An SSTO as "God and Robert Heinlein intended".

[Loru]

We have to make similar calculation for Kerosene/LOX launch vehicle

 

[RGClark]

And one more thing about SSTO with current technology.
Most current engines are throtable in range 70-100%. Asuuming you're using 1 stage with one set of engines (not to carry on dead mass into orbit) you encounter more problem:
During lift-off you need a big thrust to weight ratio to overcome gravity and clear the atmosphere.
This high thrust gives you a problem in latest stage of boost phase. Engine - that has to work with at least 70% of it's nominal thrust, will create so much acceleration that many components (human crew included) may not survive boost phase.
Let's do the numbers.
As the example I'm using first stage of my ETS launch vehicle which has powerfull 1st stage(current configuration):

Themis LV Stage I

structural mass + engine               30 000 kg 
RP1/LOX Isp 309              400 000 kg 
                             430 000 kg total
Engine:
1 x RD-180: 3.83 MN at sea level

Let's add typical Soyuz spacecraft as payload: 7000kg

At full thrust rocket is incapable of launching:
T/W Ratio (lift off) = 8.76 means it can't even lift itself from a pad...

For SSTO you want to use weight optimized structures. SpaceX has already achieved a 20 to 1 mass ratio for its Falcon 9 first stage:

SPACEX ACHIEVES ORBITAL BULLSEYE WITH INAUGURAL FLIGHT OF FALCON 9 ROCKET.
"The Falcon 9 first stage, with a fully fueled to dry weight ratio of over 20, has the world's best structural efficiency, despite being designed to higher human rated factors of safety."
http://www.spacex.com/press.php?page=20100607

And they claim they will be able to achieve a 30 to 1 mass ratio for the side boosters used on the Falcon Heavy:

Falcon Heavy.
"Anticipating potential astronaut transport needs, Falcon Heavy is also designed to meet NASA human rating standards. Falcon Heavy is designed to higher structural safety margins of 40% above flight loads, rather than the 25% level of other rockets, and triple redundant avionics. Despite being designed to higher structural margins than other rockets, the Falcon Heavy side booster stages have a mass ratio (full vs. empty) above 30, better than any launcher in history. By comparison, the Delta IV side boosters have a mass ratio of about 10."
http://www.spacex.com/falcon_heavy.php

If your Themis LV first stage used the SpaceX structural design you could carry 600,000 kg propellant in that same sized stage.


Bob Clark

 

[T.Neo]

Yes. I already stated this:

On the other hand, one could argue that the ET is pretty unoptimised for the task, and a propellant tank that uses shared bulkheads for example, and a semi-pressure-supported structure (like the Falcon propellant tanks) would be better. This would likely improve the associated problems, but not get rid of them entirely.

The Falcon stages are so lightweight (at least in the case of the Falcon 1) because they use internal pressure to stiffen themselves. The centaur stages and early Atlas rockets had a similar arrangement, but entirely relied on internal pressure for support- meaning that they would crumple on the ground if not kept pressurised by inert gas or stiffened by a support structure.

The falcon stages strike a middle ground by having enough of their own structural integrity to stay intact for ground handling, but reach their full strength once pressurised. This allows the stages to achieve a mass ratio that is striking in comparison to other designs (such as the Delta rockets, etc).

But a flimsy stage is not without problems. For example a flimsier stage is more likely to be damaged during reentry and recovery. And a flimsier structure might be, nearer the limit of its capabilities, costlier to refurbish and reuse.

And then you have the engine problem. If you have to shut down all but one of your engines late in the ascent to prevent the vehicle from crumpling in on itself, you better have a very good reason to keep all that parasitic mass aboard the vehicle.

In most cases it would likely be more advantageous both economically and physically, to jettison the superfluous engines. You now lose SSTO status, but you have a more capable vehicle.

And I think... a 1.5 stager, might be a better bet than an obligate 2 stager.

 

[Urwumpe]

20:1 structural mass fraction just means that you have about one percent payload mass fraction left when reaching orbital speed (with a kerosene/LOX SSTO). Sadly, a SSTO makes no sense without reuse, since a twin stage rocket with the same structural mass fraction for every stage will outperform it by large, when expendable.

Since RGClark is not open for using mathematics, the lingua franca of science, let me do that:

The SSTO will reach the following payload mass ratio at a structural mass fraction of 0.05 and an specific impulse of 3300 m/s:
[math]\lambda_{SSTO} = \frac{e^{\frac{-9200 \frac{m}{s}}{3300 \frac{m}{s}}} - 0.05} {1 - 0.05} = 0.0122[/math]
Just 1.22% of the mass will be available for payload (and any advanced recovery and landing systems, if desired)

The TSTO will at equal parameters and approximately optimized stage ratio get:

[math]\lambda_{TSTO} = \left (\frac{e^{\frac{-4600 \frac{m}{s}}{3300 \frac{m}{s}}} - 0.05} {1 - 0.05} \right ) ^2 = 0.0435[/math]
That means 4.35% of the lift off mass will be available for payload. The SSTO will weight 3.57 times more for the same payload as the TSTO. That is about the difference between Soyuz and Space Shuttle.

