3.1 Input configuration data

Each part of ‘configuration data’ employed by the present method corresponds to one of the following categories:

• • Aircraft performance – aircraft-specific linear interpolation tables and data.

• • Aircraft configuration – the zero-fuel gross weight (zfgw), fuel weight (fuel), zero-weight centre-of-gravity position (zfwcg), and one or more values of the expected landing or End of Descent (EOD) gross weight.

• • Atmosphere – the air temperature, defined by the corresponding standard temperature deviation (ISADev).

• • Navigation – the departure and destination airports’ and EOD altitudes; minimum and maximum cruise altitude limitations; climb, cruise and descent speed schedules, EOD speed (a ‘speed schedule’ denotes a pair of Indicated Air Speed (IAS) and Mach index values).

An aircraft's performance model^{(Reference Liden1,Reference Liden2)} supplies all the data necessary for the calculation of aircraft and flight path parameters, such as the maximum flight altitudes, fuel burn, altitudes, and still-air flight distances and flight path angles. Each calculation employs one or more linear interpolation tables specific to the particular performance parameter and flight phase, and the calculation may depend on one or a combination of parameters such as aircraft weight and balance configuration, altitude, speed, air temperature, etc. The present method considers that for each flight phase, the air temperature (defined using the standard temperature deviation) is constant; thus, it does not change with the geographical position and time.

The advantage of considering the set of expected landing/EOD gross weight values as an input to the method is that it allows the advanced computation of the set of expected vertical descent paths to be stored in the vertical flight path look-up structure and in the vertical flight path graph. The selection of these values may be performed following an analysis of historical flight data corresponding to the aircraft's type, departure and destination airports, etc. Moreover, it is known that the ‘descent’ flight paths’ performance parameters are less sensitive with respect to gross weight variation (and thus, the estimated landing/EOD gross weight variation) than those corresponding to ‘cruise’ and especially ‘climb’ flight path performance parameters^{(Reference Gerretsen and Swierstra50)}. Therefore, a judiciously chosen set of landing gross weights may also allow the use of pre-computed descent paths for performance computations corresponding to other landing gross weight values, by employing interpolation algorithms, which will result in path predictions within an acceptable error margin.

3.2 Gross weight and centre-of-gravity position

For some aircraft models, the performance interpolation tables may impose calculations as a function of the centre-of-gravity position. Consequently, the expression linking the fuel weight, the total weight, and the centre-of-gravity position must be established prior to the construction of the vertical flight path look-up structure. This expression is a function of the aircraft's take-off weights and balance configuration and relies on a set of aircraft performance tables. It does not change for the entire extent of the flight, thus for any flight phase, segment type, flight speed, altitude or atmospheric conditions.

As illustrated in the literature^{(Reference Dancila, Botez and Labour29,51)} , the aircraft's total gross weight gw and the position of its centre of gravity cg specified as a percentage of the mean aerodynamic chord length (% MAC) are dependent on the aircraft's zero fuel gross weight zfgw, zero fuel weight centre-of-gravity position zfwcg, and fuel weight fuel, as described in Equations (15) and (16):

(15) $$\begin{equation} gw &=& {f_1}\left( {{\hbox{\it zfgw}}{\rm{,}}\;{\rm{fuel}}} \right), \end{equation}$$

(16) $$\begin{equation} cg &=& {f_2}\left( {{M_a}\left( {{\hbox{\it zfgw}}, {\hbox{\it zfwcg}}} \right),{M_f}\left( {{\rm{fuel}}} \right), {\hbox{\it CGREFDIST}}, {\hbox{\it LEMAC}}, {\hbox{\it MAC}}} \right), \end{equation}$$

3.3 Maximum flying altitude as function of the gross weight

The vertical flight paths assembled in the vertical flight path look-up structure must conform to a minimum set of two conditions: account for the aircraft's performance and their limitations and cover the maximum set of altitude and gross weight configurations (the flight envelope). Both conditions require a proper characterisation of the maximum flying altitude, which depends on the aircraft's performance, and which could also be a function of one or more parameters related to the particular aircraft's configuration (gw, cg), and flying conditions (speed, air temperature, etc.).

The proposed method addresses these requirements first by determining the relationship between the maximum altitude and the aircraft's gross weight, and for the flying conditions for each phase (climb, cruise, and descent) using the appropriate set of aircraft performance data. Secondly, for each flight phase, a table is constructed that provides the maximal set of altitudes and the corresponding maximum allowed aircraft gross weight.

