# What would the Δv cost of bringing the space shuttle external tank to orbit be?

There was an independent proposal that the space shuttle external tank could have been lifted all the way to orbit, and then used as a structural material in space stations.

In terms of propellant budget, how much would it have cost to do this? Presumably, you would impart more Δv to the external tank, which would have reduced the payload you can take to orbit. How close was the external tank to orbital velocity, how much extra propellant would it have taken to get it the rest of the way, and would this have been mechanically possible with the space shuttle design?

Update: I corrected a (huge) mistake that incorrectly penalized the vehicle for lifting the nominal payload to MECO-1, when the question was asking about eliminating a nominal payload in favor of boosting the empty ET into a stable orbit instead.

Using rough numbers, it would cost everything / not work. Putting the ET in orbit would have eliminated the ability of the shuttle to carry any other payload, and an ET used during launch would need significant retrofit to be useful for anything else.

First the math, then a few other reasons why this seems like a bad idea.

## Math

### Calculations

For a nominal ascent trajectory 140,000 kg can be put into the MECO-1 orbit, which is divided between the ET, Orbiter, and Payload.

Nominally, the ET is then staged, which reduced the mass prior to the OMS circularization burn to 105,000 kg. Using the rocket equation we can calculate the OMS propellant required for that burn:

$$mp_{nominal} = mf_{nominal} \cdot \left(e^{\frac{\Delta v}{g \cdot I_{sp}}} - 1\right)$$

$$I_{sp} = 361 s$$

$$g = 9.81 \frac{m}{s^2}$$

$$\Delta v = 150 m/s$$

$$mf_{nominal} = 105,000 kg$$

$$mp_{nominal} = 4,542.91kg$$

If instead we want to raise the orbit of the entire MECO-1 mass, we get a higher propellant weight.

$$mp_{BoostET} = mf_{BoostET} \cdot \left(e^{\frac{\Delta v}{g\cdot I_{sp}}} - 1\right)$$

$$mf_{BoostET} = 140,000 kg$$

$$mp_{BoostET} = 6,057.22 kg$$

So boosting the ET requires an additional 1,514 kg of OMS propellant. This is less than the 22,700 kg payload allocation, so it appears possible (although the Shuttle would have to be retrofitted to hold additional OMS propellant in the cargo bay and supply it to the OMS engines — surely possible, but not trivial).

Note: One obvious option for increasing performance is using the higher specific impulse SSMEs rather than the OMS engines for the circularization burn. This would either require a direct-ascent trajectory (possible, but likely only for low-altitude orbits), or an ability to restart the SSMEs (or at least one of them). Again possible but non-trivial.

## Challenges

But despite the first-order technical feasibility, there would be significant challenges associated with this approach.

The main issue is that upon reaching orbit the tank would need significant rework to be useful. Remember, it wasn't designed to be a habitat, it was designed to hold fuel and oxidizer for the shuttle during ascent. Any accommodations for it to serve a dual purpose would have a cost or weight penalty. More importantly, any on-orbit modifications would be additional missions — probably EVAs by astronauts on follow-up missions.

Once empty, the tank is also a (relatively) light-weight object for its size (i.e. it has a low ballistic coefficient). This would cause it to re-enter more quickly than typical payloads, which might be 2/3 the mass but (maybe) 1/10 the cross section. This would require putting the ET in a higher than normal orbit (reducing mass available for other payload) or working on a clock to add adjunct station-keeping propulsion to the ET husk (before de-orbit).

So I'll temper my original response and say technically this approach was probably feasible, but likely to be expensive and represent a non-trivial evolution for a program that historically struggled to maintain a high flight rate, demonstrate a good safety record, or operate affordably.

