#include <Kinematics.h>

Static Public Member Functions
static double	turnRadius (double speed, double bank, double g)

static double	turnRadius (double speed, double bank)

static double	turnRadiusByRate (double speed, double omega)

static double	speedOfTurn (double R, double bank)

static double	turnRate (double speed, double bankAngle)

static double	bankAngleRadius (double R, double speed)

static double	bankAngleRadius (double speed, double R, bool turnRight)

static double	bankAngle (double speed, double turnRate)

static double	bankAngleGoal (double track, double goalTrack, double maxBank)

static double	turnRateGoal (const Velocity &vo, double goalTrack, double maxBank)

static bool	turnDone (double currentTrack, double targetTrack, bool turnRight)

static double	turnTime (const Velocity &v0, double goalTrack, double maxBank, bool turnRight)

static double	turnTime (const Velocity &v0, double goalTrack, double maxBank)

static double	turnTime (double groundSpeed, double deltaTrack, double bankAngle)

static double	turnTime (double deltaTrack, double trackRate)

static bool	turnRight (const Velocity &v0, double goalTrack)

static std::pair< Vect3, Velocity >	linear (const std::pair< Vect3, Velocity > &sv0, double t)

static std::pair< Vect3, Velocity >	linear (Vect3 so, Velocity vo, double t)

static std::pair< Vect3, Velocity >	turnOmega (const Vect3 &s0, const Velocity &v0, double t, double omega)

static Vect2	center (const Vect3 &s0, const Velocity &v0, double omega)

static std::pair< Vect3, Velocity >	turnByDist2D (const Vect3 &so, const Vect3 &center, int dir, double d, double gsAt_d)
	‍ * EXPERIMENTAL *** More...

static Vect3	turnByDist2D (const Vect3 &so, const Vect3 &center, int dir, double d)

static Vect3	turnByAngle2D (const Vect3 &so, const Vect3 &center, double alpha)

static std::pair< Vect3, Velocity >	turnOmega (const std::pair< Vect3, Velocity > &sv0, double t, double omega)

static std::pair< Vect3, Velocity >	turn (const Vect3 &s0, const Velocity &v0, double t, double R, bool turnRight)

static std::pair< Vect3, Velocity >	turn (const std::pair< Vect3, Velocity > &sv0, double t, double R, bool turnRight)

static std::pair< Vect3, Velocity >	turn (const Vect3 &s0, const Velocity &v0, double t, double bank)

static std::pair< Vect3, Velocity >	turnUntil (const Vect3 &so, const Velocity &vo, double t, double goalTrack, double maxBank)

static std::pair< Vect3, Velocity >	turnUntil (const std::pair< Vect3, Velocity > &sv0, double t, double goalTrack, double maxBank)

static std::pair< Vect3, Velocity >	turnUntilTimeRadius (std::pair< Vect3, Velocity > svo, double t, double turnTime, double R, bool turnRight)

static std::pair< Vect3, Velocity >	turnUntilTimeOmega (const Vect3 &so, const Velocity &vo, double t, double turnTime, double omega)

static std::pair< Vect3, Velocity >	turnUntilTimeOmega (const std::pair< Vect3, Velocity > &svo, double t, double turnTime, double omega)

static Vect3	positionAfterTurn (const Vect3 &so, const Velocity &vo, double goalTrack, double bankAngle)

static double	closestTimeOnTurn (const Vect3 &s0, const Velocity &v0, double omega, const Vect3 &x, double endTime)

static double	closestDistOnTurn (const Vect3 &s0, const Velocity &v0, double R, int dir, const Vect3 &x, double maxDist)

static std::pair< Vect2, Vect2 >	directTo (const Vect2 &bot, const Vect2 &v0, const Vect2 &goal, double R)

static Quad< Vect3, Velocity, double, int >	directToPoint (const Vect3 &so, const Velocity &vo, const Vect3 &wp, double R)

static Triple< Vect3, double, double >	genDirectToVertex (const Vect3 &so, const Velocity &vo, const Vect3 &wp, double bankAngle, double timeBeforeTurn)

static Vect2	centerOfTurn (const Vect2 &so, const Vect2 &vo, double R, int dir)

static Vect2	centerOfTurn (const Vect2 &so, const Vect2 &vo, double bankAngle, bool turnRight)

static bool	testLoSTrk (const Vect3 &so, const Velocity &vo, const Velocity &nvo, const Vect3 &si, const Velocity &vi, double bankAngleOwn, double stopTime, double D, double H)

static Vect3	gsAccelPos (const Vect3 &so3, const Velocity &vo3, double t, double a)

static std::pair< Vect3, Velocity >	gsAccel (const Vect3 &so3, const Velocity &vo3, double t, double a)

static double	gsAccelTime (double gs0, double goalGs, double gsAccel)

static double	gsAccelTime (const Velocity &vo, double goalGs, double gsAccel)

static Triple< Vect3, Velocity, double >	gsAccelGoal (const Vect3 &so, const Velocity &vo, double goalGs, double gsAccel)

static std::pair< Vect3, Velocity >	gsAccelUntilRWB (const Vect3 &so3, const Velocity &vo3, double t, double goalGS, double gsAccel)

static std::pair< Vect3, Velocity >	gsAccelUntil (const Vect3 &so3, const Velocity &vo3, double t, double goalGS, double gsAccel)

