A kerosene-fueled X-33 as a single stage to orbit vehicle.

Table of Contents.
I.)Introduction.
II.)Lightweight propellant tanks.
III.)Kerosene fuel and engines for the X-33/VentureStar.
IVa.)Aerodynamic lift applied to ascent to orbit.
b.)Estimation of fuel saving using lift.
V.)Kerosene fueled VentureStar payload to orbit.

I.) A debate among those questing for the Holy Grail of a reusable, single-stage-to-orbit vehicle is whether it should be powered by hydrogen or a dense hydrocarbon such as kerosene. Most concepts for such a vehicle centered on hydrogen, since a hydrogen/LOX combination provides a higher Isp. However, some have argued that dense fuels should be used since they take up less volume (equivalently more fuel mass can be carried in the same sized tank) so they incur less air drag and also since the largest hydrocarbon engines produce greater thrust they can get to the desired altitude more quickly so they also incur lower gravity drag loss.
Another key fact is that for dense fuels the ratio of propellant mass to tank mass is higher, i.e., you need less tank mass for the same mass of propellant. This fact is explored in this report:

Single Stage To Orbit Mass Budgets Derived From Propellant Density and Specific Impulse.
John C. Whitehead
32nd AIAA/ASME/SAE/ASEE Joint Propulsion ConferenceLake Buena Vista, FLJuly 1-3, 1996
http://www.osti.gov/bridge/servlets/purl/379977-2LwFyZ/webviewable/379977.pdf

Whitehead notes that the propellant mass to tank mass ratio for kerosene/LOX is typically around 100 to 1, while for liquid hydrogen/LOX it's about 35 to 1, which would result in a significantly greater dry mass for the hydrogen-fueled case just in tank weight alone. Based on calculations such as these Whitehead concludes the best option for a SSTO would be to use kerosene/LOX.
The case for the X-33/VentureStar is even worse because the unusual shape of the tanks requires them to use more tank mass than a comparably sized cylindrical tank. This is discussed here:

Space Access Update #91 2/7/00.
The Last Five Years: NASA Gets Handed The Ball, And Drops It.
"...part of L-M X-33's weight growth was the "multi-
lobed" propellant tanks growing considerably heavier than promised.
Neither Rockwell nor McDonnell-Douglas bid these; both used proven
circular-section tanks. X-33's graphite-epoxy "multi-lobed" liquid
hydrogen tanks have ended up over twice as heavy relative to the
weight of propellant carried as the Shuttle's 70's vintage aluminum
circular-section tanks - yet an X-33 tank still split open in test
last fall. Going over to aluminum will make the problem worse; X-
33's aluminum multi-lobed liquid oxygen tank is nearly four times as
heavy relative to the weight of propellant carried as Shuttle's
aluminum circular-section equivalent."
http://www.space-access.org/updates/sau91.html

The X-33's twin liquid hydrogen tanks had a weight of 4,600 pounds each, and the liquid oxygen tank a weight of 6,000 pounds, for total of 15,200 pounds for the tanks:

Marshall Space Flight Center
Lockheed Martin Skunk Works
Sept. 28, 1999
X-33 Program in the Midst of Final Testing and Validation of Key Components.
http://www.xs4all.nl/~carlkop/x33.html

The weight of the propellant carried by the X-33 was supposed to be 210,000 lb. So the propellant to tank mass ratio for the X-33 was only about 14 to 1(!). This would be a severe problem for the full-scale VentureStar. Its gross lift off weight was supposed to be 2,186,000 lbs with a fuel weight of 1,929,000 lbs:

X-33 Advanced Technology Demonstrator.
http://teacherlink.ed.usu.edu/tlnasa/OtherPRINT/Lithographs/X33.Advanced.Technology.Demonstrator.PDF

So the VentureStar would have a dry mass of 257,000 lbs. Since the same design would be used for the VentureStar tanks as those of the X-33, the propellant mass to tank mass ratio would also be 14 to 1, so the tank mass would be 138,000 lbs. But this means the empty tank mass alone would be over half of the vehicle's dry weight (!)
It would have been extremely difficult for the VentureStar to have made orbit with such a large weight penalty from the start. From all accounts the weight problem with the tanks drove other problems such as the need to add larger wings, increasing the weight problem further. NASA wound up canceling the program when Lockheed couldn't deliver the working liquid hydrogen tanks even at this excessive weight. However, rather than canceling the program I believe the better course would have been to open up competition for coming up with alternative, creative solutions for reducing the weight of the tanks. This would also have resolved some of the problems with the vehicles weight growth.

II.) I have proposed one possibility for lightweighting the X-33 tanks on this forum:

http://www.bautforum.com/space-expl...ital-hypersonic-transports-5.html#post1495726

The idea would be to achieve the same lightweight tanks as cylindrical ones by using multiple, small diameter, aluminum cylindrical tanks. You could get the same volume by using varying lengths and diameters of the multiple cylinders to fill up the volume taken up by the tanks. The cylinders would not have to be especially small. In fact they could be at centimeter to millimeter diameters, so would be of commonly used sizes for aluminum tubes and pipes.
The weight of the tanks could be brought down to the usual 35 to 1 ratio for propellant to tank mass. Then the mass of the tanks on the X-33 would be 210,000 lbs/35 = 6,000 lbs, saving 9,200 lbs off the vehicle dry weight. This would allow the hydrogen-fueled X-33 to achieve its original Mach 15 maximum velocity.
The same idea applied to the full-scale hydrogen-fueled VentureStar would allow it to significantly increase its payload carrying capacity. At a 35 to 1 ratio of propellant mass to tank mass, the 1,929,000 lbs propellant mass would require a mass of 1,929,000/35 = 55,000 lbs for the tanks, a saving of 83,000 lbs off the original tank mass. This could go to extra payload, so from 45,000 lbs max payload to 128,000 lbs max payload.
An analogous possibility might be to use a honeycombed structure for the entire internal makeup of the tank. The X-33's carbon composite tank was to have a honeycombed structure for the skin alone. Using a honeycomb structure throughout the interior might result in a lighter tank in the same way as does multiple cylinders throughout the interior.
Still another method might be to model the tanks standing vertically as conical but with a flat front and back, and rounded sides. Then the problem with the front and back naturally trying to balloon out to a circular cross section might be solved by having supporting flat panels at regular intervals within the interior. The X-33 composite tanks did have support arches to help prevent the tanks from ballooning but these only went partially the way through into the interior. You might get stronger a result by having these panels go all the way through to the other side.
These would partition the tanks into portions. This could still work if you had separate fuel lines, pressurizing gas lines, etc. for each of these partitions and each got used in turn sequentially. A preliminary calculation based on the deflection of flat plates under pressure shows with the tank made of aluminum alloy and allowing deflection of the flat front and back to be only of millimeters that the support panels might add only 10% to 20% to the weight of the tanks, while getting similar propellant mass to tank mass ratio as cylindrical tank. See this page for an online calculator of the deflection of flat plates:

eFunda: Plate Calculator -- Simply supported rectangular plate with uniformly distributed loading.
http://www.efunda.com/formulae/solid_mechanics/plates/calculators/SSSS_PUniform.cfm

Note you might not need to have a partitioned tank, with separate fuel lines, etc., if the panels had openings to allow the fuel to pass through. These would look analogous to the wing spars in aircraft wings that allow fuel to pass through. You might have the panels be in a honeycomb form for high strength at lightweight that still allowed the fuel to flow through the tank. Or you might have separate beams with a spaces between them instead of solid panels that allowed the fuel to pass through between the beams.
Another method is also related to the current design of having a honeycombed skin for the composite hydrogen tanks. Supposed we filled these honeycombed cells with fluid. It is known that pressurized tanks can provide great compressive strength. This is in fact used to provide some of the structural strength for the X-33 that would otherwise have to be provided by heavy strengthening members. This idea would be to apply fluid filled honycombed cells. However, what we need for our pressurized propellant tanks is *tensile strength*.
A possible way tensile strength could be provided would be to use the Poisson's ratio of the honeycombed cells:

Poisson's ratio.
http://en.wikipedia.org/wiki/Poisson's_ratio

Poisson's ratio refers to the tendency of a material stretched in one direction to shrink in length in an orthogonal direction. Most isotropic solid materials have Poisson's ratio of about .3. However, the usual hexagonal honeycombed structure, not being isotropic, can have Poisson's ratios in the range of +1. This is mentioned in this article about non-standard honeycombed structures that can even have negative Poisson ratios:

Chiral honeycomb.
http://silver.neep.wisc.edu/~lakes/PoissonChiral.html

However, note that from the formula for the volumetric change in the Wikipedia Poisson's ratio page, a stretching of a material with a +1 Poisson's ratio implies a *decrease* in volume; actually this is true for any case where the Poisson's ratio is greater than +.5. Then fluid filled honeycombed cells would resist the stretching of tensile strain by the resistance to volume compression. This would be present with both gases and liquids. Gases are lighter. However, they are highly compressible and it might take too large an internal pressure in the cells to provide sufficient resistance, and so also too thick cell walls to hold this pressure. Liquids are heavier but they are highly non-compressible so could provide strong resistance to the volume compression and thereby to the tensile strain.
Then for liquid hydrogen tanks we might use liquid hydrogen filled cells within the skin of the tanks. Hydrogen is rather light compared to other liquids at a density of only about 72 kg/m^3. This then could provide high tensile strength at a much lower weight than typical solid wall tanks.
Kerosene and liquid oxygen would be used in the honeyombed cells for their corresponding tanks, to keep the storage temperatures comparable. These are heavier liquids than liquid hydrogen, approximately in the density range of liquid water. Still these liquid filled honeycombed cells would provide much lighter tanks than comparable solid wall tanks.
III.) Any of these methods might allow you to reduce the weight of the tanks to be similar to that of cylindrical tanks and thus raise the payload to over 100,000 lbs. This would be for keeping the original hydrogen/LOX propellant. However, in keeping with the analyses that show dense propellants would be more appropriate for a SSTO vehicle I'll show that replacing the hydrogen-fueled engines of the X-33/VentureStar with kerosene ones would allow the X-33 to actually now become an *orbital* craft instead of just suborbital, and the payload capacity of the VentureStar would increase to be comparable to that proposed for Ares V.
The volume of the X-33 liquid hydrogen tanks was 29,000 gallons each and the liquid oxygen tank, 20,000 gallons, for a total of 78,000 gallons volume for propellant. This is 78,000gal*3.8 L/gal = 296,000 liters, 296 cubic meters. How much mass of kerosene/LOX could we fit here if we used these as our propellants? Typically the oxidizer to fuel ratio for kerosene/LOX engines is in the range of 2.5 to 2.7 to 1. I'll take the O/F ratio as 2.7 to 1. The density of kerosene is about 806 kg/m^3 and we can take the density of liquid oxygen to be 1160 kg/m^3 when densified by subcooling:

Liquid Oxygen Propellant Densification Unit Ground Tested With a Large-Scale Flight-Weight Tank for the X-33 Reusable Launch Vehicle.
http://www.grc.nasa.gov/WWW/RT/RT2001/5000/5870tomsik.html

These requirements of the propellants' total volume and densities, result in a total propellant mass of 307,000 kg, with 83,000 kg in kerosene and 224,000 kg in LOX. Kerosene/LOX tanks weigh typically 1/100th the propellant mass, so the tank mass would be 3,070 kg. The current X-33 LH/LOX tanks weighed 15,200 lbs, or 6,900 kg. So the empty weight of the X-33 is reduced from 63,000 lbs, 28,600 kg, to 28,600kg - 6,900kg + 3070kg = 24,800 kg.
How about the engines? The X-33 is to be reusable so you want to use reusable kerosene engines. The RS-84 might be ideal when it is completed for the full-scale VentureStar, but it turns out it's a bit too heavy for the X-33. It would have a weight of about 15,000 lbs, 6,800 kg:

RS-84.
http://www.astronautix.com/engines/rs84.htm

about the weight of the two aerospike engines currently on the X-33:

Bringing launch costs down to earth.
"Three federally funded projects are underway to develop new rocket engines that can make it more affordable to send payloads into orbit."
http://www.memagazine.org/backissues/membersonly/october98/features/launch/launch.html

With 307,000 kg kerosene/LOX fuel and 24,800 kg dry weight, the mass ratio would be 13.4. According to the Astronautix page, the sea level Isp of the RS-84 would be 301 s, and the vacuum 335 s. Take the average Isp as 320s. The total Isp for a rocket to orbit including gravity and air drag losses is usually taken to be about 9,200 m/s. Then an average exhaust velocity of 3200 m/s and mass ratio of 13.4 would give a total delta-v of 8,300 m/s. Even if you add on the 462 m/s additional velocity you can get for free by launching at the equator this would not be enough for orbit.
So for the X-33 I'll look at the cases of the lighter for its thrust NK-33, used as a trio. Note that though not designed to be a reusable engine to make, say, 100 flights, all liquid fuel rocket engines undergo extensive static firings during testing so the NK-33 probably could make 5 to 10 flights before needing to be replaced.The NK-33 is almost legendary for its thrust to weight ratio of 136. According to the Astronautix page its weight is 1,222 kg , with a sea level Isp of 297 sec and a vacuum Isp of 331:

NK-33.
http://www.astronautix.com/engines/nk33.htm

I'll take the average Isp as 315 s. With three NK-33 engines the mass of the X-33 becomes 21,700 kg, and the mass ratio becomes 15.15. Then with an average Isp of 315 s, the total delta-v would be 8561 m/s and if you add on the 462 m/s additional equatorial velocity it's 9,023 m/s. Still slightly below the delta-v typically given for orbit of 9,200 m/s.
However, it should be noted that the extra delta-v required beyond the 7,800 m/s orbital velocity is highly dependent on the vehicle and trajectory. Here's a page that gives the gravity loss and air drag loss for some orbital rockets:

Drag: Loss in Ascent, Gain in Descent, and What It Means for Scalability.
Thursday 2008.01.10 by gravityloss
* Ariane A-44L: Gravity Loss: 1576 m/s Drag Loss: 135 m/s
* Atlas I: Gravity Loss: 1395 m/s Drag Loss: 110 m/s
* Delta 7925: Gravity Loss: 1150 m/s Drag Loss: 136 m/s
* Shuttle: Gravity Loss: 1222 m/s Drag Loss: 107 m/s
* Saturn V: Gravity Loss: 1534 m/s Drag Loss: 40 m/s (!!)
* Titan IV/Centaur: Gravity Loss: 1442 m/s Drag Loss: 156 m/s
http://gravityloss.wordpress.com/20...in-descent-and-what-it-means-for-scalability/

