Monday, June 10, 2024

Low cost approach to winged, air-breathing and rocket SSTO's, Page 1.

 Copyright 2024 Robert Clark


 I'll take a few approaches to estimate the technical feasibility of a combined jet/rocket SSTO. But first, note quite key to its financial feasibility is that costs can be 1/100th that of what you get from traditional NASA estimates. First, it is just filtering in to the general mindset of those in the space industry how important it was that SpaceX demonstrated 90%(!) reduction in development costs by the private financing approach of commercial space. ESA for example had to be dragged kicking and screaming into the idea of using the private financing approach to new launchers and spacecraft. They are finally following that approach now, though.

 Secondly, anyone familiar with the space program knows development cost for a new system developed entirely from scratch is far more than the individual cost of the launchers or spacecraft that result. So base your system around components already developed and in service. This can cut development costs again by an additional factor of 10, and commonly more.
 These two factors together mean you can cut costs by more than 1/100th what you would expect by traditional NASA cost estimates.

 Then the technical plan is to base the airframe for the air-breathing portion of the flight on existing jet airframes. Then that airframe would carry an existing hydrolox rocket stage that would provide the rocket propelled portion of the flight. In this regard, you may be able to save additional dry mass by integrating the airframes fuselage and hydrolox core into one unit, rather than placing the hydrolox stage inside the existing fuselage.

 To the end of reducing development costs and towards getting an operational prototype vehicle flying quickly, this next suggestion is key: use kerosene(jet) fuel for the first air-breathing portion of the flight.

 First, it was long thought for SSTO’s that it had to be hydrogen fueled because it offered the highest ISP. Then later it was realized because of the heavy tankage mass for hydrolox rockets, that dense propellants actually were preferred for SSTO’s. Further analysis showed if you could have a tripropellant engine burning both kerosene and then hydrogen, you could improve performance further.

 But an even more important practical consideration is that we don’t have an operational hydrogen-fueled turbojet engine operating now. For example, the jet engine company Rolls Royce is researching hydrogen fueled jet engines, but their CEO seemed to poor cold water on their own research program suggesting they won’t come into operation until the 2040’s. Remember now though, key to my approach is to use existing, operational components. 

 Now, what airframe to use? For jet aircraft, very different from rockets, the mass ratio between gross fully fueled weight and the empty weight is rather low, commonly only between 2 and 2.5. So, I was looking for aircraft that had the highest mass ratio. I was interested to see the legendary B-58 Hustler had a mass ratio of over 3. The B-58 is long retired now but it may be possible to buy one for renovation for operational use.

 And its futuristic look would make it utterly badass for a SSTO-design as an actual rocketship that flies to space:


Specifications (B-58A)

3-view line drawing of the Convair B-58 Hustler

General characteristics

Performance

  • Maximum speed: 1,146 kn (1,319 mph, 2,122 km/h) at 40,000 ft (12,000 m)[95]
  • Maximum speed: Mach 2.0
  • Cruise speed: 530 kn (610 mph, 980 km/h)
  • Range: 4,100 nmi (4,700 mi, 7,600 km)
  • Combat range: 1,740 nmi (2,000 mi, 3,220 km)
  • Service ceiling: 63,400 ft (19,300 m)
  • Rate of climb: 17,400 ft/min (88 m/s) at gross weight[97]
  • Lift-to-drag: 11.3 (subsonic, "clean configuration")
  • Wing loading: 44 lb/sq ft (210 kg/m2)
  • Thrust/weight: 0.919

https://en.m.wikipedia.org/wiki/Convair_B-58_Hustler#Specifications_(B-58A)


 It doesn't have to be the B-58 though. Other in use or recently in use jets have mass ratios in the range of 2.5 might be used such as the McDonald A-4 Skyhawk:


https://en.m.wikipedia.org/wiki/Douglas_A-4_Skyhawk#Specifications_(A4D-5_/_A-4E_Skyhawk)


 Such retired aircraft probably could be purchased at relatively low cost as surplus. 

 Note, also that airframes based on fighters or bombers would get great attention to be supported by air forces around the world. But when they offer to finance the project, politely say, No. Remember key to keeping the development cost low is to use private financing. But you could use the interest the various air forces have in purchasing the vehicle as a selling point to get that private financing. (It would be quite amusing to see the Air Force officers jaws drop when they offer to pay for the development, and you respond, "Nah, we don't need that.") 

Reducing Structural Weight.

