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

ISProgram

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The problem is, the basic structure of the first and upper stages are set in stone, so to speak. I could tweak their propellant capacity slightly, probably design different engines, but I really can't extensively modify the stage as it is.

I'm basically stuck trying to tease out as much performance as possible. Kind of like what NASA had to do with the Ares I. That's a bad omen.

Among the first things I'm doing at the moment is lengthening the second stage, by increasing the propellant tank length, but decreasing the forward skirt by the same amount, so the rocket doesn't get "taller". Drawback of this is that it takes up more space inside the fairing.

I'm also considering going with a J-2 derived engine (which weighs only 1,788 kg, compared to the 3,301 kg for the previous engine).

A common bulkhead for the first stage is also an option going through my mind right now.

A question I have to ask, though, is the 8mm and 6mm tank skin figures you used earlier in your calculations. How exactly do you come up with these numbers?

I ask this because if I can find a "thinner" tank skin figure that can still support its own weight, I would like to use that figure for dry mass calculations.

Also tried another simulation:

First stage flight. Pitched over 10 degrees beginning 11 seconds into flight. Gradually pitched over through flight, more so near the end of the first stage burn, until staging.

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Second stage flight. Pitched over to near prograde attitude after staging. Maintained this attitude until cutoff, which resulted in a somewhat elliptical orbit.

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It has consistently reached orbit, so I think the only real problem, barring any performance shortfalls, is a proper pitch program. Looking into that now. Still got a long way to go.

---------- Post added at 11:12 PM ---------- Previous post was at 08:23 PM ----------

Excerpt from Saturn V flight manual.

The 345,000 gallon lox tank is the structural link between the forward skirt and the intertank section. The cylindrical tank skin is stiffened by "integrally machined" T stiffeners. Ring baffles attached to the skin stiffeners stabilize the tank wall and sense to reduce lox sloshing. A cruciform baffle at the base of the tank series to reduce both slosh and vortex action. Support for four helium bottles is provided by the ring baffles. The tank is a 2219-T87 aluminum alloy cylinder with ellipsoidal upper and lower bulkheads. The skin thickness is decreased in eight steps from .254 inches at the aft section to .190 inches at the forward section.

Due to this, I've decided to go with 4mm(?) and 3mm(?) for the tank skin thickness. Also, 2219-T87 is 2.84 g/cc. Another alloy used on the Saturn was 7075-T6, with a density of 2.81 g/cc, but it was only used on the intertank and skirt assemblies. These should be accounted for too.

So now calculations. Does anyone think 4mm and 3mm is too thin? Not looking for balloon tanks here.
 

Phil Smith

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First off - my congratulations about reaching the orbit! + this big elliptical one shows you have extra deltaV budget so you can increase your payload mass if you will.

About skin thickness.
saturn V tanks (on first and second stages) was made of 2 inch thick 2219-T87 aluminum slab that is "integrally machined" to its final shape with skin thickness decreasing in eight steps from .254 inches at the aft section to .190 inches at the forward section and T-stringers.
2219-T87 alloy has very good welding properties, so it's used in all sections where segments need to be welded.
7075-T6 - for riveted sections (w/o welding),
My numbers if thickness were average approximation to calculate skin and all its ribs masses at one digit.

If you wanna know exactly thickness of your tank walls you need calculate bending moments and axial loads of the vehicle.

3 - 4 mm thickness is good, but stringers and rings are needed anyway to help skin withstanding all rocket flight and transportation loads. For this propose I added extra 3-4 mm and got my approx. 6-8 mm skin
 
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ISProgram

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Recalculated the second stage with 7mm and 5mm tank skin figures, and the 2219-T87 and 7075-T6 alloys.

So now:

First Stage
Thrust (Vac): 17,920 kN
Specific Impulse (Vac): 338 s
Dry Mass: 44,981 kg
Propellant Mass: 874, 606 kg

Second Stage
Thrust (Vac): 1,085 kN
Specific Impulse (Vac): 421 s
Dry Mass: 8,179 kg (it got smaller!)
Propellant Mass: 86,513 kg

Neither stage's propellant numbers account for ullage or internal tank structure. Forgot how to calculate that. The second stage has a new engine, essentially a modernized J-2 (NOT J-2X), with a dry weight of 1,705 kg.

