# Trajectory Management of the Unmanned Aircraft System (UAS) in Emergency Situation

## Abstract

**:**

## 1. Introduction

- -
- It does not influence the performance of the engine system, however, it limits the time for the UA to get to a destination or an alternative aerodrome.
- -
- It causes a partial loss of performance (power) of the engine system, which necessitates performing a horizontal flight or a flight with a small altitude loss.
- -
- It causes complete power loss, which necessitates performing a gliding flight only.

## 2. Problem Formulation

_{f}and speed V

_{f}, which, for example, can follow from the conditions of performing a safe landing. Assuming the final time t

_{f}, it is possible to avoid exceeding the maximal time of the flight following, for example, from the amount of accumulated energy in the accumulator (in the case of alternator or main accumulator damage).

- -
- durability of the airframe construction, engines, and other elements of the aircraft,
- -
- controllability and stability of the aircraft,
- -
- phenomena connected with low and high flight speeds (stall, aerodynamic phenomena, etc.),
- -
- performance limitations (e.g., absolute ceiling),
- -
- influence of a stormy atmosphere,
- -
- change of the performance caused by different emergencies (limitation of the power proceeded by the power unit, limitation of the time of the power unit work, complete power loss, etc.).

_{i}—state variables; u

_{j}—control variables; t

_{0}, t

_{f}—initial and final times.

_{0}, t

_{f}) has to be found that minimizes the functional:

_{L}is, in general, a function of the angle of attack α and the Mach number M, i.e., C

_{L}= C

_{L}(α,M). The lift coefficient is used as a variable rather than the angle of attack. The aircraft performance model was calculated on the basis of [11,12,13,14,15,16].

## 3. Method of Taking into Account of Limitations

_{min}, f

_{max}are known functions describing limitation.

**Figure 2.**The principle used to determine the minimal flight altitude and checking the required separation above the territory.

## 4. Analyzed Case: Total Power Loss of the Power Unit

_{f}, y

_{f}, z

_{f}, γ

_{f}, ψ

_{f}, e

_{cf}and initial conditions z

_{0}, V

_{0}, γ

_{0}, ψ

_{0}, will guarantee maximal distance covered by the aircraft to the final point:

_{0}and y

_{0}are also determined. However, in this task they are subject to variation. The three-dimensional motion of the aircraft is described by Equation (7) for the thrust equaling zero and a constant weight of the aircraft. That is why the aircraft is controlled by only two parameters: coefficient of load n

_{z}and roll angle φ. Symmetrical coefficients of the load are determined on the basis of:

_{z}are determined. From the fourth, fifth, and sixth equation values, λ, sinγ and tgψ, are determined. The derivatives γ' and ψ' are determined on the basis of:

## 5. Results and Discussion

Parameter | Value | Unit |
---|---|---|

Length | 1.80 | m |

Wingspan | 2.53 | m |

Wing area | 0.86 | m^{2} |

Gross weight | 9.69 | kg |

Maximum speed | 35.65 | m/s |

Cruise speed | 29.40 | m/s |

Stall speed | 12.67 | m/s |

Rate of climb | 4.30 | m/s |

**Figure 7.**3D form of the optimal trajectory with the high population area of Rzeszow as the prohibited zone.

## 6. Conclusions

- -
- it does not influence the performance of the engine system, however, it limits the time for the UA to get to the destination,
- -
- it causes a partial loss of performance (power) of the engine system, which necessitates performing a horizontal flight or a flight with a small altitude loss,
- -
- it causes complete power loss, which necessitates performing a gliding flight only.

## Conflicts of Interest

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**MDPI and ACS Style**

Majka, A.
Trajectory Management of the Unmanned Aircraft System (UAS) in Emergency Situation. *Aerospace* **2015**, *2*, 222-234.
https://doi.org/10.3390/aerospace2020222

**AMA Style**

Majka A.
Trajectory Management of the Unmanned Aircraft System (UAS) in Emergency Situation. *Aerospace*. 2015; 2(2):222-234.
https://doi.org/10.3390/aerospace2020222

**Chicago/Turabian Style**

Majka, Andrzej.
2015. "Trajectory Management of the Unmanned Aircraft System (UAS) in Emergency Situation" *Aerospace* 2, no. 2: 222-234.
https://doi.org/10.3390/aerospace2020222