For the cruise phase, the table provides the necessary information regarding the maximum altitude envelope for the particular aircraft configuration and flying conditions, as well as the maximum gw value (earliest point) at which a flight is possible, as function of the cruise altitude. This information in turn allows the computation of the earliest climb start points (gw values), and the earliest possible climb flight paths that lead to each cruise altitude, thereby maximising the range of flight paths available for the flight plan computation phase.

3.4 The climb flight path and the Top of Climb

The climb phase extends from the take-off altitude or from the aircraft's initial altitude to the Top of Climb (TOC), reached at the point where the climb flight path arrives at the minimum cruise altitude. The proposed method considers that the climb path is an unconstrained, continuous climb, meaning that there are no waypoint-imposed altitude and speed restrictions, nor mandatory level-off segments.

The climb path is decomposed in sub-segments, and its parameters are computed for these sub-segments corresponding to altitude differences of a maximum of 1,000 ft. Therefore, each such sub-segment usually starts and/or ends at an altitude multiple of 1,000 ft. and is characterised by a set of parameters which may include:

• • The aircraft's initial and final flying altitudes;

• • The aircraft's initial and final gw, cg, and fuel weight;

• • The aircraft's initial and final IAS/Mach and TAS values;

• • The sub-segment's still-air horizontal distance and flight path angle (FPA); and

• • The sub-segment's flight time, fuel-burn, and average TAS.

As mentioned above, the climb flight path computation takes into account all procedural speed and altitude constraints, including the take-off speed as well as the thrust reduction, acceleration, speed restriction, and crossover altitudes. The sequence of steps employed for the computation of the climb vertical flight path and the TOC parameters is presented in Fig. 8, below.

Figure 8.

The climb vertical flight path computation workflow.

An illustration of a climb vertical flight path, including its altitude-based segmentation, and the corresponding performance parameters is presented in Fig. 9.

Figure 9.

The pre-computed climb vertical flight path parameters.

Complementary to the climb vertical flight path data, an additional set of parameters associated with the TOC characterises the climb path as a whole and may include:

• • TOC altitude;

• • TOC gw, fuel, and cg;

• • TOC IAS/Mach and TAS;

• • Still-air, horizontal distance measured from aircraft location to the TOC, as the sum of the still-air horizontal distances of the composing climb segments;

• • Time to TOC as the summation of the composing climb path segments’ flight times; and

• • Climb fuel-burn as the sum of the fuel burns of the composing climb path segments.

The individual segments’ flight times as well as the time to TOC computed in still-air conditions remain valid during the lateral path calculations, as the winds are assumed to have no vertical components. However, during the lateral path computations, the still-air, vertical path-computed speed, horizontal distance, and flight path angle parameters are adjusted as function of each segment's particular wind conditions, as illustrated in Figs. 1-4 and Equations (7)-(9).

3.5 Descent flight paths and the set of Top of Descent points

For the descent phase, the set of computed descent vertical flight paths are connecting the EOD altitude to the maximum valid cruise altitude. They may incorporate the required level-flight deceleration segments at each cruise altitude, which correspond to the aircraft's deceleration from cruise to the descent speed. The set of points situated at the start of the deceleration segments represents the set of Top of Descent (TOD) points. The number of descent vertical paths is equal to the number of expected EOD gross weight values provided as input data. For each descent path, the number of TOD points is identical to the number of altitudes, positioned in the selected range of cruise altitudes, provided as input data, which meet the aircraft's maximum altitude and gross weight flight envelope limitations.

Each descent vertical flight path's parameters are divided in two groups. The first group characterises the set of ‘level-flight deceleration segments’, one segment per valid cruise altitude, and the second group characterises the ‘actual descent path’, which is performed at the descent speed schedule, from the corresponding maximum valid cruise altitude to the EOD altitude. The approach used in the construction of the descent paths ensures that for any selected TOD (corresponding to a descent flight path and cruise altitude), the aircraft's parameters at the end of the deceleration segment are equal to those of the selected actual descent flight path at the TOD's cruise altitude (as illustrated in Fig. 7).

Figure 10 illustrates the sequence of steps employed for the construction of the descent paths, from the EOD altitude up to the maximum cruise altitude, which include the actual descent and the flight paths’ level-flight deceleration segments.

