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Rocket equations and mathematical modeling Q&A by su_liam on 02 Jul, 2012 23:08
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Didn't know where else to plant this, so here goes...
Hi. Unlike some of the people on this site I am not an aerospace engineer, but I do like to play with rocket design as a hobby.
I'm familiar with the Tsiolkovsky rocket equation, I can calculate instantaneous drag(I have no idea how to integrate that to figure out total atmospheric losses, though) and with a bit of work I can figure out delta-V requirements for simple orbital changes.
When it comes to estimating system masses and the like, I'm limited to playing with proportions and info I have on existing rocket systems. My library is pretty much limited to stuff on the Saturn V and Space Shuttle. Other than that I'm limited to legos and things I composited from engine information in Astronautix and vehicle design rules from role-playing games.
My google-fu failed miserably when I tried to look up propellant volumes for the Delta IV and Atlas V, but I found a couple of documents I thought might prove very useful in improving my space lego collection if I could figure out what all the variables meant.
This place seems to be loaded with smart people who are reasonably tolerant of silly people like me. So I'm going to see if I can get any help here.
The first document I found really useful was http://www.ssdl.gatech.edu/papers/phdTheses/YoungJ-Thesis.pdf. There is a lot of meat to wade through in this one, especially as I begin to understand what it all means, but my focus for the moment is on the Cargo Launch Vehicle Mass Estimating Relationships on page 304 of the PDF(pg. 287 on the footer).
My first question is what is the CF? Is this the complexity factor? Is that a constant for all relationships on a given vehicle or is the CF different for each formula? That may have been more than one question…
My second(or fourth) question is in the formula for primary structural mass. What does SAStage signify?
My third(or fifth) question is in the formula for power. What does MAP signify?
Down the line, I may have some questions regarding the LSAM mass estimating relationships on page 307(290), but for now… I need to focus my efforts.
Mostly I add www.nasa.gov/pdf/382034main_018%20-%2020090706.05.Analysis_of_Propellant_Tank_Masses.pdf for the benefit of other people in my rough position. It's a nice little resource. The tank weight formula, ms = 0.19 mp0.848 (or ms = 0.1583 mp0.848) seems to be specific to LH2/LO2 tankage. I tried to generalize this to,
ms = k (BDpropellant / BDhydrolox)0.582 mp0.848,
where k===0.19 for conventional tanks or 0.1583 for common bulkhead tanks, BDpropellant is the bulk density for the propellants of interest at the ratios used by the given stage's engines, BDhydrolox is the bulk density of propellants in an LH2/LO2 system(about 320 kg/m3 for a O:F ratio of 4.83)*, mp is the propellant mass and ms is essentially the tankage mass(empty stage mass minus the engine mass, so it presumably includes all of those weights for thrust structure, feed, power, avionics and such).
I based my adaptation on the assumption that an exponent of 0.666 would represent surface area coverage and the remaining 0.582 exponent would be related to supporting the weight of the fuel.
Does my adaptation actually make any kind of sense?
That's my last question at the moment.
Thank you for your assistance.
* Taken from http://en.wikipedia.org/wiki/Liquid_rocket_propellants -
#1 by Chris Bergin on 06 Jul, 2012 00:14
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Moved and a bump. Member was very patient and asked for this to be moved....so any help with the questions?
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#2 by su_liam on 19 Jul, 2012 01:27
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Bumpity.
I know the question kind of earns me my newbie-doofus wings, but even with a re-reading of the document, I can't seem to find an explanation for these variables. When I see unexplained variable names, I assume(rightly or not) that these are fairly standard nomenclature. With that in mind, I thought I would put the question to the apparently very knowledgeable people on this board to see if anybody could recognize the jargon.
If the answer is terribly simple and obvious, I beg of you to take mercy on this doofus.
I promise to use the knowledge thus gained only to make my pretend spaceships more plausible and never to second guess the decisions of real rocket scientists at NASA or SpaceX or such.
Thank you for your help,
Colin -
#3 by sdsds on 19 Jul, 2012 04:18
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I've looked at the Young thesis paper and will gladly give you my thoughts about the the paper in general and the mass estimating relationships it provides in particular.
