staticStability
Class: Aero.FixedWing
Namespace: Aero
Syntax
stability = staticStability(aircraft,state)
stability = staticStability(___,Name,Value)
[stability,derivatives] = staticStability(___)
Description
calculates the static stability stability
= staticStability(aircraft
,state
)stability
of a fixedwing aircraft
aircraft
at an Aero.FixedWing.State
state
. This method calculates static stability from changes in body
forces and moments due to perturbations of an aircraft state. By default, these states are
airspeed, angle of attack, angle of side slip, and body roll rates. To change these states,
see criteriaTable
.
The staticStability
method evaluates the changes in body forces and
moments after a perturbation as either greater than, equal to, or less than 0 using the
matching entry in the criteria table.
If the evaluation of a criterion is met, the aircraft is statically stable at that condition.
If the evaluation of a criterion is not met, the aircraft is statically unstable at that condition.
If the perturbation value is set to
0
, the aircraft is statically neutral at that condition.
calculates the static stability result with the specified stability
= staticStability(___,Name,Value
)Name,Value
arguments. Specify any of the input argument combinations in the previous syntaxes followed by
Name,Value
pairs as the last input arguments.
[
returns the body forces and moments derivatives table along with the static stability. Specify
any of the input argument combinations in the previous syntaxes.stability
,derivatives
] = staticStability(___)
Input Arguments
aircraft
— Aero.FixedWing
object
scalar
Aero.FixedWing
object, specified as a scalar.
Data Types: double
state
— Aero.FixedWing.State
object
scalar
Aero.FixedWing.State
object, specified as a scalar.
Data Types: double
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'RelativePerturbation','1e5'
CriteriaTable
— Static stability test criteria
6by8 table (default)  6byN table
Static stability test criteria, specified as a 6byN table, where N is number of variables.
If the value being evaluated is 0, it is neutral.
If the value being evaluated does not meet the criteria, it is unstable.
If the criterion is an empty string or is missing, then the stability result is an empty string.
The criteria table has these requirements:
Each entry in the criteria table must be
'<'
,'>'
,''
, or missing.The table must have six rows:
'FX'
,'FY'
,'FZ'
,'L'
,'M'
, and'N'
.N number of variables for columns.
By default, this table appears as:
U  V  W  Alpha  Beta  P  Q  R  

FX  '<'  ''  ''  ''  ''  ''  ''  '' 
FY  ''  '<'  ''  ''  ''  ''  ''  '' 
FZ  ''  ''  '<'  ''  ''  ''  ''  '' 
L  ''  ''  ''  ''  ''  '<'  '<'  '' 
M  '>'  ''  ''  '<'  ''  ''  '<'  '' 
N  ''  ''  ''  ''  '>'  ''  ''  '<' 
Data Types: string
RelativePerturbation
— Relative perturbation
1e5
(default)  scalar numeric
Relative perturbation of the system, specified as a scalar numeric. This perturbation takes the form of:
Perturbation Type  Definition 

System State perturbation 

System input perturbation 

To calculate the Jacobian of the system, linearize
uses the
result of these equations in conjunction with the
'DifferentialMethod'
property.
Example: 'RelativePerturbation',1e5
Data Types: double
DifferentialMethod
— Direction while perturbing model
'Forward'
(default)  'Backward'
 'Central'
Direction while perturbing, specified as 'Forward'
,
'Backward'
, or 'Central'
.
Direction  Description 

 Forward difference method that adds 
 Backward difference method that adds statePert and
ctrlPert to the base states an inputs,
respectively. 
 Central difference method that adds and subtracts