static std::pair< Vect3, Velocity >	gsAccelUntil (const std::pair< Vect3, Velocity > &sv0, double t, double goalGS, double gsAccel)

static std::pair< double, double >	gsAccelToRTA (double gsIn, double dist, double rta, double gsAccel)

static std::pair< double, double >	gsAccelToDist (double gsIn, double dist, double gsAccel)

static double	distanceToGsAccelTime (double gs, double gsAccel, double dist)

static std::pair< double, double >	distanceWithGsAccel (double gs0, double gsTarget, double gsAccel, double dt)

static double	neededDistGsAccel (double gsIn, double gsTarget, double gsAccel)

static double	gsAccelDist (double gs1, double gs2, double a)

static bool	testLoSGs (const Vect3 &so, const Velocity &vo, const Velocity &nvo, const Vect3 &si, const Velocity &vi, double gsAccelOwn, double stopTime, double D, double H)

static double	elevationAngle (Velocity v)

static Vect3	vsAccelPos (const Vect3 &so3, const Velocity &vo3, double t, double a)

static std::pair< Vect3, Velocity >	vsAccel (const Vect3 &so3, const Velocity &vo3, double t, double a)

static std::pair< Vect3, Velocity >	vsAccel (const std::pair< Vect3, Velocity > &sv0, double t, double a)

static double	vsAccelTime (double vs, double goalVs, double vsAccel)

static double	vsAccelTime (const Velocity &vo, double goalVs, double vsAccel)

static Triple< Vect3, Velocity, double >	vsAccelGoal (const Vect3 &so, const Velocity &vo, double goalVs, double vsAccel)

static std::pair< Vect3, Velocity >	vsAccelUntil (const Vect3 &so, const Velocity &vo, double t, double goalVs, double vsAccel)

static std::pair< Vect3, Velocity >	vsAccelUntil (const std::pair< Vect3, Velocity > &sv0, double t, double goalVs, double vsAccel)

static bool	testLoSVs (const Vect3 &so, const Velocity &vo, const Velocity &nvo, const Vect3 &si, const Velocity &vi, double vsAccelOwn, double stopTime, double D, double H)

static StateVector	vsLevelOutFinal (const std::pair< Vect3, Velocity > &sv0, double climbRate, double targetAlt, double a, bool allowClimbRateChange)

static StateVector	vsLevelOutFinal (const std::pair< Vect3, Velocity > &sv0, double climbRate, double targetAlt, double a)

static bool	overShoot (const std::pair< Vect3, Velocity > &svo, double climbRate, double targetAlt, double accelup, double acceldown, bool allowClimbRateChange)

static Tuple5< double, double, double, double, double >	vsLevelOutTimes (double s0z, double v0z, double climbRate, double targetAlt, double accelup, double acceldown, bool allowClimbRateChange)

static Tuple5< double, double, double, double, double >	vsLevelOutTimes (const std::pair< Vect3, Velocity > &svo, double climbRate, double targetAlt, double accelup, double acceldown, bool allowClimbRateChange)

static Tuple5< double, double, double, double, double >	vsLevelOutTimes (const std::pair< Vect3, Velocity > &svo, double climbRate, double targetAlt, double a, bool allowClimbRateChange)

static Tuple5< double, double, double, double, double >	vsLevelOutTimes (const std::pair< Vect3, Velocity > &svo, double climbRate, double targetAlt, double a)

static double	vsLevelOutClimbRate (const std::pair< Vect3, Velocity > &svo, double climbRate, double targetAlt, double accelup, double acceldown, bool allowClimbRateChange)

static double	vsLevelOutTime (const std::pair< Vect3, Velocity > &sv0, double climbRate, double targetAlt, double a, bool allowClimbRateChange)

static double	vsLevelOutTime (const std::pair< Vect3, Velocity > &sv0, double climbRate, double targetAlt, double a)

static std::pair< double, double >	vsLevelOutCalc (double soz, double voz, double targetAlt, double a1, double a2, double t1, double t2, double t3, double t)

static std::pair< Vect3, Velocity >	vsLevelOutCalculation (const std::pair< Vect3, Velocity > &sv0, double targetAlt, double a1, double a2, double t1, double t2, double t3, double t)

static std::pair< Vect3, Velocity >	vsLevelOut (const std::pair< Vect3, Velocity > &sv0, double t, double climbRate, double targetAlt, double accelUp, double accelDown, bool allowClimbRateChange)

static std::pair< Vect3, Velocity >	vsLevelOut (const std::pair< Vect3, Velocity > &sv0, double t, double climbRate, double targetAlt, double a, bool allowClimbRateChange)

static std::pair< Vect3, Velocity >	vsLevelOut (const std::pair< Vect3, Velocity > &sv0, double t, double climbRate, double targetAlt, double a)

static double	tau (const Vect3 &s, const Vect3 &vo, const Vect3 &vi)

static double	distAtTau (const Vect3 &s, const Vect3 &vo, const Vect3 &vi, bool futureOnly)

Static Private Member Functions
static double	dirSign (bool turnRight)

static std::pair< Vect3, Velocity >	vsLevelOutCalculation (const std::pair< Vect3, Velocity > &sv0, double t, double T1, double T2, double T3, double climbRate, double targetAlt, double a1, double a2)

static Tuple5< double, double, double, double, double >	vsLevelOutTimesBase (double s0z, double v0z, double climbRate, double targetAlt, double accelup, double acceldown, bool allowClimbRateChange)
	‍** More...

