A delta vee requirement and capability calculation spreadsheet

[deltaV]

Hi everyone,

I made an Excel spreadsheet to estimate vehicle performance during launch and orbital maneuvers. It helped me understand things better so I’am sharing it to help others understand things too. It’s actually two parts (tables), one for estimating the delta vee requirements (and other orbital parameters) of a sequence of orbit transfers, and the second for estimating the delta vee provided by a given multi-stage launch vehicle with a given payload.

This is of course similar to what Schillings (http://www.silverbirdastronautics.com/LVperform.html) does. My tool is unlikely to be as good as Schillings at what Schillings does, namely estimating launch vehicle performance. My tool’s simplicity and open source nature however means it is better for learning than Schillings. It also handles orbital maneuvers such as Hoffman transfers, whereas Schillings only handles launch to a single orbit.

Unlike Schillings my spreadsheet does not attempt to estimate gravity and aero losses. The user must provide the sum of these loses as input. The way I estimate these losses is to load a professionally studied launch vehicle configuration that's similar to the one I care about and tune the loss figure until the spreadsheet correctly predicts the performance of this surrogate launch vehicle.

I'm releasing this spreadsheet under the open source CC-BY-SA 4.0 license so please post new and improved variants of this.

Please use and comment.

-deltaV

Edit: this spreadsheet has a bug: I calculated the geosynchronous orbit 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.

[Hop_David]

I keep seeing mentions of these Monkey Wrench Gang transfer orbits. Hope you'll  replace those with Hohmann.

Playing with spreadsheets I frequently overwrite a non-input cell. They're vulnerable to damage. I'd recommend protecting the sheet and format the input cells so they can be changed. It'd be helpful to more clearly mark the input cells, maybe put a bold border around them.

Q: What is the C3 and velocity at apogee of a 100x200km LEO?
A: Use first main table. Enter 200 for initial altitude and an altitude of 100 for h2. Read off C3=-61.1 and v1=7.75 from the "orbit 1" column.

Into which cell do I input 100 for h2?

[deltaV]

I keep seeing mentions of these Monkey Wrench Gang transfer orbits. Hope you'll  replace those with Hohmann.

Thanks, I fixed the spelling of Hohmann.

Playing with spreadsheets I frequently overwrite a non-input cell. They're vulnerable to damage. I'd recommend protecting the sheet and format the input cells so they can be changed. It'd be helpful to more clearly mark the input cells, maybe put a bold border around them.

1. The input cells appear with an orange background for me, which is quite visible. Do they appear that way for you? I added some thicker borders to make them even more visible.

2. I'm using the "Excel starter" that came with my computer, which does not appear to support protecting sheets. So I can't implement that suggestion easily.

Q: What is the C3 and velocity at apogee of a 100x200km LEO?
A: Use first main table. Enter 200 for initial altitude and an altitude of 100 for h2. Read off C3=-61.1 and v1=7.75 from the "orbit 1" column.

Into which cell do I input 100 for h2?

Oops I removed the h2 terminology and neglected to update the examples. Put the 100 in the cell at the intersection of "Orbit 1" and "Altitude r2-r_Earth (km)".

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Do you think I should "ship" the spreadsheet with an example input already filled in, or blank?

[Lar]

Filled in would be helpful.

Thanks for sharing this.

[Hop_David]

1. The input cells appear with an orange background for me, which is quite visible. Do they appear that way for you? I added some thicker borders to make them even more visible.

You also include comments in inputs? That threw me as I've been in the habit of just doing numerical inputs.

2. I'm using the "Excel starter" that came with my computer, which does not appear to support protecting sheets. So I can't implement that suggestion easily.

I would guess that option is available somewhere in your program. Sadly Microsoft often rearranges their pull down menus and user interface.

In my version there's a pull down menu called Format. Format:Cells:Protection and then I uncheck the locked button if it's an input cell. There's a Tools pull down menu where I choose Protection:Protect Sheet.

Oops I removed the h2 terminology and neglected to update the examples. Put the 100 in the cell at the intersection of "Orbit 1" and "Altitude r2-r_Earth (km)".

Intersection of "Orbit 1" and "Altitude r2-r_Earth (km)"? That would be cell D50? Attached is a screen shot of the orbit 1 column. Not exactly as you describe. But I think I'm making progress in understanding the sheet. Cell D41 seems to be the perigee. And cells on row 50 (E50 through I50) seem to the apogees of various orbits.

