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Takeoff optimisation of coaxial compound helicopter with uncertainty quantification

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Abstract

This paper focuses on the optimal takeoff of a coaxial compound helicopter, considering the possibility of engine failure. When one engine fails during takeoff, a twin-engine helicopter must either reject the takeoff (RTO) before reaching the takeoff decision point (TDP) or continue the takeoff (CTO) after the TDP. This study aims to determine the theoretical TDP by striking a balance between CTO and RTO while considering uncertainties that arise during takeoff. To achieve this goal, a multistep optimisation structure that involves uncertainty quantification is proposed. Firstly, an aircraft with a developed engine power dynamics model is established for the one-engine-inoperative problem. The entire takeoff procedures, from all-engine-operating (AEO) takeoff to CTO/RTO, are formulated as nonlinear trajectory optimisation problems. A typical takeoff is analysed to illustrate the takeoff characteristics and the conventional procedure to determine the TDP of a coaxial compound helicopter. It is found that the interference between the coaxial rotor results in an inevitable height increase during landing, with each 1-m increase in failure height resulting in 2.28 m of additional height rising. Then a robust TDP and AEO takeoff are identified by applying a multistep optimisation structure, where the influences of uncertainties are discussed. Results indicate it is feasible to define TDP as a single speed or height indicator despite the uncertainties. The recommended speed indicator is slightly lower than the takeoff safety speed, and the speed ensures a short runway length and successful CTO regardless of the AEO takeoff. In addition, an AEO takeoff path is recommended, which shortens the runway length by 10%, and the corresponding liftoff speed is slightly lower than the TDP speed. Overall, the proposed multistep optimisation structure and uncertainty quantification approach help to achieve a robust takeoff performance for a coaxial compound helicopter with consideration of engine failure.

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Abbreviations

\(\varvec{A},\varvec{B},\varvec{A}_{\varvec{B}}^i\) :

Sobol matrices for sensitivity qualification;

\(H_{\textrm{OEI}}\) :

Height when engine failure;

J :

Cost function;

\(P_{A1}\),\(P_{A2}\) :

Power from two engines, kW;

\(P_{R}\),\(P_{P}\) :

Rotor/propeller power required, kW;

\(P_{\mathrm {OEI\ HI}}\) :

30 S One-engine-inoperative power, kW;

\(P_{\mathrm {OEI\ LO}}\) :

2.5 Min One-engine-inoperative power, kW;

\(P_{\mathrm {OEI\ CT}}\) :

One-engine-inoperative contingency power, kW;

\(P_{\textrm{TO}}\) :

Maximum takeoff power, kW;

\(S_i\) :

First-order sensitivity index;

\(S_{Ti}\) :

Total-effect sensitivity index;

\(t_d\) :

Total delay time, s;

\((U_e,V_e, W_e)\) :

Velocity components to ground axes, m/s;

\(\varvec{U}\) :

Control variables vector, \(s^{-1}\);

\(V_{c \max }\) :

Maximum climb rate constraint, m/s;

\(V_{\textrm{LO}}\) :

Liftoff speed, m/s;

\(V_{\textrm{TOSS}}\) :

Takeoff safety speed, m/s;

\(\varvec{X}\) :

State variables vector;

\(\varvec{\delta }\) :

Stick movements vector;

\(\Omega \) :

Rotor rotation speed, rad/s;

\((\Phi ,\Theta ,\Psi )^T\) :

Rigid body Euler angles, rad;

\(\tau _p\), \(\tau _{p1}\), \(\tau _{p2}\) :

Engine time constants;

\(\eta \) :

Engine efficiency factor;

AEO :

All engine operating

CTO:

Continued takeoff

H-V:

Height-velocity

OEI:

One engine inoperative

RTO:

Rejected takeoff

TDP:

Takeoff decision point

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Authors and Affiliations

  1. National Key Laboratory of Rotorcraft Aeromechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, Jiangsu, China

    Yanqin Zhao & Renliang Chen

  2. Department of Aerospace Engineering, Swansea University, Bay Campus, Swansea, Wales, SA1 8EN, UK

    Ye Yuan

Authors
  1. Yanqin Zhao
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  2. Ye Yuan
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  3. Renliang Chen
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Correspondence to Renliang Chen.

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Appendix

Appendix

Table 4 shows the typical path and terminal constraints for all scenarios, including normal takeoff, CTO and RTO. The data in Table 4 aligns with those in Tables 1 and 2. The remaining constraints are loosely defined not to restrict the search area for optimisation while ensuring realistic flight paths.

Table 4 Typical path and terminal constraints in takeoff optimisation
Full size table

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Zhao, Y., Yuan, Y. & Chen, R. Takeoff optimisation of coaxial compound helicopter with uncertainty quantification. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09832-w

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  • DOI: https://doi.org/10.1007/s11081-023-09832-w

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