Detailed Description

A library of functions to aid the computation of the kinematics of an aircraft. This library is currently under development and is far from complete. The majority of the functions handle constant velocity turns and movement with constant ground speed acceleration.

Unless otherwise noted, all kinematics function parameters are in internal units – angles are in radians, linear speeds are in m/s, distances are in meters, time is in seconds.

Member Function Documentation

◆ bankAngle()

double larcfm::Kinematics::bankAngle	(	double	speed,
		double	turnRate
	)

static

Returns the calculated bank angle for a turn that has specified turnRate. Assumes sea-level gravity.

Parameters

speed	ground speed (speed ≥ 0.0)
turnRate	(positive is a right turn)

Returns: bank angle (positive = turn right, negative = turn left)

◆ bankAngleGoal()

double larcfm::Kinematics::bankAngleGoal	(	double	track,
		double	goalTrack,
		double	maxBank
	)

static

Find the minimum turn for the to reach the goal and returns the maxBank angle, with the correct sign to achieve that goal. Assumes sea-level gravity.

Parameters

track	the current track
goalTrack	the goal track angle
maxBank	the maximum bank angle, must be in (0,pi/2)

Returns: bank angle (positive = turn right, negative = turn left)

◆ bankAngleRadius() [1/2]

double larcfm::Kinematics::bankAngleRadius	(	double	R,
		double	speed
	)

static

Calculates the bank angle used for a given turn radius and ground speed.
Because this method does not have enough information, it always returns a positive bank angle (indicating a right hand turn). Assumes sea-level gravity. If R <= 0.0, this returns 0.

Parameters

speed	ground speed
R	radius

Returns: bank angle (positive)

◆ bankAngleRadius() [2/2]

double larcfm::Kinematics::bankAngleRadius	(	double	speed,
		double	R,
		bool	turnRight
	)

static

Calculates the bank angle used for a given turn radius and ground speed. Assumes sea-level gravity.

Parameters

speed	ground speed (speed ≥ 0.0)
R	radius (R > 0.0)
turnRight	true, if a right turn is desired

Returns: bank angle (positive = turn right, negative = turn left)

◆ centerOfTurn() [1/2]

Vect2 larcfm::Kinematics::centerOfTurn	(	const Vect2 &	so,
		const Vect2 &	vo,
		double	bankAng,
		bool	turnRight
	)

static

find center of turn determined by line (so,vo) with bankAngle and direction (turnRight)

Parameters

so	position
vo	velocity
bankAngle	bank angle
turnRight	right turn (left otherwise)

Returns: two dimensional position of turn

find center of turn determined by line (so,vo) with bankAngle and direction TurnRight

Parameters

so
vo
R
dir	direction: 1 = right, -1 = left

Returns

◆ centerOfTurn() [2/2]

Vect2 larcfm::Kinematics::centerOfTurn	(	const Vect2 &	so,
		const Vect2 &	vo,
		double	R,
		int	dir
	)

static

find center of turn determined by line (so,vo) with radius R and direction dir

Parameters

so	position
vo	velocity
R	radius of turn
dir	direction: 1 = right, -1 = left

Returns: two dimensional position of turn

find center of turn determined by line (so,vo) with radius R and direction dir

Parameters

so
vo
R
dir	direction: 1 = right, -1 = left

Returns

◆ closestDistOnTurn()

double larcfm::Kinematics::closestDistOnTurn	(	const Vect3 &	s0,
		const Velocity &	v0,
		double	R,
		int	dir,
		const Vect3 &	x,
		double	maxDist
	)

static

Calculate when during the turn we will be closest to the given point.

Parameters

s0	turn start position
v0	turn start velocity
R	turn radius
dir	direction of turn
x	point of interest
maxDist	distance at which turn finishes. If ≤ 0, assume a full turn is allowed.

Returns: distance on turn when we are closest to the given point x, or -1 if we are precisely at the turn's center This will be bounded by [0,maxDist]

◆ closestTimeOnTurn()

double larcfm::Kinematics::closestTimeOnTurn	(	const Vect3 &	s0,
		const Velocity &	v0,
		double	omega,
		const Vect3 &	x,
		double	endTime
	)

static

Calculate when during the turn we will be closest to the given point.

Parameters

s0	turn start position
v0	turn start velocity
omega	rate of turn (+ = right, - = left)
x	point of interest
endTime	time at which turn finishes. If ≤ 0, assume a full turn is allowed.