 Now, the reason why we may not need the high mass ratio of the B-58 airframe is from a rather surprising fact about the B-58. The B-58 was quite innovative and still is for the weight saving measures it undertook. It turns out it's structural empty weight fraction, the fraction of its structural weight to its maximum takeoff weight, was only 13.8%. This corresponds to structural mass ratio of over 7.

 The structural weight as the name implies includes the structural members only of the craft, such as wings, fuselage, tail, landing gear, engine nacelles. It excludes engines, avionics, wiring, APU's, hydraulics, instruments, seats, etc.

 But after looking up references I found it is common for the structural empty weight to be significantly less than just the empty weight, more than can be accounted for by just removing the engine weight:

 From:

Bonded Bomber — B-58.
Author(s): L. M. Smith and C. W. Rogers
Source: SAE Transactions , 1962, Vol. 70 (1962), pp. 477-486 Published by: SAE International
Stable URL: https://www.jstor.org/stable/44469505

 You see in Table 2 the structural empty weight is much less than the known empty weights for all the aircraft in the table, in the range of half as much. The B-58 was designed in the late 50's. Then with modern materials we may be able to cut the structural weight again by an additional factor of two.

 See this graphic of some modern high strength aluminum alloys:


 There are some high strength steel alloys that also improve over standard aluminum in strength-to-weight ratio, by better than a 2 to 1 factor. Because of the heat induced by the high Mach flight we may want to use these or titanium over the high strength aluminum alloys. See discussion here:

DARPA's Spaceplane: an X-33 version, Page 2.
https://exoscientist.blogspot.com/2018/06/darpas-spaceplane-x-33-version-page-2.html

 Other techniques that might be used to reduce structural weight is that of the "isotruss":

Isotruss Tower
280' tower installed in Spanish Fork, Utah



 It is 4 times better in strength-to-weight in bending and 7.5 times better in buckling than standard aluminum grades. And compared to standard steel grades it is 10 times better both in bending and bucking on strength-to-weight basis. This would quite helpful in reducing the weight of wings.

 The isotruss gets its great strength even beyond carbon-fiber composites from its geometry. However, like carbon composites the different strands have to be epoxied together. And like carbon composites also this is where it loses some of its strength. Then we may also try to form the isotruss from high-strength aluminum or steel alloys. These would be isotropic in strength so would not lose strength at the joints. See discussion here:

Horizontal landing for the BFR on Earth. UPDATED, 12/15/2018.
https://exoscientist.blogspot.com/2018/11/horizontal-landing-for-bfr-on-earth.html

 Another possibility for reducing wing weight would be the idea proposed for the horizontal lift-off SSTO proposal from the 70's called Star-Raker. The technique the Star-Raker used for the wings was innovative. They used multiple cylindrical tanks in the wings such that weight of the wings as tanks was close to that of normal cylindrical tanks: 

BLAST FROM THE PAST; a few good ideas may return to the light of day…

https://horizontalspace.wordpress.com/2015/08/10/blast-from-the-past-a-few-good-ideas-may-return-to-the-light-of-day/

 As a familiar example of heavy tank weight, recall the X-33. The non-cylindrical shape of the tanks resulted in poor weight efficiency. That poor weight efficiency led to the perceived idea carbon fiber tanks were needed to save weight. The failure of those tanks led to the program cancellation. In effect, the poor weight efficiency of non-cylindrical tanks led to the program cancellation.


Reducing Weight of Ancillary Systems.

 The amount by which the structural weight is less than the empty weight is not accounted for by just subtracting the engine weight. In fact, the ancillary systems beside the structures and engines, such as avionics, wiring, APU's, hydraulics, instruments, seats, etc. weigh nearly as much as the engine weight. In this regard then its quite important to note than we may be able to cut the weight of these systems by significantly more than by just 50%.

 See this table of weights of the various systems in the Boeing 737-200 to get an idea of the weights of the ancillary systems on aircraft:


From:

The Flight Optimization System Weights Estimation Method.
https://ntrs.nasa.gov/api/citations/20170005851/downloads/20170005851.pdf 

 
The 737-200 was designed in the 60's. Quite likely the ancillary weights on the B-58 can also be reduced. 

 First, "Surface Controls", means "control surfaces", ailerons, elevators, rudder, flaps, etc. Like structural weight this can be reduced better than 50% with modern lightweight materials. 

