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From my visual inspection, the third engine (the engine on the horizontal stabilizer) is slightly "nose up", especially compared to the engines on the wing. That means, the front part of the engine is lifted slightly. Am I correct? If yes, what is the intention?

McD11 with its third engine

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Yes, there is a slight tilt to the engine. Engines are heavy, so placing them on the tail shifts the center of mass towards the tail, which is not good for stability. To counter this, aircraft with rear engines often tilt the engines slightly, so the thrust they produce can offset their own weight, helping with stability. It's extremely slight though, as large angles can produce major pitch oscillations with power changes (something known as pitch coupling).

enter image description here

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I believe it has a 4deg incline to align the exhaust with the drag from the fuselage.

It appears more because the inlet is higher than the engine.

http://drawingdatabase.com/mcdonnell-douglas-md-11/

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It may be for the same reason down thrust angle is commonly put into tractor engine mounts - to compensate for pitch up tendency of air craft as they accelerate from added thrust leading to increased velocity.

The third engine of the tri-jet is simply pushing the tail up as thrust is applied. This is something very beneficial in the event of a power-on stall as it assists the elevator in lowering the nose.

Adding up thrust in the back to compensate for weight imbalance would have to be questioned from an engineering point of view, as failure of this engine would create a dangerous aft CG imbalance. It is wise not to rely on thrust or trim to correct an out of safe range CG. Better to move the wing back a bit, as long as it is still directionally stable.

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