Returns: time on turn when we are closest to the given point x (in seconds), or -1 if we are precisely at the turn's center This will be bounded by [0,endTime]

◆ directTo()

std::pair< Vect2, Vect2 > larcfm::Kinematics::directTo	(	const Vect2 &	bot,
		const Vect2 &	v0,
		const Vect2 &	goal,
		double	R
	)

static

Given an initial position, initial velocity, and goal position (outside of the turn radius) calculate the end of turn and center of turn

Parameters

bot	initial position (i.e. beginning of turn)
v0	initial velocity
goal	goal position
R	turn radius

Returns: end of turn, center of turn

◆ distanceToGsAccelTime()

double larcfm::Kinematics::distanceToGsAccelTime	(	double	gs,
		double	gsAccel,
		double	dist
	)

static

The time required to cover distance "dist" if initial speed is "gs" and acceleration is "gsAccel"

Parameters

gs	initial ground speed
gsAccel	signed ground speed acceleration
dist	non-negative distance

Returns: time required to cover distance

Warning: This function can return NaN

◆ distanceWithGsAccel()

std::pair< double, double > larcfm::Kinematics::distanceWithGsAccel	(	double	gs0,
		double	gsTarget,
		double	gsAccel,
		double	dt
	)

static

distance traveled when accelerating from gs0 to gsTarget for time dt (acceleration stops after gsTarget is reached)

Parameters

gs0	initial ground speed
gsTarget	target ground speed
gsAccel	positive ground speed acceleration
dt	total time traveling

Returns: total distance traveled

Note: if gsAccel = 0 it returns gs0*dt

◆ distAtTau()

static double larcfm::Kinematics::distAtTau	(	const Vect3 &	s,
		const Vect3 &	vo,
		const Vect3 &	vi,
		bool	futureOnly
	)

static

distance at time of closest approach

Parameters

s	relative position of aircraft
vo	velocity of ownship
vi	velocity of traffic
futureOnly	if true then in divergent cases use distance now

Returns: distance at time of closest approach

◆ elevationAngle()

double larcfm::Kinematics::elevationAngle ( Velocity v )

static

Return the elevation angle (alternatively the negative glide-slope angle) for a climb (descent)

Parameters

v velocity

Returns: elevation angle [radians]

Return the elevation angle (alternatively the negative glide-slope angle) for a climb (descent)

Returns: elevation angle [radians]

◆ gsAccel()

std::pair< Vect3, Velocity > larcfm::Kinematics::gsAccel	(	const Vect3 &	so3,
		const Velocity &	vo3,
		double	t,
		double	a
	)

static

Position/Velocity after a constant GS acceleration for t seconds

Parameters

so3	current position
vo3	current velocity
t	amount of time accelerating
a	acceleration, i.e. a positive or negative acceleration

Returns: position/velocity at time t

◆ gsAccelDist()

double larcfm::Kinematics::gsAccelDist	(	double	gs1,
		double	gs2,
		double	a
	)

static

Distance traveled when accelerating from gs1 to gs2

Parameters

gs1	starting ground speed
gs2	ending ground speed
a	acceleration value (unsigned)

Returns: distance needed to accelerate from gs1 to gs2 with acceleration a. This returns 0 if a=0 or gs1=gs2.

Distance traveled when accelerating from gs1 to gs2

Parameters

gs1	starting gs
gs2	ending gs
a	acceleration value (unsigned)

Returns: distance needed to accelerate from gs1 to gs2 with acceleration a. This returns 0 if a=0 or gs1=gs2.

◆ gsAccelPos()

Vect3 larcfm::Kinematics::gsAccelPos	(	const Vect3 &	so3,
		const Velocity &	vo3,
		double	t,
		double	a
	)

static

Final 3D position after a constant GS acceleration for t seconds

Parameters

so3	current position
vo3	current velocity
a	acceleration, i.e. a positive or negative acceleration
t	amount of time accelerating

Returns: final position

◆ gsAccelTime() [1/2]

double larcfm::Kinematics::gsAccelTime	(	const Velocity &	vo,
		double	goalGs,
		double	gsAccel
	)

static

returns time required to accelerate to target ground speed GoalGs

Parameters

vo	current velocity
goalGs	ground speed where the acceleration stops
gsAccel	ground speed acceleration (a positive value)

Returns: acceleration time

◆ gsAccelTime() [2/2]

double larcfm::Kinematics::gsAccelTime	(	double	gs0,
		double	goalGs,
		double	gsAccel
	)

static

returns time required to accelerate to target ground speed GoalGs

Parameters

gs0	current ground speed
goalGs	ground speed where the acceleration stops
gsAccel	ground speed acceleration (a positive value)

Returns: acceleration time

◆ gsAccelToDist()

std::pair< double, double > larcfm::Kinematics::gsAccelToDist	(	double	gsIn,
		double	dist,
		double	gsAccel
	)

static

Accelerate for a given distance. Return the end gs and time. Negative time indicates an error.

◆ gsAccelToRTA()

std::pair< double, double > larcfm::Kinematics::gsAccelToRTA	(	double	gsIn,
		double	dist,
		double	rta,
		double	gsAccel
	)

static

Compute the goal ground speed and time needed to accelerate in order to reach a point at a given required time of arrival.

Parameters

gsIn	Current ground speed (m/s)
dist	Current horizontal distance to goal point (m)
rta	(relative) required time of arrival (s)
gsAccel	maximum ground speed acceleration or deceleration (positive, m/s^2)

Returns: the goal ground speed and acceleration duration needed in order to cover the given distance in the given time. The time will be negative if the rta is not attainable.

◆ gsAccelUntilRWB()

static std::pair< Vect3, Velocity > larcfm::Kinematics::gsAccelUntilRWB	(	const Vect3 &	so3,
		const Velocity &	vo3,
		double	t,
		double	goalGS,
		double	gsAccel
	)

static

Position after t time units where there is first an acceleration or deceleration to the target ground speed goalGS and then continuing at that speed for the remainder of the time, if any.