In terms of costs, this is all advantageous for the TSTO: while it needs a staging system, it can use less complex engines, since it needs less throttle range. And since it is much lighter than the SSTO for the same payload, it will fly with much cheaper engines anyway. Also the TSTO will be able to use better optimized engines - regardless which technology you use on the SSTO for making the engines less sensible to ambient pressure, the TSTO can also use it for its advantage.

And the indigenous modular construction of a TSTO also makes it much cheaper to construct it: The main parts are smaller, while a SSTO has to be pretty monolithic.

 

[Loru]

Ergo - SSTO is possible but makes no sense with current technology.

 

[RGClark]

...
The SSTO will reach the following payload mass ratio at a structural mass fraction of 0.05 and an specific impulse of 3300 m/s:
[math]\lambda_{SSTO} = \frac{e^{\frac{-9200 \frac{m}{s}}{3300 \frac{m}{s}}} - 0.05} {1 - 0.05} = 0.0122[/math]
Just 1.22% of the mass will be available for payload (and any advanced recovery and landing systems, if desired)

The TSTO will at equal parameters and approximately optimized stage ratio get:

[math]\lambda_{TSTO} = \left (\frac{e^{\frac{-4600 \frac{m}{s}}{3300 \frac{m}{s}}} - 0.05} {1 - 0.05} \right ) ^2 = 0.0435[/math]
That means 4.35% of the lift off mass will be available for payload. The SSTO will weight 3.57 times more for the same payload as the TSTO. That is about the difference between Soyuz and Space Shuttle.

Thanks for the calculation.
It is a very important point to keep in mind that dense propellant SSTO's actually require less delta-V to orbit than hydrogen fueled SSTO's. This is true even when the two cases have the same liftoff T/W ratio.
See the discussion here:

Hydrogen delta-V (Henry Spencer; Mitchell Burnside Clapp).
The bottom line, when all this converges -- including a small gain from
lower drag on a more compact vehicle, and a very small bonus from lower
drag making the acceleration still higher -- is that a standard orthodox
NASA LOX/LH2 SSTO needs 31000ft/s to reach the space-station orbit, and an H2O2/kerosene SSTO needs only 29050ft/s.
(In fact, the explanation came after the numbers -- when good trajectory
simulations kept coming out with lower delta-Vs for H2O2/kerosene, Mitch
decided he had to understand what was going on.)
Now, consider. The H2O2/kerosene SSTO is operating in a very steep part
of the mass-ratio curve. A 6% saving in delta-V is *not* trivial. For
engines with a vacuum Isp of 320, the required mass ratio drops from 20 to
16. Given the aforementioned sophisticated scaling models, at this mass
ratio, the H2O2/kerosene SSTO's payload at the same GLOM is now equal to that of the LOX/LH2 design.
So the dense-fuel SSTO has lower dry mass, smaller vehicle size, cheaper
and easier-to-handle propellants, and now suffers no GLOM penalty... Just
what was the advantage of LOX/LH2 supposed to be again?
http://yarchive.net/space/rocket/fuels/hydrogen_deltav.html

For a kerosene fueled SSTO the delta-V to orbit is often taken as 8,900 m/s. To do a simple calculation, I'll use some estimated numbers for the Falcon 9 first stage: a dry mass of 15,000 kg and a propellant mass of 285,000 kg, to give a mass ratio of 20 to 1. Let's suppose we swapped out the low efficiency Merlin engines for an engine with an Isp of 3,300 m/s. Then we could get 5,600 kg payload:

3,300ln(1+285/(15+5.6)) = 8,900 m/s.

This is a payload fraction of 5.6/(300+5.6) = .0183, or 1.8%. It is indeed true though that SSTO's are best used as reusable. I gave an estimate before that perhaps 28% of the landed mass has to be set aside for reentry/landing systems. However, with modern materials such as composites quite likely less than half this would be required. So .14*15,000 kg = 2,100 kg for the R/L systems. This gives us 3,500 kg left over for payload.
Since this is to be a reusable system we would need the maintenance costs to be kept minimal. The big focus of X-33/VentureStar program was to cut support staff by two orders of magnitude over that of the shuttle, from literally ten's of thousands to a few hundred. Also, the engines and thermal protection system were designed to require minimal maintenance between flights. If you suppose then the reusable kerosene engines used could manage 100 flights, then this could indeed cut the costs to orbit significantly.
Another factor to keep in mind though is that payload fraction really is not a good measure, figure of merit, to use to measure the efficiency of a launch system. The reason is that the cost of the propellant is a trivial component to the cost of the launch but makes up the great majority of the mass you're comparing the payload to in calculating the payload fraction.
Many in the industry now say a much better measure would be to compare the payload to the dry mass, as this much better tracks the cost of the vehicle. The dry mass remember is the stuff that actually has to be constructed and tested.
For this SSTO, this payload to dry mass ratio, for the expendable case to make an apple to apples comparison, is 5.6/15 = 0.37, 37%.
What is it for the TSTO case you are considering?


