# Vertical Flight Efficiency during Climb and Descent

This document provides a technical description on the methodology used in the analysis of the vertical profile of the aircraft’s trajectory during climb and descent phases of flights. The objective of the methodology is to measure and observe vertical flight efficiency without highlighting specific reasons for the observed behaviour. More detailed case studies are needed to find out reasons for particular observations.

## Acronyms and terminology

Term | Definition |
---|---|

CPF | Correlated Position reports for a Flight |

PRISME | Pan-European Repository of Information Supporting the Management of EATM |

## Methodology

The main assumption for the analysis of vertical flight efficiency during climb and descent is that, all other factors being equal, level flight is considered as inefficient. The methodology presented here is very similar for the climb and descent phases so the results for the climb and descent phases are directly comparable.

### General overview

The analysis is performed in 5 major steps. First, the trajectory data has to be loaded into the analysis software. Then the climb or descent part is identified in these trajectories. In these parts of the trajectories the level segments are detected and saved and additional filters are applied. The next step is the determination of the Top of Climb or Top of Descent. Finally, the results are calculated and processed for presentation. This process is visualised in Figure 1.

### Loading of the trajectories information

The data used for the analysis are downloaded from the PRISME database. CPF data is used in order to assess the actually flown trajectories.

The most important data fields that are of interest for the analysis are the altitude, position (latitude and longitude) and time information.

### Identification of the climb or descent part of the flight

For each flight, the climb part is defined as the part of the trajectory before the Top of Climb (ToC) and the descent part as the part of the trajectory after the Top of Descent (ToD).

Optimal climb and descent parts until/from the cruising altitude generally require less than 200NM of track distance from/until the airport, especially when the cost index is low or high for respectively the climb and descent (Airbus 1998; Sam Peeters 2013). With this in mind, the analysis is limited to the parts of the trajectories within a 200NM radius around the departure/arrival airport. This is to avoid including into the analysis climbs during the cruise phase which are used to optimise the flight altitude to account for the reducing weight of the aircraft.

The identification method of the climb or descent part corresponds strongly to the method proposed by the CCO/CDO Task Force and is further detailed below. It should be noted that the CCO/CDO Task Force uses a 300NM radius for the climbs instead of 200NM as used in this analysis. The reasons for choosing a 200NM radius for the climb are threefold:

Having the same radius for both the climb and descent analysis enables a direct comparison between the climb and descent results; and

Examination of aircraft trajectories showed that when a radius of 300NM is used, a lot of level flight at slightly lower altitudes than the cruising altitude is detected as inefficient, while this could be a consequence of the optimisation of the cruising altitude with respect to the aircraft’s weight. This type of level flight should not be seen as being inefficient and can influence the final results significantly in such a way that the results are not representative; and

300NM was chosen by the CCO/CDO Task Force because some very heavy aircraft could not be able to reach the cruising altitude within a 200NM radius. Nevertheless, it is preferred to have a stable methodology that suits best the behaviour of most of the flights and provides statistically correct results and analyses.

### Identification of the climb part of a flight

For each flight, the 4D point where the flight crosses the 200NM radius around the departure airport (for the first time) is determined. This point is defined as D200. Within the part of the trajectory from take-off until D200 included, the first 4D point at which the aircraft reaches the highest altitude is defined as the ToC-D200. If the aircraft is still climbing when passing the 200NM radius, D200 and ToC-D200 are the same.

The climb phase is considered to start at 3000 feet AGL since the Noise Abatement Departure Procedures (NADP) defined by ICAO end at this altitude (ICAO 2006).

Overall, the part of the trajectory considered for the analysis goes from 3000 feet AGL (included) until ToC-D200.

The CCO/CDO Task Force uses 2500 feet as lower limit which is chosen in relation to the availability of trajectory data.

### Identification of the descent part of a flight

For each flight, the 4D point where the flight crosses the 200NM radius around the destination airport (for the last time) is determined. This point is defined as A200. Within the part of the trajectory from A200 included until touchdown, the last 4D point at which the aircraft leaves the highest altitude is defined as the ToD-A200.

