Why has the maximum service ceiling of Boeing and Airbus products remained about the same for 30 years? [duplicate]

Question

When Boeing introduced the 747-100 in 1969, its maximum ceiling was 45,100 feet; half a century later, when Boeing introduced the 777x, its maximum ceiling was 43,100 feet.

Similarly, the maximum ceiling of the Airbus A300, introduced in 1972, is 40,000 feet, while the ceiling of the A350, introduced 2 years ago, is 43,100 feet.

Given the all the other advances in aircraft design between the past and current generation of airliners, why has the ceiling remained unchanged?

Answer 1

Mainly, the optimum cruise altitude is where thrust and lift requirements for both take-off and cruise balance well. An additional benefit is the colder air which increases the efficiency of heat engines. Since this helpful drop in temperature ceases once the aircraft climbs above the tropopause, the benefits of flying higher increase most below the tropopause.

With increasing flight altitude, the airliner needs:

1. Bigger engines to create the needed thrust in thinner air
2. Bigger wings to create the needed lift

With the wings, the size of the tailplanes will also grow; this effect alone likely will weigh more than the beefing up of the fuselage structure for the increased cabin pressure. Flying higher will make almost all parts bigger and heavier.

Note that Mach 0.85 is a hard limit for efficient flight; airliners cannot compensate for lower density by flying faster. The only way to allow higher flight levels is to attach bigger wings and tails.

Another consideration is Breguet's formula: Jet aircraft have their optimum cruise lift coefficient at a value of $c_L = \sqrt{0.6\cdot c_{D0}\cdot\pi\cdot AR\cdot\epsilon}$, if we assume the thrust of high-bypass-ratio engines to vary with speed proportional to $v^{-0.5}$, which is a reasonable assumption. This means the airliner cannot fly higher by flying at a higher lift coefficient: This would decrease efficiency.

(Nomenclature: $c_{D0}$ = zero-lift drag, $AR$ = wing aspect ratio, $\epsilon$ = span efficiency)

With the wing size and the engines needed for flight at Mach 0.82 in the tropopause (Mach 0.85 is really not as efficient; follow the link to find out why this is the quoted cruise speed for long-range airliners), the take-off distance is quite reasonable and approximately matches the airports which had been defined by NATO during the cold war. Flying any higher into the stratosphere would increase the aircraft's mass due to bigger engines and wings, but would not incur the efficiency gains of increasing cruise altitude in the troposphere, where temperature drops with altitude.

Conversely, picking a lower design cruise altitude would allow to make both wings and engines smaller, but this would translate into:

1. Higher take-off and landing speeds, and critical speeds during take-off due to the smaller wing,
2. Lower take-off acceleration due to smaller engines,
3. For twins: Not enough thrust during take-off when one engine fails,
4. Lower climb speeds, so it would take longer to reach cruise altitude, and
5. Not fully taking advantage of the cold air up in the tropopause.

Designing for a lower cruise altitude would translate into much longer runways and less efficient flight overall.

Designing for cruise in the tropopause is simply the sweet spot for airliner designers where all conditions match well and produce a balanced outcome.

Answer 2

The aircraft are optimized to fly at a particular altitude, which has not changed over the years. There are multiple reasons for this:

• The higher you go, the less denser air becomes; So, for flying at higher altitude (i.e. for same lift), the aircraft has to fly at higher angle of attack (increasing drag; the wing will stall at some altitude anyway) or greater speed (requiring more thrust due to increased drag).

• As the altitude increases, the thrust produced by the engine falls, and at some point, the thrust produced isn't just enough for flight. This is the most important limitation for service ceiling.

• In commercial airliners, the cabin pressure altitude is held constant (usually ~8000 ft ISA) and the differential pressure will cause stresses on the fuselage; As the air density decreases with altitude, this stress increases and strengthening the structure will increase weight, resulting in poor performance.

• In case of transport aircraft, the service ceiling may sometimes be limited by the maximum altitude from which they can descend to 14,000 ft in less than a specified time (4 min). Commercial airliners are usually limited by this certification altitude.

• Even if the engine thrust is increased and the aircraft can fly at higher altitudes (at more speed), at some point another limitation will manifest itself- The air being accelerated over the wing will reach supersonic speeds and form shock waves, leading to a paradoxical situation where you can neither increase the speed (which will increase drag due to shock waves) nor decrease speed (which will stall the aircraft).

However, some aircraft have flown at higher altitudes where their design was optimal. For example, Concorde flew at ~55,000 ft due to lower drag and consequential heating of the airframe from supersonic speeds.

As an interesting (and unrelated) side note, any aircraft, however powerful, cannot fly above certain altitude as the atmosphere becomes too thin and it would have to fly faster than orbital velocity to generate necessary lift. This is taken as the point where outer space begins and is called the Kármán line