Bob Clark

 

[Urwumpe]

Yes - but their conclusions are wrong, so better not jump on them too much. All they have is an net effect by having a shorter burn time (A hydrogen/oxygen rocket with the same acceleration capability could also use it).

Now, in practical spaceflight, you don't get much there. Simply because your choice of propellants also means:

1. Different mass ratios and engine performances - while you need less DV (spacecraft independent, only result of the trajectory), your spacecraft will need much more fuel for following the trajectory.
2. A TSTO using the same trajectory to orbit would still brutally outperform the SSTO, the general calculations remain the same.
3. You can't increase the acceleration ad infinitum - throttle limits and wetware limits will make it impossible to get much shorter ascents.

But that is an old answer, you used this typical example of American guessing what the simulation results mean pretty often already. A short look at the ascent equation would have been better and would have wasted less bits for the reply. (Read the textbook, stupid!)

PS: If you read my math again, you might find out that I used no special TSTO case. I used concrete numbers for specific impulse and construction mass ratio (which is, engines, electronics and structure, but not payload, to propellant mass) for visualization, but the performance of the TSTO being better than the SSTO in pure physics will always remain.

Only in economics, there is an SSTO "island" possible - but you won't get there by evolution of existing economics. It is also very unlikely to be better than the TSTO "island", since, as shown above, the pure physical superiority exists.

 

[T.Neo]

I am skeptical of the diminutiveness of the 'SSTO window', over deep time...

Let's go back to the ET figures for a bit here;

Let's imagine that we have one SSME, and three RS-68A engines. This should provide enough thrust at liftoff to adequately lift the vehicle.

Assuming an engine mass of 6600 kilograms for the RS-68 engines, this is a total mass of 19 800 kg for the RS-68 engines, and a total mass of 3177 kilograms for the SSME. We will suggest that 50% of the engine mounting structure is jettisoned with the RS-68 engine cluster, and 50% remains fixed to the vehicle. We will not consider staging systems or disconnectable fluid transfer systems, as the original mass of the ET already includes these (for the Orbiter Vehicle).

This leads to a dry mass of 53 077 kilograms.

We will break launch into three phases:

1. 2000 m/s of dV, all engines, sea-level ISP figures.
2. 1000 m/s of dV, all engines, vacuum ISP figures.
3. 7000 m/s of dV, SSME only, vacuum ISP figures.

With these figures, it seems like the vehicle could make it to orbit using under 345 tons of its propellant only. It must be noted, however, that for phases 1 and 2 the exhaust velocity was based on the individual exhaust velocity of all engines, averaged together, and did not take into account any relationship with mass flow. Any wisdom regarding calculating the effective average exhaust velocity of different engines operating together would be much appreciated.

For 20 tons, the vehicle would use around 570 tons of its propellant to get to orbit.

For a payload of 30 tons, under 650 tons of the propellant would be used to get to orbit; 30 250 kilograms or so seems to be the total limit.

With a 10 ton fairing, a 3 ton payload interface and a 23 ton payload, it seems as if the vehicle could reach orbit using only around 595 tons of its propellant. The upper limit for payload at these figures is presumably slightly higher than 23 tons.

Assuming that the RS-68 engines each have a cost of $15 million, the SSME has a cost of $50 million, the rest of the hardware has the same cost of $60 million, and the additional hardware (fairings, etc) add $10 million, then the vehicle would have a cost to LEO of under $7200/kg, based on hardware cost alone and not including other factors. While this is not magic-$100-low, and isn't even exceptionally-realistic low, it is perhaps approaching modern US launchers, and is at least on a par with the lowest cost estimates of STS.

As for acceleration, with the RS-68 engines still attached and working off lowest throttle settings at vacuum thrust, the vehicle will reach 4G when it masses in total around 190 tons. The minimum acceleration that the vehicle would experience just before MECO, would be just under 2 G at minimum thrust from the SSME; at maximum thrust, it would be under 3G.

Obviously you would want to dump the engine package as soon as it is not needed. Of course, this is just one arrangement, you could maybe have two engines staying with the vehicle, for example.

Another option might be to change the type of engine- using the RS-68B as a compromise between the RS-68 and the SSME, still costing far less than the SSME.

This is all just hot air, of course; a far better experiment would be to try this concept out in Orbiter.

It is important to note that engines account for roughly 30% of of the dry mass of the vehicle at launch, minus payload, and would comprise an even larger amount of the mass of the vehicle with optimised propellant tanks.