Figure 10.

The descent vertical flight paths’ computation workflow.

An example of a descent vertical flight path and the relationship between the TODs, the deceleration segments, the actual descent, and the EOD is presented in Fig. 11, where k represents the index of the selected landing/EOD gross weight value, and N+i represents the index of the selected cruise altitude value.

Figure 11.

Example of a descent flight path – the deceleration and descent segments.

The actual descent vertical flight path data is similar to the climb vertical flight path data in terms of number and type of parameters, as well as in terms of the sub-segments’ 1,000 ft. altitude decomposition.

Each ‘level-flight deceleration’ segment represents the flight path segment connecting the corresponding pair of level-flight constant speed cruise, and actual descent paths. The deceleration segment is characterised by a set of parameters which include:

• • Aircraft's altitude;

• • Aircraft's initial and final gw, cg, and fuel weight;

• • Aircraft's initial and final IAS/Mach and TAS values;

• • Segment's still-air horizontal distance; and

• • Segment's flight time, fuel-burn, and average TAS.

The resulting descent vertical flight paths’ data can be assembled as a 2 × K × N structure, where N represents the number of cruise altitudes, and K represents the number of descent paths (expected gross weight landing/EOD values). The element (1, i, j) stores data characterising the ‘deceleration segments’ corresponding to the descent path i ‘at’ the cruise altitude j, and the element (2, i, j) stores the data characterising the ‘actual descent segments’ corresponding to the descent path i ‘from’ the cruise altitude j.

Complementary to the descent segments’ vertical flight path data, an additional set of parameters corresponding to the computed TODs provides a global characterisation of the set of available descent paths. The TOD data may be organised as a function of the EOD gross weight and initial cruise altitude, where the parameters describing each TOD may include:

• • TOD gw, fuel, and cg;

• • TOD IAS/Mach and TAS;

• • Still-air distance from the TOD to the EOD as the sum of still-air horizontal distances of the ‘deceleration in cruise’ and ‘descent’ segments;

• • TOD to EOD flight time, as the sum of the corresponding ‘deceleration in cruise’ and ‘descent’ flight times; and

• • Descent fuel-burn as the sum of the fuel burns of the corresponding ‘deceleration in cruise’ and ‘descent’ flight path segments.

3.6 Cruise vertical flight paths

For the cruise phase, the set of vertical flight paths consists of flight path segments that may be employed to link the TOC (if the aircraft is in climb) or the actual aircraft position (if the aircraft is already in cruise) with the set of TODs. These segments are positioned between the minimum cruise altitude and the maximum altitude in the set of TOD altitudes. The present method limits the cruise segments’ types to ‘constant-speed level-flight’ and ‘constant-speed step-climb’. As previously mentioned, the proposed method considers constant climb, cruise and descent speed schedules. As well, it considers only climb in cruise segments in accordance with the usual tendencies of searching higher cruise altitudes which yield better flight performance. Cruise step-descents are usually performed as a consequence of an ATC request or extreme weather avoidance manoeuvers and are not a part of pre-planned flight paths. Thus, cruise ‘step-descents’, acceleration or deceleration segments are not considered.

3.6.2 Level-flight cruise vertical flight paths

The level flight cruise vertical flight paths are constructed for altitude multiples of 1,000 ft. The performance parameters of the segments composing the level-flight cruise path were calculated using the fuel burn computation algorithm developed at the LARCASE laboratory^{(Reference Dancila, Botez and Labour29)}. This algorithm constructs and uses a fuel burn look-up table that describes the correlation between the gross weight at the beginning of the segment, cruise altitude, segment flight time, and the aircraft's gross weight at the end of the segment -the fuel burn. Figure 12 illustrates the sequence of steps employed for the construction of the level-flight cruise vertical path data.

Figure 12.

The level-flight cruise vertical flight path computation workflow.

The constant-speed level flight look-up table is calculated once and is valid for the entire cruise flight. This table makes it possible to perform more flexible fuel burn computations than the existing on-board fuel burn algorithms (i.e. ‘fuel burn’ as a function of the ‘flight time’, and ‘flight duration’ as a function of the ‘fuel burn’), and eliminates the restrictions presently imposed on the maximum length of a level-flight cruise segment (50 to 100 Nm) by the existing FMS algorithms^{(Reference Liden1,Reference Liden2)} .

