Launch vehicle calculations

Phil Smith

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So long time ago I found myself in rocketry and now I think about Launch vehicle project for little satellite (about 2-10 lbs). Just in theory for a while.
And I've read a lot of books and projects descriptions and didn't figured out one question: how i can find required propellant masses at first steps of calculations?
There is two stage vehicle.
i tried this equation:

2nd stage propellant mass:
M(f2) = (M0*k*(exp(V/Isp))/(k+1-exp(V/Isp));

2nd stage dry mass:
M(d2) = M(f2)/k;

2nd stage total mass:
M(2)=M(d2)+M(f2);

1st stage propellant mass:
M(f1) = ((M(2)+M0)*k*(exp(V/Isp))/(k+1-exp(V/Isp));

1st stage dry mass:
M(d1) = M(f1)/k;

1st stage total mass:
M(1)=M(d1)+M(f1);

(M0 - payload mass;
k - ratio of propellant mass to dry stage mass;
V - stage delta V;
Isp - Specific impules of stage engine(s) )

But in my opinion it's very very approximate calculation.
So where I can find the right way of doing that (some kind of book) or tell me how please :hailprobe:
 
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Jarvitä

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The delta v of a stage is its exaust velocity multiplied by the logarithm of the mass ratio:

[MATH]\Delta v = v_{ex} \times log \frac{m_{fuel}+m_{stage}}{m_{stage}}[/MATH]
If you solve for the mass ratio, you get the following relation:

[MATH]\frac{m_{fuel}+m_{stage}}{m_{stage}} = e^{\frac{\Delta v}{v_{ex}}}[/MATH]
Of course, for the lower stages, you must also take the mass of everything above them into account by adding it to the stage mass. It comes down to determining the right ratio of total mass between stages and cargo.
 
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Urwumpe

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I can post you more formulas later, I have the functions for calculating payload mass fraction and optimizing stage ratios somewhere in my university shelf.
 

Phil Smith

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2 Jarvitä: yeah i know it - there are the same formulas what i wrote above -just another point of view
2 Urwumpe: ok man i'm waitin to check em out:thumbup:

BTW - kinda strange think - i found a lot of book about calculation ballistics missiles (when you have payload mass and range) but no one for satellite launch vehicles :( maybe anybody knows some sort of good book about that thing (in english or russian)? will very appreciate for helping :cool:
 

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2 Jarvitä:BTW - kinda strange think - i found a lot of book about calculation ballistics missiles (when you have payload mass and range) but no one for satellite launch vehicles :( maybe anybody knows some sort of good book about that thing (in english or russian)? will very appreciate for helping :cool:

Hi.

Space Mission Analysis and Design by James Wertz describes basically how to design a satellite mission. Some parts might be legacy of the cold war, like the provision on how to build a communication satellite able to function for a month in a "radiation enhanced" (i.e. nuked to hell) Van Allen belts. However it is a good book.

Besides, the requirement of the space launcher stem from your mission: what is your satellite designed to perform? What are you planning for its orbital parameters?
 

Urwumpe

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Ok, better late than never... the formulas:

Definition payload mass ratio:

[math]\lambda=\frac{m_N}{m_0}[/math]
[math]m_N[/math] is payload mass, [math]m_0[/math] is total mass at ignition (of stage)

Payload mass ratio of stage (i):

[math]\lambda^{(i)} = \frac{e^{\frac{-{\Delta v}^{(i)}}{w^{(i)}}} - \sigma^{(i)}}{1-\sigma^{(i)}}[/math]
[math]\sigma^{(i)}[/math] is the structural mass ratio of the rocket or stage, the ratio of dry mass to total mass:

[math]\sigma = \frac{m_d}{m_0}[/math]
Multiple stages:

[math]\lambda = \lambda^{(1)} \cdot \lambda^{(2)} \cdot \dots \cdot \lambda^{(n)}[/math]
 

Phil Smith

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Hi.

Space Mission Analysis and Design by James Wertz describes basically how to design a satellite mission. Some parts might be legacy of the cold war, like the provision on how to build a communication satellite able to function for a month in a "radiation enhanced" (i.e. nuked to hell) Van Allen belts. However it is a good book.

Besides, the requirement of the space launcher stem from your mission: what is your satellite designed to perform? What are you planning for its orbital parameters?

thanks for book, strongly need to read!
it's just little tiny capsule with transmitter and 360 grad camera. And i prefer to use abort system in a case of launch vehicle failure, that pushes the satellite away from rocket like a escape tower.
Orbit - Ae and Pe ~ 200 km.
I got my first results with the booster yesterday and set the orbit at Ae = 3200 km and Pe = 120 km. (just need to correct pitch program).
there are some my drawings bellow (electric diagram and first drawing of satellite. All dims are in MILLIMETERS).





Ok, better late than never... the formulas:

Definition payload mass ratio:

[math]\lambda=\frac{m_N}{m_0}[/math]
[math]m_N[/math] is payload mass, [math]m_0[/math] is total mass at ignition (of stage)

Payload mass ratio of stage (i):

[math]\lambda^{(i)} = \frac{e^{\frac{-{\Delta v}^{(i)}}{w^{(i)}}} - \sigma^{(i)}}{1-\sigma^{(i)}}[/math]
[math]\sigma^{(i)}[/math] is the structural mass ratio of the rocket or stage, the ratio of dry mass to total mass:

[math]\sigma = \frac{m_d}{m_0}[/math]
Multiple stages:

[math]\lambda = \lambda^{(1)} \cdot \lambda^{(2)} \cdot \dots \cdot \lambda^{(n)}[/math]

very appreciate your help!!! thanks alot!!!
 