Parachuting, recovering, shipping, refurbishing, and stacking an engine module could be easier and cheaper than doing the same with a flimsy propellant tank. The only thing that worries my simplistic mind is corrosion from salt water, and there is probably a way around that as well.

 

[RGClark]

Yes - but their conclusions are wrong, so better not jump on them too much. All they have is an net effect by having a shorter burn time (A hydrogen/oxygen rocket with the same acceleration capability could also use it).

Now, in practical spaceflight, you don't get much there. Simply because your choice of propellants also means:

Obviously, I don't agree with that. These were very smart guys who actually spent their careers in the industry designing rockets. But more importantly the same effect works for multi-staged rockets and has been proven in practice. That is, dense propellant first stages, such as kerosene or using SRB boosters, result in a lower gravity loss and therefore lower delta-V to orbit.


Bob Clark

---------- Post added at 06:15 AM ---------- Previous post was at 04:21 AM ----------

PS: If you read my math again, you might find out that I used no special TSTO case. I used concrete numbers for specific impulse and construction mass ratio (which is, engines, electronics and structure, but not payload, to propellant mass) for visualization, but the performance of the TSTO being better than the SSTO in pure physics will always remain.

Again I have to emphasize the payload fraction is a very poor measure to use to evaluate the efficiency of a launch vehicle. Many in the industry now realize a much better "figure of merit" is the payload mass to dry mass(empty mass) ratio.
This is because when computing the payload fraction you're comparing to something that contributes virtually nothing to the launch cost (the cost of propellant.) A more relevant comparison is to the dry mass.
See for example this report:

A Comparative Analysis of Single-Stage-To-Orbit Rocket and Air-Breathing Vehicles.
http://govwin.com/knowledge/comparative-analysis-singlestagetoorbit-rocket-and/15354

From the report:

From the many vehicle parameters used in the design of an RLV, a few parameters were assumed to be the most significant and used as figures of merit in this study. In both aircraft and spacecraft design, a vehicle’s empty mass is used as a guide to predict the vehicle’s design, materials, manufacturing, quality control and operational costs [2, 21]. Smaller vehicle empty mass is considered favorable.
p. 5.

Compared to the cost of the RLV, the cost of fuel is relatively insignificant [5]. Vehicle gross mass, consisting mostly of mass due to fuel, was therefore not considered to be a major figure of merit in this study.
p. 5.

4.2 Empty Mass Trends
The gross takeoff mass and empty mass are plotted for all vehicles in this study in Figure 20. Gross mass does not indicate where mass is allocated (structure, payload or mass) and consists of mostly inexpensive propellant. It is presented here for reference. Empty mass is a good indication of procurement and operational costs because it consists of the expensive structure of the vehicle.
p. 52.

and

Empty weight is considered a good figure of merit for the total cost of procuring a vehicle and one of the main figures of merit for maintaining and operating a vehicle.
p. 67.

For your proposed TSTO you can get a dry mass estimate by using some reasonable values for the dry mass and propellant masses for your two stages, assuming say a 20 to 1 mass ratio for each stage. For instance for the Falcon 9 first stage I estimate a dry mass of 15,000 kg and propellant mass of 285,000 kg.


Bob Clark

---------- Post added at 07:06 AM ---------- Previous post was at 06:15 AM ----------

...
Now, do you really want whole huge ET-based launcher just for launching a measly 20 tons? In practice, less than 20 tons?
If we assume that the modified ET costs $60 million and each SSME costs $50 million, we get a cost to LEO of $18 000 per kilogram, which is far from the oft-repeated $100/kg figure. This is considering hardware cost only, and neglecting launch-related and other costs.
And there is no ability to make this vehicle reusable, of course. Already adding such simple systems as a fairing would cut into the payload figure severely, adding a TPS, parachutes, and some sort of landing system would obliterate it entirely if not make the vehicle outright incapable of attaining orbit.

Of course, the key justification for why the cost could be brought down to the few hundred dollars per kilo range was that it would be reusable.
Say if you had a version of the SSME's that had low maintenance costs over a service life of 100 flights, then that cost to orbit could be brought down to $180/kilo.
Since you are in the mood for doing sample calculations perhaps you could try this on the S-II upper stage of the Saturn V, perhaps the most weight optimized hydrogen stage ever made. You'll have to swap out the J-2 engines for SSME's.


Bob Clark

---------- Post added at 07:43 AM ---------- Previous post was at 07:06 AM ----------

Can you explain how you arrive at this conclusion?

(PS: I know what you are likely to say, so I warn you, I am aware of the big text bubble with "something magical happens here")

Also, the full weight of the HL-20 was 25,000 lb, a tiny bit more than what you state for the HL-20, the exact mass of the Dream Chaser is unknown, there are only guesstimates for the suborbital version without heat shield and simpler subsystems, based on the fact that it was meant to be launched by a white knight.