Note that the gravity loss for the Delta 7925 is particularly small. As a general principle the gravity loss can be minimized if you have a high thrust vehicle that rapidly develops high vertical velocity sufficient to reach the altitude for orbit. For then it can more quickly apply the horizontal thrust required to achieve the 7,800 m/s orbital, tangential, velocity, there being no gravity loss over the horizontal thrust portion. Note then the liftoff thrust to liftoff weight ratio for the Delta 7925 is the relatively large 1.4; in comparison for the Saturn V it was only 1.14. And note now also that the X-33 with three NK-33 engines has total mass of 328,700 kg and total thrust of 4,530,600 N giving a liftoff thrust to liftoff weight ratio of 1.4. Then this reconfigured X-33 would likely have comparable gravity drag loss as the Delta 7925. When you take into account the high thrust means it would rapidly reach high altitude, implying the Isp would quickly get close to the vacuum Isp, the average Isp over the trajectory is most likely closer to the 331 s vacuum Isp than just 315 s giving an actually higher achieved delta-v.
IV.a) It's capability of reaching orbit and possibly even with a small payload could be increased with another additional factor. Among the questors for a SSTO vehicle, the idea to use wings for a horizontal landing has been derided because of the view they were just dead weight on ascent and you need to save as much weight off the empty weight of the vehicle as possible to achieve orbit. However, the key fact is that wings or a lifting body shape can reduce the total delta-v for orbit by using aerodynamic lift to supply the force to raise the vehicle to a large portion of the altitude of orbit rather than this force being entirely supplied by the thrust of the engines. This fact is discussed on page 4 of this report:

AIAA 2000-1045
A Multidisciplinary Performance Analysis of a Lifting-Body Single-Stage-to-Orbit Vehicle.
Paul V. Tartabini, Roger A. Lepsch, J. J. Korte, Kathryn E. Wurster
38th Aerospace Sciences Meeting & Exhibit.
10-13 January 2000 / Reno, NV
"One feature of the VentureStar design that could
be exploited during ascent was its lifting body shape.
By flying a lilting trajectory, it was possible to significantly
decrease the amount of gravity losses, thereby
improving vehicle performance and payload capability.
Yet increasing the amount of lift during ascent generally
required flight at higher angles-of-attack and resulted
in greater stress on the vehicle structure. Accordingly,
the nominal trajectory was constrained to keep the parameter
q-_ below a 1500 psf-deg structural design limit
to ensure that the aerodynamic loads did not exceed
the structural capability of the vehicle. The effect of this
trajectory constraint on vehicle performance is shown
in Fig. 3. There was a substantial benefit associated with
using lift during ascent since flying a non-lifting trajectory
resulted in a payload penalty of over 1000 lbs compared
to the nominal case."
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20000031364_2000025539.pdf

Then the gravity losses could be further reduced by flying a lifting trajectory, which would also increase the payload capability by a small percentage.

The trajectory I'll use to illustrate this will first be straight-line at an angle up to some high altitude that still allows aerodynamic lift to operate. At the end of this portion the vehicle will have some horizontal and vertical component to its velocity. We'll have the vertical component be sufficient to allow the vehicle to reach 100 km, altitude. The usual way to estimate this vertical velocity is by using the relation between kinetic energy and potential energy. It gives the speed of v = sqrt(2gh) to reach an altitude of h meters. At 100,000 m, v is 1,400 m/s.
Now to have orbital velocity you need 7,800 m/s tangential, i.e., horizontal velocity. If you were able to fly at a straight-line at a constant angle to reach 7,800 m/s horizontal velocity and 1,400 m/s vertical velocity and such that the air drag was kept at the usual low 100 to 150 m/s then you would only need sqrt(7800^2 + 1400^2) = 7,925 m/s additional delta-v to reach orbit. Then the total delta-v to orbit might only be in 8,100 m/s range. Note this is significantly less than the 9,200 m/s delta-v typically needed for orbit, including gravity and air drag.
The problem is with usual rocket propulsion to orbit not using lift the thrust vector has to be more or less along the center-line of the rocket otherwise the rocket would tumble. You can gimbal the engines only for a short time to change the rocket's attitude but the engines have to be then re-directed along the center line. However, the center line has to be more or less pointing into the airstream, i.e., pointing in the same direction as the velocity vector, to reduce aerodynamic stress and drag on the vehicle. But the rocket thrust having to counter act gravity means a large portion of the thrust has to be in the vertical component which means the thrust vector has to be nearly vertical at least for the early part of the trip when the gross mass is high. Then the thrust vector couldn't be along the center line of a nearly horizontally traveling rocket at least during the early part of the trip.
However, using lift you are able to get this large upwards vertical component for the force on the rocket to allow it to travel along this straight-line. A problem now though is that at an altitude short of that of space, the air density will not be enough for aerodynamic lift. Therefore we will use lift for the first portion of the trajectory, traveling in a straight-line at an angle. Then after that, with sufficient vertical velocity component attained to coast to 100 km altitude, we will supply only horizontal thrust during the second portion to reach the 7,800 m/s horizontal velocity component required for orbital velocity.

IV.b) How much fuel could we save using a lifting straight-line portion of the trajectory? I'll give an example calculation that illustrates the fuel savings from using aerodynamic lift during ascent. First note that just as for aircraft fuel savings are best at a high L/D ratio. However, the hypersonic lift /drag ratio of the X-33/VentureStar is rather poor, only around 1.2, barely better than the space shuttle:

AIAA-99-4162
X-33 Hypersonic Aerodynamic Characteristics.
Kelly J, Murphy, Robert J, Nowak, Richard A, Thompson, Brian R, Hollis
NASA Langley Research Center
Ramadas K. Prabhu
Lockheed Martin Engineering &Sciences Company
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040087108_2004091447.pdf

This explains the low increase in payload, about 1,000 lbs., less than .5% of the vehicle dry weight, by using a lifting trajectory for the VentureStar. However, some lifting body designs can have a lift/drag ratio of from 6 to 8 at hypersonic speeds:

Waverider Design.
http://www.aerospaceweb.org/design/waverider/waverider.shtml

The L/D is usually optimized for a specific speed range but we can imagine "morphing" wings that allow a good L/D ratio over a wide speed range. For instance note on the "Waverider Design" web page the vehicles optimized for the highest hypersonic speeds have a long, slender shape, compared to those for the slower hypersonic speeds. Then for an orbital craft we could have telescoping sides of the vehicle that would be extended when full of fuel at the slower speeds, and retracted, producing a slimmer vehicle, when most of the fuel is burned off and the vehicle is flying faster. Note that a good L/D ratio at the highest hypersonic speeds means the vehicle will experience less aerothermal heating on return.
Then we can imagine a second generation lifting trajectory vehicle having this high L/D ratio over a wide speed range. So in the example I'll take the supersonic/hypersonic L/D ratio as 5, and for lack of a another vehicle I'll use the reconfigured kerosene-fueled X-33's thrust and weight values.
Here's the calculation for constant L/D at a constant angle θ (theta). I'll regard the straight-line path as my X-axis and the perpendicular to this as the Y-axis. Note this means my axes look like they are at an angle to the usual horizontal and vertical axes, but it makes the calculation easier. Call the thrust T, and the mass, M. Then the force component along the straight-line path, our X-axis, is Fx = T - gMsin(θ) - D and the force component along the Y-axis is Fy = L - gMcos(θ). We'll set L = gMcos(θ). Then the force along the straight-line is Fx = T - gMsin(θ) - gMcos(θ)/(L/D). As with the calculation in the horizontal case, divide this by M to get the acceleration along this line, and integrate to get the velocity. The result is V(t) = Ve*ln(M0/Mf) -g*tsin(θ) - g*tcos(θ)/(L/D), with M0 the initial mass, and Mf, the mass at time t, a la the rocket equation. If you make the angle θ (theta) be shallow, the g*tsin(θ) term will be smaller
than the usual gravity drag loss of g*t and the (L/D) divisor will make the cosine term smaller as well.
I'll assume the straight-line path is used for a time when the altitude is high enough to use the vacuum Ve of 331s*9.8 m/s^2 = 3244 m/s. According to the Astronautix page, 3 NK-33's would have a total vacuum thrust of 4,914,000 N and for an Isp of 331s, the propellant flow rate would be 4,914,000/(331x9.8) = 1,515 kg/sec. I'll use the formula: V(t) = Ve*ln(M0/Mf) - g*tsin(θ) - g*tcos(θ)/(L/D) , to calculate the velocity along the inclined straight-line path. There are a couple of key facts in this formula. First note that it includes *both* the gravity and air drag. Secondly, note that though using aerodynamic lift generates additional, large, induced drag, this is covered by the fact that the L/D ratio includes this induced drag, since it involves the *total* drag.
I'll take the time along the straight-line path as 100 sec. Then Mf = 328,700kg -100s*(1,515 kg/s) = 177,200 kg. After trying some examples an angle of 30º provides a good savings over just using the usual non-lifting trajectory. Then V(t) = 3244*ln(328,700/177,200) - 9.8*100(sin(30º) + cos(30º)/5) = 1,345 m/s. Then the vertical component of this velocity is Vy = 1,135*sin(30º) = 672.3 m/s and the horizontal, Vx = 1,135*cos(30º) = 1,164.5 m/s.
To compare this to a usual rocket trajectory I'll calculate how much fuel would be needed to first make a vertical trip to reach a vertical speed of 672.3 m/s subject to gravity and air drag, and then to apply horizontal thrust to reach a 1,164.5 m/s horizontal speed.
The air drag for a usual rocket is in the range of 100 m/s to 200 m/s. I'll take the air drag loss as 100 m/s for this vertical portion. Then the equation for the velocity along this vertical part including the gravity loss and the air drag loss would be V(t) = 3244*ln(M0/Mf) - 9.8*t - 100 m/s, where M0 =328,700 kg and Mf = 328,700 - t(1,515). You want to find the t so that this velocity matches the vertical component in the inclined case of 672.3 m/s. Plugging in different values of t, gives for t = 85 sec, V(85) = 680 m/s.
Now to find the horizontal velocity burn. Since this is horizontal there is no gravity loss, and I'll assume this part is at very high altitude so has negligible air drag loss. Then the velocity fomula is V(t) = 3244*ln(M0/Mf). Note in this case M0 = 328,700 - 85*1,515 = 199,925 kg, which is the total mass left after you burned off the propellant during the vertical portion, and so Mf = 199,925 - t*1,515. Trying different values of t gives for t = 40, V(40) = 1,171.5 m/s.
Then doing it this way results in a total of 125 sec of fuel burn, 25 percent higher than in the aerodynamic lift case, specifically 25s*1,515 kg/s = 37,875 kg more. Or viewed the other way, the aerodynamic lift case requires 20% less fuel over this portion of the trip than the usual non-lift trajectory. With a 307,000 kg total fuel load, thus corresponds to a 12.3% reduction in the total fuel that would actually be needed. Or keeping the same fuel load, a factor 1/.877 = 1.14 larger dry mass could be lofted, which could be used for greater payload. For a reconfigured X-33 dry mass of 21,700 kg, this means 3,038 kg extra payload. Remember though this is for our imagined new X-33 lifting shape that is able to keep a high L/D ratio of 5 at hypersonic speed, not for the current X-33 shape which only has a hypersonic L/D of 1.2.
With the possibility of using morphing lifting body or wings with high hypersonic L/D ratio allowing a large reduction in fuel requirements to orbit, this may be something that could be tested by amateurs or by the "new space" launch companies.

V.) Now for the calculation of the payload the VentureStar could carry using kerosene/LOX engines. The propellant mass of the VentureStar was 1,929,000 lbs. compared to the X-33's 210,000 lbs., i.e., 9.2 times more. Then its propellant tank volume would also be 9.2 times higher, and the kerosene/LOX they could contain would also be 9.2 times higher, or to 9.2*307,000 = 2,824,400 kg.
We saw the VentureStar dry mass was 257,000 lbs, 116,818 kg, with half of this as just the mass of the LH2/LOX tanks, at 138,000 lbs, 62,727 kg. However, going to kerosene/LOX propellant means the tanks would only have to be 1/100th the mass of the propellant so only 28,244 kg. Then the dry mass would be reduced to 82,335 kg. We need kerosene/LOX engines now. I suggest the RS-84 be completed and used for the purpose. You would need seven of them to lift the heavier propellant load. They weigh about the same as the aerospike engines on the current version of the VentureStar so you wouldn't gain any weight savings here.
To calculate how much we could lift to orbit I'll take the average Isp of the RS-84 as 320. Then if we took the payload as 125,000 kg the total liftoff mass would be 2,824,400 + 82,335 + 125,000 = 3,031,735 kg, and the ending dry mass would be 207,335 kg, for a mass ratio of 14.6. Then the total delta-v would be 3200ln(14.6) = 8,580 m/s. Adding on the 462 m/s equatorial speed brings this to 9042 m/s. With the reduction in gravity drag using a lifting trajectory this would suffice for orbit.


Bob Clark

 

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A quote from Robert Zubrin's book Entering Space: Creating a Spacefaring Civilization brought to mind a key advantage of this reconfigured X-33/VentureStar that I hadn't considered before:

"The shuttle is a fiscal disaster not because it is reusable, but
because both its technical and programmatic bases are incorrect. The
shuttle is a partially reusable launch vehicle: Its lower stages are
expendable or semi-salvageable while the upper stage (the orbiter ) is
reusable. As aesthetically pleasing as this configuration may appear
to some, from an engineering point of view this is precisely the
opposite of the correct way to design a partially reusable launch
system. Instead, the lower stages should be reusable and the upper
stage expendable. Why? Becasue the lower stages of a multi-staged
booster are far more massive than the upper stage: so if only one or
the other is to be reusable, you save much more money by reusing the
lower stage. Furthermore, it is much easier to make the lower stage
reusable, since it does not fly as high or as fast, and thus takes
much less of a beating during reentry. Finally the negative payload
impact of adding those systems required for reusability is much less
if they are put on the lower stage than the upper. In a typical two-
stage to orbit system for example every kilogram of extra dry mass
added to the lower stage reduces the payload delivered to orbit by
about 0.1 kilograms, whereas a kilogram of extra dry mass on the upper
stage causes a full kilogram of payload loss. The Shuttle is actually
a 100-tonne to orbit booster, but because the upper stage is a
reusable orbiter vehicle with a dry mass of 80 tonnes, only 20 tonnes
of payload is actually delivered to orbit. From the amount of smoke,
fire, and thrust the Shuttle produces on the launch pad, it should
deliver five times the payload to orbit of a Titan IV, but because it
must launch the orbiter to space as well as the payload, its net
delivery capability only equals that of the Titan. There is no need
for 60-odd tonnes of wings, landing gear and thermal protection
systems in Earth orbit, but the shuttle drags them up there (at a cost
of $10 million per tonne) anyway each time it flies. In short the
Space Shuttle is so inefficient because it is built upside down."
{emphasis in the original.}
Entering Space, p. 29.