Parameters

so	starting position
vo	initial velocity
goalGS	the ground speed where the acceleration stops
gsAccel	the ground speed acceleration (a positive value)
t	time of acceleration [secs]

Returns: Position after time t

◆ linear()

std::pair< Vect3, Velocity > larcfm::Kinematics::linear	(	const std::pair< Vect3, Velocity > &	sv0,
		double	t
	)

static

Parameters

sv0	Pair (initial position, initial velocity)
t	time of travel

Returns: new position after traveling straight for t units of time

◆ neededDistGsAccel()

double larcfm::Kinematics::neededDistGsAccel	(	double	gsIn,
		double	gsTarget,
		double	gsAccel
	)

static

distance traveled when accelerating from gsIn to gsTarget

Parameters

gsIn	initial ground speed
gsTarget	target ground speed
gsAccel	positive ground speed acceleration

See also gsAccelDist will give same answer

Returns: total distance traveled when accelerating from gs0 to gsTarget

◆ positionAfterTurn()

Vect3 larcfm::Kinematics::positionAfterTurn	(	const Vect3 &	so,
		const Velocity &	vo,
		double	goalTrack,
		double	bankAngle
	)

static

Position after turning to track goalTrack, assumes less than 180 degree turn

Parameters

so	starting position
vo	initial velocity
goalTrack	the track angle where the turn stops
bankAngle	the bank angle of the aircraft making the turn

Returns: Position after time t

◆ speedOfTurn()

double larcfm::Kinematics::speedOfTurn	(	double	R,
		double	bank
	)

static

Calculates ground speed of the vehicle from radius R and the bank angle. Assumes sea-level gravity.

Parameters

R	radius, must be non-negative
bank	bank angle, must be in (-pi/2,pi/2)

Returns: speed

◆ tau()

static double larcfm::Kinematics::tau	(	const Vect3 &	s,
		const Vect3 &	vo,
		const Vect3 &	vi
	)

static

time of closest approach, if parallel return Double.MAX_VALUE

Parameters

s	relative position of aircraft
vo	velocity of ownship
vi	velocity of traffic

Returns: time of closest approach (can be negative)

◆ testLoSGs()

bool larcfm::Kinematics::testLoSGs	(	const Vect3 &	so,
		const Velocity &	vo,
		const Velocity &	nvo,
		const Vect3 &	si,
		const Velocity &	vi,
		double	gsAccelOwn,
		double	stopTime,
		double	D,
		double	H
	)

static

Test for LoS(D,H) between two aircraft when only ownship gs accelerates, compute trajectories up to time stopTime

Parameters

so	initial position of ownship
vo	initial velocity of ownship
nvo	the target velocity of ownship (i.e. after turn maneuver complete)
si	initial position of traffic
vi	initial velocity of traffic
gsAccelOwn	ground speed acceleration of the ownship
stopTime	the duration of the turns
D	horizontal distance
H	vertical distance

Returns: minimum distance data packed in a Vect4

◆ testLoSTrk()

bool larcfm::Kinematics::testLoSTrk	(	const Vect3 &	so,
		const Velocity &	vo,
		const Velocity &	nvo,
		const Vect3 &	si,
		const Velocity &	vi,
		double	bankAngleOwn,
		double	stopTime,
		double	D,
		double	H
	)

static

Test for LoS(D,H) between two aircraft when only ownship turns, compute trajectories up to time stopTime

Parameters

so	initial position of ownship
vo	initial velocity of ownship
nvo	the target velocity of ownship (i.e. after turn maneuver complete)
si	initial position of traffic
vi	initial velocity of traffic
bankAngleOwn	the bank angle of the ownship
turnRightOwn	the turn direction of ownship
stopTime	the duration of the turns
D	horizontal distance
H	vertical distance

Returns: minimum distance data packed in a Vect4

◆ testLoSVs()

bool larcfm::Kinematics::testLoSVs	(	const Vect3 &	so,
		const Velocity &	vo,
		const Velocity &	nvo,
		const Vect3 &	si,
		const Velocity &	vi,
		double	vsAccelOwn,
		double	stopTime,
		double	D,
		double	H
	)

static

Test for LoS(D,H) between two aircraft when only ownship gs accelerates, compute trajectories up to time stopTime

Parameters

so	initial position of ownship
vo	initial velocity of ownship
nvo	the target velocity of ownship (i.e. after turn maneuver complete)
si	initial position of traffic
vi	initial velocity of traffic
vsAccelOwn	ground speed acceleration of the ownship
stopTime	the duration of the turns
D	horizontal distance
H	vertical distance

Returns: minimum distance data packed in a Vect4

◆ turn() [1/3]

std::pair< Vect3, Velocity > larcfm::Kinematics::turn	(	const std::pair< Vect3, Velocity > &	sv0,
		double	t,
		double	R,
		bool	turnRight
	)

static

Position/Velocity after turning t time units right or left with bank angle bank

Parameters

sv0	Pair (initial position, initial velocity)
t	time of turn
R	turn radius
turnRight	true iff only turn direction is to the right

Returns: Position/Velocity pair after t time

◆ turn() [2/3]

std::pair< Vect3, Velocity > larcfm::Kinematics::turn	(	const Vect3 &	s0,
		const Velocity &	v0,
		double	t,
		double	bank
	)

static

Position/Velocity after turning t time with bank angle bank, direction of turn determined by sign of bank

