No. I was directly answering the assertion that the non-linearity of drag around the transonic regime somehow implied a supersonic craft would have lower drag than a subsonic one. The faster you move air to exert a force on yourself, the less energy efficient it is. KE=1/2 mv^2 and P=mv It is very simple physics.
You're making a similarly dishonest equivocation by carefully trying to frame the problem as if it were a mystery and the problem hadn't been reduced to lift/drag ratios 70 years ago. Which have an easily calculable upper bound for supersonic flight, by the way.
A supersonic craft has a much worse lift to drag ratio than a subsonic one. A supersonic craft even has a worse lift to drag ratio than the same supersonic craft at subsonic speed.
You can't even optimize your craft for that high altitude high speed regime because it still has to fly at lower speed and altitude and make it through the sound barrier without getting destroyed.
You will be using at least three times the fuel, so will need at least three times the ticket price. But that's not the only place a basic understanding of kinetic energy disqualifies the entire concept. Your engines/fans will also need at least double the effective exhaust velocity so their energy needs per unit of thrust will be doubled.
With this we can predict that all other things being equal, a supersonic craft will use about 6-10x the fuel per passenger mile as a subsonic one. A 747 has a bit over double the range and 4-6 times the passenger count as a concorde, so the naive approach got us in the ballpark.
Then for long haul flights (the only kind where supersonic will save time) existing airliners are almost half fuel by mass, which means you're in the regime of the rocket equation rather than having fuel scale linearly with distance. Then you can't offset business and first class with economy tickets and freight because noone is going to fly economy supersonic for 6-10x the cost or pay 6-10x the shipping for no perceptible time saving. With the previous in mind though, the supersonic craft is going to be limited to about 4 hours in the air before you start to lose passenger capacity to fuel. So it's not even great for long haul.
In short. Unless fuel prices drop dramatically ticket prices for a new supersonic craft would be commensurable with a new apartment for time savings of around 4 hours or at best 30% of the total door to door time.
>A few lines down in your link you have this: "At about Mach 2, a typical wing design will cut its L/D ratio in half (e.g., Concorde managed a ratio of 7.14, whereas the subsonic Boeing 747 has an L/D ratio of 17)".
That is literally proving my point. Thanks for agreeing with me?
>Sure, at trans-sonic speeds the coefficient of drag is horrible, but a supersonic commercial jet doesn't spend more than the minimum time necessary in that speed range.
And the wave drag is still bad even at supersonic speeds. The planes still have to spend a significant amount of time subsonic (take off, approach, landing, etc.) even if it's minimalized, it's still a significant amount.
>What's more, improvements are possible even for the trans-sonic range. The planned Concorde B was projected to have dramatic fuel consumption improvement of 25% at Mach 1.2 [1].
Still worse than subsonic at that time. Since then, subsonic, high bypass engine design has made that gap even wider.
I don't personally want to make a value judgment about whether or not you could call supersonic air travel sustainable, particularly since it's fairly meaningless to remark on outside of a broader conversation (in much the same way that the "greenness" of electric cars is more complicated than saying they're zero-emissions, since you need to consider the power plants that are ultimately fueling them, plus the batteries, motors, manufacturing...).
But I do want to note that supersonic aerodynamics are extremely complicated, and I think it's just as disingenuous to say that drag always increases with the velocity squared in supersonic regimes. Strictly speaking you're right, but the drag coefficient itself is changing too, and in fact it converges to a value below that of its approximately-constant subsonic value. Also note that airlines are already traveling thoroughly within the transonic region.
I do agree that ultimately, in-atmosphere supersonic flight will consume more fuel than commercial airlines today. However, to say anything more specific than that, I think you really need to start doing a proper aero analysis; once you're transonic (or beyond), you've stepped outside the realm where napkin math is physically valid.
> Air pressure difference between FL350 (traditional airliners) and FL600 (Concorde) is about 1/2. But the speed difference was about 2.5x, so overall you would expect Concorde to need to expend about 3.125 times as much energy per flight hour.
