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All jet airliners have a cruise speed between Mach 0.82 and Mach 0.85.

At those speeds the aircraft are flying at their maximum subsonic speed. Any greater cruise speed would only be possible with major design changes.

My question is about fuel efficiency.

As drag increases with the square of speed, would a slower cruise speed lead to better fuel efficiency?

So why are jet aircraft never designed with a slower cruise speed?

If transonic phenomena didn't exist, would a faster speed be more fuel efficient?

Currently some airliners, after flying a 12-hour route, stay on ground for a long time before returning. Wouldn't a slow flight (if it is more fuel efficient) be better in this scenario? So not to waste time on ground?

On long-range flights, any fuel saving significantly increases the flight's profitability.

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  • $\begingroup$ related: aviation.stackexchange.com/questions/3748/… $\endgroup$ – Peter Kämpf Jun 23 '16 at 20:50
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    $\begingroup$ Only the long-range aircraft all cruise between M0.82 and M0.85. Short-range ones may cruise at less. For example A320 cruises at M0.78 (and yes, the reason is fuel efficiency). $\endgroup$ – Jan Hudec Jun 23 '16 at 21:17
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    $\begingroup$ The statement "All jet airliners have a cruise speed between M0.82 and M0.85" is absolutely false. Far more airliners cruise in the range .74-.80 mach than cruise in the range stated. For example, M0.82 is MMO for the 737; the 737 Next Gen cruises between roughly .77-.80, while the 737 Classics typically cruise around .74-.76. $\endgroup$ – Ralph J Jun 24 '16 at 3:21
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    $\begingroup$ In a single word, lift. The speed moving forward is also what keeps the plane up, and compensating for lower speed would cause more drag. $\endgroup$ – Mason Wheeler Jun 24 '16 at 15:38
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    $\begingroup$ The whole point of boarding a jet to get somewhere is to get there as quickly as possible - the Concorde had a market opportunity because it was so fast. Unfortunately, there are a whole lot of technical challenges with supersonic cruise which makes it unaffordable to the average ticket buyer. Add to that a few additional safety challenges and that is why the Concorde had a limited market all to itself and ultimately stopped flying. High subsonic is currently the optimum point for speed and affordability. $\endgroup$ – Anthony X Jun 25 '16 at 21:45
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There is indeed a benefit in flying more slowly, but the aircraft needs to be designed that way to profit from slower speeds. You can see that wing sweep has been slightly reduced in the more modern airliners, but this is also due to better airfoils with higher Mach drag rise onset.

But some things will also cost more when you slow down: You have to pay the crew for more hours, and the aircraft cannot be utilized as often. To transport the same number of passengers requires more aircraft when they fly at a lower speed. The cost versus speed relationship is not linear, but it should have a minimum somewhere below today's operating points. Aircraft with a slower design cruise speed can be lighter and smaller for the same payload, but for now airlines don't have a choice of slow or fast jets; all manufacturers try to design their long-range airplanes for at least Mach 0.83.

This has a lot to do with marketing: The aircraft with the higher speed will show a shorter travel time for the same distance, so it will show up first in the booking systems of travel agents. Of course, now you will argue that most people book on the internet and will try to get the lowest cost, regardless of travel time. True. But this is not the sort of customer the airlines are after. Their profit comes from people in First and Business class, and these still book predominantly via travel agents. Therefore, Airbus and Boeing try to market their planes as the ones which come first on the Amadeus and Sabre screens.

If you would single-mindedly optimize a configuration for the best fuel efficiency, you would arrive at something close to the MIT D8 design or Boeing's SUGAR study. Note that both are designed to fly quite a bit slower than current airliners at Mach 0.72. These designs are for a world in which fuel costs 200 USD per barrel or more, while the current designs are based on the expected prices at the time of their design start.

When fuel prices were low, the optimum speed for the best transport performance was indeed above Mach 1. The Vickers VC-10 of 1964 sported a maximum cruise Mach number of 0.886 and still holds the record for the fastest commercial Atlantic crossing. When Concorde was developed, the general consensus was that future air travel would be supersonic. Only the jump in oil prices after the 1973 oil crisis put those plans to rest. Large business jets today can cruise at up to Mach 0.935 because their owners are less concerned with saving money by flying more slowly. Technically, there is still room for cruising above Mach 0.85; it's economics that keeps airliners back.

If airplane companies were free to pick the optimum Mach number, they would today choose a speed between Mach 0.78 and 0.82 with fuel prices around 50 USD per barrel. Note that this is the design Mach number range for regional jets which fly short hops in which the increase in trip time from the reduced speed is insignificant. Also, especially in times of high fuel prices airlines operate their gear at lower speeds in order to conserve fuel. But if you follow this link, you will learn that airplane companies don't have that freedom.