• I hope to come back and do the calculation you suggest. For now, however, I do want to note that I don't understand how adding 150 m/s to a 35 ton tank replaces a 20 ton payload (and more!) that is lifted to a speed of 7,900 m/s. Something clearly seems off about that. Obviously it's not simply (mass)x(deltaV). I'm going over the details carefully hoping to nail down the issue. – AlanSE Jul 18 '13 at 12:08
• I tried to allude to that above. You'd probably have to put tanks in the Orbiter payload bay and modify the propulsion system to plumb them in, which would be a huge pain. There'd be all sorts of little details there, from propellant loading CONOPS to thermal issues, to modifying the avionics to control additional valves and gather additional telemetry. – Adam Wuerl Jul 19 '13 at 5:37
• This does not account for the use of the more efficient SSMEs and leftover propellant in the ET to complete the orbit insertion and circularization. I could imagine getting even more payload into orbit by holding on to the ET. – Mark Adler Jan 4 '14 at 22:34
• @PearsonArtPhoto: "The worst-case scenario envisions Hubble crashing back to Earth in 2028, and most models suggest an uncontrolled re-entry wouldn't happen until the mid-2030s" -- space.com/29206-how-will-hubble-space-telescope-die.html – Keith Thompson Jan 13 '18 at 20:33
• @AlanSE: If I'm modifying a tank to be useful in orbit I'll gladly also modify it to hold 1.5 more tons. – Joshua May 27 '18 at 20:24

AlenSE, Erik has the heart of the answer.

Simply put, at the time of the Shuttle External Tank separation the ET has full orbital velocity along with the rest of the Shuttle. But because the ET is not part of the Shuttle when the Shuttle circularizes its orbit with an OMS burn, the orbit of the ET intersects with the surface of the Earth at the point of the Indian Ocean.

If a fully laden Shuttle tried to circularize its orbit with the ET still attached, the OMS would have to expend approximately 35% more propellant for the burn than normal. Off hand I do not know if the OMS has that kind of excess capacity though I believe it does. But at the very worst I expect that if the payload in the Shuttle bay is ejected into orbit after the circularization burn that the OMS would have the total capacity necessary.

So the short answer is, I believe a fully loaded Shuttle could have carried the ET up to LEO, provided the mission of the payload required it be left behind in orbit.

• The ET impact point would only be in the Indian Ocean for a standard-insertion mission (last flown on STS-38 in November 1990); a direct-insertion mission (first flown on STS-41C in April 1984, and used for most missions after then, and all missions from STS-35 on, as it allowed for a heavier payload and/or a higher orbit) incorporated a longer-duration SSME burn, increasing the vehicle's speed at MECO (and, thus, its speed at ET separation) and pushing the ET impact point into the central-to-eastern Pacific. – Sean Nov 15 '19 at 23:34

We have the rocket equation over two segments.

• v_e = 4,440 m/s
• v2 = 150 m/s
• v1 = 7,900 m/s - 150 m/s = 7,750 m/s
• Orbiter mass itself = m_o = 68,585 kg
• Payload (inside orbiter) = m_p = 24,400 kg
• external tank = m_t = 35,000 kg

I will refer to 4 different mass values.

• mL - the mass at launch
• m2 - the mass right before MECO
• m2' - the mass right after MECO (if there is a seperation)
• m3 - the mass that makes it to orbit

The essence of the problem is that we have a reference case where the mass drops by the mass of the external tank at seperation, and then we want to find out how much we have to decrease the payload weight in order to still reach orbit with the external tank, meaning that m2=m2'. But first, we need to fill in all the values for the reference case.

• m3 = m_o + m_p = 68,585 kg + 24,400 kg = 92,985 kg

The mass after seperation can be found from the rocket equation. Add the external tank mass to find the mass right before seperation.

• m2' = (92,985 kg) * exp( (150 m/s) / (4,440 m/s) ) = 96,180 kg
• m2 = 96,180 kg + 35,000 kg = 131,180 kg

Apply the rocket equation yet again to find the mass at liftoff.

• mL = (131,180 kg) * exp( 7,750 / 4,440 ) = 751,496 kg

The actual weight on the launchpad is 2 million kg. However, I just need something to apply consistently right now between the two cases. This degree of error was actually rather predictable, since I used a fuel velocity that's too high and didn't account for other structural materials.

-------- end reference case ---------

Returning to the premise, we get the ET into orbit by sacrificing payload weight. That will change the weight of the space shuttle on the launchpad, and therein lies the difficultity. For this problem, however, we can actually apply a single stage rocket equation to full orbital velocity because in our false model there are no seperations at all.

I'll introduce new primed variables. Consider them to be defined by the following equations.

