# Basic Flight Mechanics

## Abstract

This book presents flight mechanics of aircraft, spacecraft, and rockets to technical and non-technical readers in simple terms and based purely on physical principles. Adapting an accessible and lucid writing style, the book retains the scientific authority and conceptual substance of an engineering textbook without requiring a background in physics or engineering mathematics. Professor Tewari explains relevant physical principles of flight by straightforward examples and meticulous diagrams and figures. Important aspects of both atmospheric and space flight mechanics are covered, including performance, stability and control, aeroelasticity, orbital mechanics, and altitude control. The book describes airplanes, gliders, rotary wing and flapping wing flight vehicles, rockets, and spacecraft and visualizes the essential principles using detailed illustration. It is an ideal resource for managers and technicians in the aerospace industry without engineering degrees, pilots, and anyone interested in the mechanics of flight.
• Provides readers with a thorough understanding of the physical principles behind flight mechanics without the need of complicated mathematics;
• Encompasses all types of flight covered in one book from the biomechanics of birds to airplanes and rockets;
• Illustrates key properties of flight with many schematic diagrams and examples to highlight important principles;
• Includes appendices on atmospheric properties as well as basic flight equations for more mathematically inclined readers.

## Chapters (6)

Aerodynamics refers to the study of forces applied to a solid object such as an airplane wing by a gas (typically air) flowing around it. Such a flow can be created either by moving the solid object through the atmosphere, or by blowing the air past a stationary object in a wind-tunnel. Since it is only the motion of the air relative to the object which creates the aerodynamic forces, it is unimportant how the flow has been generated as long its velocity and acceleration relative to the object are the same. For this reason, aerodynamic behavior of an airplane in actual flight can be understood by studying a model of a similar shape placed in a wind-tunnel. The relationship of the actual airplane’s dimensions with those of the model is called scaling, which also affects the flow conditions (density, velocity, temperature, etc.) required for simulating the actual aerodynamic properties in a wind-tunnel test. The fluid being an infinite medium can have its properties changing from point to point. Let us define the flow properties as those of a tiny volume of fluid called a fluid element. This element can move by translation and rotation, and its shape can also deform due to internal stresses. It is useful to define the properties of the flow far upstream of the object. These are called the freestream properties. The relevant freestream properties which dictate the magnitudes of the aerodynamic forces experienced by an airplane wing are the relative airspeed, the atmospheric density, and air temperature.

Airplane and glider flight is enabled by aerodynamic lift, and essentially takes place in a straight line, punctuated by brief periods of maneuvering, which by definition, consists of curved flight paths. Except while making a horizontal turn, the flight of an airplane or a glider always takes place in the vertical plane, which is defined as the plane formed by any two radial lines emanating from the earth’s center. That is why all airplanes and gliders are designed to have a plane of symmetry. By keeping the gravity vector in the plane of symmetry, all the forces can be kept naturally balanced in order to produce an equilibrium flight condition in a vertical plane. As soon as the plane of symmetry does not contain the gravity vector, an asymmetry exists in the aerodynamic forces and gravity, causing the vehicle to depart from the vertical plane in a horizontal maneuver.

Maneuvering in a horizontal plane becomes necessary for airplanes and gliders, whenever there is a need to change the direction of flight. Actually, this can also be done by performing a vertical maneuver.

In the previous chapters, we saw the flight of airplanes and gliders requires that a downwash must be created by the fixed wing as it moves through the air. The aerodynamic lift thus created depends crucially upon the speed relative to the atmosphere (airspeed), as well as on the incidence angle (angle-of-attack) made by the flight direction with the chord of the wing. As the speed falls below a certain level (called stall speed), the lift is insufficient to support the weight of the vehicle at even the largest possible angle-of-attack, and a stall results. Therefore, the fixed-wing flight requires a certain minimum forward flight velocity called the stalling speed. This severe limitation of airplanes and gliders is removed by having either a flapping wing or a rotary wing, which can generate the lift by the motion of a wing relative to the vehicle. In this manner, the vehicle can either ascend of descend vertically, or even remain stationary in the air (hover) like a hummingbird. In other words, while an airplane gently coaxes the air to follow the contours of its fixed wings, a flapping vehicle and a helicopter beat the air into submission with their moving wings.

Space flight is the ultimate form of travel which takes humans from the confines of the earth, and space exploration is an important means of expanding the frontiers of science. However, there are many prevalent misconceptions regarding space flight, which are probably derived from the popular science fiction. One of them is the issue of weightlessness. Astronauts are supposed to become weightless as soon as they get into the space. This is far from being true. Our weight is the reaction we feel from the ground as we stand, sit, or lie on it, or from any platform which has a zero vertical acceleration relative to the ground. By Newton’s third law of motion (see Chap. 1), if any object (such as yourself) exerts a force on any other object (like a platform), the second object also applies an equal and opposite force (called the reaction) on the first object. The magnitude of the force applied is equal to your own mass times the acceleration relative to the platform, according to the second law of motion (Chap. 1). If the platform itself does not have any vertical acceleration, the reaction experienced by you from the platform is equal to your mass times the acceleration due to gravity, which is your weight. Now, suppose you are in an elevator which is accelerating upward relative to the ground (see Fig. 6.1). The net acceleration experienced by you from the platform is now greater than that due to gravity, and it seems as if your weight has increased because the platform exerts a larger reaction on you. If a tragedy were to happen in which the elevator’s cable snaps, then both you and the elevator would be falling down with the same acceleration due to gravity (this situation is called a free fall), therefore your relative acceleration due to the platform would be zero. Since now you will not feel any reaction from the platform, it would seem as if your weight has become zero. In fact, your weight is still the same as it was before you got into the elevator. Similarly, an astronaut only feels a zero reaction from the spacecraft, whereas both the astronaut and the spacecraft are falling freely with the same acceleration due to gravity. The same weightless sensation is produced in an airplane which is making a vertical turn in a downward direction with a rate such that the lift acting on the aircraft is exactly zero, and the centripetal acceleration is provided only by the gravity. Such a zero-lift (or ballistic) flight is used to train astronauts for space missions.

