Falcon 9 vs Ariane 5 in terms of GTO insertion

[ZachS09]

I’m beginning a new thread about comparing Falcon 9 and Ariane 5 based on their GTO capabilities. It’s also to continue the discussion I had with GWR64 in the Ovzon 3 mission thread.

Using the delta-v to GEO calculator at https://gtocalc.github.io/, it'll take 1,707 m/s of delta-v for Ovzon 3 to get to its destination in GEO.

267 by 47,368 kilometers, inclined 26.81 degrees = 1,707.057 m/s

If Ovzon 3 was launched on Ariane 5 as originally planned, and put into the supersynchronous transfer orbit (71,000 kilometer apogee) per the Ovzon 3 brochure from long ago, the delta-v result would've been 1,431 m/s.

250 by 71,000 kilometers, inclined 3 degrees = 1,431.094 m/s

Then again, the first stage returning to LZ-1 ate up a lot of performance, meaning Ovzon 3 needs to use about 276 m/s of extra delta-v. But it's a good thing at the same time; the more RTLS landings, the more launches SpaceX can conduct to hopefully reach the 144 mark.

[ZachS09]

I thought that since the originally combined stack of Eutelsat Konnect VHTS and Ovzon 3 was below Ariane 5’s maximum GTO capability of just over 11 tons (~8.9 tons including adapters and SYLDA)…

…and combined with the fact of the ESC-A second stage stretched a little bit, Ariane 5 would’ve been powerful enough to achieve the hypothetical SSTO parameters I listed in my post.

[deltaV]

Your delta vees are slightly higher than ideal since you're using a calculator that puts all the inclination change in one burn rather than doing a portion of the inclination change in each burn. With inclination change split optimally between the two burns the 1707 m/s is reduced to 1698 m/s. The 1431 m/s doesn't change significantly, i.e. still 1431 m/s after rounding to the nearest multiple of 1 m/s. I calculated these using a spreadsheet. See posts by BowShock and others in https://forum.nasaspaceflight.com/index.php?topic=36954.msg1341826#msg1341826.

[ZachS09]

I’ve always used the GTO delta-v calculator link I mentioned in my original post, which was made by LouScheffer.

But I’ll look at your spreadsheet and maybe Steven Pietrobon’s calculator too (I also tried out Steven’s version back then).

[deltaV]

But I’ll look at your spreadsheet and maybe Steven Pietrobon’s calculator too (I also tried out Steven’s version back then).

1. Where is the Steven Pietrobon calculator you are referring to?

2. If you're wondering which spreadsheet I used, the answer is the one I posted a decade ago (first post of https://forum.nasaspaceflight.com/index.php?topic=33897.0). Note that it has a bug: I calculated the geosynchronous radius assuming a 24 hour period instead of the correct sidereal day. To fix this replace cell D24 with "=POWER(SQRT(D19)*(86164.0905)/2/PI(), 2/3)-D21". This bug doesn't make a significant difference though.

To do a super-synchronous GTO to GEO calculation with my spreadsheet, fix the buggy D24 as mentioned above, clear all the input (i.e. orange) cells in the "first main table", and then set the following input cells: D41="267", D44="super GTO", D50="47368", E45="1", E47="25.8", E50="=D24", F44="GEO", F45="1", F47="=26.81-E47", F50="=D24". The overall delta vee of 1.698 km/s appears in cell F58. I determined the inclination change in E47 by trial and error approximately minimizing cell F58. Note that if you set E47 to 26.81, which puts all the inclination change in the first burn, it gets the same 1.707 km/s as the calculator you used.

Someday I may get around to polishing that spreadsheet some more and making it more user friendly.

[ZachS09]

Short story:

About a month before the Iridium-NEXT F6 & GRACE-FO launch, I was predicting how many M-Vac burns would be needed to deploy all seven satellites into their respective orbits.

https://forum.nasaspaceflight.com/index.php?topic=35275.msg1808990#msg1808990

In the link above, Steven showed the most efficient way to get from the GRACE-FO orbit (490 km, 89 degrees) to the Iridium-NEXT orbit (625 km, 86.66 degrees).

That’s where I discovered his calculator.

[deltaV]

Short story:

About a month before the Iridium-NEXT F6 & GRACE-FO launch, I was predicting how many M-Vac burns would be needed to deploy all seven satellites into their respective orbits.

https://forum.nasaspaceflight.com/index.php?topic=35275.msg1808990#msg1808990

In the link above, Steven showed the most efficient way to get from the GRACE-FO orbit (490 km, 89 degrees) to the Iridium-NEXT orbit (625 km, 86.66 degrees).

That’s where I discovered his calculator.

If I do the same problem as in Steven's post with my spreadsheet I get 318 m/s of delta vee, which differs from the 427 m/s he reported. It seems either his calculator or my spreadsheet have a bug.

