Calculating the dry mass of a 5m+ diameter stage.

[ISProgram]

As in, calculating the dry mass of a 5m rocket stage, like Atlas V Phase 2.

Previously, a technique for finding out the dry mass of the stage was to make my dry mass:fuel mass ratios similar to that of actual rocket stages.

All I do is make my dry mass:fuel mass ratios similar to real rocket stages. Astronautix is a good resource for rocket stage data.

However, I noticed two potential problems with this:
- to get a accurate/realistic result, you also have to mimic the mixture ratio of the fuel/oxidizer, since that determines propellant mass.
- if a analog stage does not exist, then you can't get a result.

The rocket I'm planning is 5.75m in diameter and is fueled by RP-1/LOX. There is no analog stage in existence to baseline a dry mass; the closest thing that could be found was the Atlas V Phase 2 proposals.

So I ended up using the Atlas CCB as a analog, and ended up with a dry mass of 65,300 kg - the hypothetical stage is virtually identical in size and width to the Delta IV CBC, which is only 26,400 kg. So I thought something was wrong.

So I did something new. I modeled a rough approximation of two analog stages and my hypothetical stage into SketchUp, measured their internal volume and divided that by that stage's dry mass for the analogs.

Using this "density" number, I then fed the information into the analog stage volume. I ended up with these results:
- Delta CBC analog gave my hypothetical stage a dry mass of 31,450 kg.
- Atlas V analog gave me a dry mass of 61,315 kg.

Now, since my hypothetical stage is based of the Atlas V Phase 2 proposal, I was tempted to go with the CBC analog, since that number looked the most realistic and because both the hypothetical stage and Phase 2 are based off/similar to the CBC and would be very similar. The result reflect this.

The problem is, the Atlas V analog is 61,315 kg, which fits rather closely to that of the previously 65,300 kg dry mass found using the ratio technique. So right now, either result appears to be valid in its own regard.

My question is, which dry mass would be better, with regards to realism? Or if you know a better way of calculating this kind of dry mass, how to do it? Help is appreciated!

I would also like to note that the fuelxidizer ratio, and the propellant mass in general, is constant ad doesn't change between the analogs.

 

[Phil Smith]

hey ISProgram!
I guess 31,450 kg is closer value than 61 tons.. But what is your stage height?
probably I can help if you'll provide me total propellant mass and Oxidizer/Fuel ratio

 

[ISProgram]

hey ISProgram!
I guess 31,450 kg is closer value than 61 tons.. But what is your stage height?
probably I can help if you'll provide me total propellant mass and Oxidizer/Fuel ratio

Sure! Here are the current statistics.

Length: 41.45 m
Diameter: 5.75 m
Fuel/Oxidizer: RP-1/LOX
Fuel Mass/Oxidizer Mass: 244,297/636,811 kg
Propellant Mass: 881,108 kg

From the information, you can see that it is similar in diameter and height to the Delta CBC. The mixture ratio is 2.6 - 2.62, as it will be using a oxidizer-rich staged combustion engine.

It might also be worth noting that the RP-1 density value is .806 g/ml, and the LOX value is 1.141 g/cc. Also, the graphic below doesn't really illustrate that I have already calculated ullage volume (so the tanks aren't filled all the way).

Thanks in advance for the assistance!

 

[Phil Smith]

ISProgram, thanks for info, so let's go (i'm about to write calculations right here):
say, we got tail unit, just like Saturn V - there are just lower fuel tank bulkhead and thrust structure. engines are outside.
Bulkhead(s) height -
h_bulk = 0.75*Stage_radius = 0.75*(5.75/2) = 2.15 m;
Height of thrust structure:
h_ts = ~1.00 m;
Distance between bulkhead and thrust structure:
h_free = ~1.00 m;
Total tail unit height:
h_tail = 2.15+1.0+1.0 = 4.15 m.
Propellant tanks.
a) Fuel tank:
Fuel volume:
V_fuel = 244,297 / 806 = 303.1 m3;
Tank ullage volume:
V_ullage = V_fuel*0.03 = 303.1*0.03 = 9.093 m3;
Total fuel tank volume (+ extra 5% for everything inside the tank):
V_f_total = (9.093+303.1)*1.05 = 327.8 m3;
Bulkhead volume:
V_bulk = (2/3)*Stage_radius^2*h_bulk*Pi = (2/3)*(5.75/2)^2*2.15*3.14 = 37.2 m3;
Volume of cylindrical portion:
V_cyl = V_f_total - 2*V_bulk = 327.8 - 2*37.2 = 253.4 m3;
Cylindrical portion height:
h_cyl_f = V_cyl / (Stage_radius^2*Pi) = 253.4 / ((5.75/2)^2*3.14) = 9.76 m.