Zubrin makes a key point about that dry weight of 80,000 kg of the orbiter, which is essentially an upper stage, that needs to be carried along to bring that approx. 20,000 kg of payload to orbit. That 4 to 1 ratio of the upper stage dry weight to payload weight struck me because the upper stage for rockets is usually a quite lightweight structure. Then the shuttle is quite poor on this measurement. I then thought of the reconfigured kerosene version of the VentureStar I was considering and realized that it was actually quite good on this scale. It could carry ca. 125,000 payload to orbit with a vehicle dry weight ca. 82,000 kg.
Actually the total shuttle system as a whole is even worse on this scale. This site gives the specifications for some launch systems:

Space Launch Report Library.
http://www.spacelaunchreport.com/library.html

Here's the page for the shuttle system:

Space Launch Report: Space Shuttle.
http://www.spacelaunchreport.com/sts.html

You can calculate the total dry weight by subtracting off the propellant weight from the gross weight for each component. I calculate a total dry weight of 310,850 kg to a payload weight of 24,400 kg, a ratio of 12.7 to 1. In contrast the reconfigured VentureStar has this ratio going in the other direction, that is, the payload weight is larger than the vehicle dry weight.
This is important because the total dry weight is a key parameter for the cost of a launch system. I looked at some of the vehicles listed on the Spacelaunchreport.com page and all the ones I looked had the total dry weight higher than the payload weight. For instance for the Delta IV, it's a dry weight of 37,780 kg to a payload weight of 8,450 kg, for a ratio of 4.5 to 1.
For the Atlas V 401 it was 25,660 kg dry weight to a 12,500 kg payload weight, for a ratio of 2 to 1. This was actually one of the better ones. All the ones I looked at, all had a total dry weight significantly higher than the payload weight, usually at least by a 3 to 4 to 1 ratio.
Then the reconfigured VentureStar would be important in that it could reverse this trend (perhaps for the first time?) in making the dry weight actually less than the payload that could be lofted to orbit. Note that not even the original, planned VentureStar could accomplish this, having a dry weight of about 100,000 kg to a payload capacity of 20,000, a ratio of 5 to 1.
The reconfigured kerosene-fueled VentureStar would have a greater propellant mass using dense propellants, but the propellant costs are a relatively small proportion of the launch costs. The more important parameter of dry weight would actually be less.
Note also that the reconfigured kerosene VentureStar could accomplish this feat of having a higher payload capacity than its dry weight, while having a payload capacity that would be close to or exceed that of all the former or planned U.S. launchers, and while being of significantly smaller dimensions. See the attached image drawn to scale showing some key U.S. launchers compared to the VentureStar. Note that despite its small size it would be carrying more payload than the shuttle, the Ares I, the Saturn V and nearly that of the Ares V.
Another factor that I somehow missed when I first wrote on this was the great reduction in launch costs. I somehow didn't make the connection between the increase in payload capacity over the original VentureStar configuration and that of the kerosene fueled one.
The development costs for the VentureStar or any launch vehicle are figured into the launch costs. Then the estimated per kg launch costs of ca. $1,000/kg for the original VentureStar are based on the late 90's estimated development costs for the VentureStar. However, a big part of that development cost was due to the composite design which was significantly more expensive then than now. Recall the point I made before about the reduction in costs of composite materials leading to auto makers including them more and more in passenger cars, and this reduction in cost makes them now economically feasible for an all composite SSTO.
Also, hydrogen engines and associated systems are generally more expensive than kerosene ones. So the reconfigured VentureStar would have a lower cost on that component as well. Then the total development cost even including inflation for the reconfigured VentureStar might be at or even below that of the 1990's estimates for the original hydrogen-fueled VentureStar. This means the per launch costs of the new version should be at or below that of the original version.
But the reconfigured VentureStar can carry 6 times the payload of the original VentureStar! This means the per kg launch costs would be 1/6th as much or only $166 per kg! This is such an extreme reduction in launch costs over the current costs, that the calculation I made for how much you could reduce the weight of the propellant tanks has to be done in a more serious fashion.
Note that all the other systems for the VentureStar were progressing well. It was only the relatively trivial problem of not using a strong enough glue for the composite propellant tanks, that led to the program being canceled. Then this is so trivial compared to the complexity of the other systems and the importance of having a fully reusable launch system is so clear, that a better course would have been to open up a competition to find ways of getting the composite tanks to work.
I gave a few different possibilities for lightweighting the propellant tanks in section II of the first post in this thread. A few were theoretical, not being tried before. However, the one involving partitioned tanks is just basic engineering so I'll present a detailed calculation for that in the next post.

Bob Clark

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kerosene weighs too much

 

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We'll view the X-33 hydrogen tanks standing vertically as conical with flattened front and back. This report on page 19 by the PDF file page numbering gives the dimensions of the X-33 hydrogen tanks as 28.5 feet long, 20 feet wide and 14 feet high:

Final Report of the X-33 Liquid Hydrogen Tank Test Investigation Team.
http://alpha.tamu.edu/public/jae/misc/tankreport.pdf

Call it 9 meters long, 6 meters wide, and 4.3 meters deep for this calculation. I'll simplify the calculation by approximating the shape as rectangular, i.e., uniformly 6 meters wide. See the attached image. Note that the rounded portions of the sides, top and bottom will be considered separately. I'll call the vertical length of each section x, and the bulkhead thickness h. Since the length of the tank is 9m, the number of sections is 9/x.
I'm doing the calculation for kerosene/LOX propellant tanks, but approx. same size as the X-33 tanks. Typically these are pressurized in the 20-40 psi range. I'll take it as 30 psi; call it 2 bar, 2x10^5 Pa. Referring to the drawing of the tank, each bulkhead takes part in supporting the internal pressure of the two sections on either side of it. This means for each section the internal pressure is supported by one-half of each bulkhead on either side of it, which is equivalent to saying each bulkhead supports the internal pressure of one section.
The force on each section is the cross-sectional area times the internal pressure, so 6m*x*(2*10^5 Pa), with x as in the diagram the vertical length of each section. The bulkhead cross-sectional area is 6m*h, with h the thickness of the bulkheads. Then the pressure the bulkheads have to withstand is 6m*x*(2*10^5 Pa)/6m*h = (2*10^5 Pa)*x/h.
The volume of each bulkhead is 6m*h*4.3m. The density of aluminum-lithium alloy is somewhat less than aluminum, call it 2,600 kg/m^3. So the mass of each bulkhead is (2,600 kg/m^3)*6m*h*4.3m = 67,080*h. Then the total mass of all the 9/x bulkheads is (9/x)*67080*h = 603,720*(h/x).
Note that additionally to the horizontal bulkheads shown there will be vertical bulkheads on the sides. These will have less than 1/10 the mass of the horizontal bulkheads because the length of each section x will be small compared to the width of 6m, and will have likewise small contribution to the support of the internal pressure.
The tensile strength of some high strength aluminum-lithium alloys can reach 700 MPa, 7*10^8 Pa. Then the pressure the bulkheads are subjected to has to be less than or equal to this: (2*10^5 Pa)*x/h <= 7*10^8 Pa, so x/h <= 3,500, and h/x => 1/3,500. Therefore the total mass of the bulkheads = 603,720*(h/x) => 172.5 kg. Note we have not said yet how thick the bulkheads have to be only that their total mass is at or above 172.5 kg, for one of the twin rear tanks. It's twin would also require 172.5 kg in bulkhead mass. The third, forward, tank had about 2/3rds the volume of these twin rear tanks so I'll estimate the bulkhead mass it will require as 2/3rds of 172.5 kg, 115 kg. Then the total bulkhead mass would be 460 kg, about 15% of the 3,070 kg tank mass I calculated for the reconfigured X-33.
This is for the bulkheads resisting the outwards pressure of the sections. Notice I did not calculate the pressure inside the tank on the bulkheads from the propellant on either side. This is because the pressure will be equalized on either side of the bulkheads. However, we will have to be concerned about the pressure on the rounded right and left sides of the tank, and the rounded top and bottom of the tank, where the pressure is not equalized on the outside of the tank.
Before we get to that, remember the purpose of partitioning the tank was to minimize the bowing out of the front and back sides from the internal pressure. Consider this page then that calculates the deflection of a flat plat under a uniform load:

eFunda: Plate Calculator -- Clamped rectangular plate with uniformly distributed loading.