The first stage has not yet been recalculated with the new tank skin figures.

Now, the rocket had previously done 54,117 kg to a 185 LEO (though I didn't disclose this), but it does only 49,895 kg to the same orbit, due to the lower Isp of the new engine (421 s). If the Isp is changed back to 453, it goes up to 54,420 kg. A nozzle extension might be employed to mitigate this low Isp.

It should be noted that I've been told that Silverbird and Orbiter have a ~10% discrepancy with their data for a given orbit, with regards to payload capacity (if my rocket can do 49895 kg to 185 LEO by Silverbird, it theoretically does around 44905 kg to that orbit in Orbiter).

With these new statistics, I did a simulation. I made probe.cfg 49895 kg, then flew. This time, I did a more aggressive pitch maneuver, yawing over 20 degrees 12 seconds after launch. The second stage pitch operation was the same as previous test.

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IMO, I am now under the impression that the rocket design is near maturity, it is the concept of operations (pitch program, for example) that is the main issue now.
 

ISProgram

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No longer under that impression. So, still trying to optimize the pitch program. For some reason, I can't find any (detailed) examples for current rocket systems. I've only found the Saturn V pitch maneuver.

That being said, I might have to temporarily stop work, since my laptop screen has cracked. So now I have black blotches all over it. but at least this isn't something that's completely stopped operations; I'm typing this from the same computer, as a matter of fact.

Anyhow, I've revised the figures for the major components of the rocket again Hoping this is the final time. However, that first stage dry mass figure is suspicious, so I doubt it.

First Stage
Thrust (Vac): 17,920 kN
Specific Impulse (Vac): 338 s
Dry Mass: 37,863 kg
Propellant Mass: 778,400 kg

Second Stage
Thrust (Vac): 1,085 kN
Specific Impulse (Vac): 421 s
Dry Mass: 8,264 kg
Propellant Mass: 69,360 kg

Those propellant number represent the amount used by the rocket, and so account for the ullage and internal tank structures. If I'm correct, it's 3% volume loss for internal structures and 5% loss for ullage, per earlier calculations.

The new engine now has a mass of 1,790 kg, the same as the J-2. Did this for margin purposes. Isp hasn't changed. Now the engine has two variants, the first of which is the J-2 derived version. The second is to be used on high performance flights, and has a different nozzle to achieve better Isp.

Having said that, does anyone have a formula for how big a nozzle extension would need to be to achieve a Isp of 440-450?

At the moment, Silverbird says the rocket can do 43,977 kg to a 185 LEO.
 

ISProgram

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Okay, decided to finish addressing that delta-v deficit.

dV = ve * ln(m0/m1) is the equation to be used. ve is the exhaust velocity (Isp * 9.81) of the vehicle propulsion. m0 is the fueled mass of the rocket/spacecraft before the burn. m1 is the mass of the rocket/spacecraft after the burn.

So, to calculate first stage flight, it should be:

ve = (338*9.81) = 3,315.78 m/s, the exhaust velocity of the RD-290

m0 = 897,718 kg, the full fueled mass of the rocket

m1 = 119,318 kg, after the rocket has expended first stage fuel.

So it's 3315.78 * In(897,718 - 119,318)

For second stage flight, the equation is 3315.78 * In(897,718 - 119,318)

Too bad I can't figure out the value for "In" 'cause I'm dumb. :)

An example on a NSF thread uses the SSME, and is 4444 * In(120 / 100), which is 810 m/s of delta-V.

So I used an online calculator to double-check this, and got 810.24. Pretty accurate for me.

So, with it, the first stage can ideally get 10,080.88 m/s of delta-V, and the second stage gets 8,257.41 m/s, which is a total of 18,338.29 for the entire rocket. Not accounting for any gravity or aerodynamic forces. Even so, it appears the (tentative) pitch programs appear to be the problem.

To reach LEO, apparently a delta-V of 8,600 m/s is needed, but to account for the atmosphere, at least a additional 1,500-2,000 m/s of delta-V is needed.

