Boomerang Air-Launched TSTO RLV Concept Part II: Carrier Plane Gamma Maneuver Safety Considerations

In this post I would like to discuss some of the key considerations and options governing the carrier plane for my Boomerang TSTO RLV concept. Specifically I’ll be covering considerations relating to safely supporting the Gamma Maneuver, and useful support hardware. I’ll also discuss specific options for the carrier plane role, and their pluses and minuses. I had originally intended to include a lot more of the math and illustrations for this post, but I’ll have to come back and provide those in a later part of this series.

Gamma Maneuver Considerations
As discussed in Part I, one of the key enabling concepts for Boomerang is the use of a Gamma Maneuver, where the rocket engines are ignited while still attached to the carrier airplane, enabling the airplane to pull up into a steep flight-path angle prior to rocket separation. For review, some of the key reasons why the Gamma Maneuver is worth considering even though it is scary include:

• Performance: The traditional straight-and-level drop-and-light approaches that have been used for most air launches to-date¹ all result in a losing most of the performance benefit from air launching. The 3-5 second delay between separation and ignition results in a significant negative component to the flight path angle (velocity vector) that now has to be made up either propulsively or via a wing. If you use the wing route, you end up driving the structural design, making liquid propulsion harder, and still taking a decent performance hit. Without the wing, you lose a significant amount of altitude, require a higher T/W ratio on the stage, and wipe out most of the saved gravity loss. With the exponential nature of the rocket equation, doing air-launch in a way to gain the full 1km/s of saved drag and gravity losses makes a huge difference, potentially allowing you to not have to push the design as hard in other areas. Often it’s best to pick one or two hard things to do that make everything else easier.
• Engine Operation Verification: Performing the Gamma Maneuver enables you to verify nominal engine operations before separation with the carrier airplane, similar to using a hold-down mechanism like SpaceX and several other ground-launch operators. Think of how many times SpaceX has decided to abort a launch due to an issue during engine startup prior to lift-off. How many launches would they have lost by now if they didn’t get to light the engines until they were already in free-fall? Drop-and-light greatly increases your odds of losing launch vehicles and payloads due to no-lights. That might be acceptable for expendable “artillery rockets”, but isn’t a good risk for RLVs.
• Eliminating or Minimizing Bending Loads: The Gamma Maneuver enables you to do your rocket vehicle in a way that avoids bending loads and large wings that are typically required on air-launched vehicles. The need to aerodynamically change the vehicle’s flight path angle using wings induces significant bending loads on the launch vehicle, which significantly decreases the achievable mass ratio of the launch vehicle, partially erasing some of the benefits of air-launching.

The problem is that most pilots consider lighting a rocket attached to their carrier plane to be extremely anti-social behavior. Specifically, from my conversations with several aircraft companies about the Gamma Maneuver, I’ve heard several concerns voiced:

1. Carrier aircraft controllability
2. Assumed risk to the carrier aircraft pilots
3. Rapid Unplanned Disassembly of the Launch Vehicle taking out the carrier aircraft
4. Separation dynamics issues resulting in post-separation recontact
5. How loads are reacted through the attachment structures/release mechanisms
6. Structural loads induced on the whole aircraft during the gamma maneuver
7. Plume heating on the carrier aircraft
8. Plume impingement on the carrier aircraft

Thrust Related Concerns
My initial plan for solving most of the thrust related problems (specifically Items #1, #4, #5, and #6) was to have the aircraft begin pitching up, and then light the rocket throttled way down, and gradually increasing it to cancel out the drag on the rocket and the component of gravity acting on the rocket parallel to the thrust of the aircraft and rocket². By doing this, you actually relieve stresses on the attachment mechanism/structure because the only net force will be one normal to the attach structure³, you shouldn’t have significant off-axis thrusts to cause control issues, and separation dynamics would be very similar to a drop-and-light, except the separation acceleration would be decreased by the higher flight path angle (possibly necessitating the use of some separation springs).