Those mass values were taken from the links I cited in post #89.

Principles of scaling in launch vehicles allow that your mass ratio increases as you scale up the vehicle. This is because propellant tank weight and engine weight scales with the gross mass. But other components such as avionics, fairings, wiring, etc. scale at a slower rate. So the dry mass is increasing at a slower pace than the gross mass, which means your mass ratio improves.
Note too that for all competing proposals for the X-33, this half scale test vehicle could only be suborbital, while the full sized version would be fully orbital. This is because the mass ratio improved as you scaled it up.
I was using this general rule of thumb to argue the scaled up twice version of the DreamChaser could be fully orbital since I estimated the actual DreamChaser could be suborbital at high Mach by filling its internal volume with propellant.
There was another reason for suggesting the scaled twice up Dream Chaser could be orbital. I saw the version of the HL-20 scaled up 40% called the HL-42 did not weigh very much more than the HL-20. So it had a better mass ratio when filled with propellant. And in fact I estimated its delta-V would not be too far off that needed for orbit.
So I reasoned the mass ratio for the twice scaled up version would have sufficient delta-V for orbit.


Bob Clark

 

[T.Neo]

Of course, the key justification for why the cost could be brought down to the few hundred dollars per kilo range was that it would be reusable.
Say if you had a version of the SSME's that had low maintenance costs over a service life of 100 flights, then that cost to orbit could be brought down to $180/kilo.

My whole point is that the ET-based SSTO can't be reusable, because it murders its payload capability. Even the 1.5 stager would have an unreasonably low payload if reusability infrastructure was included.

The refurbishment cost for the SSMEs can be partially calculated using the figures here. If we assume that the TPS refurbishment takes 40 000 man-hours, and TPS refurbishment takes up 40% of the man-hours of vehicle refurbishment in total, then the SSMEs, comprising 8.85% of the refurbishment man-hours, will take 8850 man-hours to refurbish, or 2950 man-hours per SSME.

If the annual salary for an aeronautical engineer in the US is $80 000 a year, and your aeronautical engineer works roughly 2000 hours per year, then the hourly rate is $40/hour. This means that at these figures, it would cost roughly $120 000 to refurbish the SSMEs, not including replacement parts, paperwork and organisation, and upkeep for the actual facilities.

If we assume that the vehicle can magically manage 20 tons payload and be reusable, that total flight cost is only $5 million, that yearly upkeep is $800 million (yearly upkeep for the STS program is apparently $1 billion), that program R&D costs were $15 billion, that there are five vehicles and each was built at a cost of $360 million, and that the program is intended to run for 20 years with a flight-rate of 10 per year (similar to the flight-rate of Proton in 2010), that is still a cost of $169 million per flight, or $8450 per kilogram.

Even if you neglected the initial development and vehicle construction costs, you would have a launch cost of 85 million or 4250/kg, comparable to Proton. This of course would make things entirely unsuitable for a private operation as there would be billions of dollars lost entirely in R&D and construction.

And this is not making up for failures- with a 2% failure rate, you can expect 4 failures out of 200 launches.

I'd like to see how you came to your $180/kg cost.

Since you are in the mood for doing sample calculations perhaps you could try this on the S-II upper stage of the Saturn V, perhaps the most weight optimized hydrogen stage ever made. You'll have to swap out the J-2 engines for SSME's.

Who says I am in the mood for anything? These calculations take time and effort, I am practically mathamatically illterate, I am likely missing certain factors, there is a high chance of inaccuracy, and everyone probably thinks I am a moron for doing so.

Nevertheless, I am sure it is pretty clear that I cannot refuse such pondering.

Launching an S-II was actually discussed as a post-Saturn concept, and is represented in Velcro Saturns. The concept is an S-II as the first stage below an S-IVB, augmented with high-pressure HG-3 engines in the place of the J-2 engines.

The three concepts depicted in Velcro Rockets are the INT-17, INT-18, and INT-19. Below are the scenario descriptions by Sputnik:

The INT-17, which eliminated the S-IC stage from the Saturn V. S-II thrust augmented by uprating to 7 high-pressure HG-3 engines. Not cost-effective and not studied further. This Orbiter implementation displays only 5 engines as this launcher does not really deserve a new mesh.

The INT-18, which eliminated the S-IC stage from the Saturn V. Sea-level liftoff of an S-II and S-IVb, with thrust augmentation from 4 UA1207 7-segment Titan motors. INT-18 also studied variants with only two UA1207's, or with the S-IVb stage removed.

The INT-19, which eliminated the S-IC stage from the bottom of the Saturn V. Sea-level liftoff of an S-II and S-IVb, with thrust augmentation from 12 (!) Minuteman motors; 8 ground-lit and 4 air-lit. Warning: smoke trails will tend to bog down your sys tem in external view.