As illustrated in Fig. 7, each level-flight cruise flight path segment starts at a gross weight value equal to that at which the climb flight path or a step-climb flight path reaches the corresponding cruise altitude and ends at a gross weight value equal to that at which the immediately succeeding step-climb or descent flight path reaches the same cruise altitude.

The set of parameters that characterises a level-flight cruise vertical path segment may include:

• • Altitude;

• • Initial and final gw, cg, and fuel weight;

• • IAS/Mach and TAS values;

• • Segment's flight time and fuel burn; and

• • Segment's still-air horizontal distance.

3.7 The vertical flight path look-up structure and the vertical flight path graph

The assembly of climb, cruise, and descent flight path segments’ performance data can be compiled into a look-up structure. The sets of climb-in cruise and descent paths are organised sequentially, in a reverse order of the gross weight at the start of the vertical flight path (minimum cruise altitude and the EOD, respectively), similar to the usual aircraft's gross weight reduction along a flight path.

The global topological relationships between the climb, cruise, and descent paths (as well as the corresponding path segments) can be described using the vertical flight path graph. Its nodes (Fig. 7) are represented by the gross weight–altitude binomials corresponding to the T/O, TOC, TODs, and the EODs, as well as by all the ‘intersection’ points between the pre-computed cruise vertical flight paths (level flight and step-climb). These intersection points are situated in the cruise phase, between the TOC and the TODs, at altitude multiples of 1,000 ft.

A succinct representation of the succession of steps employed for the construction of the vertical flight path look-up structure and the vertical flight path graph is presented in Fig. 13.

Figure 13.

The vertical flight path look-up structure and vertical flight path graph computing workflow.

For any flight phase, given an aircraft's vertical flight plan position defined by an altitude and gross weight, the vertical flight plan graph provides a way for detecting whether that position is situated at a graph node or on an edge and consequently, the number and type of vertical path segments that can be employed for building the subsequent vertical and lateral flight path segment. It also facilitates the detection of the transition points from one flight phase to the next. For example, the graph node corresponding to the TOC designates the transition point from climb mode to cruise. Similarly, upon reaching any graph node corresponding to a TOD, its set of parameters can be used by itself or in conjunction with other parameters (such as the distance to the EOD/destination airport) to decide whether the exploration of a ‘descent path’ is appropriate.

Once the vertical path segment is selected, the vertical flight path graph facilitates the retrieval of the corresponding performance information from the vertical flight path look-up structure, either as general segment description data (say for the entire descent segment as a whole) or as detailed segment description data (say for the set of data of each sub-segment composing the selected descent vertical flight path).

The two sets of data describing the ensemble of available vertical path segments also allow the construction of a complete stand-alone vertical flight plan and the computation of the corresponding set of altitudes, still-air distances, flight times, fuel burns, and flight costs. The construction of the vertical flight plan may also target specific goals including flight time, fuel burn, or flight cost minimisation. However, knowing that such a vertical flight plan is constructed for still-air conditions, its suitability for the construction of the final lateral and vertical flight plan is dependent on the flight's particular navigation (composing segments’ lengths and headings), and wind conditions. Nonetheless, the ability to construct and evaluate such profiles may provide useful insight regarding the relationship between the criteria used for the selection of a vertical flight path and an aircraft's performance, configuration, and navigation conditions.

3.8 The vertical and lateral flight plan computation using the vertical flight plan look-up structure and the vertical flight plan graph

The proposed method considers that the vertical flight path look-up structure and graph are employed in a scenario in which the full vertical and lateral flight plan parameters are computed in a manner similar to the scenario considered by the existing on-board algorithms, one segment at a time, from the aircraft's actual position to the destination airport. The performance parameters of the vertical flight plan segments, however, are not recalculated at every reconstruction/evaluation of the corresponding flight plan segments. Instead, the segment's performance parameters are extracted from the look-up structure and processed along with the corresponding lateral navigation and wind data to determine the full vertical and lateral flight path description (flight plan).

The flight plan computations may be performed with respect to the selected vertical flight path look-up structure segment's entire still-air horizontal distance (H _dist), or for just a fraction (k) of it. For the climb, step-climb, and descent segments, the computations may also be performed relative to the look-up structure segment's entire altitude difference (d _alt), or for just a fraction (k) of it. These computations allow the determination of the aircraft's parameters at a particular location or altitude on the flight plan.

