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Decided to revisit that question of maximum GTO performance for the current incarnation of Falcon 9.

As previously noted, the Intelsat-35e webcast telemetry showed startup-1 at 2.606 km/s, SECO-1 at 7.46 km/s, startup-2 at 7.362 km/s, and SECO-2 at 9.855 km/s. So the first burn provided 4.854 km/s net and the second burn provided 2.493 km/s prograde.

With a vacuum isp of 348 seconds, the second stage would need to burn 11.5 tonnes of fuel for the second, prograde-only burn.

This tells us that during the boost to orbit (from staging at 2.606 km/s to SECO-1 at 7.46 km/s), S2 burned 96 tonnes of fuel for an effective isp of just 296 seconds. That's not too surprising; even at GTO-mass payloads, the F9 upper stage flies a sharply lofted trajectory. The difference between 296 seconds and the true isp of 348 seconds consists of gravity losses. You can also calculate it the other way around; if you set isp at 348 seconds, you get 5.71 km/s for gravity losses of 853 m/s.

I'm not sure if or when SpaceX's live-feed telemetry factors in the rotation of the Earth...the Kerbal equivalent being the switch between "Surface" view and "Orbit" view. So that's a grain of salt to take.

The first stage has a vacuum isp of 311 seconds. Rather than integrating to go from surface isp to vacuum isp, let us merely treat gravity drag, aerodynamic drag, and isp drag as a single value. Using the vacuum isp of 311, burning the entire fuel capacity of the first stage delivers 4.17 km/s of dV...but since staging took place at 2.606 km/s, we can set isp drag, gravity drag, and aerodynamic drag at a sum total of 1.564 km/s.

Elon said that Intelsat-35e was contracted at an apogee of 28,000 km but ultimately achieved an apogee of 43,000 km. A quick glance at an orbital solver tells us the perigee burn for a 28,000x262 km Hohmann transfer is 2,285 m/s of dV, so that's our theoretical minimum dV for insertion from a nominal parking orbit to a 28,000 km Ap GTO.

For reference, the perigee burn for insertion to a 43,000x262 km Hohmann transfer is 2.541 km/s of dV, within 2% of the observed change in velocity on the webcast telemetry. (Differences are probably due to the fact that the parking orbit was not exactly circular, the final Ap was probably not exactly 43,000 km, and there was probably a slight plane change that didn't show up in the prograde dV.)

The difference between these two is just 256 m/s, so that's the overperformance of the Falcon 9 in this mission. Obviously, the first stage would need much more than 256 m/s of dV reserved for a landing attempt, so it's safe to say the overperformance was not so great that it could have allowed recovery.

Edited by sevenperforce
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Based on these values, let's take a look at the F9's performance at the advertised maximum GTO payload, 8.3 tonnes.

First stage burns all 411 tonnes of its propellant, delivering 4.14 km/s of dV. Subtracting the losses I calculated earlier, this places staging at 2.58 km/s. The second stage ignites and pushes to 7.46 km/s, requiring 4.88 km/s of dV plus the 853 m/s of gravity drag I previously calculated. This burns 97.5 tonnes of propellant, leaving the second stage with a net mass of 22.3 tonnes and just 2.03 km/s of remaining dV.

This is about 11% (255 m/s) short of a full GTO injection burn. So either there is margin somewhere else (like a lower perigee or a shorter coast period), or the 8.3-tonne advertised payload is calculated for Block V booster and upper stage rather than Block III or Block IV.

The Iridium-2 launch used a Block IV upper stage with a Block III first stage. Does anyone know whether the Intelsat-35e mission used a Block III or Block IV upper stage?

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12 minutes ago, sevenperforce said:

Bahaha!

I swear, if I could get paid to just sit around and run astrodynamics calculations/simulations all day, I'd be the happiest man in the world.

So why haven't you submitted your resume to NASA, then? SpaceX? ULA? That other rich guy? They have peeps who are paid to do exactly that. :wink:

 

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21 minutes ago, CatastrophicFailure said:

So why haven't you submitted your resume to NASA, then? SpaceX? ULA? That other rich guy? They have peeps who are paid to do exactly that. :wink:

 

I only have a B.S. in physics. Not enough to do anything but sweep the floor at NASA, BO, SX, or ULA. Also I don't live anywhere near any of their offices.

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2 hours ago, CatastrophicFailure said:

So why haven't you submitted your resume to NASA, then? SpaceX? ULA? That other rich guy? They have peeps who are paid to do exactly that. :wink:

 

Also they computers to do that most of the time, most of the people involved are basically there just to maintain the computers and feed them input data.

