Advanced Question Launch Vehicle Capacity Calculations

[Capt_hensley]

I want to calculate the capacities of launch vehicles to "Fill in the blanks" of this table derived from Wikipedia. See attached spread sheet.

Assume all capacities given in the table are correct(even though it's from a wiki source)
1. Fill in the Numbers only in the blank fields. No negative numbers.
2. For all other numbers give "theorhetical" or "Derived" capacity to the given target orbit.
3. Payload Physical dimension is irrelevant for this exercise. Simply assume the dimensions will fit the fairing configuration of the LV. Drag and gravity are not considered directly, assume maximum aerodynamic efficiency.
4. If no value exist for any target orbit, assume next lower capacity for the nearest rocket in the family plus 1%. (this will work for my appliciation)
5. This is the table of LVs I want to use disreguard any other LV, real or fictional.

A mathmatician should be able to create a simple excel formula to extrapolate the data for a given field, derived from one with a value, or from several values for the record in question.

I assume the following, but if you know better, please reorder or correct the altitude

1. HCO 600–800 km
2. SSO 600–800 km
3. LEO 2000 km
4. GTO 20,000-40,000 km
5. GEO 42,164 km
6. TLI 384,403 km

There are 226 records, some more complete than the others, some LV records are empty.

I'm sure if every rocket had a LEO capacity it would be easier to calculate what the highest target(TLI) capacity would be, provided the LV had enough delta v to get there.

I'm sure there are questions, let em fly'

Like ohms law there is a formula for every value in the table, I figure there must be a way to formulate this launch vehicle table of capacities.

 

[Notebook]

Nice spreadsheet Capt_H, must have took some work.

I'm no expert, but I can't see how one formula will fill in all your blank cells?

Looking at one I'm vaguely familiar with, Black Arrow. That was a developement vehicle, not desgned to get above LEO as far as I know, so no new cells there!

Have you tried looking for a formula at a sample that has all the cells filled?
The Delta II series seems to have most data available there.

I'll have a play around, make a change from banging my head against C++!

N.

 

[Capt_hensley]

Nice spreadsheet Capt_H, must have took some work.

I'm no expert, but I can't see how one formula will fill in all your blank cells?

Looking at one I'm vaguely familiar with, Black Arrow. That was a developement vehicle, not desgned to get above LEO as far as I know, so no new cells there!

Have you tried looking for a formula at a sample that has all the cells filled?
The Delta II series seems to have most data available there.

I'll have a play around, make a change from banging my head against C++!

N.

Yeah, this one sent me for a loop, although One formula wouldn't do.

With ohms law, there are three formulas that use different factors to come up with the same end value. Because the spread sheet has 5 values I need to get from one given factor, I think something can be done, like you said, by using a nearly filled in record to figure out the differences, and creating a formula for one value, against that outcome, and then the next and so on.

If you could get say the GTO from the LEO, then together the GTO, and LEO could be used to get the next value(like the GEO) for the same record, and so on until all six values are filled in, then using the filled record you could work on the next and graduate to filling in all the blanks based on a common formula for each column. One column using the other factors to calculate its own value.

Say that GTO is a percentage of LEO, then you could use a formula to use the same percentage for all GTO values if you can provide the LEO factor. but what do you do when you have a completely unrelated value, and you need to get the LEO factor.

The problem of this hypothisys is that there is no common percentage of LEO that equals GTO, each is dependant on the engines used, and the dynamics of the LV. Even with that being said, I still think a formula is possible. Call me Crazy!:rofl:

With Black Arrow, and some other models, a zero is appropriate in the higher altitudes, that's fine. But most multistage rockets can take a lighter payload all the way to GEO or even TLI on the same Delta V budget. Allot lighter but a payload none-the-less. from what I can see it's 1/3, or even 1/5 of LEO, but nothing consistant.

Remember the list came from Wikipedia, but it's valid to about 98% of the values given with references, so it makes a great starting point.
http://en.wikipedia.org/w/index.php..._systems&printable=yes#cite_note-GSP-Delta-17 is the table source that I've removed the hyperlinks and references.

Thanks for giving it a try.

 

[Notebook]

Not sure if this help, or just confuses the issue!