It is also implied that 9,500 to 9,700 m/s is needed to reach LEO, accounting for atmospheric drag and gravity.
 

kocmolyf

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So, with it, the first stage can ideally get 10,080.88 m/s of delta-V, and the second stage gets 8,257.41 m/s, which is a total of 18,338.29 for the entire rocket...it is also implied that 9,500 to 9,700 m/s is needed to reach LEO...

This should be a "reality check" moment. :) 18 km/s is far too much for a rocket intended to reach LEO. To give you a frame of reference, the LR1 Skyhammer has almost exactly 9,500 m/s available for ascent with 40,000 kg of payload. This is just barely enough to reach a 60 degree, 135 km x 400 km orbit.

I suspect you are not taking the second stage into account during the first burn, or the payload during the second burn. I'll lay out the numbers you provided above:

Payload:
Empty mass: 50,000 kg

Stage 2:
Empty mass: 8,264 kg
Propellant mass: 69,360 kg
Gross mass: 77,624 kg
Exhaust velocity: 4,129 m/s

Stage 1:
Empty mass: 37,863 kg
Propellant mass: 778,400 kg
Gross mass: 816,263 kg
Exhaust velocity: 3,314 m/s

OK. Now let's compute the delta velocity for each burn. Remember that each stage has to carry not only its own empty mass, but also the gross mass of all stages above it.

dV = Ve * ln(mg / me)

Burn 1:
Empty mass: 165,487 kg = 37,863 kg [stage 1] + 77,624 kg [stage 2] + 50,000 kg [payload]
Propellant mass: 778,400 kg [stage 1]
Gross mass: 943,887 kg = 165,487 kg + 778,400 kg
Exhaust velocity: 3,314 m/s [stage 1]
Delta V: 5,770 m/s = 3,314 m/s * ln(943,887 kg / 165,487 kg)

Burn 2:
Empty mass: 58,264 kg = 8,264 kg [stage 2] + 50,000 kg [payload]
Propellant mass: 69,360 kg [stage 2]
Gross mass: 127,624 kg = 58,264 kg + 69,360 kg
Exhaust velocity: 4,129 m/s
Delta V: 3,238 m/s = 4,129 m/s * ln(127,624 kg / 58,264 kg)

Total Delta V: 9,008 m/s = 5,770 m/s [burn 1] + 3,238 m/s [burn 2]

As you can see, your total velocity with 50,000 kg of payload is only 9 km/s. That is almost certainly too low to overcome gravity and aerodynamic losses if you have "normal" thrust-to-weight ratios and drag. Let's check:

Stage 1:
Gross weight: 9,256 kN = 943,887 kg * 9.806 m/s2
Thrust: 17,920 kN
Thrust-to-weight: 1.935 = 17,920 kN / 9,256 kN

Stage 2:
Gross weight: 1,252 kN = 127,624 kg * 9.806 m/s2
Thrust: 1,085 kN
Thrust-to-weight: 0.867 = 1,085 kN / 1,252 kN

Whoa! Your second stage is spot-on, but your first stage thrust-to-weight is huge. I would expect something more in the range of 1.2 - 1.3. With such an extreme thrust/weight ratio you will reduce your gravity losses, but your rocket will have to be super strong to withstand the aerodynamic forces during ascent (you will be going really fast).

I would also comment that your first stage and second stage seem a bit mismatched. Generally you should have roughly equal delta-V on each stage. If one stage has a significantly higher exhaust velocity (Isp) than the other, you should try and put more delta V on that stage. Your situation is sort of the opposite, almost two-thirds of the delta V is on the first stage, which has a lower Isp. That kind of mismatch can happen for historical reasons ("we had a couple stages off the shelf and bolted them together"), but it wouldn't be a good idea to design a new rocket with those ratios.

