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I'd like to know how you choose the location of the engines under the wings, in the case of a 4-engines aircraft with low wings (and therefore with engines under the wings).

Concerning the longitudinal location, what are the constraints? Nacelles are usually in front of the wing, but why? I know there is a security constraint, especially with high bypass ratio engines, but is that all?

Concerning the lateral position, you want to reduce the bending moment of the wings, and therefore have your engines close to the wing tips during flight. But one could also say you want the engines close to the CG to reduce bending moments on the ground... Which constraint is dominant? And why can't we have to engines close to each other? (far enough to avoid flow interactions)

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  • $\begingroup$ for the forward position, see here (and the other linked question): aviation.stackexchange.com/questions/16499/1467 $\endgroup$ – Federico Dec 3 '15 at 14:36
  • $\begingroup$ Possible duplicate of Why do we use pylons to mount engine on jet airliners? $\endgroup$ – fooot Dec 3 '15 at 16:10
  • $\begingroup$ @fooot, I disagree with the duplicate - that question does a nice job of addressing how far below the wing to hang the engine and why, but not how far away from the wing root. It does cover some of the how far in front of the leading edge should it go, but I'd imagine we'll get even more detail about that on this question. $\endgroup$ – FreeMan Dec 3 '15 at 16:19
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After having read aeroalias' picture collection, I feel an urge to chime in.

Longitudinal position

The main reason to place them ahead of the wing is flutter suppression. Flutter is an oscillation caused by the interaction of elastic and aerodynamic forces. In case of the wing, it is an up-down bending motion. Since air takes its time to flow over the wing, at a certain airspeed the air pressure change on the wing is so much out of phase with the motion that it amplifies the elastic motion of the wing. By placing the center of gravity of the aircraft part ahead of its elastic axis, flutter can be suppressed. This is true of flaps (where a mass balance is added ahead of the hinge line) as of full wings (where engines take the part of the mass balance).

Imagine the wing bending up, and now add the inertial forces of an engine connected to this wing and also moving up. If it is placed ahead of the elastic axis, it will induce a torsion moment into the wing, such that the local angle of attack is reduced, which in turn will reduce lift and the forces which cause the wing to bend upwards. The same happens in opposite direction when the wing bends downwards. Since the biggest thickness of the wing is in its forward section (which shifts the elastic axis forward) and the heavy flap mechanism is in its rear section (which shifts the local center of gravity back), a wing without an engine mounted forward of it needs a much heavier structure or less heavy, but otherwise unproductive, balance weights.

Placing the engine ahead of the wing brings some more benefits:

Why engines are not placed on top of the wing is discussed in this answer.

Lateral position

In two- and three-engined jets you put them at the wing station where the inner wing ends. The main reasons are:

  • There is a major rib anyway to support the wing's skin, so the structure for attaching an engine is easier to add.
  • There is a gap between inner and outer flaps (at least in Boeing designs), so the engine blast will not hit the flaps.
  • They are still relatively close to the center of the airplane to not require an excessively large vertical tail to cancel the yawing moment in single-engine flight.

Boeing 737 bottom view

Boeing 737 bottom view (picture by Adrian Pingstone). The inner wing section has an unswept trailing edge while the outer wing has less taper and a swept trailing edge. The engines are exactly where both meet.

Aircraft like the DC-8 had their inner engines at the wing rib which supported the inner flap tracks of the outer Fowler flap, because they had no gap between inner and outer flaps. On the DC-10, Douglas placed the wing engines at the break between inner and outer wing, however.

In four-engined jets the inner engines are placed like those on two-engined jets, while the outer engines are placed at the end (or slightly outside) of the outer Fowler flaps, about midway between the inner engine and the wing tip. Note that again a rib is needed where the aileron cutout starts - this rib doubles as the engine mount. There the engines can contribute a lot to bending relief, and since a single engine contributes only 25% of the total thrust, the yawing moment of the outer engine in the engine-out case is roughly equal to that of a single engine of a two-engined jet.

Airbus A340 bottom view

Airbus A340 bottom view (picture by Adrian Pingstone).

Why it is better to separate the engines and spread them out over the wing instead of collecting them in a single nacelle is explained in this answer.

In some cases, the engine location is dictated by other requirements. On the Antonov An-70 the inner engines need to be far enough out to allow to drop paratroopers from the front door, for example.

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Any design decision is an optimization problem which involve a number of diverse factors. There are multiple parameters to consider while determining the location of engines in the wings.

Longitudinal location

  • Clearance- In case of high bypass turbofans, farther the engine is out in the wing, greater is the clearance in ground (and require less landing gear length). In some cases where high bypass engines were retrofitted on aircraft, the engine inlet shapes had to be non-circular to get the required clearance.

Inlet

CFM56 engine on Boeing 737, Image from asec.ir

  • Interference- The engine mounting (pylon and nacelle) interferes with the airflow over the wing, which affects the longitudinal location.

  • Safety- Any uncontained failure of the engine disks should not damage the primary structure of the wing, which influences the longitudinal location of the engine. Also, any engine (part) failure should not affect the wing leading edge devices. For this reason, the engines are mounted well in front of the wings.

Forward mounting

Typical engine mounting, from adg.stanford.edu

  • The longitudinal location is also affected by the requirement of operating thrust reversers, which basically deploys a section of the nacelle aft and out.

787 Thrust reversers

Boeing 787 thrust reverser operation. Image from www.pbase.com

  • The location of the engine center of gravity forward of the wing produces a torsional moment, which has the effect of increasing wing stiffness.

Lateral Location:

  • Stability- Closer the engines are to the fuselage, lesser the yawing moment in case of an engine failure.

  • Control surfaces- Usually, control surfaces i.e. flaps are not present aft of the engine as the high temperature flow requires special materials. This leads to reduced Cl_max. The following figure clearly shows the absence of high lift surfaces aft of the engine.

Engine aft

"Undercarriage.b747.arp" by Arpingstone - Photographed by Adrian Pingstone in August 2002 and released to the public domain.. Licensed under Public Domain via Commons.

  • Drag- In this case, engines buried in the wing root is the best location. However, it is rarely used due to various reasons- difficult engine maintenance, wing redesign required if a new engine is to be used, elimination of inboard flap, etc. The location of the engine also affects the interference drag (with the fuselage).

Interference

Effect of large engine on interference drag, image from adg.stanford.edu

  • Wing loads- The location of the engine in the wing helps to relieve the wing bending moment in flight (as for reducing the bending moment in ground, compare the flight and ground loads).

The location of engine is determined after considering all these (and many other) factors.

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