"Auxiliary Power" unit, APU, is used to start up the engines. For the Boeing 737-200 it can put out 45 KVA, 56 kW. For that 56 kW it weighs 800 kg. Now see the lists here for power-to-weight ratios of heat engines and electric engines:

https://en.m.wikipedia.org/wiki/Power-to-weight_ratio#Engines

You see several that are in the range of a few tens of kW, a la the 56 kW APU of the 737-200, have power-to weight ratios of 5 to 10 kW/kg. That would result in their weights being in the range of only 5 to 20 kg.

For example, Honeywell produces a 45 kVA electric generator at only 28.3 pounds, 13 kg.

For our unmanned launcher, the 400 kg for the "Instruments" would be removed.

For "Hydraulics", they can be replaced by electromechanical motors at about 60% the weight:

HYDRAULIC ACTUATOR REPLACEMENT USING ELECTROMECHANICAL TECHNOLOGY WEIGHT REDUCTION.
The primary reason the Aircraft Industry moved away from hydraulic actuation and into electro- mechanical actuation is the reduction in overall systems weight. In a case study completed for a small business jet. The weight of a full hydraulic system for landing gear actuation was compared to an electromechanical system. The weight savings for a 28VDC system was 15 pounds over the hydraulic system with tubing and actuators. For the electromechanical system the weight was 24 pounds as compared to 39 pounds for the hydraulic system. This represents approximately a 40% weight saving for the employment of electromechanical actuators.
https://www.jdtechsales.com/wp-content/uploads/2018/12/Hydraulic-Actuator-Replacement-using-Electromechancial-Technology_Whitepaper.pdf

 For electrical systems, carbon nanotubes can cut weight by 80% over copper:

Can Carbon Nanotubes Replace Copper?
By John Sprovieri

But perhaps the most intriguing way to use CNT fibers is to spin them into conductive yarns that could someday replace copper wire in wiring harnesses and motor windings. The driving force behind this application is weight reduction.

Consider an RG-58 coaxial cable. The weight of a standard copper construction is 38.8 grams per meter, says Stefanie E. Harvey, Ph.D., senior manager for corporate strategy at TE Connectivity. Replacing the copper braid with CNT tape would reduce the weight to 11.5 grams per meter. Replacing the center conductor with CNT yarn would further reduce the weight to 7.3 grams per meter, for a total weight savings of 80 percent.

Such a reduction equates to hundreds of pounds in an aircraft, says Harvey. For example, the F-35 fighter contains approximately 15 miles of cable. If the copper shielding on all that cable were replaced with CNT tape, the total weight of the cabling could be reduced by approximately 1,180 pounds, she says. If the shielding and the conductors were replaced with CNT materials, the total weight savings would be 1,975 pounds.
https://www.assemblymag.com/articles/93180-can-carbon-nanotubes-replace-copper

 For the "Avionics", that would be practically nothing in weight now compared to its weight in the 50's and 60's. Recall, back then we were still using vacuum tubes and relays.

 No "Furnishings and Equipment" for our unmanned, cargo vehicle.

 No "Air Conditioning + Anti-Icing" for our unmanned, cargo vehicle.

 Putting these weight savings together we can reduce the ancillary weights from 16,900 lbs of the 55,000 lbs empty weight, about 30%, down to only 1,300 lbs, only 2%.

Combined-cycle Engines.

 There is still the issue of the combined-cycle engines. Reaction Engines did testing of their precooler for their Skylon Sabre engine by sending the exhaust of a small jet engine into it to confirm it could deal with the high temperatures.

 However, since we would be using a kerosene turbojet, I advise testing their precooler by placing it in front of an existing kerosene turbojet engine and confirming they could get the needed cooling in that case. For the cooling you could still use the hydrogen or perhaps kerosene in this case.

 In this scenario, we would use oxygen-rich combustion for the jet engine Reaction Engines in their tests places in front their precooler, so that the exhaust exiting the precooler has enough oxygen to support combustion of a jet engine placed after the precooler. 

 Alternatively, instead of using a jet engine to send exhaust into the precooler we could use, for example, electrically heated air that is then accelerated by a de Laval nozzle, to have the needed speed and temperature to emulate air flowing into the precooler at ramjet speeds.