The actual computation of the flight plan parameters for a fraction k of a look-up structure flight path segment depends on the type of the segment itself and takes advantage of the fact that the look-up structure and the composing segments were computed considering the linearity domains of the aircraft's performance model. Therefore, some of the fractional (k) still-air flight path segment parameters’ values (such as the fuel burn, altitude difference, and horizontal distance) are equal to the same fraction k values of the corresponding full-length still-air flight path segment's parameters. If the segment is flown at constant IAS/Mach, the final TAS is computed using the corresponding speed conversion equation as a function of the final altitude; the segment flight time is equal to the quotient between the segment's still-air distance fraction and its average TAS.

For the constant-speed climb segment example presented in Fig. 14, considering the fuelburn and H _dist values retrieved from the look-up structure, the still-air performance parameters for the segment P₁P₂ (representing a k fraction of the entire constant speed climb segment) are computed as follows:

(17) $$\begin{equation} {K_1} &=& {K_0} + k, \end{equation}$$

(18) $$\begin{equation} {P_1}{P_{2 - {\rm{hdist}}}} &=& k*{H_{{\rm{dist}}}}, \end{equation}$$

(19) $$\begin{equation} {P_1}{P_{2 - {\rm{fuelburn}}}} &=& k*\;{\rm{fuelburn,}} \end{equation}$$

(20) $$\begin{equation} {P_1}{P_{2 - {\rm{dalt}}}} &=& k*{d_{{\rm{alt}}}}, \end{equation}$$

(21) $$\begin{equation} {a_1} &=& {K_0}*{d_{{\rm{alt}}}}, \end{equation}$$

(22) $$\begin{equation} {a_2} &=& {a_1} + k*{d_{{\rm{alt}}}}, \end{equation}$$

(23) $$\begin{equation} {\hbox{\it TAS}}\_{P_2} &=& {\hbox{\it TAS}}({\hbox{\it IAS}}/Mach,{a_2}), \end{equation}$$

(24) $$\begin{equation} TA{S_{avg\_{P_1}{P_2}}} &=& {\hbox{\it TAS}}\left( {{\hbox{\it IAS}}/Mach,{a_1} + {d_{alt}}\frac{k}{2}} \right), \end{equation}$$

(25) $$\begin{equation} {t_{{\rm{still}} - {\rm{air}}\_{P_1}{P_2}}}& =& \frac{{{P_1}{P_{2 - {\rm{hdist}}}}}}{{TA{S_{avg\_{P_1}{P_2}}}*\cos \left( {{\hbox{\it FPA}}} \right)}} = \frac{{k*{H_{{\rm{dist}}}}}}{{TA{S_{avg\_{P_1}{P_2}}}*\cos \left( {{\hbox{\it FPA}}} \right)}}, \end{equation}$$

Figure 14.

Example of fractional constant-speed climb segment performance computation.

‘Acceleration-in-climb’ and ‘deceleration-in-descent’ segments consider a uniform variation of the IAS/Mach. Consequently, the segment's final speed is calculated as a function of the initial and final IAS/Mach values, as well as of the fraction of the look-up structure flight path segment for which the computations are performed. The corresponding final TAS value is computed using the corresponding speed conversion equations. The flight time for the fraction of the segment is computed as the quotient between the actual still-air horizontal distance fraction and its average TAS.

Considering the look-up structure segment presented in Fig. 14, the acceleration-in-climb and deceleration-in-descent segments are characterised by an additional set of parameters: initial speed IAS₀/Mach₀, and final speed IAS_f/Mach_f, and thus the IAS/Mach speed variation d_IAS/d_Mach. The IAS fractional segment's final and average speed values, and the flight time are computed using the following equations (similarly for Mach segments):

(26) $$\begin{equation} {\hbox{\it IAS}}\_{P_1} &=& IA{S_0} + {K_0}*{d_{\scriptsize{\hbox{\it IAS}}}}, \end{equation}$$

(27) $$\begin{equation} {\hbox{\it IAS}}\_{P_2} &=& {\hbox{\it IAS}}\_{P_1} + k*{d_{\scriptsize{\hbox{\it IAS}}}} = IA{S_0} + \left( {{K_0} + k} \right)*{d_{\scriptsize{\hbox{\it IAS}}}}, \end{equation}$$