This is false. First, drag is proportional to air density, not pressure, with density at FL600 being 30% of FL350. Drag is increased by 1.728 times[1], which means thrust required is increased by 1.728 times, but energy required is not linearly proportional to thrust required. As a jet engine moves at higher speeds and through less dense air, it's efficiency increases and therefore the power required to produce a unit of thrust decreases. So even though you need 1.728 times the thrust, you need less that 1.728 times the power. Even if it were the same amount of power, at 2.44 times the speed you are only expending that power for 41% of the time, and thus the energy consumption would be 73%.
There are plenty of very valid concerns with regards to the concorde and supersonic transport in general. For starters, you can't simply slap a modern turbofan on there and call it a day, you'd have to sacrifice decades of lessons learned to make high bypass turbofans of the necessary size, so they're still going to be inferior to more refined engines on subsonic aircraft. But the belief that the laws of physics force SSTs to be ridiculous gas guzzlers and no amount of technological refinement can overcome it is misguided at best.
[1] This is actually an oversimplification. Drag does not scale perfectly with qV^2 through the transonic and low supersonic regimes. Wave drag dramatically increases drag close to Mach 1 (which as an aside is the source of the term sound barrier). Wave drag becomes less significant past Mach 1.4 though and by the time you get to supercruise qV^2 is once again a good approximation.
It is, and you're misunderstanding some of the basics of supersonic flight.
"As speeds approach the speed of sound, the additional phenomenon of wave drag appears. This is a powerful form of drag that begins at transonic speeds (around Mach 0.88). Around Mach 1, the peak coefficient of drag is four times that of subsonic drag. Above the transonic range, the coefficient drops drastically again, although remains 20% higher by Mach 2.5 than at subsonic speeds. Supersonic aircraft must have considerably more power than subsonic aircraft require to overcome this wave drag, and although cruising performance above transonic speed is more efficient, it is still less efficient than flying subsonically."[1]
Factoring in that supersonic airplanes are significantly heavier, have lower L/D, must spend more fuel getting to higher altitudes, still have to fly subsonic a considerable amount of the flight time/path, etc. means that it's a matter of physics.
U miss the point entirely that supersonic planes work differently from “traditional” subsonic planes. Just assuming that “faster equals less fuel efficient” is not really correct. Turbofan engines are kind of draggy and not so fuel efficient close to Mach 1. Ramjets change your equation… :-)
>A few lines down in your link you have this: "At about Mach 2, a typical wing design will cut its L/D ratio in half (e.g., Concorde managed a ratio of 7.14, whereas the subsonic Boeing 747 has an L/D ratio of 17)".
Do you not understand what that means? It's literally proving my point. Thanks for agreeing with me.
>Sure, at trans-sonic speeds the coefficient of drag is horrible, but a supersonic commercial jet doesn't spend more than the minimum time necessary in that speed range.
And the wave drag is still bad even at super sonic speeds. The jets still have to spend a significant amount of time subsonic even if it's minimalized, it's still a significant amount.
>What's more, improvements are possible even for the trans-sonic range. The planned Concorde B was projected to have dramatic fuel consumption improvement of 25% at Mach 1.2 [1].
Still worse than subsonic at that time. Since then, subsoni, high bypass engine design has made that gap even wider.
A few lines down in your link you have this: "At about Mach 2, a typical wing design will cut its L/D ratio in half (e.g., Concorde managed a ratio of 7.14, whereas the subsonic Boeing 747 has an L/D ratio of 17)".
Sure, at trans-sonic speeds the coefficient of drag is horrible, but a supersonic commercial jet doesn't spend more than the minimum time necessary in that speed range.
What's more, improvements are possible even for the trans-sonic range. The planned Concorde B was projected to have dramatic fuel consumption improvement of 25% at Mach 1.2 [1]. This projection was made around 1980. In the 40 years since, computers have advanced a bit, so there's a chance the Boom guys know what they are talking about.
You are overlooking the obvious problem. Subsonic planes already existed. Even it it was just as efficient at subsonic speed, I doubt if it was as cost effective as a 737, for example.
The Concorde seated 100 people, in first class. If you can’t fly at supersonic speeds, you aren’t going to spend the extra money.
Again, I'm not saying the concorde is a more efficient vehicle, I'm saying flying supersonically is more efficient than flying subsonically. The concorde was an extremely inneficient plane because it used inneficient engines. Were it to use engines with the same efficiency as modern turbofans, it would be more efficient overall.
