel load seems like about 110t, but it's not well constrained.

Offline LouScheffer

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[...] For what it's worth, here is the output from my Inmarsat-5 sim. The orbit at SECO1 is about 160 x 590 kms, and mass is 25.5mT. At SECO2, mass is 11.6mT. A 4° plane change from 28.5 to 24.5° would require an additional 540m/s, for a burn to depletion S2 total of 9.9mT. Subtracting 6.1mT for the satellite, gives 3.8mT S2 dry mass, a touch lower than I would have expected.

The plane change plus the GTO injection sum as vectors, not as scalars, and they are at right angles.  From this orbit, straight GTO injection needs about 2400 m/s.  Adding 540 m/s at right angles means a total burn of sqrt(2400^2 + 540^2) = 2460 m/s.  So adding the plane changes needs only an additional 60 m/s.   That should give a more realistic second stage mass.

Offline OneSpeed

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The plane change plus the GTO injection sum as vectors, not as scalars, and they are at right angles.  From this orbit, straight GTO injection needs about 2400 m/s.  Adding 540 m/s at right angles means a total burn of sqrt(2400^2 + 540^2) = 2460 m/s.  So adding the plane changes needs only an additional 60 m/s.   That should give a more realistic second stage mass.

Yes, I was treating them as two separate burns. Combining them would be only 200kg of fuel, making S2 5.3mT dry.

Offline LouScheffer

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The http://www.spacex.com/falcon9SpaceX web site says the second stage has ISP 348, burn time 397 seconds, and thrust 934000 N.  The burn time appears accurate for this mission 5:42 for the first burn, 56 seconds for the second, according to the press kit, for a total of 398 seconds.  The actual GTO burn was a few seconds longer, which makes sense for a burn to depletion using the last 1% or so.

But the evidence above is pretty strong that the actual thrust during the GTO burn is quite a bit less than the 934kN quoted, at least 10% less.  Possible explanations are that it is a block 4 engine but the web site spec is for a block 5, or that they throttle it back for reliability. 

But this contradicts the burn time.  If the tank is sized for 934 kn at 397 seconds, then at 10% less thrust you should run for 10% (40 seconds) longer, but it didn't.  (In theory, your ISP could be correspondingly less, but it's unlikely to vary that much between versions.)

My first thought is that only the second burn operates at reduced thrust, which would reduce the discrepancy.   But the end of the first burn (where gravity effects are minimal) is at 32 m/s^2, just like the start of the second burn.  So both burns seem to be operating at the same reduced thrust.

One possible explanation is that they don't fill the tank completely when using non-block 5 engines.  This would give up performance and margin for no reason, and I don't believe it.   More likely, in my mind, is that the web site is wrong, with a mixture of block 5 specs (thrust) and block 4 specs (burn time).  This is an occupational hazard of tea-leaf reading using public-facing web sites as a data source.

Offline envy887

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The 934 kN thrust has been listed since 2015 when v1.2 specs were first posted. I rather doubt they were looking forward to Block 5 way back then.

Does the data fit better if this was not in fact a burn to depletion, and there was 2,000 kg (or any arbitrary number) of propellant left at the end of the second burn?

Offline Semmel

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We have seen that the second stage throttles down before. See the attachments to my post here:

[...]

PS: Sorry, still no time to do programming at home and advance the script.

@edit: added the plot for convenience.
« Last Edit: 06/22/2017 01:12 pm by Semmel »

Offline llanitedave

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The 934 kN thrust has been listed since 2015 when v1.2 specs were first posted. I rather doubt they were looking forward to Block 5 way back then.

Does the data fit better if this was not in fact a burn to depletion, and there was 2,000 kg (or any arbitrary number) of propellant left at the end of the second burn?


One would think that there would be reserve propellant in the second stage to make up for potential shortfalls in first stage performance, although maybe the flyback and landing propellant constitutes all the reserve.
"I've just abducted an alien -- now what?"

Offline envy887

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The 934 kN thrust has been listed since 2015 when v1.2 specs were first posted. I rather doubt they were looking forward to Block 5 way back then.

Does the data fit better if this was not in fact a burn to depletion, and there was 2,000 kg (or any arbitrary number) of propellant left at the end of the second burn?


One would think that there would be reserve propellant in the second stage to make up for potential shortfalls in first stage performance, although maybe the flyback and landing propellant constitutes all the reserve.

Inmarsat was an expendable mission, so there was no landing reserve for the booster. We assumed the second stage was a burn to depletion, but several things make more sense if it wasn't:
1- The apparent "excess" mass in the second stage.
2- The accuracy of the injection to the predicted orbit. Depletion burns tend to vary a bit.
3- The apparent gain in performance for Block 5.

Offline LouScheffer

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We have seen that the second stage throttles down before. See the attachments to my post here:

[...]

PS: Sorry, still no time to do programming at home and advance the script.

@edit: added the plot for convenience.
The M1D throttle change is pretty small (perhaps 4-5%).  Perhaps it's a mixture ratio switch.  In Apollo, they ran the second stage with a "maximum thrust" mixture ratio for the first part of the burn (where gravity losses are most important), then switched to a lower-thrust, maximum ISP mixture ratio for the rest of the burn.  ( Described here.)  This would generate a profile just like that shown in the plot.

Offline intrepidpursuit

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We have seen that the second stage throttles down before. See the attachments to my post here:

[...]

PS: Sorry, still no time to do programming at home and advance the script.

@edit: added the plot for convenience.
The M1D throttle change is pretty small (perhaps 4-5%).  Perhaps it's a mixture ratio switch.  In Apollo, they ran the second stage with a "maximum thrust" mixture ratio for the first part of the burn (where gravity losses are most important), then switched to a lower-thrust, maximum ISP mixture ratio for the rest of the burn.  ( Described here.)  This would generate a profile just like that shown in the plot.

That also answers the question of why they would throttle there rather than later in the burn. ISP is generally highest near maximum throttle so ISTM they wouldn't throttle until there is an acceleration limit, which is nowhere near that point in the mission.

Offline envy887

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We have seen that the second stage throttles down before. See the attachments to my post here:

[...]

PS: Sorry, still no time to do programming at home and advance the script.

@edit: added the plot for convenience.
The M1D throttle change is pretty small (perhaps 4-5%).  Perhaps it's a mixture ratio switch.  In Apollo, they ran the second stage with a "maximum thrust" mixture ratio for the first part of the burn (where gravity losses are most important), then switched to a lower-thrust, maximum ISP mixture ratio for the rest of the burn.  ( Described here.)  This would generate a profile just like that shown in the plot.

That also answers the question of why they would throttle there rather than later in the burn. ISP is generally highest near maximum throttle so ISTM they wouldn't throttle until there is an acceleration limit, which is nowhere near that point in the mission.
They wait to throttle because of gravity losses, ISP is basically constant for an engine in vacuum over that small a throttle range.

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