Evaluation of the power required in level flight is essential to any new or modified helicopter performance flight-testing effort. The conventional flight-test method is based on an overly simplification of the induced and profile power components required for a helicopter in level flight. This simplistic approach incorporates several drawbacks that not only make execution of flight sorties inefficient and time consuming, but also compromise the level of accuracy achieved. This paper proposes an alternative flight-test method for evaluating the level-flight performance of a conventional helicopter while addressing and rectifying all identified deficiencies of the conventional method. The proposed method, referred to as the corrected-variables screening using dimensionality reduction (CVSDR), uses an original list of 36 corrected variables derived from basic dimensional analysis principles. This list of 36 corrected variables is reduced using tools of dimensionality reduction to keep only the most effective level-flight predictors. The CVSDR method is demonstrated and tested in this paper using flight-test data from a MBB BO-105 helicopter. It is shown that the CVSDR method predicts the power required for level flight about 21% more accurately than the conventional method while reducing the required flight time by an estimate of at least 60%. Unlike the conventional method, the CVSDR is not bounded by the high-speed approximation associated with the induced power estimation, therefore it is also relevant to the low airspeed regime. This low-airspeed relevancy allows the CVSDR method to bridge between the level-flight regime and the hover. Although demonstrated in this paper for a specific type of helicopter, the CVSDR method is applicable for level-flight performance flight testing of any type of conventional helicopter.

