Copyright 2024 Robert Clark
Specifications (B-58A)
![3-view line drawing of the Convair B-58 Hustler](https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Convair_B-58_Hustler_3-view_line_drawing.svg/500px-Convair_B-58_Hustler_3-view_line_drawing.svg.png)
General characteristics
- Crew: Three
- Length: 96 ft 10 in (29.51 m) [95]
- Wingspan: 56 ft 9 in (17.30 m) [95]
- Height: 29 ft 11 in (9.12 m)
- Wing area: 1,542 sq ft (143.3 m2)
- Aspect ratio: 2.09
- Airfoil: root: NACA 0003.46; tip: NACA 0004.08[96]
- Empty weight: 55,560 lb (25,202 kg)
- Gross weight: 67,871 lb (30,786 kg)
- Max takeoff weight: 176,890 lb (80,236 kg)
- Zero-lift drag coefficient: CD0.0068
- Frontal area: 10.49 sq ft (0.975 m2)
- Powerplant: 4 × General Electric J79-GE-5A afterburning turbojet, 10,400 lbf (46 kN) thrust each dry, 15,000 lbf (67 kN) with afterburner
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)
https://en.m.wikipedia.org/wiki/Douglas_A-4_Skyhawk#Specifications_(A4D-5_/_A-4E_Skyhawk)
en.m.wikipedia.org |
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":
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…
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.
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)
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:
Where is the density of air at the flight condition (a constant), A is any reference area on the aircraft, usually wing area, and 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:
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
- Compressor: 3-stage fan, 6-stage high-pressure compressor
- Combustors: annular combustor
- Turbine: 1-stage high-pressure turbine, 2-stage low-pressure turbine
- Bypass ratio: 0.57:1
Performance
- Maximum thrust:
- 28,000 lbf (125 kN) military thrust,
- 43,000 lbf (191 kN) with afterburner
- Overall pressure ratio: 28:1
- Turbine inlet temperature: 3,600 °F (1,980 °C; 2,260 K)
- Thrust-to-weight ratio: 7.47:1 military thrust, 11.47:1 augmented
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