The risk of aircraft collision in the air is the most dangerous phenomenon in aviation. In connection with the growing air flow to Turkey, this risk cannot be underestimated. In this study, a calculation of the probability of the aircraft going beyond the established route will be made based on the static analysis of the data regarding the flight of the aircraft along the routes. The data were collected using Automatic Dependent Surveillance-Broadcast (ADS-B) transmitters and then processed in the Python programming environment. The risk is calculated using the probability density function as the area under the function bounded by the lateral boundaries of the route.
The world is currently in a very difficult period when many military conflicts are arising
across the globe. It affected every sphere of the economy at different levels, and aviation
was no exception. In its annual report for 2023, the International Air Transport Association
(IATA) [
Turkey has always had an advantageous position as a bridge between Europe and Asia.
At the moment, this position has only been consolidated, because due to the Russian
invasion of Ukraine, many Western countries have imposed sanctions on Russia, including
the aviation industry. Because of this, the main air flow from Europe to Asia now passes
through Turkey [
The lack of air space arises because of the concept of air space construction, as planes fly
on predetermined routes. One of the options for solving the problem is the transition to an
alternative concept, which is currently being actively implemented in European countries,
Free Route Airspace (FRA) [
The problem of the collision of planes in the air has been studied for many years, because
this is the most deadly event that can happen in aviation. Therefore, to determine the risk,
there is a collision risk model (CRM) that calculates the probability of a collision. To
calculate the CRM in the horizontal plane, the ICAO uses Reich mode, which represents the
plane as a box whose parameters are equal to the echelon minimums, therefore, if there is
an overlap of the area of the boxes of two different planes, this indicates a violation of the
minimums and, accordingly, the risk of an increase in the risk of collision [
In the paper a specialized software is developed for automatic safety level detection based on airplane trajectory input.
Airspace is a designated volume of the atmosphere that is under the control of a certain
state, and this is the part that is above its land territories and territorial waters. For the
convenience of organizing air traffic, airspace is divided into controlled and uncontrolled.
Controlled is the one where dispatching service is provided. Uncontrolled is the one where
dispatching service is not provided. In addition, the airspace can be divided into upper and
lower echelon 275 (8400 m). Moreover, in order to divide the areas of management and
responsibilities of various dispatching services, the airspace is divided into the following
elements: Control Area (CTA), Terminal Control Area (TMA), Control Zone (CTR), Flight
Information Region (FIR), Flight Information Zone (FIZ), Aerodrome Flight Information
Zone (AFIZ) and Aerodrome Traffic Zone (ATZ). ICAO also applies a special classification of
airspace (seven classes from A to G) to determine which dispatching service to apply and
what are the requirements for airspace users in this class [
The dispatching authority of the respective country is responsible for the organization
of air traffic. The controller's task is to provide safe, economical and effective air traffic
control. To perform this task, the dispatcher uses the most important tool at his disposal
separation. Separationing is vertical and horizontal (the latter is divided into longitudinal
and lateral separationing. It should also be said that there is separationing by time and by
distance (we will consider the latter during the study). Vertical separationing has two
values: 300 m for aircraft flying up to 290 FL and for aircraft permitted to fly in the zone of
reduced vertical separation minima (RVSM) between 290 and 410 FL (excluding
government aircraft) and 600 m for all aircraft flying above 290 FL and which are not
permitted to fly in RVSM. Horizontal separationing depends on the navigational aids used
and the navigational methods. The width of the route along which the aircraft flies is also
determined by the navigational aids. If we are talking about the zonal navigation method
(RNAV), then the aircraft can fly not from one radio beacon to another, but it must be able
to fly in the center of the determined route during 95% of the flight [
RNAV 10 for oceanic routes, route width 50 NM; RNAV 5 for en-route leg routes, route width 5 NM; RNP 4 for oceanic routes, route width 23 NM;
RNP 1 for the approach/takeoff phase, route width 1 NM.
There are different types of routes. When talking about the route of the airspace, we are talking about a clearly defined segment of airspace that is used to direct the flow of airships. In a general sense, it combines all types of air routes: • • •
Advisory service is performed in uncontrolled airspace, where advisory service is provided; An uncontrolled route is also in uncontrolled airspace, but only emergency service is provided;
Controlled is the one on which dispatching service is provided.
Air routes that will be described later will be the last type of control. Because it is on them that commercial aviation makes flights.
We use static and analytical research methods to obtain results, as well as the Python
programming environment and probability density function to obtain the probability of the
aircraft leaving the set limits. At, the first step to be taken is to collect data on the movement
of aircraft over the territory of Turkey using the Python software environment and
additional libraries. The data is obtained from Automatic dependent surveillance-broadcast
(ADS-B) transmitters, which are an element of Communication, Navigation, Surveillance
(CNS) of aviation, which refers to surveillance in the same way as primary, and secondary
radars. ADS-B get location of the aircraft from global navigation satellite systems (GNSS),
and transmits this data not only to ground stations (which include dispatchers) but also to
nearby airships [
To calculate the deviation of the plane from the center of the route, we used the level of a straight line. Having two points: the beginning and the end of the route get the equation of the straight line passing through them:
+ + = 0, (1) where (x, y) are the coordinates of the point, a, b, c are free changes that we will get in the following way: ( 2 − 1) − ( 2 − 1) − 2 1 2 = 0, (2) where (x1, y1) are the coordinates of the first point on the route segment, (x2,y2) are the coordinates of the segment end.