The problem is that for a non-winged VTVL rocket vehicle, you need to be in a flight path angle >60 degrees above horizontal. I thought this wouldn’t be a problem–after all, WhiteKnightTwo has an unloaded takeoff T/W ratio > 1, so I figured it shouldn’t be a problem. Unfortunately, when I ran the numbers on how much thrust you lose by the time you get to 30kft/9km, it turns out you only get ~33% of the thrust at that altitude. Neglecting drag, and assuming the rocket is offloading all the drag and the parallel component of the rocket’s weight, you need a T/W ratio greater than ~0.85 to get to a 60 degree flight path angle⁴. With the data I have for WK2, it can only get up to a ~25 degree flight path angle using a Gamma Maneuver that only cancels out the drag and weigh components of the rocket. There are several ways to deal with this:

1. You could use a winged RLV first stage. By getting up to a 25 degree flight path angle, you’re already near the optimal flight path angle for a lightly-winged rocket stage. For instance the SpacePlane concept Dan DeLong came up with at Teledyne Brown would’ve used separation at a 25 degree flight path angle, with the RL-10 engines lit to compensate for drag losses. Unfortunately this trick doesn’t work so well for VTVL designs that tend to need much higher separation flight path angles (60-75 degrees).
2. You could settle for only a 25 degree initial flight path angle. This would likely require a turning wing, big gravity losses, or a very high vehicle T/W ratio combined with high maximum dynamic pressures⁵. Without running the numbers more I don’t know how bad this.
3. You could do a “zoom climb”. This is one where your vehicle is not able to maintain speed at the higher angle, but you pull up and then separate before your aircraft has slowed down to too close to its stall speed. This has the penalty that your velocity is now lower, erasing some of the benefit of a gamma maneuver. However, I’d have to do a lot of additional analyses to figure out if the losses are showstoppers or nuisances.
4. If the aircraft’s launch vehicle support structure can support enough net thrust from the rocket to enable reaching the desired flight path angle/velocity, but the separation mechanism can’t handle large net shear forces, you could throttle up the rocket enough to get to the right flight path angle and velocity, and then throttle down to just drag/weight makeup shortly before separation, and then re-throttle up after departure. This is more complex on engine operations though, and might not be possible with COTS carrier vehicles like WK2.
5. If the aircraft’s launch vehicle support structure can support some net thrust, but not enough to maintain velocity at the desired flight path angle, you could do a hybrid between #4 and #3, where you pull up to the desired flight path angle, providing enough net thrust to minimize the velocity loss before separation. You might or might not have to throttle down prior to separation, but this option would likely work on existing COTS carrier vehicles, and would minimize the velocity losses from option #3.
6. The best option would be to modify the carrier aircraft to have a support/release mechanism that can handle the rocket operating at enough thrust to maintain speed at the desired flight-path angle. The control, structural design, and separation analyses would all be more complex, but this would give the best performance, with the least complexity on the rocket side.

My preference would be to check the numbers on  #3 first, followed by #2, and then #5 because those could likely work without much/any modifications to the carrier vehicle. It would also be worth seeing if the shear load capability of the pylon and release mechanism are sufficient to support something like #4, but the odds of it working for #6 with COTS aircraft is small. Only if none of #2-5 work would #6 be that interesting, because it likely implies either a clean-sheet carrier aircraft design or significant modifications to the carrier plane, which might be hard to get approvals for on a COTS carrier plane.

The best way to retire risks for many of these concepts, after picking the approach that at least appears to look best on paper, would be to test in subscale using something about the size of the TGALS system developed at NASA Dryden. This is a scale small enough that the rocket can be low-cost, and many different ideas can be tried out quickly, and verified in a way that doesn’t risk a pilot or an expensive, full-scale operational aircraft.

Towed Glider Air-Launch System and its Towing Plane on the Ground with Ground Crew for Sense of Scale

Other Gamma Maneuver Safety Concerns and Mitigations:
Relative to thrust, separation, and control related concerns, the others seem a lot more easily addressable. Specifically:

• Assumed risk to the carrier aircraft crew can be mitigated either by eliminating the hazards or by going with an optionally piloted or completely unmanned carrier aircraft design (or preferably both). The main fear most of the pilots seem to have are the rocket exploding, structural failure of the aircraft due to rocket thrust, or loss of control due to the coupled behavior of the aircraft or plume impingement after separation. Most of those can be tested-out in subscale, as mentioned in the last section.
• Engine explosions taking out the aircraft can be mitigated primarily by providing shrapnel protection “armor” around the engine hardware. While hybrids rockets, pressure-fed liquids, and solids all tend to have a large pressure vessel storing large amounts of pressure energy, pump-fed liquid rockets tend to have their high-pressure parts all down in the engine area. For an RLV, you already want to protect engines from each other, and the stage itself from the engines. Also, there are many directions shrapnel can be allowed to travel in that do not endanger the carrier aircraft, so the blast shields only have to divert the blast, not completely absorb it. While all of this takes some engineering, a lot of it are things you’d already want to do for an RLV, and doesn’t necessarily need to take a lot of weight. Making armor so that a worst case engine failure doesn’t damage the aircraft, and doesn’t propogate to a total launch vehicle failure is probably achievable. Though you’d likely want to do a few engine fraticide tests to be really sure. More benign engine cycles like expander cycles and electropumps tend to be less likely to explode in heinous ways than cycles like staged combustion or high-pressure gas generator cycles. Fortunately, air launch makes expander and electropump cycles more feasible than for ground-launched rockets.
• Separation dynamics risks could also be potentially mitigated (if necessary) by doing some form of separation thrusters on the launch vehicle. If you’re planning on doing a DTAL/Xeus style lander you might already have the plumbing for rockets in the right class out where you’d want to apply separation thrust. Though there are obvious plume impingement issues you’d need to look into–for instance, the separation thrusters could be timed to operate for a short enough duration that the rocket hasn’t had time to move forward enough relative to the carrier plane for the separation engines to have their plumes impinge on the aircraft. Obviously you’d only do this if the separation looked marginal or unsafe without them, as that’s an extra piece that has to work correctly for a safe separation.
• Plume heating from the rocket can be mitigated by either picking a propellant combination whose exhaust is relatively low luminosity (LOX/alcohol, LOX/Methane, LOX/Propane, and LOX/LH2 are all pretty good), or by making the aircraft more tolerant of radiative heating, or both. Fortunately, at realistic air-launch altitudes, the engine won’t be so overexpanded that the plume actually contacts the aircraft prior to separation, so you’ll have cool air flowing over the surfaces, and heat transfer primarily by radiation heat transfer, so this problem might not be as scary as it sounds. SS2 had to do some modifications to its tails because they operate fairly close to the rather luminous hybrid exhaust. The solution appeared to be adding a layer of metalized mylar or kapton to the skin of the tails to reflect the radiated heat away. The structure of the carrier plane are likely going to be much further away, and if you use a propellant combo that isn’t very luminous, you might not even need something as fancy as that.
  

  SS2 with Reflective Coating on Wings Clearly Visible (Credit Virgin Galactic, Jan 2014)

So to recap, the biggest adaptations that might need to happen to a COTS carrier plane to enable the Gamma Maneuver include: potentially going with an unmanned or optionally-piloted configuration, potentially needing to strengthen the aircraft-to-launch vehicle support structure, potentially needing to redesign the release mechanism to operate under load, and potentially needing to add a metalized layer to the carrier aircraft’s tail sections. Most of these aren’t potential show-stoppers, but they do point to the trade between using a COTS carrier aircraft, and a Gamma Maneuver-Optimized clean sheet design.

I’ll continue this in Part III where I’ll discuss additional carrier plane support subsystems, and my thoughts on the best type of carrier aircraft for a Boomerang-type air-launched RLV.

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Jonathan Goff

President/CEO at Altius Space Machines

Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and the founder and CEO of Altius Space Machines, a space robotics startup that he sold to Voyager Space in 2019. Jonathan is currently the Product Strategy Lead for the space station startup Gravitics. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.

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1. Pegasus, SS1 & SS2, AirLaunch QuickReach, and proposed for use on LauncherOne, and the various Stratolaunch concepts shown to-date.
2. As you pitch your aircraft up, you get a -m*g*sin(gamma) weight component acting against the thrust of your carrier plane
3. Just as you would see in level flight, but in this case the weight would only be -m * g * cos(gamma).
4. If you manipulate the equations I’ll show in a later blog post, you get sin(gamma)=T/W
5. Highly depressed flight paths are possible with high T/W stages, but you take a hit on drag losses and max-q