Finally, huge kudos for digging into the math. Most people never even get this far! :tiphat:
 

Phil Smith

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Hey!:hello:
LN is just natural logarithm - [ame="http://en.wikipedia.org/wiki/Natural_logarithm"]Natural logarithm - Wikipedia, the free encyclopedia[/ame]
It can be easily computed with windows calculator (example - https://www.riskprep.com/blog/73-using-the-windows-calculator )
For second stage flight, the equation is 3315.78 * In(897,718 - 119,318)
You should divide M0 and M1 not subtract, so:
deltaV for first stage = 3315.78 * In(897,718 / 119,318) = 6691.46 m/s;
same for the second stage (I'm using parameters from your previous post):
deltaV for second stage = 421 * 9.81 * Ln ((2nd stage fuel mass + 2nd stage dry mass + payload mass)/(2nd stage dry mass + payload mass)) = 4,130.01 * LN ((69,360 + 8,264 + 43,977)/(8,264 + 43,977) = 3,489.35 m/s.

PS I correct some for first stage. it will be:
delta V_1_stage = 338*9.81 * LN ((1st stage prop. mass + 1st stage dry mass + 2nd stage fuel mass + 2nd stage dry mass + payload mass)/(1st stage dry mass + 2nd stage fuel mass + 2nd stage dry mass + payload mass)) = 3,315.78 * LN((778,400 + 37,863 + 69,360 + 8,264 + 43,977)/(37,863 + 69,360 + 8,264 + 43,977)) = 5,874.86 m/s;
Total vehicle ideal delta V = 5,874.86 + 3,489.35 = 9,364.21 m/s

I suggest you to create an excel sheet and type all this formulas and just tweaking masses and see what's goin on

Having said that, does anyone have a formula for how big a nozzle extension would need to be to achieve a Isp of 440-450?
there is some huge formula.. best way to make this analysis with "RPA light" software - it's free and will give you whole picture changing Ae/At ratio.
Here we go - http://www.propulsion-analysis.com/downloads.htm - download latest light version and install on your machine and you'll be ok:probe:
Cheers!
 
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ISProgram

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Whoa! Your second stage is spot-on, but your first stage thrust-to-weight is huge. I would expect something more in the range of 1.2 - 1.3. With such an extreme thrust/weight ratio you will reduce your gravity losses, but your rocket will have to be super strong to withstand the aerodynamic forces during ascent (you will be going really fast).

I would also comment that your first stage and second stage seem a bit mismatched. Generally you should have roughly equal delta-V on each stage. If one stage has a significantly higher exhaust velocity (Isp) than the other, you should try and put more delta V on that stage. Your situation is sort of the opposite, almost two-thirds of the delta V is on the first stage, which has a lower Isp. That kind of mismatch can happen for historical reasons ("we had a couple stages off the shelf and bolted them together"), but it wouldn't be a good idea to design a new rocket with those ratios.

So, the upper stage needs to take more of the dirty work. That means either an increase in propellant mass OR a different engine which has better Isp. As it currently stands, both are an option, since the recent engine downgrade actually shrank the rocket a bit (its 71.47 m at the moment, compared to 71.94m earlier, which might go towards stretching the second stage). If I go for a Isp increase, which is the one I would rather do, a nozzle extension will be required, perhaps deployable.

The excessive thrust to weight resulted because the first stage lost weight from its earlier baseline. The thrust-to weight was probably more benign earlier. That being said, a engine capable of just 12,040 kN should solve this. Engine throttling could also solve the issue, though the former solution leaves open the possibility of weight reduction...which is something to be avoid on the first stage right now...:hmm:

I try to address these concern later today. My time zone's telling me I'm up way too early right now.

Half of my brain is in sleep mode, so I'll continue the rest of this post later, if no one minds....:coffee:

---------- Post added at 12:38 PM ---------- Previous post was at 06:28 AM ----------

best way to make this analysis with "RPA light" software - it's free and will give you whole picture changing Ae/At ratio.
Here we go - http://www.propulsion-analysis.com/downloads.htm - download latest light version and install on your machine and you'll be ok:probe:
Cheers!

So, just tried it out, and was a bit surprised by the results.

The data inputted was:

Chamber pressure: 763 psi
Mixture ratio (O/F): 5
Expansion area ratio: 28

perhaps it needed more data, but it processed the results regardless. First thing I noticed was that vacuum Isp was 447.43; way higher than the J-2's 421. However, the optimum expansion for that was just 426.58, and seems more accurate.

