Aerospace and Electronic Systems Magazine April 2018 - 39
Tang, Zhu, and Fan
TCAS/TCAS COORDINATION
Range and altitude tests are performed on each altitude-reporting
intruder. For Aircraft i and Aircraft j, if the TA tau and either the
time to coaltitude or relative altitude criteria associated with the
current SL are met, the intruder is declared a threat [4].
TtCPA , h =
(x
i
t
−
ij
(v
i
t, x
− vt,jx
) + (v
2
i
t, y
− vt,j y
)
2
− xtj
) +(y
2
i
t
− ytj
)
Dtij, h =
vi − v j
xi − xtj
·cos arctan ti, x t,jx − arctan ti
j
vt, y − vt, y
yt − yt
zti − ztj
vti, z − vt,jz
(x
i
t
− xtj
(9)
) +(y
2
i
t
− ytj
)
2
(10)
Dtij, z = zti − ztj
(11)
(
) (
)
0 < Tt ij , h < TimeTA ∧ 0 < Tt ij , z < TimeTA
CPA
CPA
(
) (
1
ij
j
ij
(14)
ALIM RA + zti − ztj + vti, z ·TtCPA
, h − vt, z ·TtCPA , h
2
ij
tai 0 = TtCPA
,h −
(T )
2
ij
taj0 = TtCPA
,h −
(T )
2
2
(8)
ij
TtCPA
,z = −
Δ ti, z = −Δ tj, z =
(12)
)
∨ Dtij, h < DMODTA ∧ Dtij, z < ZTHR TA
) (
(
ij
tCPA , h
ij
tCPA , h
)
−2Δ it + ti , z a0
(15)
−2Δ ti + tj , z a0
(16)
If Aircraft i is in the RA process and encounters another vehicle Aircraft k, Aircraft i would increase acceleration a0 0.35 g
with the response time ti′ ( 0 ≤ ti′ ≤ 2.5s ) to resolve the new secondary threat. When the RA is removed, a "Clear of Conflict" would
be announced to inform the flight crew that the encounter has been
successfully resolved
( tCoC > tCPA ) ∨ ( Dtij
CoC , h
) (
> DMOD RA ∨ DtijCoC , z > ZTHR RA
)
(17)
WIND DISTURBANCE
The basis for the atmosphere and air data model is an implementation of the International Standard Atmosphere model, in which
the mean wind speed is altitude dependent, and directly associated
with the wind speed V30 as measured at 30 feet above ground level
(AGL). The calculation of the mean wind speed Vwind(z) is defined
as follows [15]
1
wherein, TtCPA, h and TtCPA, z respectively indicate the TA Tau in horizontal and altitude, while TimeTA is the corresponding criteria; Dtij, h
and Dtij, z express the horizontal and vertical distances; and DMODTA
and ZTHRTA constitute the dimensions of the protected airspace.
In a TCAS/TCAS encounter, the two aircraft declare each other
as threats that need to be resolved when
ij
ij
(
) (
)
0 < Tt,ijh < Time RA ∧ 0 < Tt,ijz < Time RA
(
) (
(13)
)
∨ Dtij, h < DMOD RA ∧ Dtij, z < ZTHR RA
TCAS is designed to select the nonaltitude crossing sense due
to the rules of aviation safety even if the altitude crossing sense
provides greater separation. In addition, both aircraft should respond to the RA positively (i.e., climb, descend) not negatively
(i.e., maintain) for the coordinated threat resolution, and then
choose the RA strength which is designed to be the least disruptive (Δ it, z and Δ tj, z) to the existing flight path, while still providing
ALIM vertical separation ALIMRA between Aircraft i and Aircraft j
at CPA. Note that in modelling the aircraft response to RAs, the expectation is that the pilot will begin the initial a0 = 0.25g acceleration maneuver within five seconds. The response time in Aircraft i
and Aircraft j can be assumed as ti ( 0 ≤ ti ≤ 5s ) and tj 0 ≤ tj ≤ 5s .
i
Their own acceleration time ta0 and taj0 can be calculated as follows:
(
APRIL 2018
)
z 7
Vwind ( z ) = V30
10
(18)
Evidently, the value of mean wind speed increases with altitude
and it can be used to determine the turbulence intensity. The initial
value measured at 30 feet AGL is given in the simulations. The different values for the mean wind speed Vwind(z) varying with altitude
are summarized in [13].
GRAPHICAL MODELLING AND ANALYSIS SOFTWARE
For the experiments, we previously used the state space analysis
tool called TIMed State space Performance Analysis Tool (TIMSPAT) [16], developed at the Logistics and Aeronautics Unit of the
Autonomous University of Barcelona. The tool has been shown to
be effective for the performance analysis of very demanding and
flexible industrial systems [17]. Yet the model architecture of the
TIMSPAT model, constituted by a set of text files, is not easy to
understand; and the errors are difficult to detect in the developing
process. In addition, as one of the most commonly used tools for
modelling and simulating discrete event systems (DESs), CPN
Tools [18] stands out as an industrial strength software that provides both a graphical editing interface and an interactive simulator
for constructing and analyzing models. However, its earlier version supports extraordinarily simple calculation only and even with
this extension, the up-to-date version still has difficulty integrating
IEEE A&E SYSTEMS MAGAZINE
39
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