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An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards. For an aircraft that flies a horizontal path at high angle of attack, the airflow approaches the engine horizontally and leaves the engine in a downward angle, close to the negative angle of attack.

In order to make the flow turn downwards, the engine must exert a downward force on the airflow. According to the third law of Newton,there is an opposite force on the engine. The component of this force that is perpendicular to the incoming undisturbed airflow is the additional lift force caused by the engine.

This additional liftenter image description here


One way to analyse the thrust of an engine is independentto look at the rate of change of momentum of the tiltedair flowing through and around the turbine.

Momentum is the product of mass and velocity: $\vec{p} = m \vec {V}$ As you see, momentum it is a vector quantity.

The rate of change of momentum $\dot{\vec{p}}$ of a mass is equal to force on the object.

By analysing the change of momentum of the air flowing around the engine, we can determine the thrust vector of the engine.

In the image below, the engine's axle is perfectly aligned with the incoming flow of air. I choose an imaginary volume around the engine, such that the static pressure at the boundary is equal to the static pressure far ahead of the engine. Because the boundary pressure = $p_0$ at every point on the boundary, the integral of pressure over the surface of the volume, the resulting net force would be zero.

enter image description here

The top and bottom boundaries are chosen to be along the streamlines.

The left boundary is experiencing a constant influx of air; the flow is uniform across the left boundary.

The right boundary is experience a constant outflux of air; the flow in non uniform due to the difference in flow velocity in the core and the bypass section of the engine.

The influx of mass through the left boundary is equal to the outflux of mass through the right boundary; I neglect the burned fuel here.

The influx of momentum through the left boundary $\dot{\vec{p}}_{in}$ is equal to $\dot{m}\vec{V} = \iint_{l} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The outflux of momentum through the right boundary $\dot{\vec{p}}_{out}$ is equal to $\iint_{r} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The difference between the inflow of momentum (indicated by the blue vector below the drawing) and the outflow of momentum (indicated by the red vector below the drawing) is the force exerted on the volume of air. The thrust (indicated by the black vector) is the reaction force.

 

enter image description here When we now introduce an angle of attack, the bounding volume will change shape. Also the influx and outflux momentum will be different. What is most important is that the thrust generated is no longer purely axial; the thrust vector develops a transverse component. This is the additional lift (and a bit of drag) that the engine creates a high angle of attack.

enter image description here

When the engine is mounted well in front of the centre of gravity, a high angle of attack / high thrust situation will cause an upward pitching moment. This is the case in the Boeing 737 MAX where this effect was changing the handling characteristics at high angles of attack. To make sure the handling would be similar to earlier 737 models, Boeing introduced the - now infamous - Maneuvering Characteristics Augmentation System (MCAS).

An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards. For an aircraft that flies a horizontal path at high angle of attack, the airflow approaches the engine horizontally and leaves the engine in a downward angle, close to the negative angle of attack.

In order to make the flow turn downwards, the engine must exert a downward force on the airflow. According to the third law of Newton,there is an opposite force on the engine. The component of this force that is perpendicular to the incoming undisturbed airflow is the additional lift force caused by the engine.

This additional lift is independent of the tilted thrust force vector.

enter image description here

An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards. For an aircraft that flies a horizontal path at high angle of attack, the airflow approaches the engine horizontally and leaves the engine in a downward angle, close to the negative angle of attack.

In order to make the flow turn downwards, the engine must exert a downward force on the airflow. According to the third law of Newton,there is an opposite force on the engine. The component of this force that is perpendicular to the incoming undisturbed airflow is the additional lift force caused by the engine.

enter image description here


One way to analyse the thrust of an engine is to look at the rate of change of momentum of the air flowing through and around the turbine.

Momentum is the product of mass and velocity: $\vec{p} = m \vec {V}$ As you see, momentum it is a vector quantity.

The rate of change of momentum $\dot{\vec{p}}$ of a mass is equal to force on the object.

By analysing the change of momentum of the air flowing around the engine, we can determine the thrust vector of the engine.

In the image below, the engine's axle is perfectly aligned with the incoming flow of air. I choose an imaginary volume around the engine, such that the static pressure at the boundary is equal to the static pressure far ahead of the engine. Because the boundary pressure = $p_0$ at every point on the boundary, the integral of pressure over the surface of the volume, the resulting net force would be zero.

enter image description here

The top and bottom boundaries are chosen to be along the streamlines.

The left boundary is experiencing a constant influx of air; the flow is uniform across the left boundary.

The right boundary is experience a constant outflux of air; the flow in non uniform due to the difference in flow velocity in the core and the bypass section of the engine.

The influx of mass through the left boundary is equal to the outflux of mass through the right boundary; I neglect the burned fuel here.

The influx of momentum through the left boundary $\dot{\vec{p}}_{in}$ is equal to $\dot{m}\vec{V} = \iint_{l} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The outflux of momentum through the right boundary $\dot{\vec{p}}_{out}$ is equal to $\iint_{r} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The difference between the inflow of momentum (indicated by the blue vector below the drawing) and the outflow of momentum (indicated by the red vector below the drawing) is the force exerted on the volume of air. The thrust (indicated by the black vector) is the reaction force.

 

When we now introduce an angle of attack, the bounding volume will change shape. Also the influx and outflux momentum will be different. What is most important is that the thrust generated is no longer purely axial; the thrust vector develops a transverse component. This is the additional lift (and a bit of drag) that the engine creates a high angle of attack.

enter image description here

When the engine is mounted well in front of the centre of gravity, a high angle of attack / high thrust situation will cause an upward pitching moment. This is the case in the Boeing 737 MAX where this effect was changing the handling characteristics at high angles of attack. To make sure the handling would be similar to earlier 737 models, Boeing introduced the - now infamous - Maneuvering Characteristics Augmentation System (MCAS).

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An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards. For an aircraft that flies a horizontal path at high angle of attack, the airflow approaches the engine horizontally and leaves the engine in a downward angle, close to the negative angle of attack.

In order to make the flow turn downwards, the engine must exert a downward force on the airflow. According to the third law of Newton,there is an opposite force on the engine. The component of this force that is perpendicular to the incoming undisturbed airflow is the additional lift force caused by the engine.

This additional lift is independent of the tilted thrust force vector.

enter image description here