It is clear that the S-II has been considered for surface liftoff, and is clearly capable of doing so, or at least was thought so by the people who came up with stuff like the Saturn INT-17.

Nevertheless the S-II itself is a pretty poor choice considering that it is not only a 1960s design, but that it might not be optimal from an aerodynamic perspective (is wider than it is tall).

Astronautix gives a wet mass of 490 778 kg and a dry mass of 39 048 kg. Wikipedia says the mass of the J-2S engine was 1400 kg. That is 7000 kg for 5 engines, leaving the S-II with an engineless dry mass of 32 048 kg.

The S-II has a propellant mass of 451 730; an enginless dry mass of 32 048 kg, and an engineless wet mass of 483 778 kg. This is a mass ratio of 15.

The STS has a propellant mass of 735 601 kg, a dry mass of 26 500 kg, and a wet mass of 762 101 kg. This is a mass ratio of over 28.

Considering that the ET has an intertank and needs to deal with asymmetric stresses during ascent, and the S-II does not, I would say that the S-II is... primitive. Or that it is reinforced for a fully fueled S-IVB and Apollo stack above it, which wouldn't be there in a self-contained launch vehicle.

I think a comparison based on the volume/mass of one of the pressure-supported Atlas rockets, or one of the Falcon vehicles, would be better in this case.

 

[Urwumpe]

Obviously, I don't agree with that. These were very smart guys who actually spent their careers in the industry designing rockets. But more importantly the same effect works for multi-staged rockets and has been proven in practice. That is, dense propellant first stages, such as kerosene or using SRB boosters, result in a lower gravity loss and therefore lower delta-V to orbit.

First of all, don't try argument by authority against me. I hate incompetence.

Second, your "authorities" are:

Henry Spencer: Famous computer programmer, newsgroup activist and space enthusiast. He has NEVER worked for a spaceflight company, but is active in the Canadian Space Society. He is no professional however, just a very good amateur - we have dozens of those in the Orbiter community.

Mitchell B Clapp: Inventor, book author, former USAF captain, military scientist/engineer - holds two patents on rocket planes, space enthusiast, had been supporting the failed Rocketplane Limited in 1997. Was employed at the Phillips Laboratory, before he joined Rocketplane Limited, today the Phillips Laboratory is split into the Space Vehicles and Directed Energy Directorates of the Airforce Research Laboratory. Was last employed the at the VT-X, the Launch Vehicle Technology Office. Nothing known about his life since 1999.

Notice something?

Also, if I remember the newsgroup discussion between the two, that you treat here like a scientific publication, correctly, Clapp did actually correct Spencer a few times, but also based his findings on the Trident 2 missile, which is having a too high acceleration for any kind of payload that isn't a warhead.

PS: For all those people that never heard of the ascent equation and are maybe feeling as surprised as Spencer:

[math]\Delta v = \Delta v^{\ast} - \mu \int_0^{t_b} \frac{\cos {\alpha}}{r^2} \mathrm{d}t - \int_0^{t_b}\frac{D}{m} \mathrm{d}t - \int_0^{t_b} \frac{F}{m} \left ( 1 - \cos{\delta} \right ) \mathrm{d}t[/math]
[math]\Delta v[/math] is the velocity change between ground velocity and orbital velocity
[math]\Delta v^{\ast}[/math] is the total velocity change as produced by the engines and calculated by the rocket equation
[math]t_b[/math] is the burn out time, the moment you reach orbit
[math]\alpha[/math] is the flight path angle (0° = straight up)
D is the drag force
m is mass
F is the engine thrust
[math]\delta[/math] is the steering angle, the angle between total thrust vector and velocity vector.

Thus, the first integral are the gravity losses, the second the aerodynamic losses and the third the control losses.

As you can easily see - the smaller the [math]t_b[/math], the lower the losses.

(Yes, I finally had the time to hack this into Latex form)

 

[RGClark]

Thus, the first integral are the gravity losses, the second the aerodynamic losses and the third the control losses.

As you can easily see - the smaller the [math]t_b[/math], the lower the losses.

Yes, the method by which the gravity losses are reduced for the dense propellants is that the time of the vertical thrust portion of the flight where the gravity drag is operating is reduced.


Bob Clark

 

[Urwumpe]

Yes, the method by which the gravity losses are reduced for the dense propellants is that the time of the vertical thrust portion of the flight where the gravity drag is operating is reduced.

Again, this isn't an exclusive realm of dense propellants. It is just a matter of thrust to weight. A hydrogen/oxygen rocket could fly the same trajectory - with less propellant mass, but more propellant volume... but the mass does usually hurt more.

also, more acceleration during the vertical part of flight means automatically more losses by drag and more aerodynamic loads on your rocket, increasing the structural mass and the SPL for the payload.

