chapter 01 - laws and definitions

8/13/2019 Chapter 01 - Laws and Definitions

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WILJAM FLIGHT TRAININGChapter 1.

Laws and Definit ions

Introduction

Before studying aerodynamics it is essential to have a thorough grounding in basic mechanicsand any related units of measurement. In aeronautics all measurements world-wide are basedon the International System (SI) of units, but in practice some anomalies exist, for examplealtitude, which is quoted in terms of feet, and airspeed which is quoted in nautical miles per hour(knots).

S I Units

The fundamental SI units are those of:

Mass

Length

Time

The amount of matter in a body; measured in kilograms (kg).

The distance between two points; measured in metres (m).

The duration of an event; measured in seconds (s).

From these, other standard units can be derived.

Derived UnitsThe following quantities and their related units of measurement are extensively used inaerodynamics:

Area

Volume

Velocity

Acceleration

Momentum

Force

A measure of a surface; measured in square metres (m2).

A measure of the bulk or space occupied by a body; measuredin cubic metres (m

3).

A measure of motion in a specified direction: measured inmetres per second (m/s).

A measure of the change of velocity of a body: measured inmetres per second per second (m/s

2).

The product of the mass and the velocity of a body: measuredin kilogram metres per second (kgm/s).

An external influence capable of altering the state of rest ormotion of a body, and is proportional to the rate of change ofmomentum of a body.

Force = Mass x Acceleration

The unit of force is the Newton (N), which is the force required

to give a mass of one kilogram an acceleration of one metre

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WILJAM FLIGHT TRAININGWeight

Work

Power

Energy

per second per second.

The gravitational force of attraction that the earth exerts on a

body of given mass: measured in kilograms (kg).

Weight = Mass x Acceleration Due to Gravity

Unlike the mass of a body, which remains constantirrespective of its location, the weight of a body varies withdistance between the body and the centre of the earth. This isbecause acceleration due to gravity varies with geographicallocation and altitude, but under standard conditions this term isassumed to be 9.81 m/s

2.

The effort needed when a force is applied to a body causes itto be lifted or moved a given distance in the same direction as

the force.

Work = Force x Distance

The unit of work is the Joule (J). One Joule is the work donewhen a force of one Newton moves a body through a distanceof one metre in the direction of the force.

Work is also stated in terms of Newton Metres (Nm), where1 Joule = 1 Nm.

The rate of doing work: measured in units of work per unittime: measured in Watts (W), where 1 watt = 1 J/s or 1 Nm/s.

Power = Force x Velocity

The capacity for doing work, which in mechanics exists in twobasic forms:

Potential energy- Due to position.

Kinetic energy - Due to motion.

The unit of energy is the Joule (J), where 1 Joule = 1 Nm.

Pressure The force per unit area acting on a surface: measured inNewtons per square metre (N/m2), which is properly called thePascal (Pa). In aviation the bar is more commonly used tomeasure pressure where 1 bar = 10

5Pa,

or 1mb = 1hPa. In

aerodynamics three types of pressure exist:

Static Pressure (PS). When air is stationary it exerts pressureequally in all directions. For example a mass of stationary airin a container, will exert a certain amount of static pressure onthe surrounding walls (Fig. 1.1)

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WILJAM FLIGHT TRAINING

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STATICPRESSURE

FIG. 1.1

Dynamic Pressure (PD). This occurs when moving air isbrought to rest on the surface of a body, i.e. when relativemovement exists between the surface and the airflow (Fig.1.2).

DYNAMICPRESSURE

(q)

FIG. 1.2

Dynamic Pressure is expressed as:

Q = RhoV2

Rho () is the air density, which decreases with altitude, and Vis the speed of the body relative to the airflow.

Total Pressure (PT). The sum of both the static and dynamicpressures. This is a very important term in aerodynamicformulae and is used in the calculation of lift, drag andindicated air speeds (these terms will be explained later).

Total pressure = Static Pressure + Dynamic pressure


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WILJAM FLIGHT TRAININGIn aerodynamics this is also referred to as Pitot Pressure.

Density The mass of material per unit volume: measured in kilogramsper cubic metre (kg/m

3). The density of air is an important

property in the study of aerodynamics and varies with changesin pressure, temperature and humidity. Such changes have asignificant effect on aircraft performance.

Temperature (T) A measure of the hotness of a body: measured in DegreesCelsius (C). The unit of thermodynamic temperature is theKelvin (K) and is the unit normally used in scientificcalculations. To convert from the Celsius system to the Kelvinsystem, 273 must be added to the temperature in C.

eg. 15C = 15+273 = 288K

Viscosity

Wing Loading

A measure of the resistance to motion. In aerodynamics it isthe resistance to movement of one layer of air over another,and in the case of a fluid, how easily it flows over a surface.For example cold engine oil has high viscosity, and hot engineoil has low viscosity.

The total aircraft weight supported per unit area of the wing:measured in Newtons per square metre (N/m

2).

Wing Loading = AUW / wing area

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WILJAM FLIGHT TRAININGAi rspeeds

Indicated Airspeed

(IAS).

CalibratedAirspeed (CAS).

EquivalentAirspeed (EAS).

TrueAirspeed (TAS).

Mach No.

The airspeed of an aircraft as shown on its pitot-static

airspeed indicator (ASI), that provides vital airspeedinformation, e.g. stalling and structural limitation airspeeds, tothe flight-crew. It is calibrated to reflect standard atmosphericadiabatic compressible flow at sea level, and is uncorrectedfor airspeed system errors.

The Indicated airspeed of an aircraft corrected for positionand instrument errors. CAS is equal to the True Airspeed(TAS) in standard atmosphere at sea level only.

The calibrated airspeed of an aircraft corrected forcompressibility error at a particular altitude. EAS is equal toIAS at airspeeds less than 300 knots, and is equal to TAS in

standard atmosphere at sea level only.

The actual speed of an aircraft through the air relative to theair that is uninfluenced by the aircraft. TAS is important fornavigation purposes only. The relationship between EAS andTAS is as follows:-

TAS = EAS ( o / )1/2

where o = density at sea level

= density at altitude

The ratio of the TAS of an aircraft to the speed of sound in the

surrounding atmosphere, i.e. the local speed of sound (LSS).

Mach No = TAS / LSS

Newtons Laws of Motion

Newtons 1st Law.

Newtons 2nd Law.

Newtons 3rd Law.

States that a body will continue in a state of rest, or in uniformmotion in a straight line, unless acted on by an external force,i.e. it has inertia.

States that a body at rest or in uniform motion will when actedon by an external force accelerate in the direction of the force.The magnitude of the acceleration for any given mass is

directly proportional to the size of the force applied, i.e. whena force of 1N is applied to a mass of 1kg it will accelerate at1m/s

2.

Force = mass x acceleration

States that for every action there is an equal and oppositereaction.

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WILJAM FLIGHT TRAINING

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chapter 01 - laws and definitions

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