Aerodynamic Forces and Moments

Calculation of aerodynamic forces and moment.

blockType: SubSystem

Path in the library:

/Aerospace/Aerodynamics/Aerodynamic Forces and Moments

Description

Block Aerodynamic Forces and Moments calculates the components of the aerodynamic force and the aerodynamic moment relative to the center of gravity of the aircraft, taking into account the selected coordinate systems for the input signals, force and moment.

The block uses coordinate systems according to the international standard ISO 1151.

The components of aerodynamic force:

where

— coefficient of longitudinal (axial) force;
— lateral force coefficient;
— the coefficient of normal force;
— high-speed pressure;
— the reference area.

Components of the aerodynamic moment:

where

— coefficient of longitudinal (axial) force;
— lateral force coefficient;
— the coefficient of normal force;
— roll moment coefficient;
— the coefficient of pitch moment;
— coefficient of yaw moment;
— high-speed pressure;
— reference area;
— wingspan (reference size for roll and yaw moments);
— average aerodynamic chord (reference size for pitch moment);
, , — coordinates of the center of gravity;
, , — coordinates of the pressure center.

Conversion of coefficients and axes

The unit supports operation in connected, semi-connected, and velocity coordinate systems for input signals, force, and moment. Internal transformations are performed using angles of attack and sliding and rotation matrices.

Rotation from a connected coordinate system to a semi-connected one:

Turning from a semi-connected coordinate system to a high-speed one:

The final turn from a connected coordinate system to a high-speed one:

The aerodynamic force can be recorded in different coordinate systems in the same way. The force coefficients are shown below. No separate new symbols are introduced for the semi-connected coordinate system: the same symbols are used as in the others (the two components match).

The coefficients of moments in different coordinate systems use the same notation. . Diagonal matrices of signs are used in the block to coordinate the standard designations of the force coefficients in the velocity and semi-connected coordinate systems.:

The relationship between the normal and vertical components in the associated coordinate system is also used.: .

Ports

Entrance

# Coef — aerodynamic coefficients

+ The vector is 6 by 1

Details

The coefficients of the components of the aerodynamic force and moment along the axes in the associated coordinate system, specified as a vector. Vector elements:

— coefficient of longitudinal force.
— the coefficient of normal force.
— coefficient of lateral force.
— roll moment coefficient ( ).
— coefficient of yaw moment ( ).
— pitch moment coefficient ( ).

Dependencies

The lower index in the port name depends on the one selected in the parameter Input axes: coordinate systems:

Body — port name Coef_body;
Stability — port name Coef_stab;
Wind — port name Coef_wind.

Типы данных	`Float64`
Support for complex numbers	None

# q_bar — high- speed pressure

+ a 3-by-1 vector

Details

The velocity pressures calculated from the components of the speed of the aircraft along the axes of the associated coordinate system, specified as a vector.

Типы данных	`Float64`
Support for complex numbers	None

# CG — coordinates of the center of gravity

+ a 3-by-1 vector

Details

Coordinates of the aircraft’s center of gravity. They are measured in units of length, specified as a vector.

Типы данных	`Float64`
Support for complex numbers	None

# CP — coordinates of the pressure center

+ a 3-by-1 vector

Details

Coordinates of the aircraft’s pressure center, set as a vector. They are measured in units of length.

Типы данных	`Float64`
Support for complex numbers	None

# Vb — components of the speed of the aircraft

+ a 3-by-1 vector

Details

The components of the speed of the aircraft, set as a vector.

Dependencies

To use this port, set at least one of the parameters Input axes:, Force axes:, Moment axes: meaning Stability or Wind.

Типы данных	`Float64`
Support for complex numbers	None

Output

# F — aerodynamic forces

+ a 3-by-1 vector

Details

The components of the aerodynamic force relative to the center of mass of the aircraft in the associated coordinate system, specified as a vector. Vector elements:

— longitudinal force.
— normal strength.
— lateral force.

They are measured in units of force.

Dependencies

The lower index in the port name depends on the one selected in the parameter Force axes: coordinate systems:

Body — port name F_body;
Stability — port name F_stab;
Wind — port name F_wind.

Типы данных	`Float64`
Support for complex numbers	None

# M — aerodynamic moments

+ a 3-by-1 vector

Details

The components of the aerodynamic force relative to the center of mass of the aircraft in the associated coordinate system, specified as a vector. Vector elements:

— longitudinal force.
— normal strength.
— lateral force.

They are measured in units of force.

Dependencies

The lower index in the port name depends on the one selected in the parameter Moment axes: coordinate systems:

Body — port name M_body;
Stability — port name M_stab;
Wind — port name M_wind.

Типы данных	`Float64`
Support for complex numbers	None

Parameters

Main

# Input axes: — coordinate system for the input aerodynamic coefficients
Body | Stability | Wind

Details

The coordinate system for the input aerodynamic coefficients.

If values are set for this parameter Stability or Wind, then the input port Vb is used in the block.

Values	`Body` \| `Stability` \| `Wind`
Default value	`Body`
Program usage name	`inputAxes`
Tunable	No
Evaluatable	Yes

# Force axes: — coordinate system for aerodynamic force
Body | Stability | Wind

Details

The coordinate system for the aerodynamic force.

If values are set for this parameter Stability or Wind, then the input port Vb is used in the block.

Values	`Body` \| `Stability` \| `Wind`
Default value	`Body`
Program usage name	`outputForceAxes`
Tunable	No
Evaluatable	Yes

# Moment axes: — the coordinate system for the aerodynamic moment
Body | Stability | Wind

Details

The coordinate system for the aerodynamic moment.

If values are set for this parameter Stability or Wind, then the input port Vb is used in the block.

Values	`Body` \| `Stability` \| `Wind`
Default value	`Body`
Program usage name	`outputMomentAxes`
Tunable	No
Evaluatable	Yes

# Reference area — characteristic area

Details

The characteristic area of the aircraft. It is measured in units of area. For an airplane, the wing area is usually taken as the characteristic area.

Default value	`1.0`
Program usage name	`S`
Tunable	No
Evaluatable	Yes

# Reference span — the average aerodynamic chord of the wing

Details

The average aerodynamic chord of the wing. It is measured in units of length.

Default value	`1.0`
Program usage name	`b`
Tunable	No
Evaluatable	Yes

# Reference length — characteristic linear size

Details

The characteristic linear size of the aircraft. It is measured in units of length. For an aircraft, the wingspan is usually taken as the characteristic linear size.

Default value	`1.0`
Program usage name	`cbar`
Tunable	No
Evaluatable	Yes