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francisdrake

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attachment.php


I took data from the upper stages of the old Scout launcher (1960s all-solids rocket) and entered a payload mass of 5 kg (~12 pounds).
The spreadsheet to play around is my trusty old DeltaVcalc:
http://orbiter-forum.com/attachment.php?attachmentid=7187&d=1303424862
 

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Mattyv

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Phil Smith

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Thanks a lot everybody! Ive done masses calculus. :probe:
Ideal deltaV - 10,040 m/s.
Max payload weight - 10 kg.
but here i got a problem with pitching program calculation.
i make flight simulation in one russian program called "sputnik". very impressive freeware. you enter all main parameters of your vehicle (masses, thrusts, specific impulses, launch site, pitching and yaw program etc) but best results i got are apogee at 3639.44 km, perigee at 120.055 (to low I guess).
Here's screenshot of program window (I marked pitch values)


BTW - start time is time in seconds after launch.

and another screen with orbit parameters:



so here's a question - how to calculate trajectory to the orbit?


for example: i need to reach orbit with perigee about 200 km. besides all masses of vehicle are known. What kinda calculation i need to perform to get my RIGHT pitch program with the RIGHT altitude? :idk:
 
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Urwumpe

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Remember that you can't have a higher perigee, than your altitude at cut-off. You can change this by:

  • Reducing pitch slower and gain more vertical speed.
  • Include a coast-phase without propulsion

I would recommend using closed-loop guidance for orbit-insertion anyway, if you need accuracy.
 

Phil Smith

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Remember that you can't have a higher perigee, than your altitude at cut-off. You can change this by:

  • Reducing pitch slower and gain more vertical speed.
  • Include a coast-phase without propulsion

I would recommend using closed-loop guidance for orbit-insertion anyway, if you need accuracy.

I tried different variations of pitch parameters but didnt get results better than 3110.24 Ap and 122.115 Pe with deltaV = 8237.35 m/s. (but i made 1,000,000 iterations and found out the satellite will survive more than 15 days :D )
I first time make such kind of trajectory calculations and need to be pushed here in that question. :facepalm:
Yesterday I start reading "Space Mission Analysis and Design" by James Wertz but dont find solve for such problem there yet.
 
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Phil Smith

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Does this "sputnik" program have an English version/counterpart?

unfortunately no.. i've installed on my second laptop RUSSIAN WINDOWS just because of that program (in english version all letters are question marks, for example word "apogee" will be "??????")
I wanted to contact with developers but i didnt find any clue about them.
Here's their official site: http://traintospace.narod.ru/ but there are just to links on their programs. at all.
 

Urwumpe

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Can you include a small phase without propulsion in your rocket? Or have a lower thrust of the second stage?
 

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If there's no way to include a coast phase, you could try a steeper launch followed by a quick pitch-down. This would make it less efficient, but allow for a higher perigee.
 

Phil Smith

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Can you include a small phase without propulsion in your rocket? Or have a lower thrust of the second stage?

ok, I try to reduce 2nd stage engine thrust little bit. it it wont work, make a small phase (but that way is more difficult - we need to start engine 2 times).
Anyway i give you all parameters of vehicle:

FIRST STAGE
First stage full mass - 11 700 kg
First stage dry mass - 1 670 kg
First stage fuel mass - 10 030 kg

First stage engine specific impulse -
Isp(sl) = 2 762 m/s
Isp(v) = 3 183 m/s
First stage engine thrust -
F(sl) = 150 kN
F(v) = 175.8 kN

SECOND STAGE
Second stage full mass - 800 kg
Second stage dry mass - 170 kg
Second stage fuel mass - 630 kg

Second stage engine specific impulse -
Isp(sl) = 1 421 m/s
Isp(v) = 3 234 m/s
Second stage engine thrust -
F(sl) = 7.5 kN
F(v) = 17 kN

Payload mass (max) - 10 kg
Total launch vehicle weight - 12 510 kg
 

Urwumpe

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You could also just ignite the second stage later, if your program permits to simulate it.
 

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unfortunately no.. i've installed on my second laptop RUSSIAN WINDOWS just because of that program (in english version all letters are question marks, for example word "apogee" will be "??????")
I wanted to contact with developers but i didnt find any clue about them.
Here's their official site: http://traintospace.narod.ru/ but there are just to links on their programs. at all.

*sigh* I wish there was an English version. It looks good for planning a launch vehicle, and is probably more advanced and accurate than this.
 

Phil Smith

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*sigh* I wish there was an English version. It looks good for planning a launch vehicle, and is probably more advanced and accurate than this.
i wish too ;)
sure it's way way more advanced and accurate than that one. Sputnik shows you what orbit you have in 3D, all kind of useful diagrams "by time" such as vehicle velocity, weight, altitude, pitch and yaw angles, air density etc) and it makes reports you can save. Here is example of the report for my booster (i zoomed it out to fit it to the screen):



There is flight plan, and ALL parameters of all flight and orbit

I wanna to translate this program myself and I hope i'll done it. sooner or later..

You could also just ignite the second stage later, if your program permits to simulate it.
it can be done by makin "ghost" stage between first and second.
BTW - THANKS ALOT! a reduce thrust from 2nd stage from 17 to 13.5 kN (in void) and get perigee at 147.1 and apogee at 2839 km. pretty cool I admit :)

---------- Post added at 06:54 PM ---------- Previous post was at 05:14 PM ----------



Bull's eye! So that program has a function "turn on/off" stage's engine when you want. so i made 20 sec delay after 1st stage burnout and ignited second - and that's it! 156.161 km Perigee!:cheers:
Satellite lifetime from launch till touchdown - 1d00:47:45.104 - not bad.
 
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