• mL = mL' + m_p = 727 096.026 kg + m_p
• m3 = m3' + m_t + m_p = 68 585 kg + m_t + m_p

• m_p = ( 727,096.026 - ( 68585 + 35000 ) * exp( 7900/4440 ) ) / exp( 7900/4440 ) = 19,120 kg

The payload mass was lowered by 5280.5 kg by my calculation. That sounds reasonable - that we lose 5 tons of payload in order to push 35 tons of tank material the last little bit of the path to orbit.

Now, regarding the other answer:

To be slightly more precise, the sum of the orbiter burnout mass and the ET, the OMS specific impulse, and the required ΔV can be plugged into the rocket equation to solve for how much excess payload mass is available. The answer is a negative number.

I think I figured out what happened here. I think it is this:

m_p = ( (106,780 kg) - (103,585 kg) exp( (150 m/s) / (4,440 m/s) ) ) / ( exp( (150 m/s) / (4,440 m/s) ) - 1) = -10 601.5052 kilograms

This calculation and number comes from applying the rocket equation to the final stage, after the MECO. The problem with that calculation is that you're reducing the payload weight, but don't account for the fact that you'll have more fuel at (what was previously) MECO because you reduced the payload. So basically, this is a one-segment application of the rocket equation and it doesn't get the right answer. Because of the nature of the beast, you need to consider two segments of application.

I'm not sure I can give you a specific amount of propllent, but I can give you a back of the envelope answer. Perhaps someone can add details from Shuttle Program documents.

The External Tank (ET) came off shortly after Main Engine Cutoff (MECO). After that, the Shuttle made one or more OMS burns depending on when the launch was made in the Program's history. These burns raised the orbit's perigee and circularized the orbit. The OMS pods had about 300 m/s delta-V available for the Orbiter alone. Making a rough estimate that half (?) of this (150 m/s) was used for orbital insertion and half was used for the deorbit burn, you would need to provide an additional 150 m/s of delta-V to the ET to get it into the shuttle's low orbit.

Keep in mind that an ET at this altitude would quickly re-enter due to the small but significant atmospheric drag. You would therefore have to either add additional delta-V to further raise the orbit or plan on reboosting the tank every 90-180 days like the ISS does.

Don't forget the rocket equation either. In addition to providing the additional delta-V to the ET, you have to provide additional delta-V for the fuel you use to provide this additional delta-V and so on, and so on, and....

• I take it that this MECO point is where the tank is normally separated and allowed to fall? Are you saying that point had 300+150 m/s left to go before reaching orbit? – AlanSE Jul 18 '13 at 1:37
• At MECO, the trajectory's apogee was correct and the Orbiter was heading uphill towards it. The perigee however was still too low and had to be raised. The OMS burn(s) did this. The number and type of OMS burns changed over the program, so some missions will have an OMS-1 burn and some will have an OMS-1 and OMS-2 burn etc. These were called direct and standard insertions. I'm pretty sure the single burn was called direct. – Erik Jul 18 '13 at 1:39

Many of the figures being offered here for masses of various components seem off, and there is definitely a typo in the Isp given for the Orbiter OMS engines--it is really 316 sec, not 361.

I believe the Orbiter actually massed more than the figures given here, and the ET generally a lot less--116-120 tonnes for Orbiter all up on the pad, 30 to 26 tonnes for a dry tank, containing 725 tonnes of oxygen and hydrogen at launch, attached to two SRBs each massing 88 tonnes empty with 500 tonnes propellant each added up to 2050 on the pad all up.

Here's a link to Norbert Brügge's site:

http://www.b14643.de/Spacerockets_2/United_States_1/Space_Shuttle/Description/Frame.htm

It gives a consistent OMS load maximum of 21.65 tonnes, implying that the load would vary from mission to mission. Liftoff weights excluding payloads vary for various generation of Orbiter and flight but are close to 100 tonnes, between 94.4 and 105.5, I believe that mass includes the OMS propellant and varies largely for that reason. The payloads given raise some serious question marks in some cases, but note how the last decade of Shuttle use brought the loads down below 15 tonnes, because presumably they were mostly missions to ISS, which is significantly higher in orbit than the lower ones that would maximize payload--also ISS is at a 51.64 degree inclination, making reaching it from Canaveral more difficult. The newer the Orbiter model, the lighter it was, and so only Endeavour, Atlantis and perhaps Discovery could be usefully used for ISS missions--Columbia was to be used for alternative, lower-altitude missions until it was lost.