b) Intertank section:
h_intank = 2*h_bulk + 1.0 = 2 * 2.15 + 1.00 = 5.30 m;

c) Oxidizer tank:
Oxidizer volume:
V_oxid = 636,811 / 1,141 = 558.1 m3;
Tank ullage volume:
V_ullage = V_oxid*0.05 = 558.1*0.05 = 27.91 m3;
Total fuel tank volume (+ extra 3% for everything inside the tank):
V_ox_total = (27.91+558.1)*1.03 = 603.6 m3;
Bulkhead volume:
V_bulk = 37.2 m3;
Volume of cylindrical portion:
V_cyl = V_ox_total - 2*V_bulk = 603.6 - 2*37.2 = 529.2 m3;
Cylindrical portion height:
h_cyl_ox = V_cyl / (Stage_radius^2*Pi) = 529.2 / ((5.75/2)^2*3.14) = 20.4 m.

d) Aft unit height:
h_aft = ~2.5 m;

Total stage height:
H_st = h_aft + h_cyl_ox + h_intank + h_cyl_f + h_tail = 2.5 + 20.4 + 5.30 + 9.76 + 4.15 = 42.11 m.
Ok, now masses.

Say all skin has average thickness of 8.00 mm made of aluminum, then:
Skin mass = Stge_dia*Pi * 0.008 * H_st * rho_aluminum = 5.75 * 3.14 * 0.008 * 42.11 * 2700 = 16,430 kg;

Say all bulkheads have average thickness of 6.00 mm made of aluminum, then:
One bulkhead mass = 43.5 * 0.006 * 2700 = 705 kg
(where 43.5 m2 - is a bulkhead area (calculated as a half of ellipsoid area ( https://www.google.com/webhp?source...1&espv=2&ie=UTF-8#q=area+of+ellipsoid&spell=1 )
Number of bulkheads - 4;
Total bulkheads mass
M_bulk = 705*4 = 2,820 kg
Mass of other small tanks, devises, etc) =
M_other = (16,430 + 2,820) * 0.15 = 2,890 kg.
Mass of engines. And I forgot to ask you about a value of your thrust..
For huge engines their mass is 1% of their thrust.
For example your vehicle got engines with~ 1,800,000 kg (17,700 kN) total thrust, then engines mass is:
1800000*0.01 = 18,000 kg;

Oh, and of course, thrust structure! for example Saturn V one weights ~ 20,000 kg (with stage total thrust of 35 MN), so you've got approx. a half of it, so:
M_ts = ~10,000 kg

And now we got total dry stage mass:
16,430 + 2,820 + 2,890 + 18,000 +10,000 = 50,140 kg

So now your Atlas V analog is little bit closer))) but we've got almost a middle between your two options - (61,315 + 31,450)/2 = 46,382.5 kg

Propellant mass / dry stage mass ratio:
881,108 / 50,140 = 17.57! - this is a pretty awesome result))

PS sorry, if i got some math or spell errors above, but I hope you catch my thoughts))

PS PS I've uploaded a quick sketch of your stage (2 F-1 engines - just for show, they got appropriate thrust and weight though) and I thing 1 m thrust structure is too small so it should be increased up to 2-2.5 meters..
Cheers man!

 

[Pipcard]

That's a lot more in-depth than my rough estimations for stages. But I've never had that kind of information (such as bulkhead thicknesses) before. Thanks!

 

[Phil Smith]

That's a lot more in-depth than my rough estimations for stages. But I've never had that kind of information (such as bulkhead thicknesses) before. Thanks!

You're welcome!
About bulkheads, I can tell you some quick trick to calculate their thicknesses quite accurate.
Upper bulkheads - easiest part - they withstand just pressure of a tank pressurization system, so thickness of upper spherical bulkhead is:
t_up_bulk = (p_w*R) / (2*sigma),
where:
p_w = p_p*1.2
p_p - internal tank pressure, Pa (pressure of pressurization system);
1.2 - 20% safety factor;
R - Tank radius, m;
sigma - bulkhead material ultimate strength (for aluminum sigma = 320 MPa), but I prefer using the maximum yield strength = 170 MPa for aluminum.
For ellipsoidal bulkhead:
t_up_bulk = (p_w*R_bulk) / (2*sigma),
where:
R_bulk - is bulkhead radius, m:
R_bulk = Stage dia^2/(8*h_bulk) + h_bulk/2;
h_bulk - bulkhead height, m.

