Bjorn’s Corner: Supersonic transport revival, Part 2

By Bjorn Fehrm

August 17, 2018, ©. Leeham News: In the last Corner we outlined several challenges facing a supersonic airliner or business jet.

We will now go through these challenges one by one. We start with the aerodynamic challenge.

Figure 1. The last Supersonic transport, the Concorde. Source: Wikipedia.

Supersonic aerodynamics

When an aircraft goes from subsonic to supersonic flight, the aerodynamic changes in a major way. We covered the changes in the Corner series on “Aircraft drag reduction”. The Transonic and Supersonic bits were discussed in Part 14 to 17. Here we are only recapping some main points.

In subsonic flight, the dominant drag types on an aircraft are Air friction drag, which is the drag due to the size of the aircraft, and Induced drag, which is the drag due to the weight of the aircraft.

For a Boeing Dreamliner, these drag types are typically around 10,000lbf each at cruise. The so-called drag coefficients are around 0.012 each, for a total drag of around 0.024.

Should we force the Dreamliner to fly supersonically, the fuselage alone would have an added drag of 0.1 or 80,000lbf. This is four times as much as the whole aircraft when flying at M0.85. To cruise the aircraft we then need two 50,000lbf engines instead of the two 10,000lbf engines of today (the developed thrust by the Dreamliner engines at a cruise altitude of 38,000ft).

Why is this?

Wave drag

Because we go from smooth subsonic aerodynamics, where the air molecules can move out-of-the-way of the approaching fuselage, warned by the pressure wave from the nose of the fuselage the aircraft is coming. This creates little air movement drag, called Form drag (Aircraft drag reduction Part 10).

When the nose of the fuselage is traveling at or over the speed of the air’s pressure wave, the air molecules can’t flow out-of-the-way anymore. We get a violent collision with the fuselage’s nose, much like when a curling stone hits another and both change their state and direction. We enter the region of “bounce aerodynamics”.

If our object hitting the air molecules has a blunt nose with a large diameter, there will be a lot of bouncing and much momentum loss for the object. The supersonic Volume Wave drag will be high.

The Volume wave drag describes how much added supersonic drag we create when we pass a body with a certain volume (like for a cabin) through the air at supersonic speed.

If we fly a fuselage the volume of the Dreamliner supersonically, but make it four meters in diameter instead of the Dreamliner’s six and compensate by doubling the fuselage length, the Volume Wave drag decreases nine times.

If we reduce the diameter to the three meters of the Concorde, we reduce the Volume Wave drag down to 3% of the original Dreamliner Wave drag, but now we need to double the length again to transport a 787 cabin volume.

We now understand why we shall make all volumes on a supersonic aircraft slim and long, with sharp and angled noses, just like the fuselage of the Concorde. Any extra diameter we want to use for cabin comfort will cost us dearly in Volume Wave or “bounce” drag.

Besides the Volume Wave drag we also add a Wave drag from the lift we create on the aircraft. We dive into this in the next Corner.

22 Comments on “Bjorn’s Corner: Supersonic transport revival, Part 2”

1. Hi! Very interesting, as always!
But, can you compensate by going higher, where the air is less dense, or you end up going into space with no drag but also with no lift at all, where lift is not really required… ?

Thank you!
Sylvain

• Hi Sylvain,

the drag coefficient is independent of air density, the drag in lbf isn’t. So yes, the actual force for the Volume wave drag will be less if you fly higher as will the friction drag force. This is why SSTs cruise around 55,000ft.

But the proportion of Wave drag to friction and induced drag will remain. To fly supersonic you need to carefully design the shape of the aircraft. It needs to have slender volumes.

2. It gets more complicated when you get into the design of Engine high efficinecy inlets/exhausts.

• Absolutely. The nacelle/engine area is the most challenging area, we will get there.

3. In the meantime, how about increasing the speed of subsonic airliners. The speeds are the same as they were in the 60’s. Going from 550 mph to about 700 to 725 mph would be a game changer. Quicker flights, more legs flown per day and less stressful flying.

• 700 mph at the same altitude (say 38,000 ft) is equivalent to M1.06, which is not subsonic. Even at a lower altitude of 22,000 ft, it would still be M0.99 at 700 mph. There’s a reason subsonic speeds haven’t increased – near M0.8 is the lower critical Mach number, where regions of supersonic flow start forming (i.e. transonic flow). High-transonic wings are difficult to design and inefficient, hence why no aircraft fly in the M0.9 – M1.0 range.