First, note the thesis is from 2009 and one of the advisors was Dr. Douglas Stanley. Yes I'm pretty sure this is the ESAS Lead Doug Stanley:
http://forum.nasaspaceflight.com/index.php?topic=5419.0
That pretty much gives the author an inside track on Constellation vehicles, but that comes with a price. He wasn't going to squeak by with vague approximations! You on the other hand are not writing a doctoral thesis, and Doug Stanley is not one of your advisors. So I doubt in your designs you need to raise anything (burnout mass or otherwise!) to the 0.7728th power, as this author apparently felt the need to do.
Others might scoff, but for in space propulsion I think it's sufficient to choose a propellant mass fraction for a stage (within reason) based on how much you're willing to pay for specialized engineering and manufacturing. Unless you're trying to shoehorn an existing vehicle design into a overly tight architecture, it doesn't seem worth paying those costs. If your vehicle design doesn't complete its mission because its pmf is 0.92 instead of 0.94 -- well then design a bigger vehicle.
If you're wanting to design launch vehicles, or stages that participate in ascent, it definitely gets trickier! Still, you wouldn't go too far wrong by extrapolating (or certainly not by interpolating) the characteristics of existing vehicle designs.
YMMV, good luck, etc, etc. -
#4 by su_liam on 19 Jul, 2012 22:29
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I've looked at the Young thesis paper and will gladly give you my thoughts about the the paper in general and the mass estimating relationships it provides in particular.
Thank you very much. Mostly, I'm just looking for explanations of what some of the variables represent. Some of my questions and attempts at self-answers may show evidence of serious misapprehensions. Hopefully, if you catch anything seriously boneheaded(other than using someone's doctoral thesis as a toy
), I'd love a head up!
After a bit of thought, I assume that SAstage represents the surface area of the stage. I further assume that's simply 2 Pi rstage Lstage.First, note the thesis is from 2009 and one of the advisors was Dr. Douglas Stanley. Yes I'm pretty sure this is the ESAS Lead Doug Stanley:
http://forum.nasaspaceflight.com/index.php?topic=5419.0
That pretty much gives the author an inside track on Constellation vehicles, but that comes with a price. He wasn't going to squeak by with vague approximations! You on the other hand are not writing a doctoral thesis, and Doug Stanley is not one of your advisors. So I doubt in your designs you need to raise anything (burnout mass or otherwise!) to the 0.7728th power, as this author apparently felt the need to do.
The've built it, so, if I can figure it out, I will play! My HP-48GX may be older than sin(or Sine), but raising a number to an arbitrary power is pretty easy. Even for me
.Others might scoff, but for in space propulsion I think it's sufficient to choose a propellant mass fraction for a stage (within reason) based on how much you're willing to pay for specialized engineering and manufacturing.
Mostly I'm just doing it this way to appeal to my own insane ideas of fun and a surprising touch of OCD. Which raises the question of why my house is such a mess. Apparently, my OCD doesn't swing that way.Unless you're trying to shoehorn an existing vehicle design into a overly tight architecture, it doesn't seem worth paying those costs. If your vehicle design doesn't complete its mission because its pmf is 0.92 instead of 0.94 -- well then design a bigger vehicle.
That does seem to be how the design cycle works.
1)Make a guess(more or less educated, depending on your level of... education). Let's call this stage, "Wash!"
2)See how well that adds up(In other words. Rinse.)
3)If you're outside your margin of error(pretty wide for pretendy science-fiction rockets), return to step 1("Repeat!").If you're wanting to design launch vehicles, or stages that participate in ascent, it definitely gets trickier! Still, you wouldn't go too far wrong by extrapolating (or certainly not by interpolating) the characteristics of existing vehicle designs.
YMMV, good luck, etc, etc.
I am looking at some LV designs...
Thank you.
Also, for anybody who's interested, I present
"Development of a Mass Estimating Relationship Database for Launch Vehicle Conceptual Design," by Reuben R. Rohrschneider.
I'm not up to touching that, yet, but someone else might find some meat in there.
), I'd love a head up!
.