For lower bulkheads - little bit more difficult - they withstand internal tank pressure and hydro-static pressure from propellant.
Foe ellipsoidal bulkhead:
t_low_bulk =((p_p*R_bulk)/2 + pho*g*n_x*H*(R_bulk/2)*(1+(R_bulk/H)*((2/3)*((1-COS(alfa^3)/(SIN(alfa)^2)) - COS(alfa)))))*1.2/sigma

where:
alfa - bulhead angle:
alfa = arcsin(R_stage/R_bulk);
rho - density of propellant kg/m3;
g = 9.81 m/sec^2 - gravity acceleration;
n_x - axial acceleration of the vehicle, m/sec^2;
H - propellant hydro-static column, m
For spherical - all the same, just R_bulk = R_stage.

So as a result, lower bulkheads are thicker than upper ones.
I hope it'll help you too.

PS have corrected formula of lower bulkhead thickness, I guess I need to attach some schematic for easier understanding

.....

OK, schematic's added

 

[ISProgram]

PS PS I've uploaded a quick sketch of your stage (2 F-1 engines - just for show, they got appropriate thrust and weight though) and I thing 1 m thrust structure is too small so it should be increased up to 2-2.5 meters..
Cheers man!

Whoa. That's in-depth (as in the whole post, not just the sketch). Thank you!

This is the concept as it currently looks. I didn't make it clear earlier, and that's on me, but that big empty space to the right of the tanks were the engines, as this illustration shows. The thrust structure isn't terribly big (it's split into two parts, since those engines are only representative of the nozzles; the turbopumps and plumbing literally hug the RP-1 aft bulkhead), but I didn't think it had to be. Antares' twin NK-33 are pretty close to the tank bulkhead, as this shows. The vehicle is also somewhat sized-constrained, since the full rocket is almost equal in height to the Delta IV Heavy (71.95 meters vs. Delta's 70.7 meter)

See, a while back I decided on a four-engine architecture for the vehicle. This was primarily because I wanted to have engine-out capability, and because it looked cool. This gradually evolved into a single four-chamber staged combustion engine, like the RD-170.

This engine put out a estimated 13,037 kN, but that assumed that the first stage had a dry mass of 65,300 kg, the original estimate. With the lower dry mass, the engine can now afford to be smaller and less powerful. I'm considering going back to a twin two chambered-engine architecture.

The reason the engines are the way they are is because I want to keep the diameter of the launch vehicle constant; it simplifies the launch pad exhaust opening and enables for triple-core configurations. So, the engines are actually contained within the 5.75 meter diameter of the stage, or are gimbaled outwards, like the Zenit's. Hopefully, the picture(s) illustrate what I mean...

I also tried to recalculate the dry mass of the first stage independently, and found that it was also in the 40,000-45,000 kg range, primarily because the engine was very heavy (16,996 kg).

That being said, your numbers were pretty much on the mark.

---------- Post added 09-23-14 at 07:41 PM ---------- Previous post was 09-22-14 at 08:42 PM ----------

A updated schematic, with the updated engine (still a 4-chambered stage combustion engine). It has been resized, so that it is proportionately the same size as the RD-170 is with the Zenit-3SLB. It's about 90% the size of the previous engine proposal. The thrust structure is now 1m, a .25m increase from what it originally was.

Still calculating thrust...

 

[Phil Smith]

Glad it helps!
btw nice 3d model! Is upper stage propelled by LH2/LOX engine?
yep, rd-170's great choice - good ol'engine, too bad it's retired.. great efficiency and pretty "green" for RP-1/LOX motor. rd-180 is the same but twice smaller - If i was Energomash employee I'd create vehicle with core stage equipped with one rd-170 and two strap-on boosters with rd-180 :lol:
So if you got another questions about rocket/engine structures - feel free to ask
Cheers!

 

[ISProgram]

Glad it helps!
btw nice 3d model! Is upper stage propelled by LH2/LOX engine?
yep, rd-170's great choice - good ol'engine, too bad it's retired.. great efficiency and pretty "green" for RP-1/LOX motor. rd-180 is the same but twice smaller - If i was Energomash employee I'd create vehicle with core stage equipped with one rd-170 and two strap-on boosters with rd-180 :lol:
So if you got another questions about rocket/engine structures - feel free to ask
Cheers!

The upper stage is indeed using a LH2/LOX engine, based of the J-2/J-2X. The first stage and the second stage engines are called the RD-290 and L-1, respectively.