 This would actually be a quite important test to do. It's long been known that the maximum speed a ramjet could be operational getting positive thrust is Mach 5 to 6. But there is little published work on this being actually achieved experimentally. The only thing I've found is almost anecdotal reports of it being achieved accidentally. For instance the research conducted by Onera in the 50's and 60's:

1946 to 1962: aeronautical research that is rapidly gaining momentum.
From the beginning, large teams (of 150 to 200 people) were assigned to the study of liquid propellant and solid propellant rocket engines, ramjets and turbomachinery. In particular, in 1951 in Hammaguir in Algeria, ONERA launched its Stataltex ramjet, which for a long time held the world record for speed and altitude for target devices of its class, reaching Mach 5 at an altitude of 38 km.
https://www.onera.fr/en/history/onera-70-years-1946-1962-aeronautical-research-that-is-rapidly-gaining-momentum

 And this test series with the Martin Marietta ASALM ramjet powered missile in the 70's:

The Air Force Almost Got A Near Hypersonic Radar Plane Killing Cruise Missile Decades Ago.
The primary goal was to give bombers, such as the B-52, a means to destroy Soviet air defense sites and airborne early warning and control aircraft.
During one of the tests, the PTV test vehicle actually exceeded expectations, reaching a hypersonic speed of Mach 5.5 at an altitude of 40,000 feet. In at least one of the launches, an A-7 Corsair II combat jet was used as the launch platform, indicating the Air Force may have considered expanding the number of aircraft certified to carry the weapon. Mockups of the ASALM missiles were also shown mounted on the rotary launcher for the B-52.
https://www.twz.com/34036/the-air-force-almost-got-a-near-hypersonic-radar-plane-killing-cruise-missile-decades-ago

 This last occurred reportedly when a fuel valve got stuck open.  

 Then if Reaction Engines with their Sabre engine could definitively show even on the test stand positive thrust from their precooled engine at Mach 5+ air inflow, that would be a significant advance for propulsion at the upper end of the the ramjet range.

 Note though strictly speaking the Sabre is not a ramjet. The unique approach of the Sabre is that it first sends the Mach 5+ incoming air into their precooler and then sends the chilled air into the standard compressors of a turbojet. 

 The difficulty of the Sabre development is that Reaction Engines wants to use hydrogen fuel. But there aren't any hydrogen fueled turbojets available. And as mentioned the leading researcher on hydrogen-fueled turbojets Rolls Royce engines feels it may take another two decades to make them viable.

 Then I advise Reaction engines try proving their concept with kerosene(jet) fuel. It may even be possible to do using existing jet engines.

 So in regards to achieving Mach 5+ air-breathing propulsion we have a scenario where we have two possible methods: the precooler with turbojet approach and the ramjet approach. Because Reaction Engines precooler has already been proven to work for cooling high velocity, high temperature incoming air, there's a high probability it will work when attached to an an actual (kerosene-fueled) turbojet. Note though we don't have the capability, yet, for using the high Isp hydrogen for the fuel for this approach.

 On the other hand for the ramjet approach we only have anecdotal evidence that it can work in the Mach 5+ speed range. But ramjets have been described as "flying stovepipes". They have no moving parts. It would seem they should be able to work up to the maximal speeds of Mach 5+, even using high Isp hydrogen fuel. Yet still we don't have definitive evidence they have been successfully accomplished at these high speeds.

 I advise both methods be tried for our proposed airbreathing/rocket SSTO.

 For the standard turbojet/ramjet approach, in keeping with the principle of using already developed components we could try adapting the famous J58 engine of the SR-71 to Mach 5+ flight. We would close off the intake's pathway to the compressors when we exceeded the Mach 3.2 operating speed of the J58, which likely can be extended to ca. Mach 3.5. We may need to replace the materials of the combustion chamber to deal with the higher temperatures of the ramjet combustion at Mach 5+ speeds. Another possibility is because we will be carrying hydrogen we can use that to cool the combustion chamber keeping the same combustion chamber materials. 

 Note also, that while getting a turbojet to operate on hydrogen fuel is a non-trivial technical problem, a ramjet is a much simpler operational engine. In that case, getting useful propulsion with hydrogen fuel is likely much simpler. So for our adapted J58 engine we may get significantly higher ISP by switching to hydrogen fuel for the ramjet portion of the flight.

 That's for using the J58. We should investigate as well though combining separate operational turbojets and ramjets. Most turbojets use for example some proportion of bypass air that is routed away from the compressors. Then we could either use this air either in the original combustion chamber when the jet is adapted to ramjet operation or we could bolt instead onto the jet engine a new combustion chamber taken from an already in use ramjet engine. 

 As before we can use kerosene or hydrogen for the cooling. The possibility of using hydrogen for the cooling leaves open the possibility that we can even use a ramjet proven to work only at, say, Mach 3+, to work at Mach 5+ due to the increased cooling made possible using hydrogen.

Could we get Mach 5+ for a kerosene-fueled air-breather vehicle?