Regarding drag:

Drag does not go up with the square of speed. When plotted over speed, the drag of an airplane will first go down, reach a minimum and only then go up. Airliners fly close to this minimum, and they fly high to shift this minimum to the highest possible flight Mach number. They do this by flying in less dense air, which requires to fly at an altitude around 30.000 - 40.000 ft. An additional benefit to flying this high is the lower air temperature which makes the engines more efficient.

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  • $\begingroup$ @ymb1: Yes - and airliners could, too, if they were designed for it. Concorde and Tu-144 flew way higher again than the biz jets. Just give airliners bigger engines and a lower wing loading. The pressurization difference is negligible if you already fly at one quarter of sea level pressure. But no sane airliner company does this and no airline wants it (witness Boeing's Sonic Cruiser). $\endgroup$ – Peter Kämpf Jun 25 '16 at 23:07
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    $\begingroup$ FYI, Jet A fuel at the self-serve pumps is between 3.50 and 7.00 dollars in California—not 50 USD. Airlines probably pay around 1.40. $\endgroup$ – JScarry Nov 12 '16 at 14:46
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    $\begingroup$ @JScarry: The quoted fuel price is $50 per BARREL, which is 42 US gallons (if I can trust Google). Which is close to your $1.40/gal. $\endgroup$ – jamesqf Nov 12 '16 at 18:39
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Short answer: No one wants a slow plane.

Long Answer: While we can talk about engine efficiency all day, we must remember that planes are designed more for missions than science in many regards. If we take the fact that generally speaking planes are built to move things (people/cargo) far and fast there is not much of a use case present for a slow but efficient plane. While this would present savings in terms of cost to the passenger, most people are willing to pay for the speed a less efficient plane offers. Perhaps the best example of this is the inefficient and expensive Concorde which many people were willing to pay large sums of money to fly just to save a matter of hours.

On long range flights, any fuel saving significantly increases the flight's profitability.

This is a bit of a blanket statement and I'm not sure "significantly" is an appropriate word. While fuel savings can increase profitability from a fuel standpoint, you do so at the cost of other expenses. For example most plane parts are serviced based on flight hours, so for a given airframe/number of flights, you will increase your spend on inspections since the plane is presumably spending more time in the air to move a given load. You also have the issues of paying the crew which can cut into costs. Considering long flights (where crew cycle on 8 hour rotations) you may require a full extra crew if time is significantly increased.

I don't have any hard stats on this (but I'll look for some) I would assume there is a safety risk involved with simply spending more time in the air. If we look at accidents per flight hour reason stands that the more time spent in the air the higher chance of an accident, but this is a bit of an educated guess.

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  • $\begingroup$ people's motivation in flying Concorde was a bit more complicated than simple time-saving. Initially, Concorde was losing money because not enough people flew on it, despite the speed advantage - then BA went with prestige marketing, and turned it into a profit-maker. $\endgroup$ – user1804 Jun 24 '16 at 0:38
  • $\begingroup$ Regarding your accidents per flight hour, as soon as I began to read that bit, I went to the opposite conclusion. Since the risk on an accident is so low, even with more planes being in the air I'd think the numbers of hours would climb much faster and drive the stats down. $\endgroup$ – simpleuser Jun 24 '16 at 2:11
  • $\begingroup$ I know I'm stupid. I like flying as passenger and therefore I would probably fly only once with the Concorde (yeah mach 2!), on every other occasion I would prefer regular jet around 0.8 - 0.95. I enjoy flying and traveling to much! Faster planes, bad. Slower planes, bad too. "Beaming" would steal my journey... $\endgroup$ – Peter Jun 24 '16 at 13:08
  • $\begingroup$ @HorusKol "During its time in service, Concorde’s profitability figures weren’t released by BA but it is understood that the service wasn’t a profitable enterprise." telegraph.co.uk/luxury/travel/98151/… $\endgroup$ – A E Jun 24 '16 at 21:38
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    $\begingroup$ A lot of that is actually speculation, the Concorde was profitable according to this interview with one of the chief pilots since its design and development was undercut by the government it cost BA/AF little to actually acquire the plane and due to some interesting ticket hike ideas became quite a money maker. You should listen to the full interview there, lots of interesting stuff. $\endgroup$ – Dave Jun 24 '16 at 23:31
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In addition to the other, more technical answers, there is another reason why aircraft aren't designed to spend more in the air rather than sitting idle at either end of the route - pilots and air crew have a maximum number of hours they are allowed to be "on duty".

Under FAA rules governing Duty Limitations, a pilot can spend no more than between 9 and 14 hours on duty, depending on certain factors such as whether there are other pilots scheduled on the same flight. In addition to that, a pilot must have at least 10 hours of uninterrupted rest time between their duty periods.

So, the slower the aircraft flies, the longer it is in the air - which means that more pilots are required to cover the same flight.

For example, if an aircraft takes 9 hours to fly a route, then under FAA rules the same crew can take a 10 hour rest break at the other end and then return the aircraft.