[deltaV]

If I do the same problem as in Steven's post with my spreadsheet I get 318 m/s of delta vee, which differs from the 427 m/s he reported. It seems either his calculator or my spreadsheet have a bug.

I looked over both his code and mine and they use slightly different formula (I compute via C_3 to support hyperbolic orbits too) but they should give the same answer. Both appear correct so I'm not sure why they're giving different results. One possibility is one of us made an error when using our respective programs. To debug this someone needs to either add some more logging statements to his code or run his code in a debugger so we can compare the values of intermediate variables (e.g. the speeds) to those in my spreadsheet to determine where exactly the programs diverge. Do you know what compiler or interpreter he uses? From the file extension it's probably https://en.wikipedia.org/wiki/Delphi_(software). Does Steven use the free version of the commercial Delphi product, the paid version of Delphi, Free Pascal, Lazarus, or something else?

[LouScheffer]

OK, I coded up both the quick method and more optimized method in somewhat documented python (I've included it as .txt since the board will not attach a .py).  If you type in the data for a transfer orbit of 200 km x 55000 km x 28 degrees, by typing

python geo.py 200 55000 28

you should get

Delta-V to GEO from transfer orbit of  200.0 km, apogee 55000.0 km, inclination 28 degrees
First try simple scheme of removing all inclination with the first (perigee raise) burn
First burn  1412.05, circularization burn   273.08, total  1685.14 m/s

Now try inclining the intermediate orbit
Optimization gives  1675.51 m/s with transfer inclination  1.31 degrees

For the two orbits in question:

Delta-V to GEO from transfer orbit of  267.0 km, apogee 47368.0 km, inclination 26.81 degrees
First try simple scheme of removing all inclination with the first (perigee raise) burn
First burn  1526.84, circularization burn   180.28, total  1707.11 m/s

Now try inclining the intermediate orbit
Optimization gives  1698.76 m/s with transfer inclination  1.02 degrees
               ------------------------
Delta-V to GEO from transfer orbit of  250.0 km, apogee 71000.0 km, inclination 3 degrees
First try simple scheme of removing all inclination with the first (perigee raise) burn
First burn  1007.51, circularization burn   423.63, total  1431.14 m/s

Now try inclining the intermediate orbit
Optimization gives  1430.99 m/s with transfer inclination  0.19 degrees
[/endquote]

[deltaV]

I think it would be nice if we had orbital calculation scripts that people could modify and run in a browser, no install required. I think we can probably do this with python. We'd want to make the scripts so they can either by run with command line arguments or imported as a module which can then be called from a Jupyter notebook. I think this can be done by putting most of the code in a class or function and then use 'if __name__ == "__main__":' around the code that reads the command line arguments. Maybe I'll try to prototype this next weekend.

LouScheffer if you release your code under an open source license, e.g. MIT license (just say so), I can start with yours.

[ZachS09]

I don't have Python, and I've little to no experience with that program.

LouScheffer, I wanted to ask since you provided the "quick method" and "optimized method" codes, could you update your GTO delta-v calculator website to include the latter one?

[LouScheffer]

I think it would be nice if we had orbital calculation scripts that people could modify and run in a browser, no install required. I think we can probably do this with python. We'd want to make the scripts so they can either by run with command line arguments or imported as a module which can then be called from a Jupyter notebook. I think this can be done by putting most of the code in a class or function and then use 'if __name__ == "__main__":' around the code that reads the command line arguments. Maybe I'll try to prototype this next weekend.

LouScheffer if you release your code under an open source license, e.g. MIT license (just say so), I can start with yours.

Sure.  I am happy to release the code above for calculating delta-v remaining to GEO, under any free public license, including the MIT license.   What additional steps do I need to take, if any?

[LouScheffer]

I don't have Python, and I've little to no experience with that program.

LouScheffer, I wanted to ask since you provided the "quick method" and "optimized method" codes, could you update your GTO delta-v calculator website to include the latter one?

I'd be happy to do this, but don't recall putting my method on a web site.  However I've done other things I don't recall.  Can you specify the URL?

[woods170]

I thought that since the originally combined stack of Eutelsat Konnect VHTS and Ovzon 3 was below Ariane 5’s maximum GTO capability of just over 11 tons (~8.9 tons including adapters and SYLDA)…

…and combined with the fact of the ESC-A second stage stretched a little bit, Ariane 5 would’ve been powerful enough to achieve the hypothetical SSTO parameters I listed in my post.

Emphasis mine.

