They are tilted down and also left or right.
The reason is that:
engines do have a torque and the torque will try turn the plane left or right. So you point the engine in a way to cancel a bit of that.
Engines will pitch the nose up the more you ask power from them, they are tilted in a way to counter the nose up they give.
These angles have the purpose to cancel the effect of engine thrust, this makes the plane deviate less when the pilot changes the throttle, and makes the plane save fuel because you need to use less flight control surfaces to keep it straight.
Aircraft engines are oriented to minimize the effect of thrust changes on the aircraft’s attitude (orientation). Where an engine is mounted below the aircraft’s centre of gravity, increasing thrust tends to pitch the aircraft up. Tilting the engines down a bit lessens this effect, so when thrust increases substantially, the aircraft tends to remain level.
The same thing applies to aircraft with engines mounted up high (such as some amphibian airplanes). In these cases, increasing thrust tends to pitch the aircraft down. These engines are tilted up slightly to minimize the pitch moment.
There are various reasons, including some already covered in other answers. Another one though is that the way an airplane wing generates lift is to gently suck suck air up and then push it down. The net result is that the air forms a bit of a “bump” from the perspective of the airplane: ⤼ (see also [this image](https://www.cam.ac.uk/sites/www.cam.ac.uk/files/news/research/news/230111-holger-babinsky-wing-lift-still.jpg)). The engines are often at the front half of this and below the wing, where the air is going up, so angling them slightly down actually means they are more parallel to the airflow. You’ll find that in airplanes where the engines are mounted on the tail (and thus in the back part of the flow, where it’s going down), they’re angled slightly up.
Engine is aligned to be straight* when the plane is in a cruising attitude.
*Engine is aligned to produce min drag in cruise. If engine thrust is not on center of mass you might change alignment slightly to minimize overall drag from trim to counter torque.
Which plane(s) are you asking about specifically and during which stage of flight. Many people planes have the engine nose up on the ground for example. Which end of the engine are you asking about? That kind of engine?
Most of these answers are somewhat right but pretty incomplete. All design choices are a tradeoff, and that’s even more true for aircraft. I’ll be mostly focusing on airliners with turbofans for this comment. Generally speaking, there are two main concerns: cruise efficiency and controllability in low speed flight. Generally cruise efficiency is going to be somewhat more important in airliners. For simplicity’s sake, I’ll be calling the air ejected from both the core and the fan “exhaust”.
If you’re designing a plane to fly efficiently at 75% to 85% of the speed of sound while still being able to land on short runways, the handling characteristics are going to be a little pathological in some flight regimes, so auto trim systems and pilot training mean that the effect of thrust angle on controllability isn’t usually the overriding concern unless it’s extremely bad. When it does come up, it’s generally because newer engines were fitted to a new variant of an old design. This is what happened with the 737-MAX. The engines being more powerful were a factor, but the main issue was that there’s little room to fit such a large engine under the wing of the 737 because of how the landing gears are designed. This required them to mount the engines forward if the wing, which at larger angles of attack could cause the intake cowling to catch the air and force the plane to pitch up. (While the MCAS system was to counter this pitch up tendency, Boeing had found that the effect was something pilot training alone could adequately address, it was just that pilots would need time in the simulator to adapt to it.)
So in cruise flight, the wing has to be tipped slightly up to make lift. This doesn’t necessarily mean that the fuselage is also tipped up, as the wings can be constructed with enough angle of incidence to keep the fuselage level, but as a general rule the nose of the plane will be tilted up relative to the oncoming air. You waste some amount of thrust if the engine exhaust isn’t aligned with your direction of flight. It’s also worth mentioning that the local direction of the airflow around the engine is disturbed by the airframe. This has some effect on the ideal direction of the exhaust flow, but is a particularly big deal with the intake, as ahead of the wing, the direction of the air slopes up. [This can be remediated by angling the engine intake direction downward.](https://c8.alamy.com/comp/EPT8R2/side-view-of-a-boeing-787-jet-engine-manchester-airport-EPT8R2.jpg)
The wrinkle to that last paragraph is that the engines aren’t perfectly in line with the center of mass of the aircraft. This means that their thrust (when mounted under a low-wing plane), causes a pitch up moment. Some of this pitching moment is helpful. A stable plane is somewhat nose-heavy, and the elevators/horizontal stabilizers have to push against the lift generated by the wing to counter this, creating drag on both themselves and the wing. Airliners generally trim the whole horizontal stabilizer up and down to account for this, so it’s not as bad as the more crude trimming systems on GA aircraft, but every airframe has a happy zone for drag based on how it’s trimmed. This means that the tilt of the engine isn’t just a function of what the reasoning in the previous paragraph would tell you.
They’re tilted down and usually angled inward. This is to do with efficiency in the local airflow.
The inward angle, or toe-in is usually 1-3°, (a 747 uses 2° on all 4 engines). This is because the local airflow is moving outward from the centerline of the aircraft slightly. In general, the fuselage and wing are pushing air out of the way and this accounts for a slight out washing effect. The toe-in is there to account for this and lower drag. I’ve heard that the angle is also there to mitigate asymmetrical thrust in a single-engine scenario. You see this with many twin engined fighters. But I’ve never heard anyone credible refer to this.
The downward angle is sometimes an illusion of the landing gear, with the nose gear being shorter. But most often it’s because aircraft don’t fly completely level, they fly with some angle of attack, particularly in the engine intensive parts of the flight envelope: climb and high weight cruise. So the engines are angled to optimize efficiency with regard to airflow. During descent, we don’t care much about engine efficiency as they’re running at a fraction of their max power, often idle.
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