Which number should I go with?

With the 447.43 figure for Isp, the second stage (with a 52,600 kg payload) gets out about 7,557 m/s of delta-V.
 

Phil Smith

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you need "estimated delivered performance" table.
According wiki ( http://en.wikipedia.org/wiki/Rocketdyne_J-2 ) I used: O/F = 5.5, Ae/At (expantion area ratio) = 27.5 and 763 psi of chamber pressure.
So after solving the problem I've got 429.83 sec of vacuum Isp - little bit higher than J-2. But reaction, nozzle and overall efficiency ratios are quite "idealistic" and can be slightly higher than you'd get on a real engine test
Check my screen in the attachments - I highlighted the line you ask for
 

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ISProgram

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So, with a design goal of 9,700 m/s of full delta-V, and with the first stage producing an ideal 5,874 m/s of delta-V, then the second stage needs to perform efficiently enough to get at least 3,826 m/s of delta-V.

I can do this without changing the rocket or its propellant ratios, but the engine would need to have a specific impulse of 485 seconds. Only the RL-10 has that, and it doesn't come close to having a high enough thrust. So it seems as if the second stage will be stretched; doing that right now, as a matter of fact.

On the bright side, the ability to throttle down to 12,040 kN is well within the capability of the RD-290, since that thrust is 70% of the full 17,920 kN. Most staged-combustion engines can throttle low; the RD-180 can go down to 40%.

Stupid second stage.

And then there are other orbits to consider. Dang.

2000px-Delta-Vs_for_inner_Solar_System.svg.png
 
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Phil Smith

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LH2 / LF2 combination gives highest Isp value (among liquid bi-propellants), but in real life fluorine is TOO toxic adn TOO active (cause it's the highest performance oxidiser) and TOO dangerous to handle (http://www.astronautix.com/props/lf2lh2.htm ). As far your project is for paper and Orbiter (am I right? :lol:) it aint be a problem.
For example I checked this propellant quick in LPA and what I got (Chamber pressure - 6.0 MPa, O/F - 10.0 (yep, it's higher than LH2 with LOX), Ae/At = 40):
Isp_vacuum = 463.87 sec.
Also this combination is good cause of its O/F ratio - you need more heavy liquid fluorine (1,510 kg/m3) and less very light hydrogen (70 kg/m3) - all that reduce tank volumes, and overall stage mass.

PS Think of making two stages with equal ideal velocity. For example, if you need total vehicle ideal deltaV = 9,700 m/s, for second and first stages it would be 9,700/2 = 4,850 m/s each.
 
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ISProgram

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Okay, stretched the second stage hydrogen compartment to the maximum extent possible without making the rocket too tall. Here are the new statistics. I didn't scale up the oxygen compartment because that would've made a redesign of the second stage more challenging. Despite this, the mixture ratio still managed to be 5; it didn't change. I think I put too much margin when I calculated volume deficit from ullage and internal structures. Probably not, though.

Second Stage
Thrust (Vac): 1,085 kN
Specific Impulse (Vac): 440 s
Dry Mass: 8,524 kg
Propellant Mass: 76,680 kg

As for the engine, I used RPA again, and imputed this data:

Chamber pressure: 763 psi
Mixture ratio (O/F): 5
Expansion area ratio: 27.5

Isp was 448.90 seconds, but considering the idealistic nature of the results, I interpreted it as just 440 seconds. 8 seconds was also the difference between your earlier estimate (429) and the J-2 (421).

With these calculations, the upper stage has a ideal delta-V of 6,507.72 m/s, with a 52,600 kg payload. If you remove 2,600 kg (the weight of the fairing), it can achieve 3,613.09 m/s.

Silverbird says the rocket gets 44,470 kg to LEO; if you lower the payload to accommodate this, the upper stage can obtain a delta-V of 4,090.06 m/s, more than enough to reach orbit.

Something that I'm going to try to factor in later is the time the fairing is jettisoned; that 267s number is preliminary, a safe baseline. If trajectory calculations show that the first stage can get the upper stack above 150 kilometers or so, then the fairing can be tossed during first stage flight, as opposed to second stage flight, which would save delta-V for the latter.