 I'll take a tentative conclusion of yes. I'll look at the SR-71. It's rated top speed was Mach 3.2. But on at least one mission it reached Mach 3.5. 

 Here are its specifications:

General characteristics

  • Crew: 2; Pilot and reconnaissance systems officer (RSO)
  • Length: 107 ft 5 in (32.74 m)
  • Wingspan: 55 ft 7 in (16.94 m)
  • Height: 18 ft 6 in (5.64 m)
  • Wheel track: 16 ft 8 in (5 m)
  • Wheelbase: 37 ft 10 in (12 m)
  • Wing area: 1,800 sq ft (170 m2)
  • Aspect ratio: 1.7
  • Empty weight: 67,500 lb (30,617 kg)
  • Gross weight: 152,000 lb (68,946 kg)
  • Max takeoff weight: 172,000 lb (78,018 kg)
  • Fuel capacity: 12,219.2 US gal (10,174.6 imp gal; 46,255 L) in 6 tank groups (9 tanks)
  • Powerplant: 2 × Pratt & Whitney J58 (JT11D-20J or JT11D-20K) afterburning turbojets, 25,000 lbf (110 kN) thrust each
JT11D-20J 32,500 lbf (144.57 kN) wet (fixed inlet guidevanes)
JT11D-20K 34,000 lbf (151.24 kN) wet (2-position inlet guidevanes)

Performance

  • Maximum speed: 1,910 kn (2,200 mph, 3,540 km/h) at 80,000 ft (24,000 m)
  • Maximum speed: Mach 3.3[N 8]
  • Ferry range: 2,824 nmi (3,250 mi, 5,230 km)
  • Service ceiling: 85,000 ft (26,000 m)


Now use the fact the max velocity for an aircraft varies by the square-root of the thrust:

Are there formulas for estimating theoretical top speeds of aircraft?

Absolutely, and it's pretty much as simple as it gets. T=D, where T is the maximum thrust of your engine, and D is the drag that corresponds to the maximum velocity of the vehicle.

Now, both of those values are functions of a few other variables, and so getting the exact numbers, especially for drag, can be a bit tedious. However, the drag equation can be simplified to a function of velocity, which looks like this:

𝐷=12𝜌𝑉2𝐴𝐶𝐷

Where 𝜌 is the density of air at the flight condition (a constant), A is any reference area on the aircraft, usually wing area, and 𝐶𝐷 is an experimentally determined value, called the coefficient of drag, using that reference area. Wind tunnel testing is used to calculate the drag coefficient (and the corresponding lift coefficient), because it's a function of a whole lot of variables that is not easy (or even analytically possible) to solve.

So, all you do is replace D in the first equation with that mess, move all constants (everything but velocity) to one side, and out pops the following formula for the max speed of your aircraft:


 Now instead of the two J58 engines on the SR-71, imagine giving the SR-71 four of the F135 engines:

F135-PW-100

Data from Pratt & Whitney,[4] Tinker Air Force Base,[51] American Society of Mechanical Engineers[52]

General characteristics

  • Type: Two-spool, axial flow, augmented turbofan
  • Length: 220 in (5,590 mm)
  • Diameter: 46 in (1,170 mm) max., 43 in (1,090 mm) at the fan inlet
  • Dry weight: 3,750 lb (1,700 kg)

Components

Performance


 Two of the J58 engines have a 300 kN thrust in afterburner, while four of the F135 engines would have a thrust of 760 kN in afterburner, larger by a factor of 2.5. Since max speed varies by the square-root of thrust, the max speed would be larger by a factor of 1.6. From a max speed of Mach 3.5 to a max speed of Mach 5.6.

 This would be just about the limit for ramjet and precooler/turbojet propulsion. 

 Note quite key about this estimated top speed is the assumption that the famous ramjet mode of the J58 engine above about Mach 2 can be extended to the Mach 5+ range. Quite likely it would require using additional cooling with either kerosene or hydrogen at these speeds. But more to the point I'm supposing replacing the J58 engine with the F135, due to its higher thrust at about the same weight.

 But the F135 does not have a ramjet mode. However, if you look at the operation of the J58 in ramjet mode, it is not particularly complex additional structures that need to be added, mostly adjusting the position of the inlet spike and opening and closing additional air inlet doors:


See also discussion here:

Turboramjet.


https://aerospaceweb.org/question/propulsion/q0175.shtml

  As a prelude to making the modifications to the F135 engine, I advise doing ground experiments on the J58 to confirm it can produce usable thrust up to Mach 5+. 