I'm saying put vehicle A's engine in vehicle B to make some far more efficient vehicle C and it'll only take 5 gallons of fuel to move 4 passengers 500 miles.
The wiki page I linked quotes an L/D ratio for Concorde (in cruise mode) of 7 to 7.5 and for Boeing 747 of 15.3 to 17.7. Taking the mid-points of 7.25 and 16.5 we get that the L/D ratio for Boeing is 2.275 higher than of Concorde. But Concorde's speed was 2.41 times higher than Boeing's (Mach 2.05 vs 0.85).
There are 2 things to go from here to actual fuel per passenger*mile. How much fuel do you need to produce the same thrust, and how much aircraft do you need to carry a passenger. On both counts, supersonic airplanes have a problem: supersonic engines have a lower bypass ratio, so they are inherently less efficient, and supersonic planes need to be sturdier, and therefore heavier than subsonic ones.
These problems are hard.
But the difficulty of building a supersonic aircraft does not come from the air resistance being the square of the speed.
By the way, the L/D ratio decreases with the speed, but it does not tend to zero in the limit. This fact is actually stunning, if you think of it. As the speed goes up, at some point the L/D ratio stops decreasing, so you end up burning significantly less fuel per mile. That's the reason some militarizes invest in hypersonic missiles: they have much longer range than their size alone would make you think.
Supersonic flight has superlinearly more drag than subsonic flight. IIRC, n^4 or n^5, while drag was normally n^2 kinda thing at subsonic speeds.
Concorde was progress, but backwards progress in terms of what matters in terms of global warming (etc. etc.)
You can reduce some drag by flying higher (thinner air, less drag effects), but that also requires more fuel to reach higher into the atmosphere. So its just inefficient all around.
> Remember kinetic energy goes up with the square of speed
More relevant is that drag goes up with the square of speed generally... in the subsonic regime... I'm not sure what happens across the sound barrier, but I believe it gets worse.
"Concorde, a supersonic transport, managed about 17 passenger-miles to the Imperial gallon, which is 16.7 L/100 km per passenger; similar to a business jet, but much worse than a subsonic turbofan aircraft. Airbus states a fuel rate consumption of their A380 at less than 3 L/100 km per passenger"
But the real comparison should not be between subsonic and supersonic trans-ocean business trips. It should be between taking the trip or not taking the trip at all. The best way to reduce emissions is to avoid long-distance air travel completely.
I strongly agree with your point, but I think some extra context is warranted.
As it stands, the economics of air travel force carriers to optimise for reducing fuel consumption, since that's (by far) the biggest fraction of a commercial aircraft's operating cost.
If supersonic transport makes a comeback, it'll be because the economics will make sense, which (in my mind) will be either because of:
- Somehow reduced fuel consumption, potentially through engines that leverage the effects of the supersonic flight regime for increased fuel efficiency (e.g. ramjets, through that likely wouldn't be possible in low-supersonic flight)
-> As another commenter in this thread mentioned, drag decreases with lower atmospheric pressure at higher altitudes, so there are fuel efficiency gains to be made just by flying higher, within the engines' design constraints.
- It'll fill the niche of richer-than-god people who use jets to skip highway traffic.
There's likely more cases than just these, but these are just the greatest hits as far as I can tell; and I say all of that as someone who's not involved in the aviation industry.
For the record, I don't support this second niche existing, but it does, and it can be an economic driver.
Again incorrect! Look at the data. In what universe is having 12x the fuel burn (per unit of time) or 5x (by mile) “more efficient”.
A Supercuruising Concorde has higher fuel flow than a (much much larger) 747.
Your whole “engines more efficient at higher speed” argument is totally unsupported by facts. Supersonic flow is a major problem is jet engines. They have to use special very-high drag inlets to slow it down to subsonic velocity to actually combust.
The air being thinner doesn’t help, either. It’s basic chemistry... every unit of fuel you burn requires X units of oxygen. The density doesn’t really matter - except that denser air moving slower decelerates less and thus causes less drag.
There aren't supersonic airliners. Anyway, let's calculate. Starship having passenger capacity about that of Concord, say 100, would burn 1000 ton, $1M, of fuel and oxygen, per a suborbital transcontinental flight. Capital cost say $100M per Starship. Say amortize over 100 flights. So $20K/ticket. Double for operations. $40K/ticket. I don't see any supersonic in near and mid future coming even close. If I remember correctly my middle school physics, ballistic trajectory is the most efficient one :)
If anything, DOD is already the first in line for suborbital cargo, not warheads mind you, delivery using Starship.
