Merlin 1A engine for a hovering Falcon 9 v1.1 first stage.

Copyright 2014 Robert Clark

  Because of the high thrust of the Merlin 1D engine and the lightweight of the reusable Falcon 9 v1.1 first stage, the stage can not hover on its return to Earth. The firing of the engine has to be precisely timed so that the rocket reaches about zero relative velocity to the Earth once it reaches the landing point. SpaceX has referred to this non-hovering mode of landing as "hover-slam". It is due to the fact the thrust to weight ratio of the stage is still above 1 with single Merlin 1 D firing when the stage is nearly empty on landing:

More on Grasshopper’s “Johnny Cash hover slam” test.
http://www.newspacejournal.com/2013/03/09/more-on-grasshoppers-johnny-cash-hover-slam-test/

 Still for safety reasons I would prefer a stage that did have the capability to hover. One concern without the ability to hover for example would be unexpected large changes in wind speed and direction known as wind shear. Airline pilots know these when they are low to the ground as "microbursts". 

Microburst schematic from NASA. Note the downward motion of the air until it hits ground level, then spreads outward in all directions. The wind regime in a microburst is completely opposite to a tornado.

 These can be potentially dangerous for pilots during takeoffs and landings since they result quickly in a large change in the aircraft's apparent airspeed, important for maintaining lift. There have been several airline accidents with wind shear identified as the cause. 

While wind shear is particularly dangerous for aircraft when near to the ground because it gives the pilots limited time to react, it does also occur at altitude. For both Space Shuttle accidents wind shear is suspected to have been a contributing factor. For the Challenger accident wind shear occurred about the same time as the shuttle reached Max Q, maximum aerodynamic pressure. This may have increased the stresses on the vehicle leading to a breach in the solid rocket boosters. In the case of Columbia, unusually strong wind shear occurred also close to Max Q that might have weakened the wing before the impact of the insulating foam.

  Recently, SpaceX had to destroy its Falcon 9R test vehicle during its last test flight:

  SpaceX has not released the cause of the accident but the rocket appeared to pitch over during the flight. There could be variety of reasons for this and not wind, but unexpected wind changes could cause it.

 The ability to hover gives you more leeway about where you land and some leeway when. You could then avoid the wind shear like an aircraft doing a go-around.

 So how to give it the ability to hover? One way would be to use a smaller engine for the landing engine. In fact SpaceX already has it in its inventory: the original Merlin 1A.

 The page on the Falcon 1 by Ed Kyle gives the Merlin 1A engine a sea level thrust of 34,900 kgf (kilograms-force). And Kyle's page on the Falcon 9 v1.1 gives the total sea level thrust using 9 Merlin 1D engines as 600,000 kgf. So one would be 66,000 kgf. Then replacing the Merlin 1D with the 1A would result in a loss of 31,000 kgf thrust. This is only a 5% loss of sea level thrust.

 Kyle's page on the F9 v1.1 though gives it dry mass of 19 metric tons (mT). Typically rocket engines leave some residual propellant left in the tanks at about 0.5%. This would be about 2,000 kg.This would give the first stage a mass at landing at about 21 mT. Then the Merlin 1A would need to be throttleable down to 60%.

 However, the Merlin 1D was made to be throttleable down to 70%, but the Merlin 1A never was. Then for this method to work the Merlin 1A would also need to be made throttleable.


       Bob Clark

Update, October 13, 2014:

 A correspondent to my Facebook page named David Whitfield suggested the possibility exhaust from the preburner alone for the Merlin 1D might be low enough to give the Falcon 9 first stage hovering capability. You might be able to use 1 to all 9 Merlin 1D preburners to provide the needed thrust.

 BTW, is this the same as the turbine exhaust that appears on the left on this image:

 UPDATE, October 25, 2014:

 Another suggestion for achieving low throttleability is to use variable size nozzles. This is discussed here:

Altitude compensation attachments for standard rocket engines, and applications.
http://exoscientist.blogspot.com/2014/10/altitude-compensation-attachments-for.html 

Dave Masten's DARPA Spaceplane, page 2: an Air Launched System.

Copyright 2014 Robert Clark

 In the blog post Dave Masten's DARPA Spaceplane, I discussed using SpaceX Falcon 1 or Falcon 9 stages to achieve DARPA's XS-1 reusable first-stage spaceplane. Another DARPA program ALASA seeks to send smaller payloads of 45 kg to orbit for $1 million using air-launch. 