Since the discussion here is putting an ET into orbit, I suppose we should look at the standards for late missions to ISS. Alternative to using an ET as a space station structural element we might want to orbit one to gradually refuel for a heavy deep space mission, but with nothing better than either a Shuttle or perhaps a Titan V heavy launcher capable of perhaps 30 tonnes to LEO, we would not be refilling such a tank fast! Also its propellants would tend to boil away, hydrogen especially,so we'd need some extra tonnage to reliquify the hydrogen (using cold hydrogen, re-condensing oxygen is a snap)--it all points to space station altitude operations.

Looking at the last couple columns of Brügge's second set of "design" tables, we have payloads just under 15 tonnes, all up launch masses almost exactly 2050 tonnes (those are very consistent across the whole range of all STS launches from 1981 to 2011), Endeavour massing 101.5 minus payload (thus 116.5 all up), dry ET 27 tonnes, 726 tonnes of fuel in it, and the SRBs massed 1178.2 tonnes total. I think we can attribute a 3.3 tonne discrepancy to additional fuel in Endeavour's OMS supply, making it mass actually nearly 120 tonnes on the stack.

If, per work done by others above, a standard MECO orbit falls short of a circularized target orbit by 150 m/sec, and in this case the target orbit is ISS, at 405 km altitude, then circular orbital speed is 7670 m/sec. Subtracting 150 m/sec would reduce the major axis from 13566 km to 13060 or by 506 km--meaning the perigee would be some 99 km below sea level! I don't know whether Endeavour ever was launched straight to an elliptical MECO orbit of this kind and did a single OMS burn to achieve 150 m/sec delta V requiring about 4.7 percent of on board mass, or 5.67 tonnes. Alternatively of course it could be put into a much lower orbit initially, by means of a MECO orbit falling short of say a nominal 200 km altitude parking orbit, then first circularizing there with a 150 m/sec burn of this same kind, wait for the phasing of its lower faster orbit to line up with the half-period of a transfer orbit up to 405 so it arrives near ISS before doing a second burn to bring it close to synch, followed of course by fussy and slow careful approach maneuvers. I suspect the latter happened, and it is also a conservative assumption it did so. But the energy difference between an orbit with -100 km perigee and 200 km apogee, and one with a 405 km apogee instead, is not tremendous--just under 975 KJ/kg, which at Earth surface gravity would be the potential difference for just under 100 km altitude. Versus the speed of the lower MECO orbit at apogee, it would take just adding 13 m/sec to that to exceed the necessary energy for the higher apogee! (That is not the way to do it of course).

However the conservative assumption is that Endeavour first climbs to a 200 km parking orbit, circularizes there, and then climbs at a calculated moment to the 405 km orbit altitude and circularizes there. This allows for flexible launch times, and to phase into the approach to the actual space station location later.

Throw in a tonne of propellant more for frittering around for a safe dock at the established station--but note on the first mission this is not necessary, since wherever the ship stops is the ISS location! Assuming 150 m/sec as given for the first circularization, which requires 5 2/3 tonnes of prop, to go into a 200-405 km transfer orbit requires delta-V of 59.525 m/sec, and then to circularize at 405 requires another 5907, or 118.595 altogether. Over three burns then just under 270 m/sec are required, and these three all apply to the same initial mass, here apparently 120 tonnes, for a total propellant burn of 10 tonnes. Note how this is close to half the maximum installed tankage allows. To return to Earth from there, I estimate 120 m/sec braking is plenty. Note also this must always be applied to a down mass (ofter the burn) less than IIRC 105 tonnes, since this is limited by the lift area and TPS maximum temperatures, and the upper limit for return applies to all models of the Orbiter, though the lighter later ones can make more of that down mass payload. Thus only a bit more than 4 tonnes is needed, and 5 allows a generous safety factor for that burn. I suspect missions to ISS involved maximum OMS propellent load, 21 2/3 tonnes, whereas we see 15 is all that is needed for the nominal mission--implying that 7 tonnes are a safety factor, in this case nearly over 44 percent. This gives the mass of Endeavour, with no payload and no OMS fuel but otherwise loaded with supplies for a nominal mission, as 83.35 tonnes, and a theoretical total delta V of 1130 m/sec, or 880 without touching the 7 tonne OMS reserve, the reserve thus raising total delta V by 28.4 percent.

