Aerodynamic Stresses on rockets and missiles in lower atmosphere

Starting from the earth’s surface, you need to put energy into two places in order to achieve orbit:

-altitude (increase your gravitational potential energy)
-speed (increase your kinetic energy)

Consider a 1-kilogram satellite to be placed in orbit at an altitude of 320 km (requiring a speed of about 7778 meters per second) . Relative to a stationary position on the earth’s surface, its GPE increases by 3.14 megajoules, and its kinetic energy increases by 30.2 megajoules. Launching from the top of Mount Everest (instead of at sea level) gives you about as big an energy boost as launching from the equator (instead of a pole), and as Francis Vaughan notes, the logistics of an equatorial launch are much less challenging.

The propellant grain in a solid rocket motor provides a negligible structural stiffness; the primary structural contribution is the mass loading (which affects structural bending modes) and structural failure due to aeroloads inevitably occurs in joints and interstage structures, and at the point of Stage 1 max-Q most of the propellant is already expended anyway. The Stuttle SRMs actually have a fairly long action time at around 125 seconds compared to typical large SRBs (the Minuteman Stage 1 M55A1 motor is less than 60 seconds and Peacekeeper Stage 1 SR118 is about 83 seconds) and, as you note, is formed to shape the trajectory so as to reduce thrust (effectively “throttling down” even there is no throttle mechanism per se) during high dynamic pressure. The parallel stacking and large forward aerodynamic profile of the STS means that it suffers both very high structural loads and a large number of low frequency bending modes during ascent, hence the need to reduce thrust at such a low altittude. Max-Q for most vehicles is usually experienced at higher altittudes (up to 60 km, depending on speed and profile) and generally limits when the vehicle can start to perform a gravity turn or how much control authority it has to maintain in order to hold within the allowable angle of attack.

That was not a ‘real’ Minuteman missile; most of the propellant in the M55 was offloaded to lighten the missile, allowing it to be extracted. This was just a stunt project to demonstrate the capability of air-launching a missile, but was never intended to be an alternate deployment mode for the Minuteman III booster. In general, air launch, even at high altitude (>20kft) doesn’t offer much advantage in the sense of making it easier to launch a space launch vehicle or gaining additional speed, and in fact the logistics are often more complex than a comparable ground launch. It does, however, offer the capability of launching from a wider array of azumiths, and to also fly above weather and near-ground wind conditions which might limit launch opportunities.

ICBMs like Minuteman and Peacekeeper are entirely capable of achieving orbital speeds with the proper guidance (and in fact are in use as the basis for the Orbital Sciences Minotaur family of space launch vehicles) and in the suborbtial trajectory apogees (~1200km) they actually fly well above most spacecraft in LEO (300-600 km).

Really, the best solution for launching from a near-equatorial location is launch from a sea platform (such as the Zenit Sea Launch), or a sea launched rocket (Truax SEALAR, Excalibur, Sea Bee, Sea Dragon). Air launch is complex, potentially hazardous to the aircraft crew, and is only marginally advantageous in terms of reducing the amount of energy spent in gravity and drag losses.

Stranger

For what it’s worth, those seem to be the main benefits that Stratolaunch is claiming. They don’t even mention the increased efficiency.

Air launching isn’t a trivial benefit due to the exponential nature of the rocket equation. Shaving off 1 km/s (say) could make an SSTO (barely) viable. But as you say, the logistics are a bitch. They’re bad enough for ground launches in equatorial locations.

An SSTO is at least ostensibly viable, as demonstrated by many studies since the 'Sixties. (The Titan II first stage is effectively an SSTO despite its low performing LR-87 engines, albeit with minimal payload capability.) A reusable SSTO is more tricky, and one that has a significant amount of payload (e.g. the Chrysler SERV) more difficult yet, requiring performance at the limits of theoretical capability with chemical propulsion systems, but still within feasibility.

Stranger

All true, but the difficulty illustrates how close to the margins they are. Supposing you need 9400 m/s deltaV and have 280 s Isp engines (ballpark for sea level with RP1/LOX), you need a 30:1 mass ratio. That’s just barely possible (as you note, the Titan II was about that), but with no payload. If an air launched rocket only needs 8400 m/s deltaV and the nozzles can be expanded to give you 300 s Isp, your mass ratio drops to 17.4:1. Now you have 2% payload! Not great, but it’s something.

'course, that’s without reusability. If we drop the payload to 1%, we get 550 m/s of deltaV back. Maybe enough to land the thing if there’s not too much extra support HW. You get even more if you left your payload in orbit.

The SERV is definitely a cool concept, but it’s “complicated” and there’s not an obvious evolutionary path between here and there. And of course, I’m not saying that air launch is the right answer–as you say, it’s a logistical nightmare. Besides, a pedant would say that an air-launched single-stage rocket isn’t an SSTO anyway; you just have a really low-performance (but reusable) first stage.

[hijack, since it came up, sort of (no pun intended)]

Is it really a trivial thing to turn a satellite launch booster (if that’s the right word) into an ICBM?