Solving equation (2), we get the values of a,b,c. After drawing a perpendicular from the straight route, at the point of its intersection with the curve of the plane's trajectory, from the obtained point to the base of the perpendicular, there will be a deviation of the plane. And so on for each subsequent point along the selected route. The distance itself can be calculated as follows: = + + , (3)
√ 2+ 2 where a, b, c are free to change what we got from (2), for the route to which the coordinates of the flight curve (xi,yi) correspond.
Now we need to use the probability density function (PDF) ρ(x), since the resulting
sample will be discrete, that is, we will not be able to accurately estimate the risk of the
plane going beyond the set limits. Therefore, we need a continuous sample of flights that
can include the completeness of information that compensates for the limited amount of
received data. PDF will be able to calculate the probability of deviation as a value that
exceeds the set limit (route width) (Figure 1) [
We can calculate the risk of the aircraft going off-route as follows: = ∫−∞ − ( )
∞ + ∫ ( ) , = 1 − ∫ ( ) , −
( ) = 2 +1σ ( +1) 1
1
(− |
1 − | ) ,
2
σ
or
form [
As a PDF a Normal (ND), Exponential (ED), Double Exponential (DED), or Univariate Generalized Error Distribution (UGED) can be used. In our research we use ND with a next where σ is the dispersion of the distribution; k is a controls the skewness; µ is a mode of the distribution; Γ(k+1) is an Eelier-gamma function.
The flexibility of UGED makes ρ(x) similar to ND if k=0.5 and to DED in case k=1.
It should also be noted that the probability of lateral deviation of the aircraft is used in
the calculation of the Reich collision risk model, which is the basis of the TLS indicator
implemented by the ICAO for calculating safety. It shows what should be the number of
plane crashes in a certain airspace per hour. It has been officially established that this value
should be equal to 5×10-9, therefore, for the services responsible for air navigation, any TLS
for their sector of responsibility with a value smaller than the established value is
considered acceptable. The value of the risk according to the Reich model [
+ 2 |̅̅̅̇̅̅|
0 2 + |̅̅̅̇0̅̅|) , 2 where |̅̅̅̇̅̅| is the average transverse speed of the aircraft on the route; |̅̅̅̇0̅̅| is the average 0 vertical speed of the aircraft on the route; | ̇( )| is the average lateral speed of the aircraft on the route; m is the minimum echelon on the route; , , are length, width, and height of the aircraft model; П is probability of lateral overlap; Pz (0) is probability of vertical overlap; Pу(0) is probability of transverse overlap. (4) (5) (6) (7)
Software has been developed in Python programming language using installed selenium library. On May 22-23, 2024, records of about 165 flights from the 10 largest airports in Turkey were obtained: IST, AYT, ESB, ADB, DLM, ADA, BJV, TZX, and GZT. As mentioned earlier, all data coordinates, whose coordinates go beyond the airspace of Turkey, were discarded, and the obtained results were visualized using OpenStreetMap Figure 2.
After that, we compare the obtained set of airplane flights with the currently existing air
route network of Turkey [
Since the collected data related to the flight of airplanes was with a frequency of 20-30s
between the coordinates. The data was interpolated to have data with a frequency 1 s [
As mentioned above, the lateral limits of the route can be different, but at the en-route stage, 10 km is usually used. Of course, the volume of the studied data is large, but they are discrete values, so we need to convert them into continuous values, for this we will use PDF (5). After processing the tuple of data regarding the deviation of the planes from the route, we got required parameters, the sampling mode µ = -1.17, the dispersion of the distribution σ = 10.12, the average value 7.17, k=0.5.
Calculate the risk of the plane leaving the route by (4) (at Figure 5 this is indicated by the area with black color). The obtained value of R = 0.33 at k=0.5. For other values of k and the route, width are indicated in Table 1.
The obtained values show that the risk of an aircraft leaving the airspace of Turkey is quite high. However, this can be explained by the significant load on this airspace, because Turkey is a popular destination for many airlines, which leads to the fact that many planes can be in it at the same time. This leads to the fact that controllers resort to flow regulation and use echeloning as a tool to ensure a minimum of safety when performing a fly-by or overtaking aircraft on a route when applying speed regulation is not possible. For case of RNAV 10, the probability of going beyond the route is negligible, but this value is used for flights on routes over the ocean, which does not allow us to talk about its relevance for Turkey for objective reasons.
In the future, it will be possible to use the obtained data to calculate the total risk in the
airspace of Turkey by (6). This will make it possible to understand whether the estimated
value of TLS will exceed the established ICAO 5×10-9 or not. At the moment, it is only
possible to compare the obtained results with similar studies where this value was
calculated for other air spaces. For example, in the study of the probability of deviation for
Ukraine [
During the study, data on the location of users in Turkish airspace relative to the routes they flew were collected and analyzed. The goal was to calculate the probability of deviation. An international network of ADS-B receivers located around the world, including one in Turkey, was used to obtain data on the location of airspace users. Statistical analysis of the accumulated data made it possible to estimate the deviation of users from the center of the route in the airspace of Turkey. Using a probability distribution function to fit the statistics. The estimated ND parameters made it possible to assess the risk of losing echelon in the lateral plane according to different navigation specifications. In the future, using the results of this study, it will be possible to calculate the risk of collision in the horizontal plane and the total risk for the airspace of Turkey as a whole according to the CRM Reich formula, in addition, it will be possible to determine the risk for the entire Black Sea region. The proposed method can also be integrated into the air traffic control system to assess the safety of the used airspace.