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"This calculator computes the maximum displacement and stress of a clamped (fixed) rectangular plate under a uniformly distributed load."
http://www.efunda.com/formulae/solid_mechanics/plates/calculators/CCCC_PUniform.cfm

In the data input boxes, we'll put 200 kPa for the uniform load, 6 meters for the horizontal distance, .3 m, say, for the vertical distance, and 6 mm for the thickness of the plate. For the vertical distance x I'm taking a value proportionally small compared to the tank width, but which won't result in an inordinate number of partitioned sections of the tank. For the thickness I'm taking a value at 1/1000th the width of the tank, which is common for cylindrical tanks. For the material specifications for aluminum-lithium we can take the Young's modulus as 90 GPa. Then the calculator gives the deflection as only 2.35mm, probably adequate.
However, we still have to consider what happens to the rounded sides and the bottom and top. Look at the last figure on this page:

Thin-Walled Pressure Vessels.

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http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfm

It shows the calculation for the hoop stress of a cylindrical pressure vessel. The calculation given is 2*s*t*dx = p*2*r*dx, using s for the hoop stress. This implies, s = p*r/t, or equivalently t = p*r/s. So for a given material strength s, the thickness will depend only on the radius and internal pressure.
However, what's key here is the same argument will apply in the figure if one of the sides shown is flat, instead of curved. Therefore in our scenario, the rounded sides, top and bottom, which we regard as half-cylinders, will only need the thickness corresponding to a cylinder of their same diameter, i.e., one of a diameter of 4.3m.
So the rounded portions actually require a smaller thickness than what would be needed for a cylinder of diameter of the full 6m width of the tank.
This means the partitioned tank requires material of somewhat less mass than a cylindrical tank of dimension the full width of the tank plus about 15% of that mass as bulkheads.


Bob Clark

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tank drawing

 

This is a great article:

Single Stage To Orbit Mass Budgets Derived From Propellant Density and Specific Impulse.
John C. Whitehead
32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Lake Buena Vista, FL July 1-3, 1996
http://www.osti.gov/bridge/servlets/purl/379977-2LwFyZ/webviewable/379977.pdf

I believe it should be regarded as a seminal article in the realm of SSTO vehicles. In it Dr. Whitehead shows that though kerosene has lower Isp than hydrogen, its denseness actually means it requires lighter tanks than hydrogen and lighter engines than hydrogen.
Reducing the dry weight is of primary importance for a SSTO vehicle. The engines and propellant tanks make up the two largest portions of the dry weight of a rocket. Then being able to significantly reduce these weights make it easier to make a SSTO using dense propellants such as kerosene or other hydrocarbons than by using hydrogen.


Bob Clark

 

thing is with the current use of carbon fiber tanks that can withstand ginormous amounts of pressure...you can squeeze that hydrogen in there quite fine and the tanks are lighter.

 

Just saw this on Hobbyspace.com:

Boeing proposes SSTO system for AF RBS program.
"The new issue of Aviation Week has a brief blurb about a Boeing
proposal for the Air Force's Reusable Booster System (RBS) program:
Boeing Offers AFRL Reusable Booster Proposal - AvWeek - June.13.11
(subscription required).
Darryl Davis, who leads Boeing's Phantom Works, tells AvWeek that they
are proposing a 3-4 year technology readiness assessment that would
lead up to a demonstration of a X-37B type of system but would be
smaller. Wind tunnel tests have been completed. Davis says the system
would be a single stage capable of reaching low Earth orbit and, with
a booster, higher orbits. The system would return to Earth as a
glider.
Davis says "that advances in lightweight composites warrant another
look" at single-stage-to-orbit launchers."
http://www.hobbyspace.com/nucleus/index.php?itemid=30110

I don't have a subscription to AV Week. If anyone does perhaps they
could look this up.
I'm curious about the statement it would be "smaller" than the X-37B.
I did some preliminary calculations that if you switched to kerosene
fuel and a high efficiency engine such as the NK-33, and filled every
scrap of internal volume with propellant, then a vehicle twice the
size of the X-37B could be SSTO. I would be surprised they are able to
get it to work with a smaller vehicle than the X-37B.
Perhaps they mean it would be smaller than the booster, Atlas V, and
X-37B system, as the Atlas V weighs upwards of 300,000 kg.

Bob Clark

 

It is my contention that the reason why launch costs are so high, the
reason why we don't have passenger access to space as routine as say
trans-Pacific flights is that the idea has been promulgated that SSTO
is impossible. That is not the case. In fact it is easy, IF you do it
in the right way. The right way is summarized in one simple
statement:
If you use both weight optimized structures and highest efficiency
engines at the same time, then what you wind up with will be SSTO
capable whether you intend it to or not.
We all know that to get a good payload to space you want a high
efficiency engine. And we all know we want to use lightweight
structures so the weight savings can go to increased payload. So you
would think it would be obvious to use both these ideas to maximize
the payload to orbit, right?
And indeed both have been used together - for upper stages. Yet this
fundamentally obvious concept still has not been used for *first
stages*. It is my thesis that if you do this, then what you wind up
with will automatically be SSTO capable. This is true for either
kerosene fueled or hydrogen fueled stages.
Part of the misinformation that has been promulgated is that the mass
ratio for SSTO's is some impossible number. This is false. We've had
rocket stages with the required mass ratio's since the 60's, nearly 50
years, both for kerosene and hydrogen fueled. Another part of the
misinformation is that it would require some unknown high energy fuel
and engine to accomplish. This is false. The required engines have
existed since the 70's, nearly 40 years, both for kerosene and
hydrogen fueled.
What has NOT been done is to marry the two concepts together for
first stages. All you need to do is swap out the low efficiency
engines that have been used for the high mass ratio stages and replace
them with the high efficiency engines. It really is that simple.
This makes possible small, low cost orbital vehicles that could
transport the same number of passengers as the space shuttle, about 7,
but would have a comparable cost to a mid-sized business jet, a few
tens of millions of dollars.
Then once you have the SSTO's they make your staged vehicles even
better because you can carry greater payload when they are used for
the individual stages of the multi-staged vehicle.
In disseminating the false dogma that SSTO's are not possible it is
sometimes said instead that they are not practical because the payload
fraction is so small. Even this is false. And indeed this is just as
damaging as making the false statement they are not possible because
the statements are often conflated into meaning the same thing. So
when those in the industry make the statement they are not
"practical", meaning actually they are doable but not economical, this
becomes interpreted among many space enthusiasts and even many in the
industry as meaning it would require some revolutionary advance to
make them possible.
The fact that you can carry significant payload to orbit using SSTO's
can be easily confirmed by anyone familiar with the rocket equation.
To get a SSTO with significant payload using efficient kerosene
engines you need a mass ratio of about 20 to 1. And to get a SSTO with
significant payload using efficient hydrogen engines you need a mass
ratio of about 10 to 1. Both of these the high mass ratio stages and
the high efficiency engines for both kerosene and hydrogen have
existed for decades now.
See this list of rocket stages:

Stages Index.
http://www.astronautix.com/stages/index.htm

Among the kerosene-fueled stages you see that several among the Atlas
and Delta family have the required mass ratio. However, for the early
Atlas stages you have to be aware of the type of staging system they
used. They had drop-off booster engines and a main central engine,
called the sustainer that continued all the way to orbit. But even
when you take this into account you see these highly weight optimized
stages had surprisingly high mass ratios.
See for instance the Atlas Agena SLV-3:

Atlas Agena SLV-3 Lox/Kerosene propellant rocket stage. Loaded/empty
mass 117,026/2,326 kg. Thrust 386.30 kN. Vacuum specific impulse 316
seconds.
Cost $ : 14.500 million. Semistage: LR89-5. Semistage Thrust (vac):
1,644.960 kN (369,802 lbf). Semistage Thrust (vac): 167,740 kgf.
Semistage specific impulse: 290 sec. Semistage Burn time: 120 sec.
Semistage specific impulse (sl): 256 sec. Semistage Jettisonable Mass:
3,174 kg (6,997 lb). Semistage- number engines: 2. Semistage: Atlas
MA-3.