• Being nitpicky here but the Citation X and Gulfstream G650 both can cruise up to mach 9 and can fly up to mach .93.
That being said they are still more efficient at lower mach numbers and private jets have different priorities than commercial aircraft.
Still very impressive engineering!

4. I cannot help but wonder if the coming nexus of commercial air travel and space flight will make the concept of supersonic transport moot? The SpaceX BFS is currently under construction in LA and the first flight tests are scheduled for early to mid 2019. They have already proven that they can land a Falcon 9 booster and rapidly reuse it. If the BFS proves to be reliable and safe there is the potential to travel anywhere on earth in under an hour. Elon Musk has said that the cost of a ticket will be about the same as what a business class ticket is currently. There is a video of his plan for Earth to earth flights on you tube. He plans to provide an update on the BFS/BFR project any day now so we will soon know how much progress has been made. It is hard to believe that this might happen but then again up to a few years ago there was no such thing as a reusable rocket. We are living in the future.

• While I love what Musk has done, I have to totally doubt that you can make orbital or sub orbital flights cost the same as a current flight.

He struggles with Tesla and while I laud the effort, it proves how difficult just that can be.

I like his thinking outside the box but no where near all of his ideas are going to come to fruition.

• Suborbital ballistic travel may eventually be more efficient than supersonic flight, but the numbers don’t quite work in the yet. Supersonic fuel use per passenger is five times higher than subsonic flight, depending on a host of assumptions. Fuel cost is about a third of airline expenses, so quintupling that means supersonic travel would still cost less than twice existing premium fares.

The most favorable comparison would be to the longest current flights. The first class halfway around the world SFO-DEL fare is \$16k, so presumably this could be done supersonically for \$32k. The BFR which is operational lifts 64tons to low earth orbit for \$90m, or \$700/lb. Earth to earth would not be much cheaper, so for \$32k you could move 45lb. A whole person would cost five times as much or \$170k. Saving a day of travel time would be worth something, but probably not \$154k.

This is eleven times the subsonic fare, so not yet realistic but not that far off either. Musk has already dropped the cost of getting a pound into space from \$10,000 to \$700, so another iteration would do it.

• I think your numbers refer to the Falcon Heavy which can lift 64 tons to LEO for \$90 million. The BFR can land 150 tons on Mars. Since it is fully reusable, the major cost is fuel which is methane and liquid oxygen. Musk says each BFR flight will cost \$2 mil or about \$8,000 per passenger.

• Musk says……. You lost me right at that point.

5. One of the dramatic areas that show how much width and shape affects the supersonic costs is the F-35.

In electing to make it STOL and the form that took with a large fan behind the cockpit, they ruined the chance to make it as efficient as possible.

As the fuselage is common to all F-25 types, all the other ones from Navy to Air force are affected by the poor drag characteristics incurred by the fan shaped fuselage.

• The width is necessary as well for inlet ducts to hide the compressor face from outside and the internal weapon bays. Other planes in this class have twin engines which add width, eg PAK FA which has the engines separated as well. Conformal fuel tanks which ‘thicken out’ the fuselage of existing aircraft show being wider is not such a disadvantage when your mission doesnt require high M speeds. After all you cant out- run a missile.
This aerodynamic analysis of both F35 models by students of Virginia Tech using publicly known information and some astute assumptions to feed into useful software shows how much more efficient the F35C is with its bigger wing area is.
http://www.dept.aoe.vt.edu/~mason/Mason_f/F35unknownS03.pdf
http://www.dept.aoe.vt.edu/~mason/Mason_f/F35ASpr11.pdf

Im assuming LNR follows similar principles but focused on airliner sizes, cruise speeds and weights( plus a lot of historical knowledge) to derive its estimate of performance of current and possible new passenger jets.
We can see the reasons why Boeing , Airbus and others hold back
from releasing all the broad parameters of their projected designs as they know they can be used to ‘reverse engineer’ fairly good estimates of performance by competitors and others.

• Hello TransWorld,

As antiaircraft missiles get better and better, fighter aircraft design seems to be placing more and more emphasis on stealth and less on speed and aerodynamic efficiency. The people who design and buy these aircraft clearly believe that given a choice between a slower more stealthy design, and a faster less stealthy design, the slower more stealthy design is often to be preferred. I believe that the F35’s shape has much to do with optimization for stealth. Maneuverability is also at least as important as cruise efficiency in fighter design, and what is good for supersonic cruise efficiency may not be what is good for maneuverability.

