A Titan II SSTO experiment - with numbers.

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Archibald

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Titan II stage 1 is often mentionned (on the Internet) as a possible SSTO. But what is lacking is the maths. So I decided to fill that gap.
Secret projects is a highly visible forum in Google searches, by the way. That's the reason why I put this here.
Feel free to pick any hole in my maths, I'll correct it.

The Titan II stage 1 still hold an amazing record for rockets. With empty propellant tanks it weighed barely 10 000 pounds. Then when the tanks were filled it weighed 250 000 pounds.

Propellant mass fraction (PMF) is the ratio between the two weights, empty tanks and tanks filled.
In the case of the Titan II, it calculates the following way

1-(10000/250000) = 0.96

What is really interesting is that such PMF would allow the Titan II first stage to launch itself into Earth orbit. No booster, no second stage. A SSTO, although an expendable one.

9.81*296*ln(250000/10000) = 9347 m/s.

And indeed Earth orbit is somewhere between 9 km/s and 10 km/s depending on gravity losses, drag losses, and propellant density. The denser the propellants, the lower the drag and gravity losses. I've seen values as low as 8.9 km/s.

So our Titan II stage 1 SSTO can loft itself into orbit, although with slim margin.

What is really interesting is that one could swap the old LR-87 (gas generator cycle) for Proton RD-253 which uses the same storable propellants but staged combustion.
Thrust are quite similar, propellants are storable in both cases.
LR-87 vacuum specific impulse: 296 seconds.
RD-253 : 316 seconds.

9.81*316*ln(250000/10000) = 9978m/s.

And then, how much payload to orbit ? Between 2000 and 3000 pounds.


9.81*316*ln(252000/12000) = 9437 m/s with 2000 pounds of payload.

That was Titan II / Proton hybrid, both using storable propellants.

But Titan I used kerolox, just like many other advanced Soviet rocket engines - the N-1 Kuznetsov or Energiya RD-170 / 180 / 190 family.
Might be interesting to get Titan I stage 1 PMF and try to replace the LR-87 with, say, a RD-191. I'll give it a try later on.

A very interesting documents detailing the Titan varied stages and PMF

http://home.earthlink.net/~apendragn/atg/coef/Structural_Coef.pdf
 
From the linked document above...

Titan I stage 1 weighed 9562 pounds and could hold 161688 pounds of propellants (kerolox).
9562 pounds with empty tanks
171250 pounds with the prop tanks filled

1-(9562/171250) = 0.944

Not as good as Titan II, but still a SSTO value.
https://en.wikipedia.org/wiki/HGM-25A_Titan_I

Now let's seek a Russian staged combustion engine with thrust and kerolox similar enough to the old LR-87...
RD-191 seems to be a very nice fit. And it is even throtteable, good for a SSTO.

9.81*337*ln(171250/9562) = 9538 m/s

Not bad, but I hoped better results.

In the end the best way to go would be to mix the Titan I and Titan II stages, notably the big stretch.
When you think about it, not only that stretch was a big one, but PMF actually improved from 0.944 to 0.96 !

Kudos to the engineers who pulled that in 1958 (!), even today Musk can't even better this.

I have a doubt however that the superior PMF of the Titan II related to storable prop density versus kerolox. Notably LOX being a cryogen hence harder to store.

What I mean is, while the Titan II PMF was exceptional (0.96) maybe it would degrade (to 0.94 ?) if storable were swapped for kerolox, despite the RD-191 very good specific impulse.

If not, then the combination of a 0.96 PMF + RD-191 specific impulse would probably get a SSTO with 10 000 m/s of delta-v or a little more.

Basically, this

9.81*337*ln(250000/10000) = 10641 m/s

Now that's interesting.

If we consider Earth orbit to be 9.2 km/s... then that thing could carry 5000 pounds.

9.81*337*ln(255000/15000) = 9366 m/s

In the end, the exercise is fun but also shows why the rocket equation is a b*tch.

Best PMF + best specific impulse = barely 5000 pounds to orbit

And a vehicle that is not even recoverable.

Try adding some TPS and grid fins (Musk style) to eventually retrieve that thing, and that would eat the 5000 pounds payload for dinner. and beyond, so the thing would no longer reach orbit anymore.

Geez... staging is our friend, really.
 
interesting study

My only issue on that concept, is use RD-253
it burn a different propellant as LR-87

Proton use NTO/UDMH
Titan II use NTO/Aerozin50 ( 50%UDMH and 50%hydrazine)
for using a RD-253 on launch infrastructure of Titan II, you need adapt the Injector-plate on that engine for burning NTO/Aerozin50
or redesign the Titan II stage and launch infrastructure for use of NTO/UDMH, what could reduce payload and increase launch cost.

on "a vehicle that is not even recoverable".
Martin mass-produce the Titan II and manage a low production price
something similar does Rocketlab with there Electron rocket, mass-production to lower the prices
 
Ah dang, storable propellants, but not the same. Point noted. The devil is in the details, really. Note that the RD-253 is also a bit more powerful than the LR-87, 150 mt of thrust vs 95 or so.

I was wondering, Elon Musk bragged about very high PMF for both Falcon 9 and Starship, but do we know the real numbers ?
I'm curious about Falcon 9 first and second stage PMF... even Ed Kyle doesn't seem to have the numbers on his website.
If Musk managed 0.97 it would be one hell of an achievement.

Still wondering how Martin Marietta engineers achieved 0.96 on the Titan II, better than Atlas and without balloon tanks or dropping engines. What kind of trick did they used ?
 
Archibald said:
Still wondering how Martin Marietta engineers achieved 0.96 on the Titan II, better than Atlas and without balloon tanks or dropping engines. What kind of trick did they used ?
Click to expand...

with experience with Titan I, Martin start "trow out" un-needed subsystem out the Titan II
the LR-87-AJ-1 Engine got 125 components in active controls system, what was reduce to only 30 in LR-87-AJ-5
Power control system were reduce from 107 to 21 components.
the autogenous pressurization of Propellants tanks used cooled gases from turbines exhaust of LR-87 engines
So no need to install system that need nitrogen or helium in heavy tanks
also the stage was build from extruded & chemical milled panels to reduce mass in non critical areas were needed (save 900 - 1000 pounds on stage mass)

Source
Titan II: a history of a cold war missile program
David K. Stumpf
ISBM 1-55278-601-9
 
I see the point... they really stripped down Titan I, plus chased any useful weight, anywhere.
 
It's all very well using the basic rocket equation, but you haven't allowed for -
1. Change in potential energy from surface to orbit height;
2. lower SI in atmosphere;
3. Air resistance.
 
Air resistance, drag losses, are part of the 9.4 km/s to Earth orbit (without the drag and gravity losses it would be only 7.7 km/s)
you are probably right about sea level ISP. I'm often wondering how much of a loss does it incures, considering how fast a rocket get out of sea level...
 

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