Also, I couldn't make a exel sheet on this computer; I lost Microsoft Word and its derivatives when I had to refresh my computer and couldn't find the product key a few months ago.

---------- Post added at 07:39 AM ---------- Previous post was at 07:14 AM ----------

I remember LH2/LF2 being incredibly potent compared to LH2/LOX, in terms of, well everything. There was actually a question I saw elsewhere asking why it wasn't used more often.

Of course, that stuff is nasty/volatile/crazy/don't let it spill. The reason I don't go for this right now is the same reason those kind of rockets aren't used now; the advantages of LH2/LF2 are overshadowed by its disadvantages. If not, LH2/LOX might've been largely phased out by now.

However, if the rocket delta-V continues to be an issue, I might resort to that propellant combination. I would have to be extremely desperate(?) to do this, I would much rather lower the payload mass.

Also, regardless, it is a little of a problem. The rocket is a paper rocket and for Orbiter, but it's also part of a fictional space agency project I've been doing online. The agency that makes this rocket already has established LH2/LOX stages, so a LH2/LF2 stage goes to a whole different level. Also, this rocket launches from a leased pad at Cape Canaveral, so there might be a few issues placing LF2 there; many pads there, however, have infrastructure for LH2 already or can be modified with little trouble.

Also, the reason I would rather lower payload mass is because the rocket has already passed expectations when I first designed it. It's baseline payload was supposed to be 30,000 kg (just to compete against DIV-H), but it ended up with almost 50,000 kg of payload instead. Mostly, reaching 50 metric tons is a little bonus I wouldn't mind accomplishing. If I can't 40mT is good too.

Perhaps the clincher against LF2 is the fact that the rocket is also expected to be man-rated at some point in the future. This is another reason for why I'm aiming for 50mT; I need some healthy margin in terms of payload capacity. There's a manned spacecraft that should eventually ride on this rocket in the storyline future, but current estimates give it a 40mT-60mT mass, and I've forgotten if that's dry or fueled. I wonder if there can be such a thing as a Velcro Antares...
 

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So, I have decided that I am essentially almost done with the full rocket design, save for a few details.

The first stage has a propellant change, in order to make a little more delta-V (I know the second stage should be making more at this point, but it's reached the cap of its modifications). So now:

First Stage
Thrust (Vac): < 17,920 kN
Specific Impulse (Vac): 338 s
Dry Mass: 37,863 kg
Propellant Mass: 780,840 kg

That's not a lot more propellant, but it'll still help. If the rocket manages 45mT to LEO, that'll be good enough for me.

As a matter of fact, according to the Delta-V Calculator, the first stage (plus the 1,231 kg interstage) can now impart about 5,801 m/s upon the rocket.

With a 45,000 kg payload (plus about 2,600 kg for the fairing), the second stage gets about 3333 m/s out.

Only about 9,134 m/s of delta-V, not enough to reach orbit.

With a 40mT payload, the rocket gets a total of about 9,238 m/s, 5,886 m/s and 3352 m/s by the first and second stages, respectively.

Still not enough to reach orbit.

Disclaimer: This included the 2,600 kg payload fairing, which normally is jettisoned during ascent. Calculation have it as part of the payload.

So now, with the stage designs essentially completed, the only real pacing elements are the payload fairing and interstage.

Namely, if anyone was to calculate their mass, which I may or may not have done accurately (used the processes described at the start of the thread), what would be the thickness of the material for either? If I can lower their mass, I can achieve more delta-V.

The other only pacing element for the rocket is the second stage engine, which still has a Isp of 421. I settled on a extendable nozzle design, to reduce height and create more Isp.