These are graphs of payload/height for the Europa 2 vehicle.

http://en.wikipedia.org/wiki/Europa_(rocket)

http://i89.photobucket.com/albums/k207/Notebook_04/Blue Streak/img038.jpg

It covers your first three height bands,and the wwikipedia gives a value of 360kg for GTO.

I'll have a play with this and see what turns up.

N.

 

[SiberianTiger]

There is a nice Launch Vehicle Performance Calculator to do that sort of calc on-line.

 

[Notebook]

Thats a very useul utilty.

N.

 

[Capt_hensley]

Interesting calculator, although it's rocket list is incomplete, it is very close. I could get a great deal of data from the calc, and verify the numbers given from Wiki to see how close the online calc is.

Just one problem, It still does not give me a couple of the pre-defined destinations. I'll have to enter those as target altitudes and go from there.

One last note, I'm not sure I like the idea of being dependent on this program, If the formula and additional para-metrics were available in a set of resource tables, I could put my database together and capitalize on this projects functionality.

While this program is very helpful, I'd like to see if there are other ideas or suggestions with the source data and para-metrics I have given above.

 

[Notebook]

doing some curve fitting for the Europa II, equatorial circular orbit data:

http://i89.photobucket.com/albums/k207/Notebook_04/Europa_II_Equatorial_3-1.jpg

Eyeballed 14 data points from that graph, and got this in Mathcad:

http://i89.photobucket.com/albums/k207/Notebook_04/EuropaIIMathcad_1_.jpg

Not a wonderfull match, but we'll see how it goes.

Did some curve fitting here:
http://www.orbiter-forum.com/showthread.php?t=21843&highlight=curve+fitting&page=2

I'll try the same on that data, should keep me busy this afternoon.

N.

 

[Notebook]

Well, as usual something odd came up...

http://i89.photobucket.com/albums/k207/Notebook_04/EuropaIIMathcad_8_.jpg

Seems the regress fit dosen't do as good a job as the median-median fit?

Any statistics folk out there?
I thought the regress fit was best(only one I got to work before...) maybe it dosent do well with sparse data.
For info, M is the height/payload matrix, h is just a one column height version of M(comes in useful), and made up the two polynomials from the returned values respectively.

N.

 

[Capt_hensley]

Way over my head, but I see some progress. Go for it!

 

[Notebook]

I doubt if its over your head CaptH, just the presentation is a cryptic, and its a bit 90 degrees to what you want.

Just to explain the Mathcad document in #9 above.

M is a matrix, 2 columns by 14 rows, I filled it in manually by guestimating from the graph in #8 above. So M is 14 pairs of x,y values, thats the working data. (h is just a 1 column copy of M's first column (the x-axis values). I thought it might be useful later).

Orbit_Height and Payload are the variable names for the first and second columns of M. It makes it them easier to work with.
Thats what the M^<0> and M^(1) do, you can select any column by that method.

Then the medfit() function is used on matrix M(it takes two paramaters), and the result given the name FitMedian.
In this case medfit returned "1825 and -1.889". These are the two co-efficients of a straight line graph y=ax+b
Then FitMedian is redined with these numbers giving the FitMedian graph.

Then do the same thing with the regress function.
Thats a bit more complex, you give it the Matrix M as with medfit, then give it a third parameter.
In this case 3.
Thats the higest order you want regress to use for curve fitting. So it would use something^3, then something^2, then linear*something, then a constant.
You give what it returns to FitRegress, I show that to the left of the M matrix.
Its a 1 column matrix of variables. Working from the bottom up, the first is the ^3 coefficient, next the ^2, then the linear, then a constant. Next is the highest order value(3), then two numbers Mathcad uses internally.
Then I redefined FitRegress using those coefficents for h.

What surprises me is the por fit for the regress function. It was best one for other curve fitting I've tried. I'll leave it for now, If I find out why, it'll get posted here.
For the moment, the FitMedian will be used.

Back to the thread!

This Europa II graph covers the first three orbits you want
1. HCO 600–800 km
2. SSO 600–800 km
3. LEO 2000 km

Take HCO as 600km, and SSO as 800km, you get.