I actually have a question concerning that 41,610 kg dry mass figure you calculated earlier. If I read correctly, it doesn't include engine mass, right? The 18,000 kg quote was just a example?

---------- Post added at 09:16 PM ---------- Previous post was at 09:08 PM ----------

Forgot to mention; the current RD-290 engine baseline has it weighing 22,841 kg and tossing out 17,920 kN of thrust (all of this coming out of four 1.90m diameter nozzles).

Is that excessive or still plausible, at least in real life? That thrust alone is 2.6 times that of the F-1.

 

[Phil Smith]

I actually have a question concerning that 41,610 kg dry mass figure you calculated earlier. If I read correctly, it doesn't include engine mass, right? The 18,000 kg quote was just a example?

It's mass with engines (+18,000 kg in my case).
But value of 41,610 kg is now 50,140 kg (first time I forgot about heavy massive thrust structure weights approx. 10,000 kg if you use crossed-beam configuration like on Saturn V first stage.
So that digit (50,140) consists:
Dry stage structure mass + engine mass:
32,140 + 18,000 = 50,140 kg

So in your case (with 22,841 kg engine):
32,140 + 22,810 = 54,950 kg.
Actually you can reduce some weight using truss thrust structure design, just like on rd-170 - all chambers and turbo pump mount on steel truss with giant ring at the top attaching to the lower stage structure.

And usually rd-170 weight already includes the mass of this truss - so 22,841 can be mass of engine + its thrust structure, then you got:
54,950 - 10,000 (mass of my crossed beam thrust structure) = 44,950 kg

Forgot to mention; the current RD-290 engine baseline has it weighing 22,841 kg and tossing out 17,920 kN of thrust (all of this coming out of four 1.90m diameter nozzles).
Is that excessive or still plausible, at least in real life? That thrust alone is 2.6 times that of the F-1.

let's see.
you got 4 chambers, so thrust of one is 17,920 / 4 = 4,480 kN (say it's sea level thrust);
from rd-170 let's take some parameters:
Sea level specific impulse - Isp_sl = 309 sec;
Thrust chamber pressure - P_c = 25 MPa;
Nozzle ration - e = 36.87.
Mass flow of one chamber - 4,480,000/9.81/309 = 1,480 kg/sec;
Thrust coefficient:
cf = 1.7351;
(I use free (lite) version of this software to calculate main combustion parameters - http://www.propulsion-analysis.com/downloads.htm );
Throat area:
A_th = Thrust / (cf * P_ch) = 4,480,000 / (1.7351 * 25,000,000) = 0.103 m2;
Throat diameter:
D_th = sqrt(4/pi * A_th) = sqrt(4/pi * 0.103) = 0.362 m;
Nozzle exit diameter:
D_e = sqrt(e)*D_th = sqrt(36.87)*0.362 = 2.19 m

So you need to add extra 2.19-1.90 = 0.29 cm to nozzle exit dia and you're ok.
But if you're gonna share one turbo-pump assembly among 4 chambers (like on RD-170 or other Russian engines), this baby will be HUGE, 2.5 times bigger than RD-170 or F-1 had and pumping 5,960 kg of propellant per second! awesome!

 

[Notebook]

This thread may help

http://www.orbiter-forum.com/showthread.php?t=6705&highlight=propellant+change+cog

Different objective, but things changed; sorry most photobucket links have gone on the first pages, but a lot of the maths is still there.

N.

 

[ISProgram]

It's mass with engines (+18,000 kg in my case).
But value of 41,610 kg is now 50,140 kg (first time I forgot about heavy massive thrust structure weights approx. 10,000 kg if you use crossed-beam configuration like on Saturn V first stage.
So that digit (50,140) consists:
Dry stage structure mass + engine mass:
32,140 + 18,000 = 50,140 kg

So in your case (with 22,841 kg engine):
32,140 + 22,810 = 54,950 kg.
Actually you can reduce some weight using truss thrust structure design, just like on rd-170 - all chambers and turbo pump mount on steel truss with giant ring at the top attaching to the lower stage structure.