Status: Out of production.
Gross mass: 117,026 kg (257,998 lb).
Unfuelled mass: 2,326 kg (5,127 lb).
Height: 20.67 m (67.81 ft).
Diameter: 3.05 m (10.00 ft).
Span: 4.90 m (16.00 ft).
Thrust: 386.30 kN (86,844 lbf).
Specific impulse: 316 s.
Specific impulse sea level: 220 s.
Burn time: 265 s.
Number: 140 .
http://www.astronautix.com/stages/atlaslv3.htm

Looking at only the loaded/empty mass you would think this stage had
a mass ratio close to 50 to 1. But that is only including the
sustainer engine. The more relevant ratio would be when you add in the
mass of the booster engines to the dry mass since they are required to
lift the vehicle off the pad. These are listed as the jettisonable
mass at 3,174 kg. This makes the loaded mass now 117,026 + 3,174 =
120,200 and the dry mass 2,326 + 3,174 = 5,500 kg, for a mass ratio of
21.85.
But this was using the low efficiency engines available in the early
60's. Let's swap these out for the high efficiency NK-33 [1]. The
sustainer engine used was the LR89-5 [2] 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 Spacelaunchreport.com site. Kyle takes the average Isp
as lying 2/3rds of the way up from the sea level value to the vacuum
value [3]. 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.
Note in fact that this has a very good value for a ratio that I
believe should be regarded as a better measure, i.e., figure of merit,
for the efficiency of a orbital vehicle. This is the ratio of the
payload to the total dry mass of the vehicle. The reason why this is a
good measure is because actually the cost of the propellant is a minor
component for the cost of an orbital rocket. The cost is more
accurately tracked by the dry mass and the vehicle complexity. Note
that SSTO's in not having the complexity of staging are also good on
the complexity scale.
For the ratio of the payload to dry mass you see this is greater than
1 for this SSTO. This is important because for every orbital vehicle I
looked at, and possibly for every one that has existed, this ratio is
going in the other direction: the vehicle dry mass is greater than the
payload carried. Often it is much greater. For instance for the space
shuttle system, the vehicle dry mass is more than 12 times that of the
payload.
This good payload fraction and even better payload to dry mass ratio
was just by using the engine in its standard configuration, no
altitude compensation. However, for a SSTO you definitely would want
to use altitude compensation. Dr. Bruce Dunn in his report "Alternate
Propellants for SSTO Launchers" [4] estimates an average Isp of 338.3
s for high performance kerosene engines when using altitude
compensation. Then we could lift 5,500 kg to orbit:

338.3*9.8ln((117,526+5,500)/(2,826+5,500)) = 8,928 m/s.

But kerosene is not the most energetic hydrocarbon fuel you could
use. Dunn in his report estimates an average Isp of 352 s for
methylacetyene using altitude compensation. This would allow a payload
of 6,500 kg : 352*9.8ln((117,526+6,500)/(2,826+6,500)) = 8,926 m/s.


Bob Clark


REFERENCES.
1.)NK-33.
http://www.astronautix.com/engines/nk33.htm

2.)LR89-5.
http://www.astronautix.com/engines/lr895.htm

3.) EELV Solutions for VSE.
Reply #269 on: 11/05/2007 09:20 PM
http://forum.nasaspaceflight.com/index.php?topic=10497.msg208875#msg208875

4.)Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
http://www.dunnspace.com/alternate_ssto_propellants.htm

Disclaimer: the citing of a particular reference should not be
construed as an endorsement by the cited authors of the viewpoint
expressed herein.

 

I argued in this thread that space costs can be reduced by two orders of magnitude in the near term. This will result in large corporations, wealthy individuals, and most national governments possessing their own manned orbital spacecraft.
This clearly will result in some national security concerns that should start being addressed now. I found this report after a web search:

National Security Implications of Inexpensive Space Access.
by William W. Bruner III
"INTRODUCTION
There has been a great deal of recent discussion in the space policy community about the technical challenges of gaining economical and routine access to space. Despite this, there has been little written about the opportunities which exist for the development of new missions for US military space forces. Neither has there been much discussion of the security challenges that any resultant proliferation of access to space may present to the United States and to the established international order. Even the most forward looking space "advocates" in the Department of Defense assume that access to space will continue to be prohibitively expensive and difficult for the foreseeable future, that an American decision not to take advantage of the military potential of space is deterministic for the rest of the world, and that "navigation, communications, and surveillance activities will likely remain the limits of space-based capabilities" for all countries.
Part of this failure to consider the possibilities of a world radically changed by inexpensive access to space is a reaction to the "expectations gap" set up by the gulf between mankind's collective dreams about its future in space and the realities of its achievements so far. The collective public and political mind has been shaped by powerful and convincing fictional images of space activities that we are not likely to see for a hundred years. Real world, but slow moving and silent, pictures of Earth from space taken from small spacecraft with cramped cabins and short mission durations suffer greatly in comparison to images of robust and operable spacecraft spanning the galaxy at faster than light speeds. A century after the Russian Konstantin Tsiolkovsky conceptually solved most of the problems involved in human space flight, over a third of a century since the Soviet Sputnik ushered in the space age, and over a quarter century since America left humanity's first footsteps on another celestial body, many thoughtful and technically literate people are conditioned by historical experience to think of access to space as an expensive enterprise that is technically difficult, dangerous, and the exclusive province of huge government and corporate bureaucracies..."
http://www.fas.org/spp/eprint/bruner.htm


Bob Clark

 

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

 

Space vehicle launches could be routine if they could take off horizontally from airliner runways as a single stage, like aircraft. It was thought that wings would just be dead weight on ascent but in fact following a lifting trajectory can cut in the range of 40% off the propellant requirements from a SSTO if it is at high lift/drag ratio. So wings can "carry their own weight", so to speak, even on ascent.
Here's a heuristic argument that an SSTO making a lifting trajectory at high L/D ratio can save on propellant requirements. I'll regard the straight-line path as my X-axis and the perpendicular to this as the Y-axis. Note this means my axes look like they are at an angle to the usual horizontal and vertical axes, but it makes the calculation easier. Call the thrust T, and the mass, M. Then the force component along the straight-line path, our X-axis, is Fx = T - gMsin(θ) - D and the force component along the Y-axis is Fy = L - gMcos(θ).
We'll set L = gMcos(θ), since the vehicle is traveling along the straight-line, our X-axis, so the force component in the Y-direction is zero. Then the force along the straight-line is Fx = T - gMsin(θ) - gMcos(θ)/(L/D). As with the calculation for the usual rocket equation, divide this by M to get the acceleration along this line, and integrate to get the velocity. The result is V(t) = Ve*ln(M0/Mf) - g*tsin(θ) - g*tcos(θ)/(L/D), with M0 the initial mass, and Mf, the mass at time t, a la the rocket equation. If you make the angle θ (theta) be shallow, the g*tsin(θ) term will be smaller than the usual gravity drag loss of g*t and the (L/D) divisor will make the cosine term smaller as well.
Now note that the equation includes *both* the gravity and air drag. Secondly, note that though using aerodynamic lift generates additional, large, induced drag, this is covered by the fact that the L/D ratio includes this induced drag, since it involves the *total* drag.
Some preliminary calculations I did suggest you could save in the range of 40% off your propellant requirements by reducing the gravity loss in this fashion if indeed your L/D ratio is 7+, at the speed range up to the high supersonic to low hypersonic.
A reduction in the propellant requirements this high means you could carry significant payload to orbit even with standard wing weight, estimated as 10% of the vehicle weight, which would be the gross takeoff weight for a horizontally launched vehicle.
However, we can cut this weight even further. First, even for standard wings you could cut this wing weight by half with modern materials. But a key fact is that you don't even need wings for a horizontal liftoff. Lifting bodies can perform horizontal takeoffs without additional wings. Lifting bodies have long been investigated for use as reentry vehicles, but it seems to have been overlooked to use them also for horizontal takeoff.
The problem though would be to get mass efficient propellant tanks for the vehicle. The propellant tanks are frequently the heaviest component of the dry weight of the vehicle, even more than the engines.
But the lifting body would have non-cylindrical shape. What killed the X-33/VentureStar program was the inability to get light-weight tanks for the X-33's conformally shaped tanks. Even using composite materials the non-circular cross sections would have resulted in tanks twice as heavy as aluminum tanks of usual cylindrical shape [1].
It turns out the determining factor for the heavy weight of rocket propellant tanks is they have to be pressurized. This is because of the requirements for proper operation of the turbopumps on rocket engines [2]. Pressurized tanks have to have a certain thickness to safely hold the contents.
However, quite key is the fact that this is a requirement of turbopumps but not other types of pumps [3]. XCOR because it's using wing tanks for its Lynx suborbital vehicle plans to use reciprocating (piston) pumps [4]. These require reduced pressurization in the tanks, if any. And the tanks in the wings on aircraft commonly are also not pressurized. XCOR had to develop these since they intend to carry the propellant in wing tanks which being non-circular would have been very heavy if they had to be pressurized.
Another possibility would be to use inflatable wings. These can also save weight over standard wings [5].