 DARPA has already awarded a contract to Boeing to produce the ALASA system:

Boeing Targets 66 Percent Launch Cost Reduction with ALASA.
By Mike Gruss | Mar. 28, 2014

The ALASA rocket, measuring 7.3 meters long, would be attached to the underbelly of a Boeing-built F-15E fighter aircraft. DARPA says taking off from a standard airport runway would allow the Defense Department to launch from almost anywhere. Credit: Boeing artist's concept.

http://www.spacenews.com/article/military-space/40023boeing-targets-66-percent-launch-cost-reduction-with-alasa

 However, using the Falcon 1 upper stage may provide a fast, low cost means to produce such a system. Masten Space Systems could develop this as well since it would provide a much reduced cost proof-of-principle for their larger spaceplane that in itself would still be profitable.

 SpaceX has said the Falcon 9 first stage accounts for 3/4 of the cost and the upper stage, 1/4. If we assume a similar ratio for the $8 million Falcon 1, then we might estimate the cost of the upper stage as $2 million. However, unlike with the Falcon 9, the Falcon 1 upper stage uses a much smaller and simpler engine in the pressure-fed Kestrel and it is a much smaller stage in comparison to the first stage than is the case with the Falcon 9. Then I'll estimate its cost to be, say, $1 million. That would already be at the $1 million max cost DARPA wants per launch for the ALASA system.

Solid Rocket Motor Expendable Stage version.
 To get the launch cost below $1 million we would need reusability. If we got 10 launches from the Kestrel powered booster, that would be $100,000 per launch for just this lower stage. Then staying below the $1 million max cost would depend on the cost of the upper stage. There were some small solid rocket stages that were below $1 million in cost such as the Star 17 solid rocket motor:

Encyclopedia Astronautica.
Star 17
Solid propellant rocket stage. Loaded/empty mass 124/14 kg. Thrust 19.60 kN. Vacuum specific impulse 280 seconds.
Cost $ : 0.580 million.
Status: Out of production.
Gross mass: 124 kg (273 lb).
Unfuelled mass: 14 kg (30 lb).
Height: 0.98 m (3.21 ft).
Diameter: 0.44 m (1.44 ft).
Span: 0.44 m (1.44 ft).
Thrust: 19.60 kN (4,406 lbf).
Specific impulse: 280 s.
Specific impulse sea level: 220 s.
Burn time: 18 s.
Number: 25 .
http://www.astronautix.com/stages/star17.htm

 This is not currently in production but there are probably some remaining in storage or some of comparable size.

 According to Ed Kyle's page on the Falcon 1, the F1 upper stage had a 0.36 metric ton (mT) dry mass, 3.385 mT propellant mass and 327 sec Isp. However, the Kestrel engine used only had a 3,175 kgf (kilogram-force) thrust, i.e., less than the stage weight. So we'll cut down the propellant load to 2.5 mT.

 Now we'll use the fact that airlaunch actually can result in a significant reduction of the required delta-v that needs to be supplied by the rocket to reach orbit and therefore a significant increase in payload. This is described in some reports by Sarigul-Klijn et.al.:

Air Launching Earth-to-Orbit Vehicles: Delta V gains from Launch Conditions and Vehicle Aerodynamics.
Nesrin Sarigul-Klijn University of California, Davis, CA, UNITED STATES; Chris Noel University of California, Davis, CA, UNITED STATES; Marti Sarigul-Klijn University of California, Davis, CA, UNITED STATES
AIAA-2004-872
42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 5-8, 2004
http://pdf.aiaa.org/preview/CDReadyMASM04_665/PV2004_872.pdf  [first page only]

 The conclusions are summarized in this online lecture:

A.4.2.1 Launch Method Analysis (Air Launch).
For a launch from a carrier aircraft, the aircraft speed will directly reduce the Δv required to attain LEO. However, the majority of the Δv benefit from an air launch results
from the angle of attack of the vehicle during the release of the rocket. An
ideal angle is somewhere of the order of 25° to 30°.
A study by Klijn et al. concluded that at an altitude of 15250m, a rocket launch with the
carrier vehicle having a zero launch velocity at an angle of attack of 0° to
the horizontal experienced a Δv benefit of approximately 600 m/s while a launch
at a velocity of 340m/s at the same altitude and angle of attack resulted in a
Δv benefit of approximately 900m/s. The zero launch velocity situations can
be used to represent the launch from a balloon as it has no horizontal velocity.
Furthermore, by increasing the angle of attack of the carrier vehicle to
30° and launching at 340m/s, a Δv gain of approximately 1100m/s
was obtained. Increasing the launch velocity to 681m/s and 1021m/s produced a
Δv gain of 1600m/s and 2000m/s respectively.
From this comparison, it can be seen that in terms of the Δv gain, an airlaunch is 
superior to a ground launch. As the size of the vehicle decreases, this superiority 
will have a larger effect due to the increased effective drag on the vehicle.

https://web.archive.org/web/20120229141110/https://engineering.purdue.edu/AAE/Academics/Courses/aae450/2008/spring/report_archive/reportuploads/appendix/propulsion/A.4.2.1%20Launch%20Method%20Analysis%20(Air%20Launch).doc

 A speed of 340 m/s is a little more than Mach 1, while subsonic transport aircraft typically cruise slightly below Mach 1. So the delta-V saving could still be in the range of 1,000 m/s with air launch even using a standard subsonic jet, a significant savings by the rocket equation.

 And this study found by using a supersonic carrier aircraft you could double the payload of the Falcon 1:

Conceptual Design of a Supersonic Air-launch System.
43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
8 - 11 July 2007, Cincinnati, OH
http://www.ae.illinois.edu/m-selig/pubs/ClarkeEtal-2007-AIAA-2007-5841-AirLaunch.pdf

 The idea had been that airlaunch can't result in much of an improvement in payload since jet transports typically cruise only around 300 m/s, so, it was thought, you would only subtract this off the delta-v needed to reach low Earth orbit (LEO), which is about 9,100 m/s. However, there is also the altitude the aircraft can achieve and another key factor is the high altitude launch means you can use the higher Isp and higher thrust vacuum versions of the engines. The Isp advantage can be quite significant. For instance the Merlin 1C only had a vacuum Isp of  304 sec, but the Merlin Vacuum, being optimized only to operate at near vacuum conditions, had an Isp of 340 sec.

 The Boeing version of the ALASA system will use the F-15E fighter jet for the airlaunch. This has a Mach 2.5 maximum speed at altitude and can carry 10,400 kg payload. So we'll use this also for our system. Following the Sarigul-Klijn et.al. paper, the Mach 2.5+ max speed of the F-15E  is above the 681 m/s air launch speed needed to reduce the delta-v to orbit by 1,600 m/s. This will bring the delta-v that needed to be delivered by the rocket down to about 7,500 m/s.

 Using the reduced propellant load for the Falcon 1 upper stage of 2.5 mT then with a 45 kg, 0.045 mT, payload, an (F1 upper stage + Star 17) rocket could get a delta-v of:

327*9.81ln(1 + 2.5/(0.36 + 0.124 + 0.045)) + 280*9.81ln(1 + 0.110/(0.014 + 0.045)) = 8,500 m/s.

 This is high enough that a cheaper subsonic carrier, which according to Sarigul-Klijn can still subtract off about 1,000 m/s from the required delta-v, could be used instead of the Mach 2.5 F-15E. 

 Let's also estimate how much higher payload we could get using the reduction of delta-v to 7,500 m/s allowed by using the F-15E. Taking the payload to be 80 kg, 0.08 mT, we get:

327*9.81ln(1 + 2.5/(0.36 + 0.124 + 0.08)) + 280*9.81ln(1 + 0.110/(0.014 + 0.08)) = 7,560 m/s.

 So we could actually exceed the DARPA requirements to get 80 kg to LEO.

Two Falcon 1 Upper Stage Version.
 Instead of using an expendable solid rocket as the upper stage, we could use instead a second Falcon 1 upper stage. This will allow the possibility of getting a fully reusable system. We'll have both stages firing in parallel to be able to get a T/W greater than 1. We'll also use cross-feed fueling to maximize payload. For the upper stage that reaches orbit, we'll give it the full 3.385 mT propellant load since this stage doesn't have to have a T/W greater than 1. Then using the reduced 7,500 m/s required delta-v to orbit, we could transport 240 kg to LEO:

327*9.81ln(1 + 2.5/(0.36 + 3.745 + 0.240)) + 327*9.81ln(1 + 3.385/(0.36 + 0.240)) =7,530 m/s.