 Experiments of this type for extending the J58 capabilities to the Mach 5 range are being done by the billion-dollar jet engine companies:

The Pentagon Is Using the SR-71's Legendary Engine for ... Something.
The Pratt & Whitney J58 made the Blackbird the fastest air-breathing plane ever. Which hypersonic aircraft needs the engine now?
BY KYLE MIZOKAMI PUBLISHED: MAR 10, 2021 2:39 PM EST

 But experiments of this type might be doable at low cost. Like with the precooler tests by Reaction Engines we can send exhaust from a jet engine using oxygen-rich combustion placed in front of the inlet to the jet engine and confirm it can make usable thrust with this providing the intake air. 

 But for small research teams, it's not likely you would be able use the J58 engine itself as it was not put in general commercial production but only used for military jets like the SR-71 or NASA experimental aircraft.

 Small research teams and small commercial establishments that renovate jet engines could investigate this using other engines than the J58. For instance this video is on a small commercial group renovating the J79 engine. Note this was the supersonic jet engine used on the B-58:



 As mentioned above, the modifications would be such that the inlet spike is adjustable in position and possibly additional air intakes along the side of the engine.

 But quite important in regards to small research or commercial teams attempting such modifications is that they are not to the engine itself. You certainly don't want to be making additional openings to the engine for example(!). As shown in the first graphic above showing the air flow to the J58 engine, these modifications would only be to the nacelle, i.e., the duct, holding the engine. 

 Still even in this case, if you want to extend the tests to simulating Mach 5+ flight, it's likely you would need more cooling than can be provided by increasing the cooling air taken in though the sides of the nacelles. Likely, heat exchangers of some type would be needed to cool this air further using the fuel for the cooling, cryogenic or not.
 
 As I suggested doing for the precooler tests for providing the air at Mach 5+ speed air to the intakes of our test engine in ground tests, we might use oxygen-rich combustion from another jet directed to the intakes of our test engine, or just use electrically heated air, or other means of heating, sent through a de Laval nozzle to get the needed speed and temperature to emulate air entering the test engine at ramjet speeds. 

 In that case, perhaps the SR-71 itself with the upgraded engines should be the airframe for our airbreathing/rocket SSTO? The reason why I wanted to focus on the B-58 was because of its lightweight structure, which likely can be even further lightweighted with modern materials. However, the SR-71 was designed from the beginning with titanium, which already has great strength for its weight, so likely can't be further lightweighted to any appreciable extent. Given engines to reach Mach 5+ however, the SR-71 may be used as a reusable first stage for a two-stage to orbit system.

 But what about the top speed of the B-58 given four P135 engines to replace the original four J79 engines? The original J79 engines put out 67 kN thrust with afterburner, while the F135 can make 191 kN on afterburner. By the increase in speed by square-root of this proportionally greater thrust would only take the max speed from Mach 2 to Mach 3.4. This would not be sufficient for our SSTO purpose. However, it may be the B-58 speed actually can reach Mach 5+ with this engine change.

 The reason is the J79's used on the B-58 did not have the ramjet mode. So likely the engines could not provide positive thrust at the only 70,000 feet operational altitude to reach the Mach 3+ speed of the SR-71. But the SR-71 flying at 80,000 feet, would have much reduced drag and using ramjet Mode at Mach 3+ would have net positive thrust. So more careful simulations would have to be used to determine if the B-58 could reach Mach 5 with four F135 engines provided with ramjet mode.

 A recent research report also concludes hydrocarbon fueled turbo/ramjets are possible at least to Mach 4+, though it advises higher energy hydrocarbons to improve efficiency:

Feasibility and Performance Analysis of High-Energy-Density Hydrocarbon-Fueled Turboexpander Engine.
August 2023 Aerospace 10(9):753
DOI: 10.3390/aerospace10090753
Jin Gao, Jin Gao, Ziyi Kang, Weiheng Sun, Wen Bao ...

 Note beyond those considerations we now have very good reason to believe a kerosene(jet fuel) turbojet engine can be modified to operate as a ramjet up to Mach 5+. That is what Hermeus has done with modifying existing turbojet engines. Remarkably, Hermeus expects to test a turbojet/ramjet vehicle at least to Mach 4+ next year:




Estimated Performance for a B-58 Based Airbreathing/Rocket SSTO.

 The 13.8% structural weight fraction for the B-58 at a max takeoff weight of 80 tons, corresponds to a structural weight of 0.136*80 = 11 tons. For a 25 ton empty weight, that's 14 tons left over. The four J79 engines weighed 1,740 kg each for a total of about 7 tons. That leaves 7 tons for ancillary systems. 