Now then, what is the cost of attempting to bring the tank to the ISS orbit by this three stage series of ascent burns, holding 12 tonnes in reserve for nominal descent plus 7 tonnes for emergency contingencies? We can't, if we refuse to touch any of those 7 tonnes because of course I figured the reserve on the basis of the nominal mission. However, we use less than 10 for the ascent phase, and a 26 tonne dry advanced tank raises the nominal 120 tonne Orbiter pre-burn mass, before all three phases of ascent burns, by 21.7 percent. Therefore we can steal less than 2.2 tonnes of OMS prop from the reserve, less than 30 percent of it, and bring the tank to orbit! Future missions that also bring another tank will cost more, because it will be necessary to add some more maneuvering to come to a gentle dock.

Also, given a nominal 725 tonnes fuel load in the tank at launch, if we shave some mass off the SSME burn load, we can save some fuel mass unburned. We are going to want to load the two sections of the tank with air later, and 80 percent of that is nitrogen. The volume of the tank (ignoring the intertank separating the LOX from the LH) holds those 725 tonnes, and at a bit more than 36 percent the density of water on average, when air is 1/800 the density of water, a load of air at 1 atmosphere nominal would be some 2.5 tonnes mass, thus 500 kilograms of it is oxygen. If we want to save half a tonne of oxygen or 1/1243 the total oxygen load in the tank, we would shave that proportion of total mass to OMS burn, or 118 kg, off the payload, and deduct the half tonne from it as well. When fully vaporized the half tonne of oxygen would expand but I believe its pressure would be well under a full atmosphere in the oxygen tank.

We otherwise do not need to skimp on the nominal payload mass at all, given that we can't trade off any of it to restore the 7 tonne OMS fuel reserve--we could, but it would involve plumbing modifications as well as tankage mass in the payload bay. Eliminating the payload completely would not bring the total mass down to nominal and so we'd need to tap into the reserve in any case.

Payload is thus down to 14 tonnes. For the first ET-based ISS assembly I suppose the entire payload should consist of initial outfitting masses, which could comprise a single module meant to be attached to the tank to provide a structural anchor and docking port for a future mission. It has been pointed out the ET is a "fluffy" object of low ballistic coefficient, its orbit will decay more rapidly than a denser object like say Skylab. But I believe ISS fully assembled is also draggy in the same way, so it won't be worse. Still, a top priority is to enable the tank to remain on orbit, and it needs orientation control too. I believe the first module would therefore be a combination of propulsion module and access dock, and much of its mass would be propellant to maintain orbit.

Glancing at the actual ISS historical timeline, the beginning was Zarya, a module of 19 and a third tonnes to which Endeavour attached the almost 12 tonne Unity module. If the tank launch is the second stage of alternate ISS assembly, Endeavour could first dock an expanded Unity module (say carrying supplemental propellant for Zarya) to the Russian beginning, and then, docked to Unity and using its Canadarm, position the tank to a specialized port opposite the Zarya end of Unity. Some of the cargo mass would be devoted to structures such as flanges specially built into the tank itself, so perhaps we can't carry extra fuel for Zarya on this mission after all. Once docked however, subsequent Shuttle missions can bring either modules to dock to Unity's 4 radial ports, or temporarily as cargo modules to be unloaded into the tank. Between the tank orbiting mission and the next visit of a spacecraft to ISS, the vents of the hydrogen tank would be opened to allow the residual hydrogen to boil off into space, while the LOX residual evaporates to fill the oxygen tank as a gas. It would then be possible, perhaps by remote control before the next mission, to close the hydrogen vent, open a special new valve built into the tank between the two tanks to fill the hydrogen tank with oxygen. Just 2 tonnes out of a nominal 15 tonne payload of the next shuttle mission (or perhaps 2 out of the 20 tonne mass of another module equivalent to Zarya also launched on a Proton) would be nitrogen to make up the rest of the air. Upon completion of that (with small mass of water and traces of CO2 added as well) the two tank segments become habitable and crew can move into them with 12 or 18 more tonnes of infrastructure and operational equipment to fit it out with.