Below is a list of radar cross sections and top seeds of some US combat aircraft. Radar cross sections are from the link after the list, top speeds are form Wikipedia. In general, it seems that radar cross sections and top speeds are both getting smaller.

Fighters
F15: 25 sq m, Mach 2.5+
F16: 5 sq m, Mach 2
F18: 1 sq m, Mach 1.8
F117: 0.003 sq m, Mach 0.92
F22: 0.0001 sq m, Mach 2.25
F35: 0.005 sq m, Mach 1.6+

Bombers
B1: 10 sq m, Mach 1.25
B2: 0.0001 sq m, Mach 0.95

• The radar cross section of 10 sq m that I listed above for the US B1 bomber is for the B-1B. When the US President Reagan resurrected the B-1 program after it had been canceled by US President Carter, the Mach 2.25 B-1A design that had been canceled by Carter was replaced by a Mach 1.25 B-1B re-design that eliminated the variable aspect engine intakes needed to reach for Mach 2 in order to reduce radar cross section. Unknown to the public at the time was that at the same time that Carter cancelled the B-1A, he had authorized work on what became the B-2 stealth bomber, slower than both the B-1A and B-1B at Mach 0.95, but with a radar cross section many orders of magnitudes lower. Note that that the maximum low level speed of the B-2 (Mach 0.95) is actually higher than that of the B-1A (Mach 0.85) or B-1B (Mach 0.92), and equal to that of the canceled Mach 3 (but at only at high altitudes where the DOD judged it would be a too-easy target for the best modern SAM’s) B-70 bomber of the 1960’s. The B-1B re-design emphasized low level penetration capability and low radar cross section over the ability to cruise at supersonic speeds at high altitude.

The excerpts below are from the Wikipedia article on the B-1.

“In January 1982, the U.S. Air Force awarded two contracts to Rockwell worth a combined \$2.2 billion for the development and production of 100 new B-1 bombers. Numerous changes were made to the design to make it better suited to the now expected missions, resulting in the new B-1B. These changes included a reduction in maximum speed, which allowed the variable-aspect intake ramps to be replaced by simpler fixed geometry intake ramps in the newer design. This reduced the B-1B’s radar signature or radar cross-section; this reduction was seen as a good trade off for the speed decrease. High subsonic speeds at low altitude became a focus area for the revised design, and low-level speeds were increased from about Mach 0.85 to 0.92. The B-1B has a maximum speed of Mach 1.25 at higher altitudes.”

“On 30 June 1977, Carter announced that the B-1A would be canceled in favor of ICBMs, SLBMs, and a fleet of modernized B-52s armed with ALCMs. Carter called it “one of the most difficult decisions that I’ve made since I’ve been in office.” No mention of the stealth work was made public with the program being top secret, but today it is known that in early 1978 he authorized the Advanced Technology Bomber (ATB) project, which eventually led to the B-2 Spirit.”

https://en.wikipedia.org/wiki/Rockwell_B-1_Lancer

• AP: Both you and Duke miss the point.

The F-22 is more stealthy than the F-35.

Its an older generation (supposedly) and it can super cruise.

Stealth has come a long way since the Wobbling Goblin.

While top speed in and of itself does not mean anything in a dog fight, dog fights are virutaly non existant as well.

What top speed does denote is both a slipper air-frame and an ability to open distance as needed (the F-35 is poor from the rear so its a dual issue, easier to see and it can’t move fast enough to delay a missile strike.

Due to its poor aerodynamics (relativity speaking) it can accelerate either. That was waved requirement.

The Fan in the middle had a major impact on SFC, acceleration and zero ability to super cruise like the F-22.

Its not a miner issue.

Assuming they can work the bugs out of it, the F-35 will do whats needed, but it has an abysmal range.

The F-22 can super cruise faster than the F-35 max speed (and the power to weight ratio is not that far apart)

When we are talking about supersonic fighters, a small deviation has a significant impact.

The shape of the fuselage is not major factor in stealth, it is in air flow. Coatings are used to deal with the surfaces.

Some shaping is done on the highly reflective parts.

If you put a fat object that is not normally there, you have a major compromise.

Ironically for the Marines its a CAS mission and that is not where a stealthy design lives and breaths.

• Hello TransWorld,

Regarding: “The shape of the fuselage is not major factor in stealth, it is in air flow. Coatings are used to deal with the surfaces”.