Bob Clark



1.)Space Access Update #91 2/7/00.
The Last Five Years: NASA Gets Handed The Ball, And Drops It.
"...part of L-M X-33's weight growth was the "multi-
lobed" propellant tanks growing considerably heavier than promised.
Neither Rockwell nor McDonnell-Douglas bid these; both used proven
circular-section tanks. X-33's graphite-epoxy "multi-lobed" liquid
hydrogen tanks have ended up over twice as heavy relative to the
weight of propellant carried as the Shuttle's 70's vintage aluminum
circular-section tanks - yet an X-33 tank still split open in test
last fall. Going over to aluminum will make the problem worse; X-
33's aluminum multi-lobed liquid oxygen tank is nearly four times as
heavy relative to the weight of propellant carried as Shuttle's
aluminum circular-section equivalent."
http://www.space-access.org/updates/sau91.html

2.)Fuel tank scaling laws (Henry Spencer).
http://yarchive.net/space/launchers/fuel_tank_scaling_laws.html

3.)NPSH.
http://en.wikipedia.org/wiki/NPSH

4.)XCOR Aerospace and United Launch Alliance.
Announce Successful Hydrogen Piston Pump Tests.
http://www.xcor.com/press-releases/2...ing_tests.html

5.)An inflatable wing using the principle of Tensairity.
http://www.empa.ch/plugin/template/empa/*/107170

 

Elon Musk has said he wants to cut the costs to space to the $100 to $200 per kg range by reusability. This is about a two order of magnitude reduction in cost. To put this in perspective, this is like a trans-atlantic flight that costs $1,000 suddenly being cut to cost $10 to $20.
Musk has said this transformation of the Falcon 9 to full reusability will be very hard. I don't believe it will be. But first, keep in mind how important that reduction in cost will be if it succeeds. If it succeeds then SpaceX will monopolize the launch business if the other launch companies do not field their own reusable vehicles. So there is a tremendous financial incentive for SpaceX to invest in reusability. Now, most in the industry believe reusability is very difficult for orbital vehicles and not even worth the expense. So if Musk reinforces that idea then he has a better chance at being able to field one without the other launch providers having one. And since they will not have even started to develop one, it will take them some time to catch up. The effect is that Musk will have a monopoly on all launches for at least a few years.
I don't know if that is Musk's intent in saying reusability is very hard. Actually I'm inclined to believe he is just saying what most in the industry believe including his own engineers. But a key reason why reusability is not very hard is because the cost in mass in reentry and landing systems is surprisingly low. In regards to the technical difficulty, there is none. We know how to do it as the shuttle orbiter and the X-37B and Dragon spacecraft has shown. I include the Dragon in the list of reusables because its heat shield showed minimal degradation on return. Musk has said the same heat shield could make hundreds of flights, at least to LEO.
I made an estimate before of about 28% of the landed mass has to go to reentry/landing systems. This was based on estimates of 15% for thermal protection, 10% for wings or for propellant for vertical landing, and 3% for landing gear. However, I said likely with modern materials this could be cut to half that. In fact, it might even be lower than 10%.

1.)Weight of thermal protection.

Robert Zubrin has given an estimate of 15% of the landed weight for the weight of thermal protection systems(TPS):

Reusable launch system.
http://en.wikipedia.org/wiki/Reusable_launch_system#Reentry_heat_shields

However, I gather this was in relation to the older capsules, Mercury, Gemini, Apollo, etc. Indeed the weight of the ablative heat shield on the Apollo capsule was about 15%:

Apollo Command/Service Module.
2.7 Specifications
http://en.wikipedia.org/wiki/Apollo_Command/Service_Module#Specifications

However, the space shuttle with its mostly silica tiles was able to reduce the TPS weight to about 8% of the maximum landing weight of 104,000 kg:

Space Shuttle thermal protection system.
3.3 Weight considerations.
http://en.wikipedia.org/wiki/Space_shuttle_thermal_protection_system#Weight_considerations

Also, for the X-37B the TUFROC leading edge material instead of the shuttles RCC and the TUFI AETB material instead of the shuttles silica tiles are either of equal or lower weight than the shuttles TPS materials while being tougher and requiring less maintenance:

X-37B Orbital Test Vehicle.
http://www.boeing.com/defense-space/ic/sis/x37b_otv/x37b_otv.html

For ablative TPS, the PICA-X material used on the Dragon capsule weights about half the weight of the AVCOAT material used on the Apollo heat shield:

Re: Dragon v/s Orion.
http://forum.nasaspaceflight.com/index.php?topic=23522.msg754168#msg754168

while being able to still survive lunar and even Martian reentry speeds.

SpaceX has found that at least for LEO reentry speed judging from the minimal degradation on the Falcon 9/Dragon test flight, the PICA-X heat shield could be reused hundreds of times.

Also, for vertical powered landings a la the DC-X, you might not even need an extra heat shield for base first landings. One proposal for a VTVL SSTO uses low thrust during the descent as well as a high temperature-resistant aerospike nozzle to serve as the reentry thermal protection. You would need to retain more mass in propellant or some inert gas for this purpose though.
Another idea for a vertical landing vehicle would be to reenter head first. This was the preferred method of the Air Force since it provided increased cross-range. In that case you would have the blunt heat shield at the top of each stage. I thought this method would be unstable with the heavy engines now at the top during reentry, but since this was considered for the orbital version of the DC-X presumably this was solved.

2.)Weight of the wings and the landing gear.

For horizontal landing, a common estimate is that the weight of wings is 10% of the landed weight. This comes from aircraft examples though where the wings have to carry the weight of the fuel which can be as much as the dry weight of the aircraft itself or more.
An example where the propellant will not be carried in the wings and lightweight composites will be used is the Skylon. According to their released specifications the wing weight will be less than 2% of the take-off weight, which is the appropriate weight to compare to for a horizontal take-off vehicle:

The SKYLON Spaceplane.
by Richard Varvill and Alan Bond
Journal of the British Interplanetary Society, Vol. 57. pp. 22–32, 2004
p. 32.
http://www.reactionengines.co.uk/downloads/JBIS_v57_22-32.pdf

On that same page the landing gear weight is the only 1.5% of the take-off weight.
Then for a vertical take-off vehicle these low weight proportions should apply to the dry, landing weight.

Bob Clark