The descent phase is considered to end at 1800 feet AGL because the interception altitude for ILS systems is generally at or above this altitude. Using 1800 feet AGL as lower limit allows capturing the level segments before ILS interception but on the other hand disregarding the trajectory below 1800 feet AGL where the aircraft are on the ILS glideslope and no level segments should occur.

Overall, the part of the trajectory considered for the analysis goes from ToD-A200 until 1800 feet AGL (included).

## Detection of the level segments

In the climb or descent parts of the trajectories the level segments should be determined. The trajectory part between two points on that trajectory is considered as level when the trajectory stays within a fictional window as can be seen in Figure 2.

This window has temporal and altitude dimensions related to a specific vertical velocity that is considered to be the limit between level flight and climb/descent. After consultation in the CCO/CDO Task Force, this vertical velocity is chosen to be 300 feet per minute. Consequently, the dimensions of the window have to adhere to the following relationship:

\[ \frac{Y}{X} = 300 \ \textrm{feet per minute} \]

E.g. when a temporal size of 10 seconds is used, the window is 50 feet high. In this case the altitude information of the climb or descent trajectory is considered at every interval of 10 seconds. However, since the CPF data are a discrete representation of the actual trajectories, the necessary altitude information is not available for every required time instance. Because of this and whenever required, a linear interpolation is done to obtain the information needed for the analysis.

## ToC/ToD determination

In order to avoid considering level segments that happen slightly below the cruising altitude of a flight, an exclusion box is defined. The exclusion box ranges from the altitude of ToC-D200 or ToD-A200 down to 90% of this altitude. When a level segment is detected inside the exclusion box and it lasts longer than 5 minutes, it is not considered in the final results. The new top of climb or top of descent is in that case put at the start of (the first of) such segment(s) for climbs or at the end of (the last of) such segment(s) for descents. This new ToC or ToD is called respectively ToC-CCO or ToD-CDO. When no level segments longer than 5 minutes are detected inside the exclusion box, ToC-CCO/ToD-CDO coincides with ToC-D200/ToD-A200.

The determination of the ToC-CCO or ToD-CDO corresponds as well to the CCO/CDO Task Force’s approach.

## Processing of the results

The final results are calculated taking into account all level segments before ToC-CCO for the climbs and after ToD-CDO for the descents.

The results of the analysis include the total number of flights, the average value and median value of the distance flown level, the percentage of distance flown level with respect to the total climb or descent distance, the average value and median value of the time flown level, the percentage of time flown level with respect to the total climb or descent time and the average value and median value of the number of level segments.

An additional metric is the median CDO/CCO altitude. This metric is calculated by taking the altitude of the lowest level segment for each flight. This information is then aggregated by taking the median value over all considered flights. The rationale for using the lowest level segment is the following. It is best to have no level flight because this increases the fuel burn. However, if needed, the higher the level segment occurs, the better because the higher the level segment occurs, the lower the fuel burn. E.g. a level segment of a fixed duration at FL100 burns more fuel than at FL300. So, the lowest level segment is considered since it has the highest environmental impact.

In addition, each flight can be assessed as being CCO (Continuous Climb Operations) or CDO (Continuous Descent Operations). The fact whether a flight is considered as being CCO or CDO depends on the allowed amount of level segments and their allowed lengths or durations.

The formulas used for the calculation of all these results are shown in Table 2.