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5 minutes ago, Steel said:

Also they computers to do that most of the time, most of the people involved are basically there just to maintain the computers and feed them input data.

Right, this too. I can do enough programming to get by, but my degree is not in computer science and I only know a couple of programming languages. I can do more than enough math by hand to make decent estimates for amateur forum discussions, but I would need to be an expert programmer to set up and run the launch simulations that SpaceX and Blue Origin rely on.

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1 hour ago, sevenperforce said:

I would need to be an expert programmer to set up and run the launch simulations that SpaceX and Blue Origin rely on.

Maybe that's a career path you should consider, then. :wink: You've obviously got the drive for it. The field's only going to expand...

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Wonder why they haven't released it yet? That must have been the most badass landing ever :cool: "Hey, look - our stuff can recover even from such seemingly hopeless situation. Aren't we awesome?" :D

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4 minutes ago, Scotius said:

Wonder why they haven't released it yet? That must have been the most badass landing ever :cool: "Hey, look - our stuff can recover even from such seemingly hopeless situation. Aren't we awesome?" :D

Oh, the suspense... release something! Anything!

(of course, I'm talking about the BulgariaSat-1 landing, but Falcon Heavy details wouldn't hurt either...)

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1 hour ago, TheEpicSquared said:

Oh, the suspense... release something! Anything!

(of course, I'm talking about the BulgariaSat-1 landing, but Falcon Heavy details wouldn't hurt either...)

Given that we only got two frames,

ThinSphericalAbalone-size_restricted.gif
I feel entitled to something more within...a few months of the landing. Especially considering the splash in the first frame.

Spoiler

Otherwise, I shall put on my tin foil hat and declare spaceflight fake, and that the Earth is not round, it is the shape of a fidget spinner/T-rex

 

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To the people asking for the landing video, there was a discussion over on the SpaceX reddit a while ago (sorry, I don't have the link) where someone who had seen the video said that it had done an "impressive one leg balancing act." Later in the discussion people arrived at the conclusion that SpaceX would probably not release the video because of all the clickbait news articles saying "SPACEX ROCKET NEARLY FAILS!!!!!111!!1" that would be bad PR for SpaceX. Now, if anyone did their research they would know that landing in such conditions a failure isn't terrible, and that landing on such thin margins is very impressive. Unfortunately, a large percentage of the general public doesn't do research...

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36 minutes ago, Ultimate Steve said:

To the people asking for the landing video, there was a discussion over on the SpaceX reddit a while ago (sorry, I don't have the link) where someone who had seen the video said that it had done an "impressive one leg balancing act." Later in the discussion people arrived at the conclusion that SpaceX would probably not release the video because of all the clickbait news articles saying "SPACEX ROCKET NEARLY FAILS!!!!!111!!1" that would be bad PR for SpaceX. Now, if anyone did their research they would know that landing in such conditions a failure isn't terrible, and that landing on such thin margins is very impressive. Unfortunately, a large percentage of the general public doesn't do research...

I dunno, they were pretty upfront about their actual failures...

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I have noticed that SpaceX hasn't published the webcast of the Intelsat mission yet. Makes me wonder if it's a technical issue with YouTube rather than an issue on SpaceX's side. Then again, if that were the case, SpaceX could have just published it somewhere else... 

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4 hours ago, TheEpicSquared said:

I have noticed that SpaceX hasn't published the webcast of the Intelsat mission yet. Makes me wonder if it's a technical issue with YouTube rather than an issue on SpaceX's side. Then again, if that were the case, SpaceX could have just published it somewhere else... 

I watched it, a few hours after the launch. Have another look?

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10 hours ago, TheEpicSquared said:

I have noticed that SpaceX hasn't published the webcast of the Intelsat mission yet. Makes me wonder if it's a technical issue with YouTube rather than an issue on SpaceX's side. Then again, if that were the case, SpaceX could have just published it somewhere else... 

Probably something internal and might be something very trivial like the guy responsible for the videos are sick. 
This day launch and landing videos is an fan service and not major news. 
They might have lost the drone filming the landing so they don't have good shots is another. 

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Maybe that water splash was caused by the engine torches?
If the rocket was slipping approaching to the barge autonomous drone ship from the left, and hit the deck at the last moment.
(A low-altitude horizontal stealth rocket).

Also this would explain that words about one-leg balancing and why they don't want to show this aerobatics.

Edited by kerbiloid
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19 hours ago, magnemoe said:

Probably something internal and might be something very trivial like the guy responsible for the videos are sick. 
This day launch and landing videos is an fan service and not major news. 
They might have lost the drone filming the landing so they don't have good shots is another. 

They didn't use a drone.

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