The Concorde had never been optimized for fuel consumption. Even for a jet of its time, it was quite wasteful of fuel. I once was told by someone who had some insight into Boing, that they had a much more efficient supersonic airliner in development in the competition to the Concorde, when the project was cancelled. So yes, supersonic airplanes would use more fuel than subsonic ones, but how much we can't know until someone builds a modern supersonic aircraft.
Again, that's not my argument. I will continue to assume good faith one last time.
Drag is proportional to density times velocity squared
flying through air with 30% the density at 2.5 times the speed thus produces (.3)x(2.5^2) = 1.875 times the drag.
Using 1.875 times the power for 1/2.5 = 0.4 times as long requires (0.4)x(1.875) = 0.75 times as much energy.
This is before you consider that jet engines moving at higher speeds and higher altitudes are more fuel efficient.
The 737 uses turbofans which are much more efficient than the concorde's turbojets. Trying to compare their fuel consumption is meaningless unless you account for this. If you compare the concorde to a subsonic turbojet of its era, like the 727, the concorde burns significantly less fuel per passenger mile.
In my opinion it is disingenuous to call any supersonic aircraft sustainable. Independently of any clever aerodynamic design to moderate the drag coefficient, aerodynamic drag always increases like the velocity squared. Doubling the speed will mean applying 4x the force for 1/2 the time, so all propulsive efficiencies being equal, you will expend twice the fuel to go the same distance - at an absolute minimum. In reality engine efficiencies decrease at high-speeds, and you won't be able to completely eliminate the Mach 1 "barrier" (drag peak), or design an aircraft that is equally efficient in takeoff/landing... so the factor will be bigger than that. But x2 fuel consumption is a hard lower bound.
I don't believe this can be called sustainable. Air transport is already a major contributor to CO2 emissions. We as a civilization badly need significantly more efficient ways to fly, not less efficient ways. To even slightly suggest that this might be helping the environment is deplorable.
Also, air transport is already miraculous. Going around the world in a day is not enough for you? Really? Buy a book.
Just for comparison the Concorde (which used engines based on a military bomber) used around 5x as much fuel as an A380 to transport passengers over the same distance - so there is a lot of room for improvement.
Economically I don't think there will ever be a market for the speed alone to command paying a much higher ticket price, but maybe technologies can be developed that will mean supersonic aircraft are as efficient (or more so) than subsonic aircraft.
You're making a similarly dishonest equivocation by carefully trying to frame the problem as if it were a mystery and the problem hadn't been reduced to lift/drag ratios 70 years ago. Which have an easily calculable upper bound for supersonic flight, by the way.
A supersonic craft has a much worse lift to drag ratio than a subsonic one. A supersonic craft even has a worse lift to drag ratio than the same supersonic craft at subsonic speed.
You can't even optimize your craft for that high altitude high speed regime because it still has to fly at lower speed and altitude and make it through the sound barrier without getting destroyed.
You will be using at least three times the fuel, so will need at least three times the ticket price. But that's not the only place a basic understanding of kinetic energy disqualifies the entire concept. Your engines/fans will also need at least double the effective exhaust velocity so their energy needs per unit of thrust will be doubled.
With this we can predict that all other things being equal, a supersonic craft will use about 6-10x the fuel per passenger mile as a subsonic one. A 747 has a bit over double the range and 4-6 times the passenger count as a concorde, so the naive approach got us in the ballpark.
Then for long haul flights (the only kind where supersonic will save time) existing airliners are almost half fuel by mass, which means you're in the regime of the rocket equation rather than having fuel scale linearly with distance. Then you can't offset business and first class with economy tickets and freight because noone is going to fly economy supersonic for 6-10x the cost or pay 6-10x the shipping for no perceptible time saving. With the previous in mind though, the supersonic craft is going to be limited to about 4 hours in the air before you start to lose passenger capacity to fuel. So it's not even great for long haul.
In short. Unless fuel prices drop dramatically ticket prices for a new supersonic craft would be commensurable with a new apartment for time savings of around 4 hours or at best 30% of the total door to door time.
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