Example: 'DifferentialMethod','Backward'
Data Types: char
 string
OutputReferenceFrame
— Output reference
"Body"
(default)  "Wind"
 "Stability"
Output reference of the forces and moments calculation, specified as:
"Body"
"Wind"
"Stability"
Example: OutputReferenceFrame="Stability"
Output Arguments
stability
— Stability of fixedwing aircraft
6byN table
Stability of fixedwing aircraft, returned as a 6byN table.
derivatives
— Forces and moments derivatives
6byN table
Forces and moments derivatives output in OutputReferenceFrame
,
returned as a 6byN table.
Examples
Calculate Static Stability
These examples show how to calculate static stability.
Calculate Static Stability of Cessna C182
Calculate the static stability of a Cessna C182.
[C182, CruiseState] = astC182(); stability = staticStability(C182, CruiseState)
stability=6×8 table
U V W Alpha Beta P Q R
________ ________ ________ ________ ________ ________ ________ ________
FX "Stable" "" "" "" "" "" "" ""
FY "" "Stable" "" "" "" "" "" ""
FZ "" "" "Stable" "" "" "" "" ""
L "" "" "" "" "Stable" "Stable" "" ""
M "Stable" "" "" "Stable" "" "" "Stable" ""
N "" "" "" "" "Stable" "" "" "Stable"
Calculate Static Stability of Cessna C182 with Custom Criteria Table
Calculate the static stability of a Cessna C182 with a custom criteria table.
[C182, CruiseState] = astC182(); CT = C182.criteriaTable()
CT=6×8 table
U V W Alpha Beta P Q R
___ ___ ___ _____ ____ ___ ___ ___
FX "<" "" "" "" "" "" "" ""
FY "" "<" "" "" "" "" "" ""
FZ "" "" "<" "" "" "" "" ""
L "" "" "" "" "<" "<" "" ""
M ">" "" "" "<" "" "" "<" ""
N "" "" "" "" ">" "" "" "<"
CT{"FX", "U"} = ">"
CT=6×8 table
U V W Alpha Beta P Q R
___ ___ ___ _____ ____ ___ ___ ___
FX ">" "" "" "" "" "" "" ""
FY "" "<" "" "" "" "" "" ""
FZ "" "" "<" "" "" "" "" ""
L "" "" "" "" "<" "<" "" ""
M ">" "" "" "<" "" "" "<" ""
N "" "" "" "" ">" "" "" "<"
stability = staticStability(C182, CruiseState, "CriteriaTable", CT)
stability=6×8 table
U V W Alpha Beta P Q R
__________ ________ ________ ________ ________ ________ ________ ________
FX "Unstable" "" "" "" "" "" "" ""
FY "" "Stable" "" "" "" "" "" ""
FZ "" "" "Stable" "" "" "" "" ""
L "" "" "" "" "Stable" "Stable" "" ""
M "Stable" "" "" "Stable" "" "" "Stable" ""
N "" "" "" "" "Stable" "" "" "Stable"
Calculate Static Stability of Cessna C182 with Central Differential Method
Calculate the static stability of a Cessna C182 using the central differential method.
[C182, CruiseState] = astC182(); stability = staticStability(C182, CruiseState, "DifferentialMethod", "Central")
stability=6×8 table
U V W Alpha Beta P Q R
________ ________ ________ ________ ________ ________ ________ ________
FX "Stable" "" "" "" "" "" "" ""
FY "" "Stable" "" "" "" "" "" ""
FZ "" "" "Stable" "" "" "" "" ""
L "" "" "" "" "Stable" "Stable" "" ""
M "Stable" "" "" "Stable" "" "" "Stable" ""
N "" "" "" "" "Stable" "" "" "Stable"
Calculate Static Stability and Derivatives of Cessna C182
Calculate the static stability and derivatives of a Cessna C182.
[C182, CruiseState] = astC182(); [stability,derivatives] = staticStability(C182, CruiseState)
stability=6×8 table
U V W Alpha Beta P Q R
________ ________ ________ ________ ________ ________ ________ ________
FX "Stable" "" "" "" "" "" "" ""
FY "" "Stable" "" "" "" "" "" ""
FZ "" "" "Stable" "" "" "" "" ""
L "" "" "" "" "Stable" "Stable" "" ""
M "Stable" "" "" "Stable" "" "" "Stable" ""
N "" "" "" "" "Stable" "" "" "Stable"
derivatives=6×8 table
U V W Alpha Beta P Q R
_______ ___________ _______ _______ _________ _______ _______ _______
FX 2486.2 3.4925e05 7.1825 1080.3 1.8242 0 0 0
FY 0 15.413 0 0 3392.4 52.945 0 151.07
FZ 23.856 4.956e07 174.01 38338 0.026253 0 374.73 0
L 0 130.31 0 0 28682 12300 0 2028
M 17.236 3.638e07 129.74 28528 0.018968 0 5863.8 0
N 0 83.934 0 0 18474 702.86 0 2391.6
Version History
Introduced in R2021a
See Also
Aero.FixedWing
 criteriaTable
 forcesAndMoments
 linearize
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