 We could also improve the mass ratio of these stages and increase the payload by switching to lightweight aluminum-lithium alloy for the propellant tanks. This could save as much as 25% off the tank weight. 

  Bob Clark

Dave Masten's DARPA Spaceplane.

Copyright 2014 Robert Clark

 Dave Masten's Masten Space Systems was recently announced as a winner of an award from DARPA to produce a reusable first-stage booster for a small orbital system:

Masten Space Systems selected by Defense Advanced Research Projects Agency for XS-1 Program.

http://masten.aero/2014/07/xs-1pr/

 It is notable their version will be a winged booster. Previously Masten had worked on VTVL, i.e., vertical, propulsive landing vehicles. Masten describes the decision to go with a winged VTHL, i.e., horizontal landing, vehicle in a video interview on SpaceVidcast:

 At about the 41 minute mark Masten describes the fact that the need to return to the launch site to maintain low cost reusability after a high Mach flight, suggests high lift/drag ratio design and therefore wings.

 However, it would also work to use a lifting body. I discussed resurrecting the X-33 for this purpose in the post DARPA's Spaceplane: an X-33 version. It turns out the problem of getting conformally-shaped composite tanks, which doomed the X-33, becomes a non-issue if the vehicle is only to be used as a first stage booster. The reason is a first stage does not have to be as mass-ratio optimized so you can just use metal tanks. Still, despite that, in an up coming post I'll describe how it IS possible to get the lightweight tanks originally envisioned for the X-33 so in fact it is to possible to produce a SSTO VentureStar.

 In the interview, Masten also discusses a key difficulty is getting low cost engines that would be reusable that fit within DARPA's low cost requirements. He mentioned possibly using the engines XCOR is developing. I want to suggest the possibility also of using the Merlin engines as used on the SpaceX Falcon 1 first stage.

 The last quoted price for the entire Falcon 1 according to Ed Kyle's SpaceLaunchReport.com page on the Falcon 1 was $7.9 million from 2008. Based on that one would expect the cost of the engine alone would be less than that. Actually rather than developing a whole new first stage from scratch on this high risk project, as a preliminary development Masten might want to base a first version of his booster on the Falcon 1 first stage. By the specifications on Ed Kyle's page the Falcon 1 using the Merlin 1C only had a 470 kg payload to LEO, well less than the 1,400+ kg DARPA wants. Still this would lead to a faster and cheaper development to a reusable winged booster rather than creating everything from scratch. There is also the fact SpaceX is committed to launcher reusability and might even donate surplus Falcon 1's now in storage to the project. And Masten himself said during the SpaceVidcast interview he is spending much of his time working on the aerodynamics of such a winged booster rather than such questions as the propulsion.

  If SpaceX ever constructed the Falcon 1e, then Masten possibly might be able to use the Falcon 1e, which was to have double the size of the Falcon 1's first stage. According to Ed Kyle's page this was to have about a 1,000 kg LEO payload, closer to the DARPA requirements.

 Another possibility might be to use the Falcon 9 v1.1 upper stage. According to Elon Musk in discussing reusability, the first stage of the F9 is 3/4ths the cost and the upper stage 1/4th. So the cost of the upper stage would be in the range of $14 million. With 20 to 30 reuses this would be well within the $5 million per flight DARPA requirement for the program.

 A problem though is that as is usually the case with an upper stage the thrust is less than the full stage weight. We would have to cut down the tank size. According to Ed Kyle's page on the F9 v1.1 the propellant mass for the upper stage is estimated to be 93 metric tons (mT) and the dry mass 6 mT. Cutting the stage to be half size, take the propellant mass as 46 mT and the dry mass 3 mT.

 We need also to replace the Merlin Vacuum which can not operate at sea level with the Merlin 1D. By Ed Kyle's page the total thrust of the 9 engines on the F9v1.1 first stage is 600,000 kgf (kilogram-force). So one Merlin 1D would have sea level thrust of  67,000 kgf. Then using the 311 sec vacuum Isp of the Merlin 1D,  this could carry 12 mT to 4,280 m/s delta-v:

311*9.81ln(1 + 46/(3 + 12)) = 4,280 m/s.

 With approx. 1,200 m/s losses due to gravity and air drag this should be close to the Mach 10 DARPA requirement for the reusuable first stage, carrying a 12 mT total load for the upper stage and payload.


  Bob Clark