Ariane 5 ECA injection mass for standard GTO was max. 11,300 kg, or 11.3 metric tons.
This included the Sylda, Cone and adapters. The heaviest combination of those four elements came in at 992 kg. Or let's say 1 metric ton.
This translates into Ariane 5 ECA being capable of deploying 10,300 kg of dual payload into GTO. (not "~8.9 tons including adapters and SYLDA").
On mission VA-255 in 2021, Ariane 5 ECA came extremely close to flying its max injection mass: VA-255 injected 11,202 kg into GTO. SYLDA, Cone and adapters came in at a combined 938 kg for that mission. Released payload into GTO was 10,264 kg, or 10.26 metric tons, consisting of two comsats: SES-17 and Syracus 4A.


When flying a single payload-to-GTO (no SYLDA, only Cone and one adapter), Ariane 5 could put a payload of max. 11,100 kg (11.1 metric tons) into GTO.

[ZachS09]

I don't have Python, and I've little to no experience with that program.

LouScheffer, I wanted to ask since you provided the "quick method" and "optimized method" codes, could you update your GTO delta-v calculator website to include the latter one?

I'd be happy to do this, but don't recall putting my method on a web site.  However I've done other things I don't recall.  Can you specify the URL?

https://gtocalc.github.io/

[LouScheffer]

LouScheffer, I wanted to ask since you provided the "quick method" and "optimized method" codes, could you update your GTO delta-v calculator website to include the latter one?

I'd be happy to do this, but don't recall putting my method on a web site.  However I've done other things I don't recall.  Can you specify the URL?

https://gtocalc.github.io/

I didn't write that web site - someone else did starting from my code.  Sorry, but I don't even know who did it.

[ZachS09]

LouScheffer, I wanted to ask since you provided the "quick method" and "optimized method" codes, could you update your GTO delta-v calculator website to include the latter one?

I'd be happy to do this, but don't recall putting my method on a web site.  However I've done other things I don't recall.  Can you specify the URL?

https://gtocalc.github.io/

I didn't write that web site - someone else did starting from my code.  Sorry, but I don't even know who did it.

It was my mistake. I thought since you wrote the code, you used that as part of building that website.

[Asteroza]

LouScheffer, I wanted to ask since you provided the "quick method" and "optimized method" codes, could you update your GTO delta-v calculator website to include the latter one?

I'd be happy to do this, but don't recall putting my method on a web site.  However I've done other things I don't recall.  Can you specify the URL?

https://gtocalc.github.io/

I didn't write that web site - someone else did starting from my code.  Sorry, but I don't even know who did it.

It was my mistake. I thought since you wrote the code, you used that as part of building that website.

The originating github repo owner is also anonymous so who knows.

https://github.com/gtocalc

[ZachS09]

I thought that since the originally combined stack of Eutelsat Konnect VHTS and Ovzon 3 was below Ariane 5’s maximum GTO capability of just over 11 tons (~8.9 tons including adapters and SYLDA)…

…and combined with the fact of the ESC-A second stage stretched a little bit, Ariane 5 would’ve been powerful enough to achieve the hypothetical SSTO parameters I listed in my post.

Emphasis mine.

Ariane 5 ECA injection mass for standard GTO was max. 11,300 kg, or 11.3 metric tons.
This included the Sylda, Cone and adapters. The heaviest combination of those four elements came in at 992 kg. Or let's say 1 metric ton.
This translates into Ariane 5 ECA being capable of deploying 10,300 kg of dual payload into GTO. (not "~8.9 tons including adapters and SYLDA").
On mission VA-255 in 2021, Ariane 5 ECA came extremely close to flying its max injection mass: VA-255 injected 11,202 kg into GTO. SYLDA, Cone and adapters came in at a combined 938 kg for that mission. Released payload into GTO was 10,264 kg, or 10.26 metric tons, consisting of two comsats: SES-17 and Syracus 4A.


When flying a single payload-to-GTO (no SYLDA, only Cone and one adapter), Ariane 5 could put a payload of max. 11,100 kg (11.1 metric tons) into GTO.

When I put the "8.9 tons" caption in parentheses, I was referring to the original stack of Eutelsat Konnect VHTS & Ovzon 3 w/ adapters and SYLDA. It had nothing to do with Ariane 5ECA's GTO capacity of 10.3 tons of dual payload.

[ZachF]

With F9 since it’s a kerolox 2 stage, it actually makes sense to drop the payload earlier if it has hypergolic orbit raising (most still do) and plop a bigger tank in.

For instance, it can send a 5,500kg sat to GTO-1800 which leads to an on-orbit mass of ~3,100kg with a 320 ISP.

Falcon has recently demonstrated 7,250kg to GTO-2200, which leads to an on-orbit mass of ~3,600kg with a 320 isp motor.

People also underestimate how good Ariane is at flinging things to GTO… 9,800kg to GTO-1500 leads to an on-orbit mass of ~6,075kg using the same motor. Very impressive for GTO