Parameters

sv0	Pair (initial position, initial velocity)
t	time of turn
bank	bank angle (-pi,pi) (positive = right turn, negative = left turn)

Returns: Position/Velocity after t time

◆ turn() [3/3]

std::pair< Vect3, Velocity > larcfm::Kinematics::turn	(	const Vect3 &	s0,
		const Velocity &	v0,
		double	t,
		double	R,
		bool	turnRight
	)

static

Position/Velocity after turning t time units right or left with bank angle bank

Parameters

s0	starting position
v0	initial velocity
t	time of turn
R	turn radius
turnRight	true iff only turn direction is to the right

Returns: Position/Velocity after t time

◆ turnByAngle2D()

Vect3 larcfm::Kinematics::turnByAngle2D	(	const Vect3 &	so,
		const Vect3 &	center,
		double	alpha
	)

static

Position after turning (does not compute altitude!!)

Note: will be used in a context where altitude is computing subsequently

Parameters

so	starting position
center	center of turn
alpha	turn angle

Returns: position after turn

◆ turnByDist2D() [1/2]

Vect3 larcfm::Kinematics::turnByDist2D	(	const Vect3 &	so,
		const Vect3 &	center,
		int	dir,
		double	d
	)

static

Position after turning (does not compute altitude!!)

Note: will be used in a context where altitude is computing subsequently

Parameters

so	starting position
center	center of turn
dir	direction of turnb
d	distance into turn (sign indicates direction)

Returns: Position after turning distance d

◆ turnByDist2D() [2/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnByDist2D	(	const Vect3 &	so,
		const Vect3 &	center,
		int	dir,
		double	d,
		double	gsAt_d
	)

static

Position/Velocity

Parameters

s0	starting position
center
d	distance into turn
gsAt_d

Returns: Position/Velocity after t time

◆ turnDone()

bool larcfm::Kinematics::turnDone	(	double	currentTrack,
		double	targetTrack,
		bool	turnRight
	)

static

Has the turn completed? Specifically, is the currentTrack at least the targetTrack given that currentTrack is roughly moving in the direction indicated by the parameter turnRight.

Parameters

currentTrack	initial track angle (radians clockwise from true north)
targetTrack	target track angle
turnRight	true iff only turn direction is to the right

Returns: true iff turn has passed Target

◆ turnOmega() [1/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnOmega	(	const std::pair< Vect3, Velocity > &	sv0,
		double	t,
		double	omega
	)

static

Position/Velocity after turning t time units according to track rate omega

Parameters

sv0	initial position and velocity
t	time of turn
omega	rate of change of track, sign indicates direction

Returns: Position/Velocity after t time

◆ turnOmega() [2/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnOmega	(	const Vect3 &	s0,
		const Velocity &	v0,
		double	t,
		double	omega
	)

static

Position/Velocity after turning t time units according to track rate omega

Parameters

s0	starting position
v0	initial velocity
t	time of turn
omega	rate of change of track, sign indicates direction

Returns: Position/Velocity after t time

◆ turnRadius() [1/2]

double larcfm::Kinematics::turnRadius	(	double	speed,
		double	bank
	)

static

Calculates turn radius from ground speed and bank angle. The function assumes standard sea-level gravity, see Units.gn.

Parameters

speed	ground speed
bank	bank angle (positive is clockwise looking out the nose of the aircraft), must be in (-pi/2,pi/2).

Returns: radius (always non-negative)

◆ turnRadius() [2/2]

double larcfm::Kinematics::turnRadius	(	double	speed,
		double	bank,
		double	g
	)

static

Calculates turn radius from ground speed and bank angle.

Parameters

speed	ground speed
bank	bank angle (positive is clockwise looking out the nose of the aircraft), must be in (-pi/2,pi/2).
g	local gravitational acceleration (must be positive)

Returns: radius (always non-negative)

◆ turnRate()

double larcfm::Kinematics::turnRate	(	double	speed,
		double	bankAngle
	)

static

Calculates turn rate (or track-rate) from ground speed and bank angle. Assumes sea-level gravity.

Parameters

speed	ground speed
bankAngle	bank angle, must be in (-pi/2,pi/2)

Returns: turn rate (ie. omega or track rate), positive turn rate is right hand turn.

◆ turnRateGoal()

double larcfm::Kinematics::turnRateGoal	(	const Velocity &	vo,
		double	goalTrack,
		double	maxBank
	)

static

Calculates turn rate (or track-rate) for the minimum turn to the goal track angle. Assumes sea-level gravity.

Parameters

vo	the initial velocity
goalTrack	the goal track angle
maxBank	the maximum bank angle, must be in (0,pi/2)

Returns: turn rate (ie. omega or track rate), positive turn rate is right hand turn.