But if the aircraft takes 10 hours to fly the route, the FAA requires another crew to ensure safety, but both crews must take their mandatory 10 hour rest break at the end of the flight, and then both crews can fly the same route back.

You haven't saved anything, but you are paying for extra crew members.

Airlines and aircraft manufacturers are in a constant push-and-pull struggle to get the most out of their aircraft at any one time, while safety bodies such as the FAA, CAA, EASA et al are constantly ensuring that the routes the airlines fly are safe.

http://work.chron.com/duty-limitations-faa-pilot-17646.html

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First you must realize that mach number is not a speed, but a ratio relating to speed and air temperature. The higher the altitude, the less dense the air. The crux of understanding the whole speed vs efficiency situation is in the difference between the different airspeed types and how they affect aerodynamics and the speed of sound. So it isn't the faster you go but the higher you go that increases efficiency.

Different types of airspeed

The ground speed is related to the true airspeed (TAS), which is how fast you are moving through the volume of air, regardless of the density. Whereas lift and drag are determined by indicated air speed (IAS), which is basically how fast you are going through the mass of air. So while maintaining the same IAS, as you ascend the TAS is higher, thus a faster ground speed. You must maintain IAS above stall, so, to get the most TAS out of it (thus better ground speed) you want to fly in the lowest air density you can.

Speed of sound

The plane is limited, as you note, by the local speed of sound (LSOS), which is affected by the TAS and the temperature. The higher you go, the colder it gets (to a certain point) and thus the lower the LSOS. So at a given IAS the lower the air temperature the higher the mach number (closer to the speed of sound).

Finding the sweet spot

Since lift is related to IAS the TAS is pretty much irrelevant to the wings as long as you stay below the point where LSOS issues arise. You must maintain IAS so that lift is equal to gravity, so it doesn't change at the same altitude. As altitude increases and temperature decreases the TAS goes up and the LSOS comes down. The mach number is the ratio between these two. So there is a point where they converge and you can't go any higher because your TAS will exceed the aircraft mach limit. That's the so-called "coffin corner." If you slow down you stall, if you speed up you exceed the mach limit. The sweet spot for efficiency will be in this area.

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Short answer - at current fuel prices, it's the most economical speed from a cost/revenue perspective.

The two biggest costs of operating an airliner are fuel, which would be reduced by a slower and more efficient aircraft, and airframe utilisation - The cost of the plane divided by how many ticket sales you get out of it over its lifespan, which, would be reduced by flying faster. Additionally flight crew are paid by the hour. Currently M0.85 or a bit less is a sweet-spot in these curves as going transonic causes fuel use to rise more aggressively with speed, but designs for slower and more efficient aircraft (even higher bypass engines; less swept high aspect ratio laminar flow wings) haven't got past concepts because their overall profitability would be despite lower fuel costs, especially when you consider that the tickets would have to be sold for less to make them compete with faster flights on current planes.

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Part 1 of answer: Maximum efficiency (minimum thrust/fuel requirement) occurs at the speed of maximum lift to drag ratio. It’s determined mainly by the wings, for jets engine efficiency as a function of speed also matters.

Sonic drag is another factor, most aircraft need very hish power to accelerate through Mach 1. Aircraft designed for supersonic flight experience decreasing drag above Mach 1 until dynamic pressure, proportional to the square of speed, overwhelms other factors.

A notable case was the Lockheed F-104 with the -19 model of its J79 jet engine. With that engine its fuel efficiency as a function of distance traveled improved above Mach 1, at least to Mach 2 — One pilot report said fuel burn for a given distance traveled was best at about Mach 2. That pilot wrote about returning from Texas to Florida doing Mach 2 at 73,000 feet, with the cruise taking an hour.

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To understand why an aircraft will be more efficient when it flies faster you must realise that the aircraft gives the air that it passes through a downward velocity. The change in the momentum of this air is what supports the mass of the aircraft. Every kilogram of the aircraft's mass will produce a downward force of about 10 newtons. This must be balanced by a change of momentum of 10 kgms-1 every second.

Now, although the change of momentum of a given mass is proportional to the change of velocity, the energy required to produce that change is proportional to the velocity squared. (In SI units the energy is (mv2)/2.) So the 1 kg mass could be supported for 1 second by accelerating 1 kg of air to 10 ms-1 or by accelerating 2 kg of air to 5 ms-1. Both will support the same mass but the first requires 50 J of energy and the second 25 J. Thus by doubling the mass of air that supports the aircraft the power required to do so has been halved.

So to get the best possible efficiency an aircraft should displace the greatest possible mass of air. However, it can only affect the air that it passes through, so in order to move a greater mas of air it must either increase its wing span (which is why high performance gliders have very long wings) or travel faster. So if all other factors were to remain the same then if an aircraft were to double its speed it would require half as much power to keep it up. In addition it would travel twice the distance, so the energy, and hence fuel, needed to travel a unit distance would be reduced by a factor of 4.

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