Can anyone figure out the Isp for the unextended and extended versions? Haven't had much luck doing it myself.

picture.php


---------- Post added at 05:01 AM ---------- Previous post was at 01:15 AM ----------

As you can see, your total velocity with 50,000 kg of payload is only 9 km/s. That is almost certainly too low to overcome gravity and aerodynamic losses if you have "normal" thrust-to-weight ratios and drag. Let's check:

Stage 1:
Gross weight: 9,256 kN = 943,887 kg * 9.806 m/s2
Thrust: 17,920 kN
Thrust-to-weight: 1.935 = 17,920 kN / 9,256 kN

Stage 2:
Gross weight: 1,252 kN = 127,624 kg * 9.806 m/s2
Thrust: 1,085 kN
Thrust-to-weight: 0.867 = 1,085 kN / 1,252 kN

Whoa! Your second stage is spot-on, but your first stage thrust-to-weight is huge. I would expect something more in the range of 1.2 - 1.3. With such an extreme thrust/weight ratio you will reduce your gravity losses, but your rocket will have to be super strong to withstand the aerodynamic forces during ascent (you will be going really fast).

Oh yeah, I forgot to mention something. The reason the first stage has high TWR is so that it wouldn't limit future upper stage evolutions. Just remembered this, and thought I share it.
 

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Can anyone figure out the Isp for the unextended and extended versions? Haven't had much luck doing it myself.
left "short" version is J-2 right? so first of all we calculate expansion ratios and then Isp's.

For the left one:
e = D_exit^2 / D_throar^2 = 2.39^2 / 0.47^2 = 25.6;
if it's J-2, say chamber pressure is 763 psi, O/F = 5
Isp(RPA) = 430 sec
Isp(real) = 421 sec
Pressure at the nozzle exit - 0.0182 MPa;
say k is some coefficient of some thrust chamber losses making real Isp little bit lower than RPA shows:
k = 421/430 = 0.979 (we'll use it for "long" nozzle configuration approximation).

Right one:
expansion ratio -
e = D_exit^2 / D_throar^2 = 3.05^2 / 0.47^2 = 42.11;
say chamber pressure is 763 psi, O/F = 5
Isp(RPA) = 439.81 sec;
Isp(real) = Isp(RPA) * k = 439.81 * 0.979 = 430.6 sec;
Pressure at the nozzle exit - 0.0093 MPa.

PS Be sure injector diameter is bigger than throat's 0.47 m - combustion chamber should be at least conical ;)

Cheers!:cheers:
 
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PS Be sure injector diameter is bigger than throat's 0.47 m - combustion chamber should be at least conical ;)

Whoops, sorry, that's the model engine for the mesh that I'm making right now. :)

Okay, so I decided to remove the 0.03% margin that had been in place for propellant values. Up to now, I had calculated the volume loss by ullage and internal structures as 0.11%, whereupon ullage is 0.03% and internal structures is 0.05%, per earlier calculations.

So now, the fuel mass of the first and second stage is 807,210 kg and 80,016kg, respectively. This amounts to about 5795.21 m/s and 3890.52 of delta-V for those stages, without the second stage's nozzle extension.

That's 9685.73 m/s of delta-V, with a 42,600 kg payload. It's reached orbit! Hopefully... :cheers:

With the nozzle extension providing an Isp of 431s, the second stage has 3982.93 m/s of delta-V with the same payload. Essentially the same result. Yay!

Still going to try to get payload to 45,000 kg or close.
 

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My congratulations! :cheers:
Waiting for the progress :cool:
 

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Thanks! :cheers:

Now, there's only a few things left to do, now that the rocket can at least reach orbit. These all have to do with mass reduction.

Would the rocket's interstage and payload fairing(s) be the same thickness as the tank skin, and if not, what could they be?

Provided, the interstage and payload fairing aren't completely made out of aluminum or carbon composite, but I've figured I can make use of the tank skin mass/bulkhead mass formula to calculate them.

Also, would I scale up tank thickness number as it is for the 5.75 m stage when I apply it to other stage diameters (5.75m = 7mm, then 2.87 = 3.5mm)?
 

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The only figure I could find for a carbon fiber aluminum core composite density came from this, and was 35-473 kg/m3, which is 0.035-0.473 g/cc, and compared to 2.81 g/cc for aluminum alloys, seems a bit too low.

Unless, of course, it isn't.

Until then, the fairing and interstage masses will remain as they are. I will probably start using more precise fuel mass numbers now, just to have that extra delta-V.

---------- Post added at 02:29 AM ---------- Previous post was at 02:26 AM ----------

Just might use this calculator to help.