Rockets are necessary to enable space flight, because any other form of propulsion cannot impart the necessary amount of velocity to put a spacecraft into orbit. Another important reason that rockets are indispensable for space flight is that they can provide thrust without requiring the presence of an atmosphere. Chemical rockets are typically employed to produce both a large thrust and a reasonable specific impulse by using a chemical reaction in a combustion chamber that generates an enormous amount of heat. This heat is then used to accelerate the resulting gases in a specially designed nozzle, which converts the thermal energy into kinetic energy of the exhaust. By Newton’s third law of motion, the exhaust gases apply an equal and opposite reaction on the rocket (the thrust) which causes it to accelerate in a direction opposite to that of the nozzle exhaust. A chemical reaction requires at least two substances, called the fuel and the oxidizer. The combined mixture of the fuel and the oxidizer is called the propellant, which results in a combustion. The propellant can either be a solid mixture which is ignited by a heat source, or two liquids which must be stored separately in tanks before being pumped into the combustion chamber and ignited. For example, a crude firecracker rocket has a mixture of powdered charcoal and sulfur as the fuel, and potassium nitrate as the oxidizer. A more sophisticated solid propellant mixture is fine aluminum powder (fuel), and ammonium perchlorate (oxidizer). Examples of liquid propellants are kerosene (fuel) plus liquid oxygen (oxidizer), hydrazine (fuel) plus nitrogen tetra-oxide (oxidizer), and liquid hydrogen (fuel) plus liquid oxygen (oxidizer). Solid rocket propellants are easier to store than liquid propellants, and do not require a sophisticated pumping mechanism. However, once ignited, it is difficult to stop the solid rocket combustion, while the combustion of liquid propellants can be controlled by manipulating the volume of the propellant pumped into the engine (called throttling). Thus liquid propellants are favored over solid propellants in space flight missions which require intermittent (or impulsive) firings. The chemical rocket principle is depicted in Fig. 7.1. Variations of the rocket principle are the acceleration of charged gases in an electromagnetic nozzle (plasma rocket), and nuclear propulsion wherein the heat is produced by a nuclear reaction rather than by a chemical combustion. However, these alternative forms of propulsion can currently produce only a very small thrust and hence cannot be used to launch a spacecraft into orbit.

... Considering the longitudinal stability, lift, lift change with respect to the angle of attack, location of the aerodynamic center, and wing downwash have an important effect and depend on the aerodynamic shape [7]. ...

In this study, the aerodynamic shape optimization of a wing is performed by using
3D flow solutions together with response surface methodology. The purpose of this
study is to optimize the aerodynamic shape of a wing to achieve the lowest possible
drag coefficient while ensuring desired maneuvering capability and lateral stability.
Aerodynamic shape optimization is performed for a wing of a turboprop trainer
aircraft. Optimization objective and constraints are determined according to mission
requirements and the dimensions of turboprop trainer aircraft already operating.
Since the objective function and the constraints consist of aerodynamic coefficients,
flow solutions are obtained to calculate aerodynamic coefficients by using an opensource RANS solver (SU2). Surrogate models that relate the design parameters to be
optimized to the objective function and the constraints are constructed as high-order
nonlinear analytical functions with the help of response surface methodology and the
design of experiment techniques. In the design of the experiment, a sequential
experimentation technique is used. The accuracies of the constructed surrogate
models are examined to validate the models. Optimization is performed by using the
surrogate models validated and the effect of the different optimization algorithms
(sequential quadratic programming and interior point) and initial conditions on the
optimized wing geometry are examined. Optimized wing geometry is compared with
the initial geometry in terms of the objective function value and the suitability of the
optimized geometry to the constraints is evaluated.

View Video Presentation: https://doi.org/10.2514/6.2021-2564.vid In this study, a wing planform optimization is performed by using 3D flow solutions together with the response surface methodology. The purpose of this study is to demonstrate an optimization approach involving aerodynamic shapes of aircraft. For this purpose, the wing planform of a turboprop trainer aircraft is optimized to achieve the lowest possible drag coefficient while ensuring the desired maneuvering capability and lateral stability. The optimization objective and constraints are determined considering mission requirements and dimensions of turboprop trainer aircraft already operating. Flow solutions are obtained by using a 3D open-source RANS solver, SU2, to calculate aerodynamic coefficients required in the objective function and constraints. Instead of using flow solutions to calculate aerodynamic coefficients at each optimization iteration, surrogate models that relate design parameters to be optimized to the objective function and constraints are used. Surrogate models are constructed as high-order nonlinear analytical functions with the help of response surface methodology. Sequential experimentation, a design of experiment technique, is used to determine design points where flow solutions are obtained to construct surrogate models. Surrogate models are validated by comparing the results of models with flow solutions and validated surrogate models are used in the optimization. Since the objective function and constraints are nonlinear functions, nonlinear optimization algorithms are used. The optimization is performed by using different optimization algorithms, the sequential quadratic programming, and the interior point, and different initial conditions to observe the effect of the optimization algorithm and the initial condition on the optimum configuration. The optimum wing planform obtained is compared with the initial configuration in terms of the objective function value, and the suitability of the optimum wing planform to the constraints is evaluated.

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