Algorithm analysis of baseline turn protection Area

Everyone is good, I am striving for the wind spiral written into the norms of the Liu Chongjun, I wish you all the year of the dog boom, thinking things into!

What I want to share with you today is the method of calculating the baseline turn protection in flight design.

First of all, to summarize, wind helix algorithm is a kind of formulation, suitable for computer automatic processing of spiral line calculation method. In the application of the wind Helix calculation method in the flight program reserve, the core step is to determine the initial parameters of the wind helix and calculate the position points of the wind helix tangent and Gongsche according to the initial parameters, and connect these points to form the flight program protected area.

The baseline turn procedure is a reverse procedure used in the entry stage. Its main characteristics are: aircraft sailing along a certain angle, through the timing or positioning point to determine the starting turn position, through a continuous turn to achieve the direction of the runway, connecting the middle and the last approaching segment (Figure 1 from a point in the blue solid trajectory).

Figure 1 Baseline Turn infrastructure

In the baseline turn protection area, the calculation formula for determining the earliest point of point B (B1, B2) is calculated as ab1= (t-5) (v-w ')-ZN. Here the t-5 (individual tends to be understood as) the timing error (-10) seconds plus the setting of the slope time (+5) seconds, combined together is t-5 seconds. From the computational process, the timing error can be as early as 10 seconds or 10 seconds. When the earliest point is calculated, the position is 10 seconds in advance, that is, the distance from point B to 10 seconds, plus 5 seconds to establish the slope time, the sum is the position of the B point before (-5) seconds. (When calculating the initial parameters of the wind helix, every second is important to determine the accuracy of the tangent position directly, so the principle of timing needs to be explained in each discussion.) ）

The last calculated formula is AB2 = (t +21) (V-W ') +zn. The 21 seconds here are the sum of the timing error (+10) seconds, the setting of the slope time (+5) seconds, and the driver response time (+6) seconds.

The baseline turn protected area is divided according to the center point of the Wind Helix (2), a total of 5 wind spirals can be found, respectively, C2, C3, C4, C5 Point and the baseline into the section of the Wind helix (take up C1 to represent).

Figure 2 Five wind spirals in the baseline turn reserve

The C2, C4 wind helix is the wind helix that begins to draw the most late turn, and the C3 Wind Helix is the wind helix drawn from the earliest point of the turn. The C5 wind helix is a wind helix drawn from the approaching direction (on the runway extension line). The C1 wind helix is a wind helix drawn from the beginning of the entry section.

The first problem that is more difficult to understand in the baseline turn protection area is the size relationship of the Phi angle to the DA angle (as shown).

Figure 3 The size relationship between phi angle and da angle in a baseline turn

If the C2, C4 wind Helix Gongsche extension and the Datum axis intersection with a point, set extension line and baseline angle is β angle, because the C2, C4 wind Helix initial parameters of the same, it can be proved that their Gongsche and sailing track phase perpendicular, that is, phi angle and β angle of 90 degrees. At the intersection of Gongsche and baseline, we know that the angle between Gongsche and perpendicular is equal to phi angle.

When the DA angle is larger than the Phi angle, 3 shows that the intersection of the DA angle and the baseline is on the right side of the Gongsche, the outer boundary of the turn is tangent to the C2 wind Helix, at which point the C4 wind Helix does not work (position relationship in 4).

Figure 4 Da angle is greater than phi angle, tangent to C2 wind Helix tangency

When the DA angle is smaller than the Phi angle, the intersection of the DA angle and the baseline is on the left side of the Gongsche, and the outer boundary of the turn is tangent to the C4 wind Helix, at which point the Gongsche of the wind helix and the tangent of the C4 wind helix work together to form the outer boundary (5).

Fig. 5 The DA angle is less than phi angle, tangent to the C4 wind Helix tangency

Using the SITA angle to describe the wind helix in the 5, the C2 wind helix starts and ends at 0 degrees to the 90+da,c4 wind helix from the starting angle of 90+da to 90+phi (in this case da<phi).

The end angle calculation process of the C4 Wind Helix is:

The vertical downward angle (90°) reverses the DA angle to get the tangent angle, then reverses 90 degrees, increases the DA angle to get the SITA angle (value 0), and subtracts rotation (value of -90-phi) to get the SITA angle actually used for the extrapolation, the formula is: (90-DA) -90+da-( -90-phi) = 90+phi.