And usually rd-170 weight already includes the mass of this truss - so 22,841 can be mass of engine + its thrust structure, then you got:
54,950 - 10,000 (mass of my crossed beam thrust structure) = 44,950 kg


let's see.
you got 4 chambers, so thrust of one is 17,920 / 4 = 4,480 kN (say it's sea level thrust);
from rd-170 let's take some parameters:
Sea level specific impulse - Isp_vac = 309 sec;
Thrust chamber pressure - P_c = 25 MPa;
Nozzle ration - e = 36.87.
Mass flow of one chamber - 4,480,000/9.81/309 = 1,480 kg/sec;
Thrust coefficient:
cf = 1.7351;
(I use free (lite) version of this software to calculate main combustion parameters - http://www.propulsion-analysis.com/downloads.htm );
Throat area:
A_th = Thrust / (cf * P_ch) = 4,480,000 / (1.7351 * 25,000,000) = 0.103 m2;
Throat diameter:
D_th = sqrt(4/pi * A_th) = sqrt(4/pi * 0.103) = 0.362 m;
Nozzle exit diameter:
D_e = sqrt(e)*D_th = sqrt(36.87)*0.362 = 2.19 m

So you need to add extra 2.19-1.90 = 0.29 cm to nozzle exit dia and you're ok.
But if you're gonna share one turbo-pump assembly among 4 chambers (like on RD-170 or other Russian engines), this baby will be HUGE, 2.5 times bigger than RD-170 or F-1 had and pumping 5,960 kg of propellant per second! awesome!

Thanks again for the help! 2.19 nozzle diameter?! :jawdrops: How am I going to get FOUR of those on a 5.75m rocket?! It's Frankenstein's monster at this point!

And I should supply more detail in the future, that 17,290 kN is its vacuum thrust, since these numbers were made to be fed into Silverbird. Sorry about that.

Also, I will try to get out another graphic with the new engine details later.

---------- Post added at 07:53 PM ---------- Previous post was at 07:39 PM ----------

Just had a thought. Does engine height still matter at this point? I'm still size-constrained on the length of the first stage, and one measure I've considered implementing to make more room for the engine was shrinking the interstage length, so that the tank bulkheads are closer together.

Antares does it too, as some cutaway images (like the previous link) will show that its propellant tanks practically touch each other.

 

[Phil Smith]

ok, no problem
so for 17,290 kN of vacuum thrust we got:
4,480 kN thrust per chamber;
Vacuum thrust coefficient:
cf = 1.8865;
Throat area:
A_th = Thrust / (cf * P_ch) = 4,480,000 / (1.8865 * 25,000,000) = 0.095 m2;
Throat diameter:
D_th = sqrt(4/pi * A_th) = sqrt(4/pi * 0.095) = 0.348 m;
Throat radius:
R_th = 0.348/2 = 0.174 m;
Nozzle exit diameter:
D_e = sqrt(e)*D_th = sqrt(36.87)*0.348 = 2.11 m
So little bit smaller))
and now engine length - you need provide proper combustion chamber volume for better combustion process and smooth contour from throat to nozzle exit.
let's make some math:
Comb. Chamber characteristic length for LOX/RP-1 application (taking it form table 4-1 in my attachments):
L* = 1.150 m;
Comb. Chamber volume:
V_c = L* * A_th = 1.150* 0.095 = 0.10925 m3;
From table 4-9 we take contraction ratio e_c = 1.7.
Use a nozzle convergent half-angle of 20 deg and circular arc of radius R = 1.5*R_th = 1.5*0.348/2 = 0.261 m, upstream of the throat, as follows:
Chamber diameter:
D_c = sqrt(e_c)*D_th = sqrt(1.7)*0.348 = 0.456 m;
Chamber radius:
R_c = 0.456/2 = 0.228 m;
Camber convergent cone length:
L_cc = (R_th*(sqrt(e_c) - 1) +R*(SEC(20degree) - 1))/(TAN(20degree)) = (0.174*(sqrt(1.7) - 1) +0.261*(SEC(20degree) - 1))/(TAN(20degree)) = 0.191 m;

Using the cone-frustum-volume equation and neglecting the slight rounding of the throat, the approximate convergent cone volume can be obtained as follows:

V_cc = (pi/3) * L_cc * [(R_c)^2 + (R_th)^2 + R_c + R_th] = (pi/3) * 0.191 * [(0.228)^2 + (0.174)^2 + 0.228 + 0.174] = 0.097 m3;

Required volume of cylindrical chamber section:
V_cyl = V_c - V_cc = 0.10925 - 0.097 = 0.0123 m3;

Required length of cylindrical chamber section:
L_cyl = V_cyl/(e_c * A_th) = 0.0123/(1.7 * 0.095) = 0.076 m;

Distance from injector face to throat:
L_chamber = L_cyl + L_cc = 0.076 + 0.191 = 0.276 m, say 0.280 m.