---------- Post added at 03:01 AM ---------- Previous post was at 02:29 AM ----------

Might also switch to a aluminum-lithium alloy. One such alloy is 2195 aluminium, which was used on the Space Shuttle's Super Lightweight tanks AND is currently in use on the Falcon 9 launch vehicle.

According to this paper, it has a density of 2685 kg/m3, which I translate as 2.69 g/cc, still less than the densities of either 2219-T87 (2.84 g/cc) or 7075-T6 (2.81 g/cc), which I've been using up to now. The only issue is whether or not this alloy could/would be used on the non-tank structures, in which case I could continue using 7075-T6.

EDIT: Most current US rockets (Alas V, Delta IV, Falcon 9) use aluminum/lithium alloys, as did the Space Shuttle. Orion, and the cancelled Ares rockets, were to use it too. That clinches it, I'm using 2195 now.

---------- Post added at 03:17 PM ---------- Previous post was at 03:01 AM ----------

Okay. Found that the Delta IV uses 2219 and Atlas V uses 2014. Both are aluminum-lithium alloys. The SLS was to use 2195, but is now using 2219.

So, I will continue to use 2219, unless 2014 is better. 2195 is too brittle and apparently difficult to weld. 2219, on the other hand, is denser, but give the first stage more stress endurance (why SLS is also using it). This will be necessary since the first stage will have to support bigger/heavier upper stages in future developments. Not sure the current upper stage are restricted by this, though since both stages are to use the same tooling, it doesn't matter anyway.

2014 has a difficult with welding, which will be a problem with the wide bodied stages. However, it is easily machine in certain tempers, has a high strength, and has a high hardness. This might be reserved for a later upper stage.

I considered 2090 as an option, used on the SLWT ET as well. Has a few problems with strength, so it's out.

So no alloy change yet.
 
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Okay, currently working on a upper stage evolution path. With regards to the specifications, at least. Th evolution path itself is already thought out. There will be a first stage upgrade as well.

The upper stage is 7.91m in diameter.

The Space Shuttle ET (8.4m) has one of 1.3cm (or at least this suggests).

I don't definitively know the tank skin thickness of the S-IVB (6.6m),but I recall that sheet stock used to make it was 1.9 cm (19mm) thick.


Based on this, I've decided to make the upper stage tank skin, for calculations, be about 0.011mm for the dry mass calculations.

---------- Post added at 06:12 AM ---------- Previous post was at 04:56 AM ----------

The upgraded upper stage is 21,702 kg dry (that's almost as much as the CCB!) and is 100,998 kg fully fueled. It is utilizing the same second stage engine as the first, and is using the nozzle extension for increased Isp (431s).

Unfortunately, it has only about 2634.57 m/s of delta-V with a 70,000 kg payload.

The first stage can only manage 5136.04 m/s of delta-V with the same configuration.

Still need about 1915.12 m/s to achieve the same delta-V that was reached earlier.

There's going to have to be a redesign. Again. :(
 

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Going back to the current upper stage, I used Silverbird to test a more plausible upper stage upgrade; namely, the 5.75m US with different engines.

This upgrade uses 4 "LR-60" engines instead of the previous single engine. Each of the LR-60 is based off the presumably defunct RL-60.

I managed to find a few statistic from these sources:

[ame="http://en.wikipedia.org/wiki/RL60"]Wikipedia[/ame]

Astronautix

PDF

So, the specs of the LR-60 are:

Total Thrust: 290 kN (Vac)
Engine Dry Weight: 501 kg
Burn Time: (dependent on host vehicle)
Specific Impulse: 470 s (Vac)
Propellants: LH2/LOX
Mixture Mass Ratio: 1:5 oxidizer to fuel

I did a rough calculation of the new upper stage and found that it has superior performance than the single engine. It got over 894 kg to a C3 of 90, which basically means it could get to Europa with just the single core launcher. Nice...

I also have some margin on these estimates, as this was a "just checking" kind of test. It gets 46,6747 kg to a 185 circular orbit at 28.7 degrees. Things are looking like I could hit 50,000 kg to LEO.

Now I'm thinking about base-lining this configuration. :cheers:
 
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