This chapter studies the algebra and calculus of vectors and matrices, as specifically applied to the USAF Test Pilot School curriculum. The course is a prerequisite for courses in Equations of Notion, Dynamics, Linear Control Systems, Flight Control Systems, and Inertial Navigation Systems. The course deals only with applied mathematics; therefore, the theoretical scope of the subject is limited.
The performance of an aircraft can adequately be described by assuming the aircraft is a point mass concentrated at the aircraft's center of gravity (cg). The flying qualities of an aircraft, on the other hand, cannot be described in such a simple manner. The flying qualities of an aircraft must, instead, be described analytically as motions of the aircraft's cg as well as motions of the airframe about the cg, both of which are caused by aerodynamic, thrust and other forces and moments. In addition, the aircraft must be considered a three dimensional body and not a point mass. The applied forces and moments on the aircraft and the resulting response of the aircraft are traditionally described by a set of equations known as the aircraft equations of motion. This chapter presents the form of the aircraft equations of motion used in the Flying Qualities phase of the USAF Test Pilot School curriculum.
This chapter reviews the mathematical tools and techniques required to solve differential equations. Study of these operations is a prerequisite for courses in aircraft flying qualities and linear control systems taught at the USAF Test Pilot School. Only analysis and solution techniques which have direct application for work at the School will be covered.
As spinning is still involved in around 60% of all aircraft accidents (BFU, 1985 and Belcastro, 2009), this aerodynamic phenomenon is still not fully understood. As U.S. and European Certification Specifications do not require recoveries from fully developed spins of Normal Category aeroplanes, certification test flights will not discover aeroplane mass and centre of gravity combinations which may result in unrecoverable spins. This book aims to contribute to a better understanding of the spin phenomenon through investigating the spin regime for normal, utility and aerobatic aircraft, and to explain what happens to the aircraft in terms of the aerodynamics, flight mechanics and the aircraft stability. The approach used is to vary the main geometric parameters such as the centre of gravity position and the aeroplane’s mass across the flight envelope, and to investigate the subsequent effect on the main spin characteristic parameters such as the angle of attack, pitch angle, sideslip angle, rotational rates, and recovery time. First of all, a literature review sums up the range of technical aspects that affect the problem of spinning. It reviews the experimental measurement techniques used, theoretical methods developed and flight test results obtained by previous researchers. The published results have been studied to extract the effect on spinning of aircraft geometry, control surface effectiveness, flight operational parameters and atmospheric effects. Consideration is also made of the influence on human performance of spinning, the current spin regulations and the available training material for pilots. A conventional-geometry, single-engine low-wing aeroplane, the basic trainer Fuji FA-200-160, has been instrumented with a proven digital flight measurement system and 27 spins have been systematically conducted inside and outside the certified flight envelope. The accuracy of the flight measurements is ensured through effective calibration, and the choice of sensors has varied through the study, with earlier sensors suffering from more drift than the current sensors (Belcastro, 2009 and Schrader, 2013). In-flight parameter data collected includes left and right wing α and β-angles, roll-pitch-yaw angles and corresponding rates, all control surface deflections, vertical speeds, altitude losses and the aeroplane’s accelerations in all three directions. Such data have been statistically analysed. The pitch behaviour has been mathematically modelled on the basis of the gathered flight test data. Nine observations have been proposed. These mainly cover the effects of centre of gravity and aircraft mass variations on spin characteristic behaviour. They have all been proven as true through the results of this thesis. The final observation concerns the generalisation of the Fuji results, to the spin behaviour of other aircraft in the same category. These observations can be used to improve flight test programmes, aircraft design processes, flight training materials and hence contribute strongly to better flight safety.
Your study of flying qualities to date has been concerned with the stability of the airplane flying in equilibrium on symmetrical flight paths. More specifically, you have been concerned with the problem of providing control over the airplane's angle of attack and thereby its lift coefficient, and with ensuring static stability of this angle of attack. This course considers the characteristics of the airplane when its flight path no longer lies in the plane of symmetry. This means that the relative wind will make some angle to the aircraft centerline which we define as Beta. The motions which result from Beta being applied to the airplane are motion along the y-axis and motion about the x and z axes.
The method used to analyze maneuvering flight will be to determine a stick-fixed maneuver point (Hm) and stick-free maneuver point (H'm). These are analogous to their counterparts in static stability, the stick-fixed and stick-free neutral points. The maneuver points will also be derived in terms of the neutral points, and their relationship to cg location will be shown.
The term 'dynamic parameter analysis' is used in this course to mean a discussion of (1) the general systems identification problem, (2) parameter estimation techniques, and (3) parameter analysis methods. Systems identification is the determination of the characteristics of a physical system from experimental test data. Parameter estimation techniques are methods used in systems identification problems, and parameter analysis is putting the results of these experiments to good use.
From the designer to the pilot, everyone associated with the flying qualities of high performance military aircraft, particularly the fighter or attack variety, is or should be aware of the importance of the high angle of attack flight regime. It is here that the aircraft will spend a significant amount of its time when performing the mission for which it was designed. It is here that the aircraft must display its most outstanding performance. It is also here that the aircraft, when pushed beyond its limits of controllability, can seemingly defy all laws of physics and principles of flight with which its surprised and often bewildered pilot is acquainted. The frequency of inadvertent loss of control at high angle of attack is such that many combat aircraft pilots are becoming firmly convinced that all pilots may be divided into two categories: those who have departed controlled flight, and those who will. Most thoroughly convinced are those pilots who fall into the former category. The unfortunate fact concerning departure from controlled flight at high angle of attack is that many aircraft and pilots are lost each year due to failure to recover from the out-of-control flight condition. The circumstances surrounding the losses are varied. Departures from controlled flight may occur unintentionally during high-g maneuvers or intentionally during a nose-high deceleration to zero airspeed in an attempt to gain an advantage over an opponent in combat maneuvering; the aircraft may spin and the gyration be identified too late for recovery or a steep spiral may be mistakenly identified as a spin, causing recovery controls to be misapplied. Whatever the circumstances, departures from controlled flight result all too often in catastrophe. For this reason, test pilots in particular must be familiar with every facet of the high angle-of-attack flight regime.
Pilot rating scales and their use in assessing aircraft handling qualities are reviewed historically, and objections that have been raised to limitations of earlier scales are considered in the development of a revised scale. Terminology used in the evaluation of handling qualities is reviewed and new definitions are proposed to improve communication and international understanding. O f particular significance is the new definition of handling qualities, which emphasizes the importance of factors that influence the selection of a rating other than stability and control characteristics. The experimental use of pilot rating is discussed in detail, with special attention devoted to (l) clarifying the difference between mission and task, (2) identifying what the rating applies to, (3) considering the pilot's assessment criteria, and (4) defining the simulation situation. The important elements of the report are then summarized in a suggested Briefing Guide, designed for guidance in planning and executing handling qualities experiments.