Israel has never demonstrated an ICBM, but for decades, supposedly, it was hardly a question because of their satellite launch capability.

ICBMs and longer range IRBMs can be reletively easily converted to an SLV. The converse is less true. Outside the practical issues, (SLVs can easily need special launch facilities, take hours to fuel and days to prepare) ICBMs need to be useable in minutes.

Agreed. ICBMs are purpose designed for not only long term storage in protected storage (typically underground silos) and short respone time, but also high launch availability regardless of weather conditions and the ability to withstand near-strike conditions (e.g. flyout through blast effects and debris cloud) to an overall reliability consistent with strategic applications. Nearly all modern ICBM systems are use solid propellant motors for main propulsion with storable liquids for the post-boost system. Nerlhy all modern purpose-designed space launch vehicles (except for ICBM derivatives like the Minotaur family or the light lift air-launched Pegasus) use liquid propellant engines for the main (core stages) and only supplement with strap-on solid boosters.

Stranger

Is there any limit to how low range is before a missile cannot be used as an SLV at all, or with useful payloads (a few hundred KG)? IRBM can be so used, but about short range missiles?

I’m not entirely certain how to answer your question other than to point to the Scout OLV, which was an enhanced version of the Scout sounding rocket system which can be used to loft smallsat class payloads (in the 300 kg range) into Low Earth Orbit. (The Scout OLV is noteworthy for being one of the few rocket systems that was actually largely developed internally by NASA instead of being developed by outside contractors.) Launchers with smaller capability are certanly plausible (see the Interorbtial Systems SR 145 vehicle) but the economics are questionable; since most of the propellant mass of the rocket is expended to do work lifting the remaining propellant and inert mass, and the smaller the rocket the larger the ratio of inert mass to propellant mass tends to grow, the less lift capability to a specified orbit you are getting per gross lift off weight of the overall vehicle.

Both the PGM-17 ‘Thor’ and the PGM-19 ‘Jupiter’ IRBMs were used as the basis for space launch vehicles as the long-lived and highly successful Thor-Delta program (which lives on today, albiet in name only, as the ULA Delta IV) and the less successful but still groundbreaking Juno II rocket, but both are significantly modified from their operational form, and in general ICBM, IRBM, and SLBM boosters are overdesigned and have features not needed for normal space launch operations.

Stranger

I find it interesting that SLVs have a much closer ancestry with early ICBMs than modern ICBMs do. For example, the current Soyuz launch system is very close to the R-7 Semyorka ICBM. The latter was not a particularly good ICBM since the non-storable propellants (LOX, in particular) ensured that it took nearly a day to prepare for launch, and could not be kept on standby for any reasonable length of time. That doesn’t matter so much for SLVs, though.

Ironically, safety (or lack thereof for liquid propellants) is a much more pressing issue for ICBMs than for SLVs. The Titan II was fully retired as a missile in 1987. A major factor was an accident in 1980 where a wrench socket was dropped near a missile, puncturing the oxidizer tank and ultimately causing an explosion. As a launcher, though, the Titan II lived on for 16 more years, and more than that for its derivatives.

How are they so over designed. Besides the longer storage and faster launch times; mentioned upthread.

ICBMs are designed to launch under more stressing conditions (high wind shear, through precipitation and blast debris, withstand extremely high neutron flux and ionizing radiation environments) with a greater degree of availability (launch at literally ninety seconds notice rather than a window of several hours) and accuracy (the “Circular Error Probable” or CEP of an RV is typically measured in hundreds of meters or less versus a typical orbital insertion accuracy in a box a few kilometers on a side) than any dedicated space launch vehicle. The amount of effort spent in development and testing for strategic applications is easily an order of magnitude more than the development of a comparable non-strategic space launch vehicle.

For instance, the LGM-118A ‘Peacekeeper’ missile program cost around US$20B (FY1982 dollars) for a total of 114 boosters produced, for an amortized per unit cost of ~US$175B. (You’ll see ‘flyaway’ cost estimates ranging from US$20M to US$70M per booster but these are build-to-print costs that do not include development and maintenance, nor the overall support system costs.) The Peacekeeper is a four stage booster with three solid propellant rocket motor lower stages and a storable liquid propellant post-boost vehicle which has since been adapted into the Minotaur IV and V family of vehicles like the one that launched the LADEE spacecraft to the Moon in 2013. By comparison, the Athena II rocket, consisting of two Castor 120 and one Orbus 21 solid rocket motors with a liquid apogee engine as the forth stage was developed for a total cost of under half a billion US dollars (~FY1995) and launches for somewhere in the range of US$50B-$US80B. (Someone will probably come by and point out that the Castor 120 is purportedly a “commercial version of the SR118 Peacekeeper Stage 1”, but in fact except for the propellant formulation and overall diameter the two motors are very different in terms of both design and manufacture, with almost no tooling or interfaces in common among the programs. The Castor 120 uses an electromechanical TVA and controller, has a completely different nozzle construction, uses a different case fiber, has a machinable propellant grain to tailor the thrust profile, lacks the EPM protective coating, has a different bolting interface, and is about two feet longer and nearly ten tons heavier, so the two motors are similar only in the grossest sense of the term.)