(28) $$\begin{equation} {\hbox{\it TAS}}\_{P_1} &=& {\hbox{\it TAS}}({\hbox{\it IAS}}\_{P_1},{a_1}), \end{equation}$$

(29) $$\begin{equation} {\hbox{\it TAS}}\_{P_2} &=& {\hbox{\it TAS}}({\hbox{\it IAS}}\_{P_2},{a_2}), \end{equation}$$

(30) $$\begin{equation} IA{S_{avg\_{P_1}{P_2}}} &=& {\hbox{\it IAS}}\_{P_1} + \frac{{k*{d_{\scriptsize{\hbox{\it IAS}}}}}}{2}, \end{equation}$$

(31) $$\begin{equation} TA{S_{avg\_{P_1}{P_2}}} &=& {\hbox{\it TAS}}\left( {IA{S_{avg\_{P_1}{P_2}}},{a_1} + {d_{{\rm{alt}}}}\frac{k}{2}} \right), \end{equation}$$

(32) $$\begin{equation} {t_{{\rm{still}} - {\rm{air}}\_{P_1}{P_2}}}& =& \frac{{{P_1}{P_{2 - {\rm{hdist}}}}}}{{TA{S_{avg\_{P_1}{P_2}}}*\cos \left( {{\hbox{\it FPA}}} \right)}} = \frac{{k*{H_{{\rm{dist}}}}}}{{TA{S_{avg\_{P_1}{P_2}}}*\cos \left( {{\hbox{\it FPA}}} \right)}} \end{equation}$$

The final gw and cg values are computed using Equations (15) and (16).

For a level-flight constant-speed cruise segment the look-up structure data provides the values corresponding to the flying altitude, IAS/Mach speed, initial gross weight, fuelburn, TAS, still-air flight time, and horizontal distance. The corresponding (P₁P₂) fractional flight path segment parameters’ computation can be performed relative to a selected fraction (k) of the fuelburn value, flight time or still-air horizontal distance. The fuelburn-based computations are performed using Equations (13) and (14), where gw _initial and gw _final are replaced by the actual gross weight at the start and at the end of the fractional segment (gw_P1 and gw_P2, respectively). Thus,

(33) $$\begin{equation} g{w_{P2}} = g{w_{P1}}\,{\rm{ + }}\,k^{\ast}{\rm{fuelburn}} \end{equation}$$

For the fractional flight time or horizontal distance-based still-air computations, the relationship between the flight time and still-air horizontal distance is described by Equation (14), and therefore:

(34) $$\begin{equation} {P_1}{P_2}_{ - {\rm{still}} - {\rm{air}} - {\rm{dist}}} = k*{H_{{\rm{dist}}}} \end{equation}$$

and

(35) $$\begin{equation} {P_{1}\,P_{2 -{\rm still} - {\rm air} - {\rm time}}} = k*{t_{{\rm{crz}} - {\rm{segm}} - {\rm{still}} - {\rm{air}}}} \end{equation}$$

The final gw and fuelburn values are computed from the cruise fuelburn look-up tables^{(Reference Dancila, Botez and Labour30)} as functions of the initial gw, altitude, and actual segment flight time:

(36) $$\begin{equation} g{w_{P2}} = f\left( {al{t_{{\rm{crz}}}},g{w_{P1}},{P_1}{P_{2 - }}_{{\rm{still}} - {\rm{air}} - {\rm{time}}}} \right) \end{equation}$$

For a selected fraction of a level-flight deceleration segment, situated between a TOD and the corresponding actual descent path, the horizontal flight distance and fuel burn values are equal to the same fractional value of the total segment's H _dist and fuelburn found in the look-up structure. The computation of the flight path segment's complete set of still-air parameters is performed in a manner similar to that used for the climb-acceleration or descent-deceleration segments, using Equations (17)-(22) and (Reference Jensen, Hansman, Venuti and Reynolds26)-(32), where d _alt = 0. The final gw and cg values are computed using Equations (15) and (16). The final speed, average segment speed, and actual segment flight time are computed considering a uniform deceleration relative to the aircraft's IAS/Mach.

Figure 15 presents a simplified description of a typical use of the vertical flight path graph and look-up structure, and Fig. 16 presents the processing steps employed for the translation of the vertical path segment data into lateral and vertical flight plan segment data.

Figure 15.

The flight plan computation workflow.

Figure 16.

The flight plan segment's computation workflow.