2-1 Basic Theory

• a quantity that represents only magnitude
• Ex: time, temperature, or volume
• It is expressed using a single number, including any units

• a quantity that represents magnitude and direction
• It is commonly used to represent displacement, velocity, acceleration, or force

• (m)
• the quantity of molecular material that comprises an object

(v) is the amount of space occupied by an object

• (p)
• mass per unit volume
• Density = mass/volume: p=m/v

• (F)
• a push or pull exerted on a body
• Force = Mass * Acceleration: F=m*a

• (W)
• the force with which a mass is attracted toward the center of earth by gravity

• (M)
• a vector quantity equal to a force (F) times the distance (d) from the point of rotation that is perpendicular to the force.
• created when a force is applied at some distance from an axis or fulcrum and tends to produce rotation about that point.
• the moment arm is the perpendicular distance from the fulcrum to the point where the force is applied

• (W)
• a scalar quantity equal to the force (F) times the distance of displacement (s).
• W = F*s
• done when a force acts on a body and moves it

• (P)
• the rate of doing work or word done per unit of time.
• P=W/t

• a scalar measure of a body's capacity to do work
• Total Energy = Potential Energy + Kinetic Energy
• TE = PE + KE

• (PE)
• the ability of a body to do work because of its position or state of being
• It is a function of mass (m), gravity (g) and height (g)
• PE = W*H = mgh

• (KE)
• the ability of a body to do work because of its motionIt is a function of mass (m) and velocity (V)
• 

• AKA Newton's First Law
• "A body at rest tends to remain at rest and a body in motion tends to remain in motion in a straight line at a constant velocity unless acted upon by some unbalanced force."
• Inertia is the tendency for the body to remain at it's current state is inertia (rather it is at rest or in motion). Inertia opposes the work on the body causing the change
• Equilibrium is the absence of acceleration, either linear or angular. Bodies in equilibrium remain at a constant speed.

Equilibrium flight exists when the sum of all forces and the sum of all moments around the center of gravity are equal to zero.

• Exists when the sum of all moments around the center of gravity is equal to zero
• Example: an airplane in a constant rate, constant angle of bank turn is in trimmed flight, but not equilibrium flight
• An airplane in equilibrium flight is always in trimmed flight.

• AKA Newton's Second Law
• "An unbalanced force (F) acting on a body produces an acceleration (a) in the direction of the force that is directly proportional to the force and inversely proportional to the mass (m) of the body"
• a=F/m or a = (Vout-Vin)/time

• AKA Newton's Third Law
• "For every action, there is an equal and opposite reaction; the forces of two bodies on each other are always equal and are directed in opposite directions"

Static pressure (PS) is the pressure particles of air exert on adjacent bodies. Ambient static pressure is equal to the weight of a column of air over a given area. The force of static pressure always acts perpendicular to any surface that the air particles collide with, regardless of whether the air is moving with respect to that surface.

Air density (ρ) is the total mass of air particles per unit of volume. The distance between individual air particles increases with altitude resulting in fewer particles per unit volume. Therefore, air density decreases with an increase in altitude.

Temperature (T) is a measure of the average random kinetic energy of air particles.

Air temperature decreases linearly with an increase in altitude at a rate of 2 °C (3.57 °F) per 1000 ft until approximately 36,000 feet. This rate of temperature change is called the average lapse rate.

Humidity is the amount of water vapor in the air.

As humidity increases, water molecules displace an equal number of air molecules. Since water molecules have less mass and do not change the number of particles per unit volume of air, density decreases. Therefore, as humidity increases, air density decreases.

Viscosity (μ) is a measure of the air’s resistance to flow and shearing. Air viscosity can be demonstrated by its tendency to stick to a surface.

• For liquids, as temperature increases, viscosity decreases.
• Air viscosity increases with an increase in temperature.

The local speed of sound is the rate at which sound waves travel through a particular air mass.

• The speed of sound, in air, is dependent only on the temperature of the air. 
• As the temperature of air increases, the speed of sound increases.

• P=ρRT
• P = Pressure
• ρ = density
• T = Temperature
• R = constant for any given gas

• Bernoulli's Equation shows that the total energy can be separated into potential energy (static pressure) and kineic energy (dynamic pressure). It applies in flictionless, incompressible airflow.
• Static pressure - pressure of air exert on adjacent bodies.
• Dynamic Pressure - impact pressure of a large group of air molecules moving together.
•           q=(1/2)ρ(V^2)
• Total Pressure - sum of static and dyanamic pressure
•          H = Ps + (1/2)ρ(V^2)

• H = Total Pressure
• Ps= Static Pressure
• ρ = density
• V = Velocity

If dynamic pressure is known, H =Ps + q

airflow in which at every point in the moving air mass, the pressure, density, temperature, and velocity are constant.

• the path that air particles follow in steady airflow.
• in steady airflow, particles do not cross streamlines.