 As discussed above I'll assume with modern materials, the structural weight can be reduced by better than 50%, to 5 tons. 

 The F135 engine at higher TWR has nearly 3 times higher thrust than the J79, but weighs about the same. So keep the same engine weight at 7 tons. As we argued above with modern materials and systems we can reduce the weight of the ancillary systems to only 2% of the empty weight. That would put it at only 0.5 tons. Then our reconfigured modern B-58 weighs 5 + 7 + 0.5 = 12.5 tons. 

 Or, given the 3 times greater thrust of the F135 engine over the original J79 we could instead use only two of them. This would reduce the empty weight to 9 tons, with the thrust still 1.5 times greater than the original amount.

 For the estimate we need to know the specific fuel consumption(sfc) of the F135 engine, the corresponding term for jet engines to Isp for rockets. It's value is in an inverse relationship to Isp by a known formula. It has not been specified for the F135 engine but estimate as in the range of other engines in its class near the top of the range for turbojet engines, of 4,000s without afterburner, and 2,000s with afterburner.

 We also need to know the specific fuel consumption for the ramjet portion of the flight. We'll estimate it from this graphic of Isp values for different types of aircraft engines:


 So from the graphic for the range of Mach 3 to Mach 5+, estimate the Isp as 1,500s, 15,000 m/s. This is not terribly much less than the Isp in afterburner mode.

 Our approach is to start with the empty mass of the reconfigured B-58, then assuming the max takeoff weight is still 80 tons, the kerosene fuel for the airbreathing portion and our added on hydrolox stage for the rocket portion of the flight will make up the rest of the 80 tons. 

 Then we need to estimate the fuel usage for the kerosene burning portion of the flight. For this we need to know how much the F135 engine burns. We'll be using it only in afterburner mode to achieve the needed speed and altitude quickly to minimize gravity drag. However, it may turn out using it first in the fuel-efficient general cruise mode, non-afterburning, is better to reduce the kerosene load that needs to be carried despite the increased gravity loss.

 ChapGPT gives as max fuel usage rate of the F135 in afterburner mode as 38,000 pounds per hour:

The F-35 Lightning II, a family of single-engine stealth multirole fighters, has significant fuel consumption when using its afterburner. The exact fuel consumption rate can vary based on several factors including altitude, speed, and specific operational conditions. However, some general estimates provide a useful approximation. The F-35's Pratt & Whitney F135 engine consumes fuel at an approximate rate of: - **Normal (non-afterburner) flight:** About 4,000 to 5,000 pounds of fuel per hour. - **Afterburner:** Fuel consumption can increase significantly, typically to around 35,000 to 38,000 pounds per hour. Given the F-35A has a total internal fuel capacity of about 18,498 pounds, using afterburner extensively would deplete its fuel in approximately 30 minutes. These numbers are rough estimates, as actual consumption can vary based on mission profile and environmental conditions.
 
 This is about 5 kg/s. So 20 kg/s for four F135 engines, or 10 kg/s for two.

 We need to estimate the total kerosene fuel load. We'll estimate it from the length of time it takes the B-58 to reach Mach 2 and then extend that length of time for it to reach Mach 5.5.

 According to ChapGPT, the time for the B-58 to reach Mach 2 was 8 to 10 minutes:

The B-58 Hustler, an early supersonic bomber, could reach Mach 2 in a relatively short period compared to other aircraft of its era. Typically, the B-58 could accelerate to Mach 2 in approximately **8 to 10 minutes** under optimal conditions. This included the initial climb to a high altitude (around 50,000 feet) where the thin air allowed for less drag and more efficient high-speed flight. The aircraft's delta wing design and powerful engines enabled it to achieve these impressive acceleration times, making the B-58 a remarkable aircraft in terms of speed and performance during its operational period in the 1960s.

 As a first level estimate, we'll take the time to get to Mach 5.5, a 2.75 times higher speed, as 2.75 times longer, so 8*2.75 = 22 minutes. Granted the ramjet portion of the flight will have reduced thrust but on the other hand it will have much reduced drag at the high altitude. 

 Not much has been published on hydrocarbon fueled ramjets so these should be taken as rough estimates. But the efficiency of the ramjets at high altitude and Mach values discussed in that cited report, "Feasibility and Performance Analysis of High-Energy-Density Hydrocarbon-Fueled Turboexpander Engine", suggest these estimates are not too far off the mark. In particular the high Isp and thrust still able to be achieved at the high altitude and very low air pressures by the ramjets should allow the rapid speed and altitude increases estimated:

Figure 12. Variation in (a) specific impulse and (b) specific thrust with different Mach numbers.
 