Now we design an 80% bell nozzle configuration. The nozzle contour downstream of the throat will be a circular arc of radius 0.382*R_th = 0.382*0.174 = 0.066 m. By definition, the nozzle length L_n will be 80% of the length of an equivalent 15-deg-half-angle conical nozzle.

So as far as you need just nozzle length, I won't write how to calculate all parabolic radii in the nozzle skirt to reduce length of the post LOL.

So nozzle length:
L_n = 0.8* [(R_th*(sqrt(e) - 1) + 0.066*(SEC(15degree) - 1))/(TAN(15degree)] = 0.8* [(0.174*(sqrt(36.87) - 1) + 0.066*(SEC(15degree) - 1))/(TAN(15degree)] = 2.642 m, say 2.645 m;

Total thrust chamber height (from injector face to nozzle exit):
L_engine = L_chamber + L_n = 0.280 + 2.645 = 2.925 m;

And dont forget about all manifolds/domes and gimbal mount on the top of the camber so you can add extra 0.2 m:
2.925 + 0.2 = 3.125 m

PS - I've taken this calculations and tables from book called "Modern Engineering for Design of Liquid Propellant Rocket Engines" pages 82-83 - https://app.box.com/s/46rhns45x6ulvukj3ryf
Awesome book and great samples!! and there you find all schematics for this mess))))

PS PS - SEC (X) = 1/(COS(X));

Enjoy!

 

[ISProgram]

I might've failed horrible in interpreting that information. At the moment, the engine (or at least one of its nozzles) looks like this. From top to bottom, it's 3.13 meters. About .18m below the very top is where the injection face is.

Hopefully, it's accurate to the information. I somewhat doubt this. :huh:

On the bright side, the engine is short enough that it can once again fit in the original thrust structure, with some margin, so the first stage will/should retain its original 41.45 m length. That margin is supposed to account for the turbopump propellant lines and the mess of piping this engine is going to be. I've also created a outline of the truss for the thrust structure.

Oh, and one other thing...

But if you're gonna share one turbo-pump assembly among 4 chambers (like on RD-170 or other Russian engines), this baby will be HUGE, 2.5 times bigger than RD-170 or F-1 had and pumping 5,960 kg of propellant per second!

With 881,108 kg of propellant, and with that monster RD-290 burning 5,960 kg of propellant per second, the first stage will have 147.83 seconds of burn time. That's somewhat short for a liquid fueled first stage, something I expect more from a solid fueled rocket.

Does this mean that it will accelerate quickly or that the second stage is powerful enough to overcome the shorter burnout time and resultant lower separation altitude? The first option could be bad for a delicate payload; the second might imply a seriously overpowered, perhaps implausibly, second stage.

See, before I made this thread, with the 65,300 kg first stage dry mass, the rocket was already capable of >48,000 kg to LEO. Now that the dry mass figure is 20,000 kg lower, that only increases.

How can a rocket with such a short burn time place that much into orbit?

BTW, thanks for the help.

 

[Phil Smith]

How can a rocket with such a short burn time place that much into orbit?

BTW, thanks for the help.

we're welcome!
So can you provide me some data about upper stage(s)? I'll run some trajectory simulations to see how far this boy will fly.

I need 2nd stage engine vacuum thrust and specific impulse, 2nd stage dry and propellant masses and if you have the 3rd stage - I need same parameters for it.

For the first stage I got all I need:
1st Stage engine vacuum thrust - 17,920 kN;
1st Stage engine vacuum specific impulse (taken from RD-170) - 338 sec;
1st stage dry mass - I'll take 45,000 kg cause we've reduced 10,000 kg from 54,950 kg by deleting the heavy crossed-beam thrust structure;
1st Stage propellant mass - 881,108 kg.

Payload mass is 48,000 kg (for the first shot will be enough, if there will be some good result we can increase it.

Also I need payload fairing length or its approximate mass.
As I see from your 3d model all stages have the same diameter of 5.75 m?

So you can quick-check your vehicle against Tsiolkovsky equation - if you'll get a value of deltaV >= 9,500 m/s - you're ok to reach LEO

PS 147 sec is pretty much standard burning time for huge pr-1/LOX stages.
Tremendous Saturn V's S-Ic was fired for 150 sec too and placing S-II at just 40 nm altitude.

 

[ISProgram]

Well, the rocket has two upper stages. Not a second or third stage, but different optional upper stages for different missions.

The first is the H-IVA. It has a dry mass of 8,733 kg, and holds 77,177 kg of propellant, of which 12,863 kg is hydrogen and 64,314 kg is oxygen. Its single engine, weighing 3,301 kg, puts out 1,470 kN of thrust, though it can go as low as 1,007 kN, and possibly higher as well. This engine has a vacuum specific impulse of 452 s.