Do you think it is a coincidence that the B-2 and B-21 have flying wing shapes like the stealthy Avro Vulcan (top speed Mach 0.95) of the 1950’s and 1960’s? Do you believe the Avro Vulcan had a lower radar cross section than other bombers of its era (100 sq m for a B-52) because it had a different surface coating, rather than a different shape? Do you believe that a B-52, 747, or A380 could be turned into a stealth aircraft by giving them some type of magic stealth surface coating? If so, you should share your coating formula with USDOD and get rich, because they are wasting billions of dollars developing aircraft with novel shapes designed to improve stealth, when they could instead just be painting the aircraft they already have with your magic stealth coating.

“The possibility of designing aircraft in such a manner as to reduce their radar cross-section was recognized in the late 1930s, when the first radar tracking systems were employed, and it has been known since at least the 1960s that aircraft shape makes a significant difference in detectability. The Avro Vulcan, a British bomber of the 1960s, had a remarkably small appearance on radar despite its large size, and occasionally disappeared from radar screens entirely. It is now known that it had a fortuitously stealthy shape apart from the vertical element of the tail. Despite being designed before a low radar cross-section (RCS) and other stealth factors were ever a consideration,[23] a Royal Aircraft Establishment technical note of 1957 stated that of all the aircraft so far studied, the Vulcan appeared by far the simplest radar echoing object, due to its shape: only one or two components contributing significantly to the echo at any aspect, compared with three or more on most other types.[24][26] While writing about radar systems, authors Simon Kingsley and Shaun Quegan singled out the Vulcan’s shape as acting to reduce the RCS.[27] In contrast, the Tupolev 95 Russian long-range bomber (NATO reporting name ‘Bear’) was conspicuous on radar. It is now known that propellers and jet turbine blades produce a bright radar image[citation needed]; the Bear has four pairs of large (5.6 meter diameter) contra-rotating propellers.”

https://en.wikipedia.org/wiki/Stealth_technology

What is your explanation for the obviously not very aerodynamically efficient shape of the F-117? According to Wikipedia, the shape was dictated by the desire to achieve low radar cross section with then available technology. See below.

“Modern stealth aircraft first became possible when Denys Overholser, a mathematician working for Lockheed Aircraft during the 1970s, adopted a mathematical model developed by Petr Ufimtsev, a Soviet scientist, to develop a computer program called Echo 1. Echo made it possible to predict the radar signature of an aircraft made with flat panels, called facets. In 1975, engineers at Lockheed Skunk Works found that an aircraft made with faceted surfaces could have a very low radar signature because the surfaces would radiate almost all of the radar energy away from the receiver. Lockheed built a model called “the Hopeless Diamond”, a reference to the famous Hope Diamond and the design’s predicted instability. Because advanced computers were available to control the flight of even a Hopeless Diamond, for the first time designers realized that it might be possible to make an aircraft that was virtually invisible to radar.”

https://en.wikipedia.org/wiki/Stealth_aircraft

• For the Avro Vulcan I should have said “near flying wing shape” instead of “flying wing shape”. The Vulcan does have a cockpit extending ahead of its large delta wing, but except for the cockpit region, the wing blends smoothly into the bump that passes for a fuselage, without there being a large vertical surface to reflect incident radar waves directly back to their direction or origin.

• AP:

I was discusin the F-35 and did not make that clear.

A bomber has a different set of aerodynamics to work with.

They don’t have to be able to maneuver like a fighter does.

And note that the B-2 is sub sonic.

B-1 is supersonic capable (sort of) and is not stealthy.

The F-117 was not nor could it fight. It was a bomb truck. Good one for what it was, but all the stealth shape compromises meant that is was its only role.

• The F-117 also was below Mach.

As we know, Mach 1 changes things dramatically

As the fuselage shape is not the worst issue reflection wise, you can coat it.

Rear engines are really bad. Intake ducts are bad

Those you have to design around and get the best you can.

• There are two reasons for the F22 ability to ‘supercruise’ and they have nothing to do with shape
1) Intake ducts which have ramps
2) Thrust to weight ratio

After all the Concorde ‘B version’ did away with ABs with changes to inlets, engines thrust and some ‘smallish’wing changes.
The other thing to consider isnt the takeoff thrust but the thrust at altitude when you want to push through the sound barrier. Even the ‘marginal stealth’ of the Typhoon can supercruise.