Result | Formula |
---|---|

Total distance flown by flight \(f\) during the climb/descent | \[D_f^+ = \begin{cases} D_{3000, f} - D_{\textrm{TOC} - \textrm{CCO}, f}, & \text{climbs} \\ D_{\textrm{TOD} - \textrm{CDO}, f} - D_{1800, f}, & \text{descents} \end{cases}\] |

Percentage of distance flown level during the climb/descent | \[D_{\textrm{perc}} = \frac{ \sum_{f} D_f}{\sum_{f} D_f^+} \cdot 100\] |

Average value of the distance flown level per flight | \[D_{\textrm{avg}} = \frac{ \sum_{f} D_f}{n}\] |

Median value of the level distance | \[D_{med} = \begin{cases} D_m & \text{$n$ is odd, $m = (n+1)/2$} \\ \frac{D_m + D_{m+1}}{2}, & \text{$n$ is even, $m = n/2$} \end{cases}\] |

Total time flown by flight \(f\) during the climb/descent | \[T_f^+ = \begin{cases} T_{3000, f} - T_{\textrm{TOC} - \textrm{CCO}, f}, & \text{climbs} \\ T_{\textrm{TOD} - \textrm{CDO}, f} - T_{1800, f}, & \text{descents} \end{cases}\] |

Percentage of time flown level during the climb/descent | \[T_{\textrm{perc}} = \frac{\sum_f T_f}{\sum_f T_f^+}\] |

Average time flown level per flight | \[T_{\textrm{avg}} = \frac{\sum_f T_f}{n}\] |

Median value of the level time | \[T_{med} = \begin{cases} T_m & \text{$n$ is odd, $m = (n+1)/2$} \\ \frac{T_m + T_{m+1}}{2}, & \text{$n$ is even, $m = n/2$} \end{cases}\] |

Average number of level segments per flight | \[_{\textrm{avg}} = \frac{\sum_f L_f}{n}\] |

Median value of the number of level segments | \[L_{med} = \begin{cases} \displaystyle L_m & \text{$n$ is odd, $m = (n+1)/2$} \\ \frac{L_m + L_{m+1}}{2}, & \text{$n$ is even, $m = n/2$} \end{cases}\] |

Percentage of flights considered as CCO or CDO | \[P = \frac{n_0}{n} \cdot 100\] |

With:

Symbol | Description |
---|---|

\(n\) | Total number of flights considered in the analysis |

\(n_0\) | Number of flights considered as CCO or CDO |

\(L_f\) | Number of level segments for flight \(f\) |

\(D_f^{+}\) | Total distance flown by flight \(f\) during the climb/descent |

\(D_f\) | Total distance flown level by flight \(f\) during the climb/descent |

\(D_{3000, f}\) | Track distance flown by flight \(f\) when passing \(3000\) feet AGL |

\(D_{\textrm{TOC} - \textrm{CCO}, f}\) | Track distance flown by flight \(f\) when passing TOC-CCO |

\(D_{\textrm{TOD} - \textrm{CDO}, f}\) | Track distance flown by flight \(f\) when passing TOD-CDO |

\(D_{1800, f}\) | Track distance flown by flight \(f\) when passing 1800 feet AGL |

\(T_f^{+}\) | Total time flown by flight \(f\) during the climb/descent |

\(T_f\) | Total time flown level by flight \(f\) during the climb/descent |

\(T_{3000, f}\) | Time at which flight \(f\) passes \(3000\) feet AGL |

\(T_{\textrm{TOC} - \textrm{CCO}, f}\) | Time at which flight \(f\) passes TOC-CCO |

\(T_{\textrm{TOD} - \textrm{CDO}, f}\) | Time at which flight \(f\) passes TOD-CDO |

\(T_{1800, f}\) | Time at which flight \(f\) passes \(1800\) feet AGL |

## Further Information

For further information please refer also to (Sam Peeters 2016; S. Peeters et al. 2016; Sam Peeters and Guastalla 2017).

## References

*Getting to Grips with the Cost Index*. Getting Grips With 2. Airbus. https://goo.gl/llIzE6.

*Doc 8168. Aircraft Operations*. Fifth. Doc 8168 OPS/611. ICAO. http://www.aptrac.co.za/file/icao_8168_5th_ed..pdf.

*2016 Integrated Communications Navigation and Surveillance (ICNS)*, 7A2-1-7A2-11. Herndon, VA, USA: IEEE. https://doi.org/10.1109/ICNSURV.2016.7486368.