So depending on how you estimate the costs the Athena is 1:20 (comparing rough development costs) or 1:2 to 1:3 (comparing flyaway costs) of the Peacekeeper. It is worth noting that Peacekeeper has an almost flawless flight record (only one failure during an early development flight test due to a misinstalled actuator, and fifty flight development and Glory Trip launches plus the six successful Minotaur IV/V flights) while the Athena family has a record of five successes in seven launches. So, at least in some sense, you get what you pay for. Of course, Peacekeeper was an actually well-managed program that was largely developed within the cost estimates and functioned as intended, in large part because of the direct oversight and management of the contractors by the Air Force Space and Missile Systems Organization (SAMSO) with independent systems engineering and technical support from TRW. It is pretty much the prime example of how to run a large system development and procurement process.

Stranger

Could the S-1C first stage of the Saturn V be used as a SSTO?

I was passing a merry-go-round in downtown Boston the other day. This merry-go-round did not have horses; there were falcons, an owl, lobsters, a sea turtle, etc. I happened to have a fairly wide-brimmed hiking hat with me. I wanted the merry-go-round to have a hydrogen bomb so I could ride and go all Slim Pickens on it.

That’s gallows humor.

I read a book in college that listed the criteria the U.S. wanted for a missile test range, and the three options considered. This was before they were planning for orbital launches, though; just things like the V-2 and its successors. They wanted to launch from land, have the missile fly over water (because it would be coming back down), with land nearby where they could put tracking stations. The options were the Washington coast (launching to the northwest, tracking stations on the Canadian coast and the Aleutians), southern California (launching south, tracking from the Baja Peninsula), and Florida (launching east, tracking from the Bahamas). The author claimed that Florida won out because of its weather as much as anything else, and that the benefits of a southerly location were a fortuitous bonus when we stepped up to orbital launches.

I’m not entirely sure I buy it. I’m not sure exactly when we started the concrete planning for launching things into orbit, but I think the idea goes back to before the era in question, and the benefits of being close to the equator wouldn’t have been hard to figure out.

Not a chance. The S-IC was designed for high thrust performance for a short duration (165 s) to get the massive Saturn V rocket moving. It’s propellant mass efficiency was low with an I[SUB]sp[/SUB] of 263 seconds and an expansion ratio of 16:1. Even if it could be throttled down to extend the duration, its performance at high altitude is too low. In general, an altitude-compensating nozzle is almost required for a true SSTO, hence why many proposals have relied on plug or aerospike nozzles in order to increase performance across the flight range sufficient to carry a useful amount of payload.

All of the American launches of the Aggregat-4 (V-2) missile launches were from White Sands Missile Range in New Mexico. What became the Joint Long Range Proving Grounds and then Cape Canaveral Air Force Station/Eastern Range. Setting aside its relative proximity to the equator the Cape is a nearly idea location because of the generally fair weather (aside from the occasional hurricane), accessible location, and wide range of broad ocean area to fly into that would not threaten shipping or inhabited areas.

It was originally assumed by early advocates that spaceports would be located on military bases or near major cities and would operate similar to flight lines and civil airports irrespective of lattitude. Many initial concepts also involved stations in polar orbits or at the Earth-Moon libration points rather than in prograde Low Earth Orbit until the difficulties of reaching these orbits and protecting the crew from radiation hazards was known. It was only with later experience in the difficulties in improving propulsive performance and controllability of orbital launch vehicles that that would need to be launched from specially designed facilities into controlled ranges and relying on the modest advantage of the Earth’s rotation to even achieve Low Earth Orbit.

Stranger

I got the impression that this was at the time the U.S. was looking for something bigger than White Sands. Do you know if western Washington or southern California were ever seriously considered?

To be honest, this is the first I’ve ever heard of Washington State being considered for selection as a launch range. There are a number of reason why it would be a poorly suited location but the biggest is the generally overcast state. While rockets are tracked by the range using C-band and S-Band radar and telemetry, visual confirmation is also highly desireable especially in the case of a flight anomaly where telemetry may be fragmented or lost.

Southern California would have been desireable as a launch location due to the then-proximity to missile and launch vehicle manufacturers. However, after the failure of the guidance system (such as it was) on an American-launched V2 which created an international incident by crashing into a hill in Juarez, Mexico, the Mexican government refused to allow the United States to perform overflights. If that wer not the case, the Oxnard/Pt. Mugu area would probably be ideal for southward polar or retrograde launch. Instead, the former Camp Cooke and Sudden Ranch was converted to Vandenberg Air Force Base, which is the headquarters of the 30SW and the US Western Range. Although there are probably better sites, CCAFS and VAFB (and the NASA Wallops Flight Facility in Virginia) have built up substantial infrastructure and support for launch vehicle operations, and building that up from scratch (e.g. the Kodiak Launch Complex in Alaska or Spaceport America in New Mexico) is an expensive and time-consuming process, hence why Orbital Sciences, SpaceX, and others generally operated from leased facilities out of government-run ranges for orbital launch.

Stranger