PS: The discussion was based on the Trident 2 performance, which had been extremely low in total velocity change compared to other ICBMs - but really not surprising if you remember that the Trident 2 is a pop-up weapon with around or less than two minutes boost phase.

 

[RGClark]

Who says I am in the mood for anything? These calculations take time and effort, I am practically mathamatically illterate, I am likely missing certain factors, there is a high chance of inaccuracy, and everyone probably thinks I am a moron for doing so.

I appreciate your taking the time to do the calculation.
About the comparison between the ET and the S-II empty weights, the more relevant comparison would be when you add the engine weight to the ET. But then you also have to add on the thrust structure which transmits the thrust evenly to the propellant tanks, the wiring, and the hydraulics for the engine gimbaling. You also have to add on the avionics but you would have to add this also to the S-II, and with modern miniaturization this should be a small component of the empty weight.
These extra weight considerations are why I prefer to do this swapping out of engines with already existing stages, such as the S-II.


Bob Clark

 

[T.Neo]

I removed the engines from the S-II for exactly this reason.

If I add a whole 6000 kg to the ET, I still get a mass ratio of over 23. I would say that this is Absolutely No Contest for the S-II, or at the least, that the S-II isn't 'the most mass optimised hydrolox stage ever', as you suggest.

If you aren't willing to explore other possibilities, just because they require more speculative effort on your part, then you will severely limit yourself.

 

[RGClark]

I removed the engines from the S-II for exactly this reason.
If I add a whole 6000 kg to the ET, I still get a mass ratio of over 23. I would say that this is Absolutely No Contest for the S-II, or at the least, that the S-II isn't 'the most mass optimised hydrolox stage ever', as you suggest.
If you aren't willing to explore other possibilities, just because they require more speculative effort on your part, then you will severely limit yourself.

The problem is the weights for those extra components that make up an actual stage are not trivial. Take a look for instance at the design of the Direct teams version of a 70 mT payload HLV that uses the shuttle ET. When 3 SSME engines are attached to the bottom of the ET and it is made into an actual stage, the dry mass balloons up to 63,725 kg. Actually even this is too small for our SSTO purpose because you would need to use 5 or 6 SSME's to be able to leave the pad and have a good enough T/W ratio to not incur a large gravity loss.


Bob Clark

 

[T.Neo]

Yes. And nearly ten tons of that is engines. And if we assume that the engine mounting structure is some 5 000 kg, we are left with a stage that is... roughly twice as heavy as the ET.

I don't know where that extra mass comes from. If you changed things inside the ET so drastically as to effectively double its mass, you would probably lose a significant fraction of DIRECT's supposed commonality with shuttle systems. Maybe. I don't know much about DIRECT.

Maybe for example that mass is some weird, huge safety margin. Or maybe part of it, at least, is part of a payload mount.

The STS ET already has propellant feed lines, to the Orbiter connection points, at least. It already has mounting points for STS, for example. On the ground- when the full weight of the vehicle is hanging off the ET, you're looking at some 100 tons hanging off the tank. And of course after booster seperation, that is reversed, basically with the tank hanging off the shuttle.

And of course, the whole thing is hanging off the boosters.

I don't really see how all the structural mass needed for that is trivial.

On the other hand, if you are suggesting some sort of... 15 ton avionics suite, then I really have no clue. Yes, electronics for space applications are generally more primitive than civillian, ground-based electronics. But they don't suddenly double the mass of your vehicle.

And when comparing the ET with a rocket stage, always subtract the mass of the engines. It isn't fair to try and compare something that isn't there. The key here is comparing the properties of the propellant tank itself.

 

[RGClark]

... this was using the low efficiency engines available in the early 60's. Let's swap these out for the high efficiency NK-33. The sustainer engine used was the LR89-5 at 720 kg. At 1,220 kg the NK-33 weighs 500 kg more. So removing both the sustainer and booster engines to be replaced by the NK-33 our loaded mass becomes 117,526 kg and the dry mass 2,826 kg, and the mass ratio 41.6 (!).
For the trajectory-averaged Isp, notice this is not just the midpoint between the sea level and vacuum value, since most of the flight to orbit is at high altitude at near vacuum conditions. A problem with doing these payload to orbit estimates is the lack of a simple method for getting the average Isp over the flight for an engine, which inhibits people from doing the calculations to realize SSTO is possible and really isn't that hard. I'll use a guesstimate Ed Kyle uses, who is a frequent contributor to NasaSpaceFlight.com and the operator of the Spacelauncereport.com site. Kyle takes the average Isp as lying 2/3rds of the way up from the sea level value to the vacuum value. The sea level value of the Isp for the NK-33 is 297 s, and the vacuum value 331 s. Then from this guesstimate the average Isp is 297 + (2/3)(331 - 297) = 319.667, which I'll round to 320 s.
Using this average Isp and a 8,900 m/s delta-V for a flight to orbit, we can lift 4,200 kg to orbit:

320*9.8ln((117,526+4,200)/(2,826+4,200)) = 8,944 m/s. This is a payload fraction of 3.5%, comparable to that of many multi-stage rockets.
...