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Flight test engineering is an interdisciplinary science that gathers flight-test data and develops methods with the objective of evaluating an aircraft or an airborne system in its operational flight environment. The need for flight testing emanates as a necessary effort that complements ground-based verification activities such as wind-tunnel testing, simulators and computational modelling. Flight testing is a broad field that involves many disciplines. Performance flight testing is one discipline that is responsible of providing answers to questions like: How high can the aircraft fly? How fast can it fly? How much power does the aircraft need in order to sustain specific flight conditions of gross-weight, altitude and ambient air temperature? Or How long can the aircraft remain airborne before it runs out of gas (or electric power)? A profound data base for the performance of any type of aircraft is essential for their safe and efficient operation. This thesis focuses on performance flight-testing methods for conventionally-configured helicopters, i.e., those that employ a single main rotor to generate lift and thrust, and a single tail rotor to counter-act the torque effect of the main rotor. More specifically, the scope of this research was limited to gas-turbine available power testing and power required for out of ground effect (OGE) hover and power required for level-flight (AKA cruise flight). The research was limited to the execution of up to ten flight test sorties on two types of helicopters; the Bell Jet-Ranger and the MBB BO-105 helicopters, both normally used for training at the National Test Pilot School (NTPS) in Mojave, California. The goal of this thesis is to develop new and improved flight-test methods to rectify existing problems associated with the conventional methods. The conventional method for the maximum available power of a gas-turbine relies on three independent, single-variable polynomials that often yield poor prediction accuracy that sometimes even defy basic engineering concepts. The conventional method for OGE hover performance is overly simplified and neglects important blade non-linear effects. This results in inaccurate empirical models for hover performance representation. The conventional flight-test method for level-flight performance incorporates several drawbacks which not only make the execution of flight-test sorties inefficient and time consuming, but also compromise the level of accuracy achieved. This conventional level-flight method fails to specifically address non-linear effects such as blade-tip compressibility and drag-divergence that often results in inaccurate predictions, especially at high altitude and low air temperature conditions. The research intended to develop new flight-test methods for the available power of a gas-turbine engine and for the power required for hover and level-flight. Both new methods are based on multivariable polynomial approach. The research was initiated with the development of a new method for the maximum available power of a gas-turbine engine. A novel method, referred to as the ‘Multivariable Polynomial Optimization under Constraints’ (MPOC), was developed. This method seeks for a third order multivariable polynomial to describe the engine output power as a function of the other three variables of the engine (compressor speed, temperature and fuel-flow). The maximum available engine power is realized by solving an optimization problem of maximization under constraints. For this optimization, the Karush-Khun-Tucker (KTT) method was used successfully. For the exemplary BO-105, the standard deviation of the output power estimation error was reduced from 13 hp (conventional method) to only 4.3 hp by using the proposed method. Expanding the flight-test data base to include seven different engines reveals that the multivariable polynomials approach of the proposed method performed much better with all seven engines, as compared to the conventional single-variable approach. The maximum average prediction error was only 0.2% as compared to a maximum average prediction error of 1.15%, yielded by the conventional method. The research effort conducted for the OGE hover performance was concluded successfully with the development of the novel “Corrected Variables Screening using Dimensionality Reduction” (CVSDR) method for hover performance. This novel method combines fundamental dimensional analysis to generate a list of candidate corrected-variables (CVs) to represent the hover performance problem, then screens for the most essential ones by means of dimensionality reduction, implemented by singular-value-decomposition (SVD). This phase of the research was executed with four sorties on the Bell Jet-Ranger helicopter and produced a total of five conclusions. The most significant conclusion was that power predictions of the CVSDR method were 1.9 times more accurate than the conventional method. At the 95% confidence level, the CVSDR method deviated by an average of only 0.9 hp (0.3% of the maximum continuous power of the example helicopter) from the actual power required to hover, whereas power predictions from the conventional method deviated by an average of 1.7 hp. The final phase of the research concentrated on developing a new flight-test method for the level-flight regime. This effort spanned over five distinct sorties using the BO-105 helicopter. Similar concepts used for the hover performance testing were expanded and adapted for level-flight performance flight testing. The CVSDR method for level flight performance can be regarded (abstractly) as an expansion of the CVSDR method for OGE hover into a higher dimensional space. This phase of the research was aimed at addressing five research questions and yielded ten conclusions. The top three conclusions were that (1) the power predictions accuracy achieved using the CVSDR method for level-flight was nearly 21% better (on average and at the 95% confidence level), as compared to the prediction accuracy yielded from the conventional method. (2) the CVSDR method made planning and execution of flight-test sorties more efficient and time conserving. It is estimated to reduce flight-time for data gathering by at-least 60%, and (3) the CVSDR method is not restricted by the high-speed approximation, hence is also appropriate for the low-airspeed regime, and can potentially bridge the empirical modelling gap between the hover and level-flight regimes. The novel flight-test methods developed within this research (the MPOC for the available power of a gas-turbine engine and the CVSDR for OGE hover and level-flight performance) are recommended to be used by the helicopter flight-testing community, as they were shown to increase accuracy and promote execution efficiency. This thesis produced six recommendations concerning possible future expansion of the work already done during the current research. These include an expansion of the CVSDR method into more areas of performance testing like vertical and forward flight climb, partial power and unpowered descent, etc. Another continued research recommendation relates to the applicability and efficiency of the CVSDR method to relevant vertical-lift aircraft that combine both RW and FW characteristics. It is also recommended that continued research look into the potential and feasibility of employing the CVSDR method for empirical modelling used by Health and Usage Monitoring Systems (HUMS) installed in helicopters. @en

The process of empirical models evaluation is at the core business of experimental flight-testing data analysis. Accurate and convenient flight-testing of helicopter engine(s) available power is crucial for predicting the total helicopter performance. Common practice in estimation of in-flight helicopter gas turbine engine power consists of a reduction of flight-test data into simplistic single-variable analysis approach. While such an approach is convenient for practical use, it often results in unrealistic predictions of the available engine(s) power. A novel approach for the helicopter available power problem is the so-called Multivariable Polynomial Optimization under Constraints method. In this method, 18 regressors, constructed from the engine non-dimensional parameters, are used to define empirical polynomial models. This paper is intended to complement the Multivariable Polynomial Optimization under Constraints method and answer the question of which multivariable polynomial can be generally used in representing helicopter gas-turbine engine performance? In this sense, a variety of seven gas-turbine engines installed on different helicopters are analyzed, each one giving 512 possible polynomial models to be used for available-power calculations. While conventional statistical methods of hypothesis-testing failed in providing the answer to the question stated above of which the best general empirical model for representing engine performance is, an alternative approach based on the Singular-Value-Decomposition theorem, was proven successful in providing the answer. Moreover, this approach presented in the paper yielded a short list of 10 simple and convenient multivariable polynomials, best representing the performance of all seven engines analyzed as a group.

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