The row 54 V1s seems to be the velocities at either perigee or apogee of different orbits? For example cell F54 looks the perigee velocity of a 200 km altitude x 60000 km orbit. But G54 looks the apogee velocity of a 200 x 35863 orbit. Not sure what row 54 is supposed to be.

[deltaV]

1. The input cells appear with an orange background for me, which is quite visible. Do they appear that way for you? I added some thicker borders to make them even more visible.

You also include comments in inputs? That threw me as I've been in the habit of just doing numerical inputs.

Yes. I guess comments are not really inputs, but they're like inputs in that they're part of the spreadsheet that I expect users to modify. Hmmmm.

2. I'm using the "Excel starter" that came with my computer, which does not appear to support protecting sheets. So I can't implement that suggestion easily.

I would guess that option is available somewhere in your program. Sadly Microsoft often rearranges their pull down menus and user interface.

In my version there's a pull down menu called Format. Format:Cells:Protection and then I uncheck the locked button if it's an input cell. There's a Tools pull down menu where I choose Protection:Protect Sheet.

I'm pretty sure protection is a feature that's omitted from the starter version of excel. Once I get the spreadsheet closer to done I'll turn on protection using another computer of mine which has the full version of excel.

Oops I removed the h2 terminology and neglected to update the examples. Put the 100 in the cell at the intersection of "Orbit 1" and "Altitude r2-r_Earth (km)".

Intersection of "Orbit 1" and "Altitude r2-r_Earth (km)"? That would be cell D50? Attached is a screen shot of the orbit 1 column. Not exactly as you describe.

Yes.

But I think I'm making progress in understanding the sheet. Cell D41 seems to be the perigee.

D41 is the perigee or apogee of the first orbit. It turns out (see below for why) that D41 remains an apside until "switch apsides = 1" is used.

Each of the numbered orbits orbit 1, orbit 2, etc. have two apsides (singular apsis). Traditionally the smaller one is called perigee and the larger apogee, but determining which is which would make the coding more complicated so for the spreadsheet they're just apsis #1 and apsis #2.  r1 and v1 are the radius and velocity at apsis #1; r2 and v2 are analogs for apsis #2. (These differ from the input altitudes by the radius of the Earth.) If you care which is the apogee and which the perigee you can look at r1 and r2 and see which is bigger.

For the first orbit the user specifies both apsides. The apside #1 is specified directly with an altitude. The apside #2 can be specified in one of three ways: directly by specifying its altitude, or indirectly by specifying velocity at apside #1, or indirectly by specifying the orbit's C3. These three options correspond to the three rows labeled "input energy".

Each orbit differs from the previous one by one burn at one of the two apsides. These burns change only one of the two apsides, so each of the orbits #2 and higher have one apsis that's inherited from the previous orbit and one apsis that's specified in the same way as apside #2 of orbit 1 is. The new apsis is always apsis #2 and the inherited apsis is apsis #1. If "switch apsides"=0 apsis #1 equals the previous apsis #1, otherwise it equals the previous apsis #2. In other words if "switch apsides=0" the burn occurred at the previous apside #1 and if "switch apsides=1" the burn occurred at the previous apside #2.

As I wrote the above I realized that "switch apsides" is rather confusing terminology. Maybe I should change it so that you enter 1 or 2 to specify which of the apsides the burn should be at?

And cells on row 50 (E50 through I50) seem to the apogees of various orbits.

Those are either apogees or perigees of the orbits.

The row 54 V1s seems to be the velocities at either perigee or apogee of different orbits?

Yep

For example cell F54 looks the perigee velocity of a 200 km altitude x 60000 km orbit.

Yep

But G54 looks the apogee velocity of a 200 x 35863 orbit. Not sure what row 54 is supposed to be.

G54 is the apogee velocity of a 60000 x 35863 orbit. The 54 row is the speed at apsis #1. See above discussion of apsides numbering.

The spreadsheet ships with the following orbits:
             Apsis 1    Apsis 2
Orbit 1: 200 x -6378
Orbit 2: 200 x 200
Orbit 3: 200 x 60000
Orbit 4: 60000 x 35863
Orbit 5: 35863 x 35863

Does it make sense now?

[JohnFornaro]

DeltaV:  Many thanks for sharing this spreadsheet.  Are you updating the OP spreadsheet attachment each time you update / correct the spreadsheet?

[deltaV]

DeltaV:  Many thanks for sharing this spreadsheet.  Are you updating the OP spreadsheet attachment each time you update / correct the spreadsheet?

I'm working on an improved and corrected version but I haven't posted it yet.