All this goes to show that the Shuttle, as it was, could indeed supply tanks to orbital destinations at a very low cost of dipping into existing fuel reserves. More efficient ways of using the tanks would emerge had we gone ahead and developed "Shuttle-C," a number of Shuttle-derived vehicle proposals that had in common using the standard equipment provided for Orbiter launches including the tank, SRBs, and a new module meant to recover the SSMEs from orbit. Now I have never been able to get any details on the nature of the engine module, but I would be amazed if a 3 engine module had to mass as much as 60 tonnes all up; more likely in the range of 35-45 I would think. (I actually have my own ideas on this line for a next-generation Space Transport system that would develop 15 tonne or less separate modules for each engine, scaled down Orbiter designs, unmanned, that would enable a very flexible national launch system using various numbers of engines and various sizes of SRB. But to keep it simple the Shuttle-C proposals were all in addition to using Orbiter as the sole crewed vehicle; Shuttle-C designs would all launch unmanned, and some of them proposed using SSMEs up on one launch, presumably old ones near end of life). As unmanned launchers Shuttle-C designs should have been at least somewhat cheaper to launch than an Orbiter, and even if the engine recovery module massed as much as 60 tonnes, half the Orbiter mass, the other 60 tonnes are 3 times the nominal 20 tonne Orbiter payload--4 times the payload to ISS.

With such a system in hand--and I think it clearly could be operational well before 2000--a single Shuttle C mission, with a cargo module permanently attached to the tank and including an OMS engine, could deliver to the orbit a tank pre-fitted for air filling, 5 tonnes of stored liquid air (2 fills of the tank), and 50 more tonnes of other supplies and equipment.

I estimate a 9 second burn of a single STS OMS engine once a month would suffice to check orbital decay, assuming similar forces to those on the existing ISS. That would consume under 80 kg of propellant each time, for under a tonne a year. Clearly the propellant reserve does not have to be tremendous!

Looking up actual figures ISS currently consumes 7.5 tonnes a year; even so, a 10 tonne reserve included in the original launch is only 20 percent of the miscellaneous tonnage available. With 40 tonnes left beyond that, this single launch would be the equivalent of both Zarya and Unity with 10 more tonnes (another Unity, almost) left over. Since Zarya is the propulsion module of the existing station, clearly we could get more utility than these two launches provided aside from the use of the tank itself.

An Orbiter, arriving after the Shuttle C launch or pre-positioned at the destination before it, coordinated with a Soyuz launch, could provide an international workforce of 10 crew to do the initial docking of a modified Zarya focused on providing power without propulsion to the Shuttle C cargo module, which I envision would have Unity style multiple docking ports built in, one with an adapter (moveable as the station grows) for Soyuz. Whether this crew could finish inflating the tanks with air depends on how fast hydrogen gets flushed out into vacuum from that tank. I'd think they could outfit it to the point of it being immediately habitable for the next crews. At 120 tonnes, it would be almost 30 percent of the mass of the current station. 3 more Shuttle-C launches delivering 3 more tanks, accompanied by 3 more Orbiter visits each bringing 15 tonnes of cargo would surpass the current assembly by 15 tonnes. Crew volume of course would be gigantic, so much so that we probably would not want to do more tank delivery missions, but even so 6 Orbiter visits would round out to the same mass as our current station, presumably a mix of cargo for interior installation and new modules and trusses and solar panel sets and so forth.

It is then a practical proposal; with Shuttle C it would have been accomplished very quickly with few launches. Whether we would want to develop the 10-tank spinning habitat proposed (an octagon of 8 tanks end to end trussed to a pair along the axis, end to end) is a question of funding, not launch capability. Such an alternative would of course require orders of magnitude more people in space to be worthwhile, and as offered seems incomplete to me--I don't see how Shuttles or any other craft would dock to it once spun up, one or both the axis tanks would need to attach to a de-spin module requiring power and probably reaction mass, attached at the other end to a microgravity station ships could dock to, which would also be the place to put solar panels and radiators I suppose. Such a station would I suspect require an order of magnitude lowering of launch costs, to be remotely fundable, bearing in mind the need to rotate hundreds of crew up every year, and vital supplies along with them. I do think developing Shuttle-C would point the way toward major cost reductions per kilogram, perhaps by a factor of 5, but not 10.