Europa II capacity:

1 HCO 600km = 922.796 kg
2 SSO 800km = 698.393 kg
3 LEO 2000km = -648.044 kg

Slight error, just realised the graph only goes up to 850 km, so you can only deliver anti-matter above that...
EDIT:
Worse that I thought, used the FitRegress for the above figures, should have used FitMedian like I said. Here's the correct values:

Europa II capacity:

1 HCO 600 km = 691.6 kg
2 SSO 800 km = 313.8 kg
3 n/a

Should have checked my results!

I'll have a go with the data in the spreadsheet, and see how it goes.

N.

 

[Notebook]

I was starting on the Atlas V 501 data, and I notice the SSO/LEO are transposed?(what is SSO, Space Shuttle /ISS orbit?)
Im assuming SSO is higher than LEO so I'll switch them in Mathcad.


EDIT:
Ignore above, had a look at this:

http://en.wikipedia.org/wiki/File:Orbitalaltitudes.jpg

and the spreadsheet order is correct.
For my effort, I'll make LEO 250 km. and SSO(ISS?) 400 km.

N.

 

[Notebook]

Tidied up the Mathcad doc:

http://i89.photobucket.com/albums/k207/Notebook_04/AtlasV501_1_.jpg

I've had a good search,but can't find any value for a HCO(Helio-Centric Orbit).

Any one got some figures?

Many thanks, N.

 

[Capt_hensley]

I was starting on the Atlas V 501 data, and I notice the SSO/LEO are transposed?(what is SSO, Space Shuttle /ISS orbit?)
Im assuming SSO is higher than LEO so I'll switch them in Mathcad.


EDIT:
Ignore above, had a look at this:

http://en.wikipedia.org/wiki/File:Orbitalaltitudes.jpg

and the spreadsheet order is correct.
For my effort, I'll make LEO 250 km. and SSO(ISS?) 400 km.

N.

Sun Synchronous Orbit(SSO) This orbits an object around the Earth, beginning with an elliptical orbit, then circularizing if the orbit is to be permanent.

It can be used for solar-polar orbits (90 degrees from earths equator), but these are far more rare. This number is low priority in the table. LEO, GTO, and GEO/GSO are the prime numbers needed for most applications. GEO/GSO is my goal.

 

[Notebook]

Tanks for that CaptH.

Just to let you know what I'm doing, and where I'll stop! Just so you don't get your hopes up...

I think with only 4 data points for most of the spreadsheet values, curve fitting will be a bit problematic.
Using the Atlas V example in #13 above, you can extapolate the TLI orbit from the FitMedian plot and get a value of -4.511E+4 kg. Obviously not a practical value!
Demonstrates one of the steps of Mathematical Modelling, check against the real world.

For fun(?) I'll try and convert the Mathcad steps into an Excel formula. Had a look at the statistics functions, and it looks like its got whats needed.

Might use excel more in the future , Mathcad seems to have gone slightly mad since PTC took them over. They were up to version 15, then they brought out a thing called Mathcad Prime. Got a good kicking on the forums for being basically useles.

i've used Mathcad since version 8, up to 14. I liked its open style and easy use of units.
Wish they would leave a product alone when it works.

N.

 

[Capt_hensley]

Go for it, lots of wiggle room.

 

[Notebook]

Talking of wriggling out of things...

This is as far as I go with this:
http://i89.photobucket.com/albums/k207/Notebook_04/AtlasV501_3_.jpg

It matches how far I got with the Mathcad document.

Cell C6 gives the intercept point =INTERCEPT function on the data range,
Cell C7 does a =SLOPE(E3:H3,E4:H4) linear regression on the data range.

Then do C7 on the x axis, and you get the blue line as a fit to the payload data.

Could interpolate and extrapolate for various orbits now you have a formula, just plug Orbit Height into the formula, and there you have it.

You have to do this for every vehicle of course...going to take somebody clever than me, and a wizz at Excel.

N.

 

[Capt_hensley]

OK I'll set this up and see how the results come out. Thanks for the effort. This looks promising

 

[Notebook]

You're welcome CaptH, excel has more functions than I thought. I'll use your data for some more curve fitting in Mathcad, if anything useful comes up I'll place it here.

Cheers, N.

 

[Capt_hensley]

Could you zip up and post the sample spread sheet shown above, please?