Physics and Maths for the PPL E-Book

Luis Burnay

• Herausgeber: Crowood
• Kategorie: Fachliteratur
• Sprache: Englisch

Veröffentlichungsjahr: 2017

Beschreibung

Many student private pilots don't realize at the start of their course that many hours of study are required on top of the in-class schedule. This book will help those trainee pilots without science backgrounds, or those that need a refresher, to brush up on the necessary theory. It covers subjects that will be encountered many times during the PPL course, such as principles of flight, aircraft general knowledge, flight performance and planning, meteorology, navigation and human factors. The content is organized around two main groups of information, namely core knowledge, concentrating more on the concepts; and a practical toolbox, dedicated to some techniques that will be required during the course. Aimed at those trainee pilots without science backgrounds or those that need a refresher on the necessary theory, this handy reference book is illustrated with 170 colour photographs10 black & white photographs.

Leseprobe

PHYSICS AND MATHS FOR THE PPL

LUIS BURNAY

First published in 2017 by

Airlife Publishing, an imprint of

The Crowood Press Ltd

Ramsbury, Marlborough

Wiltshire SN8 2HR

www.crowood.com

This e-book first published in 2017

© Luis Burnay 2017

All rights reserved. This e-book is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorised distribution or use of this text may be a direct infringement of the author’s and publisher’s rights, and those responsible may be liable in law accordingly.

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

ISBN 978 1 78500 315 8

Dedication

To Joe – for that first flight on the left seat in October 1999, your enthusiastic support and … your flying-wisdom quotes!

CONTENTS

Preface

Introduction

CORE KNOWLEDGE

1   Laws of Motion

2   Energy and Power

3   The Behaviour of Air

4   Aerodynamics

PRACTICAL TOOLBOX

5   Trigonometry

6   Sexagesimal Operations

7   Interpolation of Tables

8   Dimensional Analysis and Units of Measurement

Index

PREFACE

The motivation to write this book sprang from my experience during the PPL ground school classes, where I observed how hard it was for some students to keep up with the pace of the course and the contents of the syllabus due, essentially, to lapses in their physics and maths knowledge or recollection.

I had in my class people from six different decades, from a teenager to a septuagenarian, with a very wide mix of backgrounds and life experiences. While it is wonderful that such diversity can be gathered in a single PPL classroom, with a passion for flying as probably the only common ground, it is natural that when there are varying levels of comfort with essential subjects in the realm of physics and mathematics, this unbalance will hinder those students less at ease with the fundamentals and slow their apprehension of the mostly technical subjects that will be taught in the course.

This is what this book is about: helping those aspiring pilots without science backgrounds, or those that need a refresher, to brush up on the matters that most will typically struggle with, and give them the solid base that is essential for understanding the course content. This will also stand them in good stead later on as pilots.

It is not meant to be a science book! The relatively informal approach is tailored to the transmission of general knowledge and will hopefully help the reader to gain some insight into matters that in real science are the object of a complex formal mathematical treatment. There are many simplifications and, although care is exercised to keep the scientific correctness in all explanations and demonstrations, I hope the more purist readers will forgive the occasional departure from formal rigor.

Remember that this book does not replace the material you will be using to guide you through your PPL course, nor does it relate in any way to the official syllabus defined by the aviation authorities. It is meant as a primer, an assistant for you to prepare yourself ahead of time for the courses you will be attending. You can come back to it for reference at any time whenever you struggle with some concepts during the course, but you will still need to follow the teaching materials that will be recommended by your school.

Happy course!

Luis Burnay

INTRODUCTION

Flying is available to people of all ages in good physical condition: with good hearing, good eyesight (even with lenses), a healthy cardio-pulmonary system and no serious conditions in other parts of the body. An average IQ suffices – apologies if this hurts some egos – but a bit of science mixed with technical knowledge is necessary.

Many student pilots don’t realize at the start of the course that many hours of study are required on top of the already intense in-class schedule, and that they will have to delve into subjects that they may well have been away from because of career options, or because they never liked them or developed them in school. It is not quite like getting a driver’s licence!

Fig 1 From How to Learn Flying – a Practical Guide in 6 Lessons, Editorial Império, 1937. JOHN CROSTON

The good news is: it’s not rocket science either. In fact, the basic ‘mechanical’ principles and skills for flying an airplane are not complex and have changed very little since the beginnings of aviation, as can be seen in Fig 1, which is taken from a 1937, 47-page booklet that ‘taught’ how to fly an airplane in … six lessons! It now takes considerably longer than that, as airplanes have become significantly more sophisticated (and safe) and as the lessons learned over 100 years of aviation come into play in the training of pilots.

Skills alone are not enough, though: a good pilot not only knows what to do with a plane, but also knows what makes it work and why some things are best left to test pilots or stunt pilots, or simply not tried at all. There’s a lot of judgement and decision-making in flying and it should be based on sound knowledge on top of experience.

Fig 2 The role of human error in accidents. WIEGMANN ET AL

In the course of your training you will hear over and over again that more than 70 per cent of accidents happen due to human error,1 the majority of which are attributable to the pilot; and as far as pilot errors are concerned, as shown in Fig 2, 80 per cent of the accidents happen due to skill factors.2 You will be given examples that will probably horrify you, making you think – and say – ‘I would never do that’.

The danger areas in terms of human physical and psychological limitations will be discussed in the human performance factors course, and you will also learn that besides recklessness and health incidents, a lot of what happens at the private pilot level comes about because some of the most basic notions behind flying aren’t taken into account.