The second is called the SPS-Aquarius. It has a dry mass of 1,121 kg, and holds 8,914 kg of propellant, of which 3,076 kg is monomethylhydrazine and 5,838 kg is nitrogen tetroxide . Its single engine puts out 28 kN of thrust, though I think it can go higher. This engine has a vacuum specific impulse of 324 s.

The payload fairing also has two variants. The first is 2,600 kg, the second is 3,100 kg. Only the first one is actually relevant. Both fairings are normally jettisoned at 267 s into flight.

If you are calculating the rocket's ascent, then the interstage will also be needed. Its mass is 1,374 kg.

 

[ISProgram]

Decided to reestimate the H-IVA-200 dry mass, since that 8,733 kg figure was getting suspicious...

Decided to burrow your equations, hope that's okay. The second stage uses much of the same toolings as the first stage, so the equation can apply to both.

Since all skin has average thickness of 8.00 mm made of aluminum, it should be:
Skin mass = Stge_dia*Pi * 0.008 * H_st * rho_aluminum = 5.75 * 3.14 * 0.008 * 12.4 * 2700 = 4835.8512 kg, going to round that to 4,836 kg;
All bulkheads have average thickness of 6.00 mm made of aluminum, per your earlier estimates, so:
One bulkhead mass = 43.5 * 0.006 * 2700 = 705 kg
(where 43.5 m2 - is a bulkhead area calculated earlier; turns out the SketchUp model's is just 40.86 m2)
Number of bulkheads is one - 1; the same calculation must now apply to the secondary common bulkhead.
Everything is the same for the previous bulkhead estimate, save the bulkhead area, so:
One bulkhead mass = 37.8 * 0.006 * 2700 = 613 kg
Total bulkheads mass
M_bulk = 613*2 = 1,226 + 705 = 1,931 kg
Mass of other small tanks, devises, etc) =
M_other = (4,836 + 1,931) * 0.15 = 1,015 kg.
Mass of engines. That's been basedlined at 3,301 kg. For thrust structure, I don't know, the engine is bolted directly to the aft bulkhead of the LOX compartment, so I'm just going to go for 840 kg (Saturn V's 20,000 kg (with stage total thrust of 35 MN), so 840 kg with total thrust of 1.7 MN).
Total dry stage mass:
4,836 + 1,931 + 1,015 + 3,301 + 840 = 11,923 kg

Slightly higher that the previous 8,733 kg dry mass figure, but still only 3,190 kg higher. And I put margin on these estimates.

Propellant mass / dry stage mass ratio:
77,177 / 3,190 = 24.19 - that's more than I expected!

 

[Phil Smith]

things get heavier as always :lol:
Now I've been trying to optimize pitch program, cause with average one you got just 5,800 m/s of total vehicle delta V. it's taking a while...
Attaching a screen with trajectory (green line - vehicle trajectory from lift-off util splashdown of the second stage, white - trajectory of separated first stage).
some parameters:
(payload mass - 48,000 kg, payload fairing mass - 2,600 kg, payload fairing jettison time - 267 sec)

first stage burn time = 155 sec;
Ideal deltaV (checked against Tsiolkovsky equation) of the stage = 5,314 m/s;
first stage delta V = 3,957.19 m/s;
vehicle velocity at the first stage cut-off = 3,957.19 m/s;
vehicle altitude at the fisrt stage cut-off = 94.1407 km;

second stage burn time = 361 - 155 = 206 sec;
Ideal deltaV (checked against Tsiolkovsky equation) of the stage = 3,897 m/s;
second stage delta V = 1,542 m/s;
vehicle velocity at the second stage cut-off = 5500.14 m/s;
vehicle altitude at the second stage cut-off = 356.402 km;

Little conclusion.
First stage "performed" normal - great delta V and altitude, Velocity loss (gravity + aerodynamic) = 5,314 - 3,957.19 = 1,357.81 m/s is a great result for the first stage - Saturn V's S-Ic got 3,660 - 46 - 0 = 2,394 m/s (ideal stage velocity - gravity loss - aerodynamic loss - steering loss = actual velocity).
Second stage got only 1,542 m/s of deltaV - something more powerful needed. Also pitch program correction will increase total performance of the stage, cause we got 3,897 - 1,542 = 2,355 m/s of velocity loss - it's way out of range for upper stage gravity losses...
Saturn V's S-II stage data for comparing:
4,725 - 335 - 0 -183 = 4,207 m/s (same here: ideal stage velocity - gravity loss - aerodynamic loss - steering loss = actual stage velocity).
S-IVb stage:
4120 - 122 - 0 - 4.5 = 3,993 m/s;
SaturnV's total ideal delta V = 12,505 m/s;
SaturnV's total gravity loss = 1,677 m/s;
SaturnV's total aerodynamic loss = 46 m/s;
SaturnV's total steering loss = 187.5 m/s
SaturnV's total actual deltaV = 10,594.5 m/s

For your second stage I recommend you to increase its deltaV from 3,897 m/s to 8,000 - 3,957.19 + ~600 = ~4,700 m/s.