When tangent and C2 wind spiral tangent, the calculated end point Sita angle is also 90+phi. Here's a very interesting conclusion: draw a horizontal line from C2 (or C4), intersect the arc drawn with the turning radius, and draw an arc from the intersecting Arc Point (90+phi) *e to the radius, which is the maximum outer expansion position of the landing section of the baseline turn protection area. When Da>phi, the tangent intersects the arc drawn by the C2 point, and when Da<phi, the tangent intersects with the arc drawn by the C4 point. because, in the calculation step (90-da) -90+da =0 means that the SITA angle is horizontal to the right parallel to the zero axis. This conclusion can be used to detect the accuracy of the distal position of the voyage section of the baseline turning protection area.

C5 Wind Helix starting point and the front section of the smooth convergence, it can be understood that when the turn from the C2 or C4 wind helix, before reaching the baseline is flying along a straight line (vertical downward), the linear flight is affected by the side wind, the external expansion angle of the DA angle, it is necessary to follow the DA angle from the baseline back to the outer boundary The outward expansion of the straight segment flight, has taken into account the impact of the wind, therefore, the C5 wind Helix Initial expansion distance of 0, and the outer boundary of the front segment is smooth tangent.

C5 Wind Helix and C3 wind Helix Gongsche, according to the general calculation method of wind helix Gongsche calculation can be.

The baseline turn enters the section wind Helix 6 as shown:

Fig. 6 The relationship between the protected area and wind helix in the baseline turning entry section

According to the basic parameters of the wind helix, the first step is to calculate the position of the N3 point. When calculating the top empty blind area of the navigation table, the angle between the outer boundary of the sail and the nominal track NDB is 25°,vor 15 °. So the angle of N3 point is Ndb:0-phi-30-25,v3 point vor:0-phi-30-15. When N3 (or V3) is found, the distance from the 11*v is moved along the 0-phi-30 direction to get the L point, and if the wind helix that is drawn from the L point is called the C1 wind Helix, its initial expansion distance (offset) is 11*v (5 seconds to establish the slope time plus 6 seconds of reaction time), the initial rotation angle (RO tation) for 0-phi-30-90.

After the initial parameters of the C1 wind helix are determined, the Gongsche of the C2 wind helix can be calculated according to the general algorithm of the Wind Helix Gongsche, and the complete tangent relation 6 is shown.

External expansion of the sub-area of 4.6km, for wind helix calculation, only need to use the same SITA angle, and specify a 4.6km offset can be achieved, no longer repeat. After completion of the baseline turn protected area as shown:

Figure 7 IAS380, height 1850 m, sailing 2 min, NDB baseline turn protection diagram

In the notes of the speedometer, the reverse program is the largest 260km/h, but the maximum speed in the ICAO 9371 template is 465km/h, so 380km/h is not too much.

One more picture of 260km/h:

Figure 8 IAS260, height 1850 m, sailing 2 min, NDB baseline turn protection diagram

The Wind helix algorithm uses the exact conversion calculation method in the maximum program, which is the basic theory necessary for the automatic processing of the program template in the future. It is the inevitable trend for the future automation development to liberate the flight program designers from the heavy protection drawing and devote more energy to the program design. As a flight programmer, you do not have to fully understand the process of software operation, but you must be able to find errors in software calculations. As a software developer, the wind spiral This lesson must be hidden away, hahaha ...

The relevant content has been published in the Journal of the College of Flight 2017 the first period, the reference format is:

[1] Liu Chongjun. Automatic algorithm analysis of baseline turning template [J]. Journal of China Civil Aviation Flight Academy, 2017, 28 (1): 33-37.

Thanks to the Journal of Flight Academy for the Strong support of wind helix algorithm, it is important for individuals to another article, "Wind helix precision algorithm in the waiting template application" will be published in the latest issue in 2018, you are welcome to subscribe in time, miss the Journal of Friends, can pay attention to this public number, I will continue to share with you the application of wind helix algorithm in all kinds of protected areas.

Algorithm analysis of baseline turn protection Area