Fig 3 Forces operating in a 60-degree bank.

It can be because the concepts were not quite understood – for example why a plane stalls at a faster speed when pulling ‘g’s and why you actually pull 2g in a 60-degree bank (Fig 3) – as you struggled to follow the maths that shows that it happens because of the physics behind flying; or it can be due to calculations gone wrong because you never grasped the logic behind them – fuel consumption estimates, mass and balance calculations, interpolations of performance tables or a bad conversion of units. Plenty to pick from!

Aircraft have gone a long, long way in terms of safety and reliability, and decades of human behaviour studies and accident analysis have introduced many improvements to pilot training. Still, humans remain the weak link and constitute the biggest liability in aviation. An essential element for reducing the human factor risks – besides training, which can obviously not be underestimated – is for pilots to understand as intimately as possible the workings of airplanes and be equipped with the necessary analytical tools to evaluate situations, calculate alternatives, understand events, diagnose problems and always stay within the safe limits of the flight envelope – the airplane’s and their own. Understanding the whys and hows of the airplane’s operation, which requires a grasp of the laws of motion, thermodynamics and fluid mechanics, plus the most elementary maths methods to link them all, is not just a ‘nice to know’ option: it is highly recommended.

This book will guide you through some concepts that will hopefully produce, somewhere along your course, that ‘aha!’ moment from which you see things in a different light. The intention is to promote understanding rather than memorization and to give you tools that allow you to find solutions to common problems when you can’t remember by heart what the answer is. Once you understand a concept it is rare for the understanding to be lost, whereas memory can (and does) play many tricks especially when we are under pressure – at that crucial moment when failure is not an option!

WHY PHYSICS AND MATHS?

Physics is the branch of science that explains, justifies and models what makes an airplane fly. As the discipline that studies matter and energy and the way the two interact, physics has many subfields, from mechanics to thermodynamics, particle physics, electromagnetism, optics and so on. It does get complex when it comes to designing and building planes, but in order to understand how and why they fly (or not!), how they are controlled and what conditions their performance, basic physics and maths will suffice. Don’t be scared, because no one will expect you to become a physics expert or a maths genius to solve Navier-Stokes equations3 or to abandon your vocation for liberal arts.

This book is not meant to be a course on physics, but only an introduction to some essentials for those less familiar with the discipline, touching on subjects that will be encountered many times during the PPL course, such as principles of flight, aircraft general knowledge, flight performance and planning, meteorology, navigation and human factors.

The content is organized around two main groups of information, namely core knowledge, concentrating more on the concepts; and a practical toolbox, dedicated to some techniques that will be required during the course.

Sir Isaac Newton’s laws of motion, the behaviour of gases and some simple aerodynamics form the mainstay of the core knowledge chapters. You will become familiar with mass, force and acceleration, moments, energy and power, as well as pressure, temperature and density. Fundamental notions about energy will be discussed because – and you will hear this expression again – an airplane is an energy-trading device par excellence, as you will learn and experience when you fly. This concept is very often overlooked and yet it forms the basis for understanding everything that moves around us, not just airplanes.

To figure out physics, and to solve practical problems in aviation, maths is the tool of choice, so there will be some important areas that you will need to refresh on: simple equation solving (yes, algebra!), and trigonometry are two of them, so that vectors such as wind velocities, lift and drag can be handled in order to understand how they interact with the airplane’s mass.

In physics, algebra is not just for equations: it’s there when you are performing operations with time and angles, using the sexagesimal system, as you will in navigation; it’s still there when you are looking at a table with figures in lines and columns and are forced to perform tabular interpolations for flight performance and planning; and it’s still there when you need to do unit conversions from the imperial to the metric system or vice versa, not to mention checking your ground speed when you are flying, calculating the temperature and pressure variations with altitude, fuel endurance and so on. These more practical areas will be dealt with in the practical toolbox chapters.

It is crucial that you become at ease with all these operations before you start your course, as this will allow you to concentrate on the relevant aspects of the syllabus, which will teach you what you need to know to become a pilot. Flying is a multi-disciplinary endeavour and it’s no good excelling at air law or communications if you don’t understand the fundamentals behind principles of flight, human factors or navigation, to name only a few courses. You will soon find out that all of the disciplines are interrelated rather than isolated entities.

Private pilots don’t have the benefit of regular professional training and recycling, and once done with the PPL course are pretty much left on their own training-wise, apart from the mandatory regular skills tests. Having a solid knowledge base that will always stay with you will be a huge asset and will give you the mental room to deal with the real important issues when things get a bit more tense. Occasional pilots often stay away from the cockpit for considerable lengths of time, which opens a lot of room for error; and errors become more likely when the core knowledge is just memorized and not understood.

Understanding the concepts – not just memorizing answers – and having the right tools will make you a safer pilot.

1 ‘The role of human factors in improving aviation safety’, Boeing Aero magazine No. 8 (1999)

2 Wiegmann, Douglas et al, ‘Human error and general aviation accidents: a comprehensive, fine-grained analysis using HFACS’, FAA report DOT/FAA/AM-05/24 (2005)

3 A set of non-linear partial differential equations that describe fluid motion.

1 LAWS OF MOTION

This chapter will start with fundamental principles that are important to understand. There will be a little bit of memorization required but intuitive cues will be given so that these concepts can be related to everyday life and the physical reality around us.