Figure 13. The (a) flight trajectory of vehicle and (b) variation in the air mass flow rate and efficiency of compressor at different Mach numbers.


Figure 14. The (a) thrust and the (b) specific impulse and specific thrust of the engine in a typical flight trajectory.


Figure 15. Variation in engine efficiency with Mach numbers.


 We also need to take into account we'll have higher thrust with the F135 engines, which will shorten the time to reach the high Mach and altitudes. With two of the F135's it'll be 1.5 times shorter to 14.66 minutes. And with 4 engines it will be 3 times shorter to 7.33 minutes.

 With two engines the kerosene fuel load will be 14.66*60*10kg/s = 8,800 kg. With 4 engines it will be 7.33*60*20kg/s = 8,800 kg also.

 Since the fuel load is the same either way is there any advantage of the heavier weight for the 4 engines? Yes, because the greater thrust will reduce the gravity loss even for winged, lifting  ascent.

 So the total of the empty mass plus kerosene fuel mass with two engines is 9,000 + 8,800 kg = 17,800 kg, leaving 62,200 kg for the hydrolox rocket stage and payload. And the total weight with four engines case is 21,300 kg, leaving 58,700 kg for hydrolox stage and payload.
 
 We'll take the total Δv to orbit as 9,000 m/s, a little less than the common estimate of 9,200 m/s to 9,500 m/s since we'll assume using lift for the first part of the flight reduces the required Δv. Assuming the ramjet is able to operate at 100,000 feet, 30km, this is equivalent to a Δv of SQRT(2*9.81*30,000) =770 m/s. Then the total Δv provided by the air-breathing part of the flight is 5.5*340 + 770 = 2,640 m/s. Then the rocket part of the flight has to provide 9,000 - 2,640 = 6,360 m/s. 

 For this rocket part of the flight we'll assume high Isp hydrolox efficiency of 4,700 m/s, achievable by using a sufficiently high expansion nozzle for a hydrolox engine in vacuum. 

 Now for our hydrolox rocket we will assume the stage dry mass can be incorporated into the aircraft fuselage. For instance the fuselage wall being using as the tank walls of the stage. And the hydrolox engine using the same combustion chamber and nozzle as the jet engine.

 However, this last may be difficult to do as they use different propellants. But even if you have to use a separate hydrolox engine this should not add too much to the dry mass because the rocket engines high thrust/weight ratio.

 In this regard it is notable there exist methane(natural gas) turbines in common use for electric generators. Then likely one of these can be adapted to act as a jet engine. Then it would be adapted further to have a ramjet mode. This has the advantage that the same fuel could be used for both the airbreathing and rocket modes, and thus also the same combustion chamber. Also, the cryogenic methane would have better cooling properties than kerosene for the ramjet portion of the flight.

Assuming little additional dry mass is added for the hydrolox stage, then take the prop load of the hydrolox stage as 45 tons, and the delta-v calculation is:

4700Ln(1 + 45/(9 + 6)) = 6,516 m/s. Normally a 45 ton propellant load hydrolox stage may have a dry mass of 5 tons. But we are assuming this mass is absorbed into the aircraft mass.

 Then we have a 6 ton payload out of a 80 ton gross mass vehicle for a payload fraction of 6/80, 7.5%, well better than the 3% to 4% even for expendable multi-stage vehicles.

 For the 4 engine case it might be the payload mass would be reduced by 3.5 tons to 2.5 tons' But keep in mind its higher thrust would result in reduced gravity loss, so the payload may actually be higher.

Use Existing Airframes for use as First Stages or Hypersonic Transports.
 
 Hermeus was able to save remarkably on cost and time by adapting already existing jet engines for their turbojet/ramjet engine. They still built their own aircraft however. I advise instead using an already existing airframe for the task for instance the Douglas A-4 Skyhawk or the F-104 Starfighter. Since you don't need the high mass ratio of a SSTO for this application, you don't have the expense of replacing the entire structure of the craft with lightweight materials.

 However, since these were both designed in the 50's and 60's, the ancillary systems for both can be greatly reduced in weight using modern systems without the expense of replacing the entire structure with lightweight materials.

 The engine also can be upgraded. We can either keep the same engine weight as the original while doubling the thrust with a modern engine, or we could keep the same thrust but at half the weight using a modern engine.


  Robert Clark

  
    


     


      





   




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