◆ turnRight()

bool larcfm::Kinematics::turnRight	(	const Velocity &	v0,
		double	goalTrack
	)

static

Returns true if the minimal (i.e. less than 180 deg) turn to goalTrack is tp the right

Parameters

v0	initial velocity vector
goalTrack	target velocity track [rad]

◆ turnTime() [1/3]

double larcfm::Kinematics::turnTime	(	const Velocity &	v0,
		double	goalTrack,
		double	maxBank
	)

static

Returns the time it takes to achieve the goal track when making the minimum turn

Parameters

v0	initial velocity vector
goalTrack	target velocity track [rad]
maxBank	maximum bank angle, must be in (0,pi/2) [rad]

Returns: time to achieve turn

◆ turnTime() [2/3]

double larcfm::Kinematics::turnTime	(	const Velocity &	v0,
		double	goalTrack,
		double	maxBank,
		bool	turnRight
	)

static

Returns the time it takes to achieve the goal track angle

Parameters

v0	initial velocity vector
goalTrack	target velocity track [rad]
maxBank	maximum bank angle, must be in (0,pi/2) [rad]
turnRight	true iff only turn direction is to the right

Returns: time to achieve turn

◆ turnTime() [3/3]

double larcfm::Kinematics::turnTime	(	double	groundSpeed,
		double	deltaTrack,
		double	bankAngle
	)

static

Returns the time it takes to turn the given angle (deltaTrack). Depending on the signs of deltaTrack and bankAngle, this turn can be more than 180 degrees.

Parameters

groundSpeed	ground speed of aircraft
deltaTrack	given angle of turn [rad]
bankAngle	bank angle (-pi/2,pi/2) [rad]

Returns: time to achieve turn

◆ turnUntil() [1/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnUntil	(	const std::pair< Vect3, Velocity > &	sv0,
		double	t,
		double	goalTrack,
		double	maxBank
	)

static

Position/Velocity after t time units turning in minimal direction until goalTrack is reached, after that continue in a straight line

Parameters

sv0	initial position and velocity
t	time of turn [s]
goalTrack	the track angle where the turn stops
maxBank	the maximum bank angle

Returns: Position/Velocity after time t

◆ turnUntil() [2/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnUntil	(	const Vect3 &	so,
		const Velocity &	vo,
		double	t,
		double	goalTrack,
		double	maxBank
	)

static

Position/Velocity after t time units turning in minimal direction until goalTrack is reached, after that continue in a straight line

Parameters

so	starting position
vo	initial velocity
goalTrack	the track angle where the turn stops
bankAngle	the bank angle of the aircraft making the turn
t	time of turn [secs]
turnRight	true iff only turn direction is to the right

Returns: Position/Velocity after time t

◆ turnUntilTimeOmega() [1/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnUntilTimeOmega	(	const std::pair< Vect3, Velocity > &	svo,
		double	t,
		double	turnTime,
		double	omega
	)

static

Position/Velocity after t time units turning at the rate of "omega," after that continue in a straight line. This function can make a turn greater than 180 deg

Parameters

so	initial position and velocity
t	time point of interest
turnTime	total time of turn [secs]
omega	turn rate

Returns: Position/Velocity after time t

◆ turnUntilTimeOmega() [2/2]

std::pair< Vect3, Velocity > larcfm::Kinematics::turnUntilTimeOmega	(	const Vect3 &	so,
		const Velocity &	vo,
		double	t,
		double	turnTime,
		double	omega
	)

static

Position/Velocity after t time units turning in direction "turnRight" for a total of turnTime secs, after that continue in a straight line. This function can make a turn greater than 180 deg

Parameters

so	starting position
vo	initial velocity
t	time point of interest
turnTime	total time of turn [secs]
R	turn radius (positive)
turnRight	true iff only turn direction is to the right

Returns: Position/Velocity after time t

◆ turnUntilTimeRadius()

std::pair< Vect3, Velocity > larcfm::Kinematics::turnUntilTimeRadius	(	std::pair< Vect3, Velocity >	svo,
		double	t,
		double	turnTime,
		double	R,
		bool	turnRight
	)

static

Position/Velocity after t time units turning in direction "turnRight" for a total of turnTime, after that continue in a straight line. This function can make a turn greater than 180 deg

Parameters

so	starting position
vo	initial velocity
t	time point of interest
turnTime	total time of turn [secs]
R	turn radius (positive)
turnRight	true iff only turn direction is to the right

Returns: Position/Velocity after time t

◆ vsAccel()

std::pair< Vect3, Velocity > larcfm::Kinematics::vsAccel	(	const Vect3 &	so3,
		const Velocity &	vo3,
		double	t,
		double	a
	)

static

Position/Velocity after a constant vertical speed acceleration for t seconds

Parameters

so3	current position
vo3	current velocity
t	amount of time accelerating
a	acceleration, i.e. a positive or negative acceleration

Returns: position/velocity at time t

◆ vsAccelPos()

Vect3 larcfm::Kinematics::vsAccelPos	(	const Vect3 &	so3,
		const Velocity &	vo3,
		double	t,
		double	a
	)

static

Final 3D position after a constant VS acceleration for t seconds

Parameters

so3	current position
vo3	current velocity
a	acceleration, i.e. a positive or negative acceleration
t	amount of time accelerating

Returns: final position

◆ vsAccelTime() [1/2]

double larcfm::Kinematics::vsAccelTime	(	const Velocity &	vo,
		double	goalVs,
		double	vsAccel
	)

static

returns time required to vertically accelerate to target GoalVS

Parameters

vo	current velocity
goalVs	vertical speed where the acceleration stops
vsAccel	vertical speed acceleration (a positive value)

Returns: acceleration time

◆ vsAccelTime() [2/2]

double larcfm::Kinematics::vsAccelTime	(	double	vs,
		double	goalVs,
		double	vsAccel
	)

static

returns time required to vertically accelerate to target GoalVS

Parameters

vs	current vertical speed
goalVs	vertical speed where the acceleration stops
vsAccel	vertical speed acceleration (a positive value)

Returns: acceleration time

◆ vsAccelUntil()

std::pair< Vect3, Velocity > larcfm::Kinematics::vsAccelUntil	(	const Vect3 &	so,
		const Velocity &	vo,
		double	t,
		double	goalVs,
		double	vsAccel
	)

static

Position after t time units where there is first an acceleration or deceleration to the target vertical speed goalVs and then continuing at that speed for the remainder of the time, if any.