Dr. John Schilling has a launch performance estimator on his company's web page based on a numerical formula:

Launch Vehicle Performance Calculator.
http://www.silverbirdastronautics.com/LVperform.html

There is a disclaimer on the page that for user-defined vehicles it is limited to only 3-stage vehicles, and indeed I found previously when I tried to use it on a SSTO it didn't supply an answer. However, recently I found it even gives an answer for an SSTO vehicle.

This is the answer I got when I used the numbers of the above example:

-------------------------------------------------------------
Mission Performance:
Launch Vehicle: User-Defined Launch Vehicle
Launch Site: Cape Canaveral / KSC
Destination Orbit: 200 x 200 km, 28 deg
Estimated Payload: 4319 kg
95% Confidence Interval: 3077 - 5820 kg

"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters
This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.
--------------------------------------------------------------


The estimator requires you to input an Isp and thrust for the engines. This is meant the vacuum Isp and thrust. The program takes into account the losses due to reduced exhaust velocity at sea level and low altitude.
For this case I used the 331 s vacuum Isp and 1,636 kN vacuum thrust of the NK-33.


Bob Clark

 

[T.Neo]

I think I was seriously, severely wrong, with my calculations, somewhere. I punched the data for my ET-derived SSTO into that calculator, with a 10 ton fairing (seperation 2 minutes in), and got roughly 38 tons to a 200x200, 28 degree LEO from KSC.

Now, initially I thought there was something seriously wrong with that calculator (which there might be).

I then created a simple Velcro Rocket of the vehicle, lacking a fairing.

I gave it a payload of 35 tons.

I achieved an orbit of ~322x215km from KSC.

Admittedly, I cheated, as I circularised at apogee, but I probably could have done a direct ascent (and achieved a less wonky orbit), if I had better style.

Where did I go wrong here? Am I being to pessimistic with sea-level figures for the first 2km/s of applied dV?

Or are Velcro Rockets and the Launch Vehicle Performance Calculator being too optimistic?

The calculator assumes full thrust throughout the mission, which, with this, means accelerations on the order of 10G or more, which probably increases payload capacity (no thought spared for structural considerations, obviously).

Velcro rockets does seem to reduce thrust at sea-level, though I'm not sure if this matches the actual figures (or if there's a relation with exhaust velocity- I'll have to look at that).

It probably isn't as simple as my calculations, or the internet calculator's calculations (hence the disclaimer), or even a simulation using Orbiter and Velcro Rockets. But they do give a hint, and maybe my hint was too pessimistic to be realistic, in which case I apologise.

That still doesn't eliminate the problems faced by SSTO vehicles (or launch vehicles in general) though.

But the Launch Vehicles Performance Calculator looks like a very interesting tool for speculating, creating Orbiter addons, and general playing around. Thanks for posting it, RGClark.

 

[RGClark]

I think I was seriously, severely wrong, with my calculations, somewhere. I punched the data for my ET-derived SSTO into that calculator, with a 10 ton fairing (seperation 2 minutes in), and got roughly 38 tons to a 200x200, 28 degree LEO from KSC.

Now, initially I thought there was something seriously wrong with that calculator (which there might be).

I then created a simple Velcro Rocket of the vehicle, lacking a fairing.

I gave it a payload of 35 tons.

I achieved an orbit of ~322x215km from KSC.

Admittedly, I cheated, as I circularised at apogee, but I probably could have done a direct ascent (and achieved a less wonky orbit), if I had better style.

Where did I go wrong here? Am I being to pessimistic with sea-level figures for the first 2km/s of applied dV?

Or are Velcro Rockets and the Launch Vehicle Performance Calculator being too optimistic?

The calculator assumes full thrust throughout the mission, which, with this, means accelerations on the order of 10G or more, which probably increases payload capacity (no thought spared for structural considerations, obviously).

Velcro rockets does seem to reduce thrust at sea-level, though I'm not sure if this matches the actual figures (or if there's a relation with exhaust velocity- I'll have to look at that).

It probably isn't as simple as my calculations, or the internet calculator's calculations (hence the disclaimer), or even a simulation using Orbiter and Velcro Rockets. But they do give a hint, and maybe my hint was too pessimistic to be realistic, in which case I apologise.

That still doesn't eliminate the problems faced by SSTO vehicles (or launch vehicles in general) though.

But the Launch Vehicles Performance Calculator looks like a very interesting tool for speculating, creating Orbiter addons, and general playing around. Thanks for posting it, RGClark.

You're welcome. Could you post the input page for the calculator where you give the data for your rocket as well as the output page?

Bob Clark