If you have any pitch program already - let me know - that make thing easier))

And probably you should try to simulate it in Orbiter and see what's going on there.

Propellant mass / dry stage mass ratio:
77,177 / 3,190 = 24.19 - that's more than I expected!

you wanted to say 77,177 / 11,923 = 6.47 ? cause it I got right - 3,190 is delta between current and previous masses

 

[ISProgram]

you wanted to say 77,177 / 11,923 = 6.47 ? cause it I got right - 3,190 is delta between current and previous masses

:facepalm:

Well, that's still something.

---------- Post added at 06:23 PM ---------- Previous post was at 06:16 PM ----------

For your second stage I recommend you to increase its deltaV from 3,897 m/s to 8,000 - 3,957.19 + ~600 = ~4,700 m/s.

If you have any pitch program already - let me know - that make thing easier))

And probably you should try to simulate it in Orbiter and see what's going on there.

How exactly do I increase delta-V? Wouldn't that require a (major) redesign for the upper stage?

No pitch program yet, was going to work on that when I started making the addon. Haven't started that yet.

I can model simulate the rocket by modifying .cfg files, right?

---------- Post added at 07:46 PM ---------- Previous post was at 06:23 PM ----------

Since I'm horrible at Orbiter, and programming, I could only do a rudimentary simulation. I used [ame="http://orbithangar.com/searchid.php?ID=6438"]an addon of Pipcard's[/ame].

Basically, I did a straight fly-up and only pitched over when staging occurred. I managed to reach orbit (I really am horrible with this kind of stuff).

So it should be able to reach orbit. Also, note the fuel and thrust gauges in the upper corners, particularly how they match the previously given values for the rocket. I take that as confirmation that I managed to successfully simulate the rocket.

---------- Post added at 10:12 PM ---------- Previous post was at 07:46 PM ----------

Decided to review some of my data and resources and came upon something rather dismaying. Whereupon the fuel/oxidizer mass for the rocket was 244,297/636,811 kg, it now appears that (not counting ullage) it is 242,426/632,180 kg instead.

The only real good news at the moment is that these calculations (derived from the latest 3D modeled rocket) assume a 14 mm tank wall/skin, so the propellant weight could possibly be higher.

The second stage manages 13,576/64,888 kg, compared to its earlier 12,863/64,314 kg figure. Again, not calculating ullage.

This figure still considers 14 mm tank wall/skin, while those earlier calculations assumed 8mm. That 6mm difference will be my margin from now on.

Working on a few calculations right now to optimize the propellants in both stages, as well as a possible second stage re-engine.

@Phil Smith: If I'm correct, you calculated ullage in your previous equations?

@Anyone in General: Anyone know a particularly better/more realistic density for RP-1 than .806 g/ml?

 

[Phil Smith]

i'm not a pro addon developer either, but as I see on your screen #2 it's a first moment of second stage firing? if so, you had very steep trajectory - 302 km is quite high altitude for first stage cut-off - it's should be around 80-110 km range in your case.

Unfortunately, if the current 2nd stage concept will fail, there will be some major redesign.. Perhaps making second stage bigger and first stage smaller gives you some result - more efficient at high altitudes LH2/LOX engine(s) will fire longer, giving bigger values of total vehicle deltaV.
But first off, try to increase second stage thrust little bit (say two engines instead of one) and try it again several times in orbiter.

@Phil Smith: If I'm correct, you calculated ullage in your previous equations?

yep, I've calculated all tank volumes with ullage space

@Anyone in General: Anyone know a particularly better/more realistic density for RP-1 than .806 g/ml?

take a look at this paper page 1, or 6th in the pdf):
http://www.dtic.mil/dtic/tr/fulltext/u2/290659.pdf
it says:

density = 0.798+- 0.0005 gm/mL (or kg/m3) at 25.00 C

There are different physical properties of RP-1 that can be useful

PS I hope some guys will help you with orbiter simulation
Cheers!