Parameters

vo	initial velocity
goalVs	the vertical speed where the acceleration stops
vsAccel	the vertical speed acceleration (a positive value)
t	time of acceleration [secs]

Returns: Position after time t

◆ vsLevelOutCalculation()

std::pair< Vect3, Velocity > larcfm::Kinematics::vsLevelOutCalculation	(	const std::pair< Vect3, Velocity > &	sv0,
		double	targetAlt,
		double	a1,
		double	a2,
		double	t1,
		double	t2,
		double	t3,
		double	t
	)

static

returns Pair that contains position and velocity at time t due to level out maneuver based on vsLevelOutTimesAD

Parameters

sv0	current position and velocity vectors
t	time point of interest
climbRate	climb rate
targetAlt	target altitude
a1	first acceleration
a2	second acceleration
allowClimbRateChange	allows climbRate to change to initial velocity if it can help.

Returns

◆ vsLevelOutFinal()

StateVector larcfm::Kinematics::vsLevelOutFinal	(	const std::pair< Vect3, Velocity > &	sv0,
		double	climbRate,
		double	targetAlt,
		double	a,
		bool	allowClimbRateChange
	)

static

Returns a statevector that holds position, velocity and relative time at final level out position

Parameters

sv0
climbRate
targetAlt
a
allowClimbRateChange

Returns

◆ vsLevelOutTimesBase()

Tuple5< double, double, double, double, double > larcfm::Kinematics::vsLevelOutTimesBase	(	double	s0z,
		double	v0z,
		double	climbRate,
		double	targetAlt,
		double	accelup,
		double	acceldown,
		bool	allowClimbRateChange
	)

staticprivate

Helper function for vsLevelOutTimesAD. Note: This could be integrated into the function vsLevelOutTimesAD as a recursive call if desired.

Parameters

s0z	initial vertical position
v0z	initial vertical velocity
climbRate	desired vertical speed for the climb/descent (positive), sign calculated in code
targetAlt	target altitude
accelup	maximum positive acceleration
acceldown	maximum negative acceleration
allowClimbRateChange	if true, if the current velocity is of greater magnitude than the specified climb rate, then continue at the current velocity (prioritize achieving the desired altitude). If false, first achieve the goal climb rate (prioritize achieving the indicated vs)

Returns: <T1 = end of first accel ,T2 = end of constant vertical speed phase, T3 = end of deceleration, a1 = acceleration for phase 1, a2 =acceleration for phase 2>

The documentation for this class was generated from the following files:

Modules/ACCoRD/inc/Kinematics.h
Modules/ACCoRD/src/Kinematics.cpp

Static Public Member Functions

Static Private Member Functions

Detailed Description

Member Function Documentation

◆ bankAngle()

◆ bankAngleGoal()

◆ bankAngleRadius() [1/2]

◆ bankAngleRadius() [2/2]

◆ centerOfTurn() [1/2]

◆ centerOfTurn() [2/2]

◆ closestDistOnTurn()

◆ closestTimeOnTurn()

◆ directTo()

◆ distanceToGsAccelTime()

◆ distanceWithGsAccel()

◆ distAtTau()

◆ elevationAngle()

◆ gsAccel()

◆ gsAccelDist()

◆ gsAccelPos()

◆ gsAccelTime() [1/2]

◆ gsAccelTime() [2/2]

◆ gsAccelToDist()

◆ gsAccelToRTA()

◆ gsAccelUntilRWB()

◆ linear()

◆ neededDistGsAccel()

◆ positionAfterTurn()

◆ speedOfTurn()

◆ tau()

◆ testLoSGs()

◆ testLoSTrk()

◆ testLoSVs()

◆ turn() [1/3]

◆ turn() [2/3]

◆ turn() [3/3]

◆ turnByAngle2D()

◆ turnByDist2D() [1/2]

◆ turnByDist2D() [2/2]

◆ turnDone()

◆ turnOmega() [1/2]

◆ turnOmega() [2/2]

◆ turnRadius() [1/2]

◆ turnRadius() [2/2]

◆ turnRate()

◆ turnRateGoal()

◆ turnRight()

◆ turnTime() [1/3]

◆ turnTime() [2/3]

◆ turnTime() [3/3]

◆ turnUntil() [1/2]

◆ turnUntil() [2/2]

◆ turnUntilTimeOmega() [1/2]

◆ turnUntilTimeOmega() [2/2]

◆ turnUntilTimeRadius()

◆ vsAccel()

◆ vsAccelPos()

◆ vsAccelTime() [1/2]

◆ vsAccelTime() [2/2]

◆ vsAccelUntil()

◆ vsLevelOutCalculation()

◆ vsLevelOutFinal()

◆ vsLevelOutTimesBase()