• a collection on many adjacent streamlines
• no mass can flow through the walls of the streamtube

• If we intersected the streamtube with two planes perpendicular to the airflow, the mass flow rate must be the same at both points.The amount of mass passing any point in the streamtube may be found by multiplying are by velocity to give volume/unit time and then multiplying by density to give mass/unit time.    
•      M = ρAV    
•      M = mass flow rate    
•      ρ = density    
•      A = Area    
•      V = Velocity

• 
• Since the guide is limited to subsonic airflow, changes to density can be ignored.
• A1V1 = A2V2

the indication on a pressure altimeter when the kollsman window is set to the current local altimeter setting

height measured with respect to the underlying ground surface.

average level for the surface of one or more of Earth's oceans from which heights such as elevations may be measured.

the height above the standard datum plane

• the altitude in the standard atmosphere where the air density is equal to local air density
• It is used as a predictor of aircraft performance rather than height reference

• Used to measure total pressure and calculate velocity.
• Pitot tube is a hollow tube open at one end and closed at the back.
• Opened end exposed into airflow to fill with air.
• Static Pressure ports on the surface are parallel to the airflow. They measure static pressure.
• Once Total Pressure is from Pitot Tube, and static pressure is from the static port, the differential pressure gauge measures the difference and has an output of dynamic pressure (q).
• 
• Now that we have Total Pressure (H), Static Pressure (Ps) and Dynamic Pressure (q), we can substitute for q.
• 
• Recalling Bernoulli's equation, we can solve for Velocity.
• 
• V = velocity
• H = Total Pressure
• Ps= Static Pressure
• p=density

• the actual instrument indication of the dynamic pressure the airplane is exposed to during flight.
• Factors such as altitude other than standard sea level, errors of the instrument, and errors due to installation, etc. may create great variances between instrument indication and the actual flight speed.
• Calibrated in knots of indicated airspeed.

Indicated airspeed corrected for instrument error

• the true airspeed at sea level on a standard day that produces the same dynamic pressure as the actual flight condition
• It is found by correcting calibrated airspeed for compressibility error

• True airspeed is the actual velocity at which an airplane moves through an air mass.
• It is found by correcting equivalent airspeed for eh difference between the local air density (ρ) and the density of the air at sea level on a standard day (ρ0)
• 
• 
• Since instrument error is typically small, and compressibility error is minor at subsonic velocities, ignore those erros and derive TAS directly from Initial Airspeed (per guide)
• 
• True Airspeed will equal IAS only under standard day conditions at sea level.
• Rule of thumb: For a constant IAS, TAS will increase approximately three knots for every thousand feet increase in altitude.

• Airplane's actual speed over the ground.
• Correct TAS for the movement of the air mass (wind) to get ground speed.
• GS = TAS - Headwind
• GS = TAS + Tailwind

• Indicated: altitude other than sea level, errors of the instrument, errors due to installation, etc
• Calibrated: angle of attack
• Equivalent: compressibility error
• True: air density, compressibility
• Ground: wind

Any device used or intended to be used for flight in the air

A mechanically driven fixed-wing aircraft, heavier than air, which is supported by the dynamic reaction of the air against its wings.

• Fuselage: basic structure of the airplane to which all other components are attached
• Wings: an airfoil attached to the fuselage and is designed to produce lift.
• It may contain control surfaces, fuel cells, engine nacelles, and landing gear.
• Empennage: the assembly of stabilizing and control surfaces on the tail of an airplane.
• It provides the greatest stabilizing influence of all the components of the conventional airplane.
• Consist of the aft part of the fuselage, the vertical stabilizer, and the horizontal stabilizer.
• Landing Gear: permits ground taxi operation and absorbs the shock encountered during takeoff and landing.
• Engine: provides the thrust necessary for powered flight.
• May be turboprop, turbojet, or turbofan engines.
• The type of engine depends on the mission requirements of aircraft.

• Modified version of monocoque
• Has skin, transverse frame members, and stringers to share stress load.
• Can be readily repaired if damaged.

All bracing is internal

• Longitudinal: passes from the nose to the tail.
• Movement around the axis is called roll
• Lateral: passes from wingtip to wingtip.
• Movement around the axis is called pitch
• Vertical: Passes vertically through the venter of gravity.
• Movement around the axis is called yaw

• 
• an infinitely long, straight line which passes through an airfoil's leading and trailing edges

• 
• the precise measurement between the leading and trailing edges measured along the chordline

• 
• the chord at the wing centerline

• 
• the chord at the wingtip

• 
• average of every chord from the wing root to the wingtip

• 
• the locus of points halfway between the upper and lower surfaces, measured perpendicular to the mean camber line

• An airfoil with zero camber.
• indicates that the MCL and the chordline are the same.
• Produces no lift at zero angle of attack.

• Airfoils that have the MCL above the chordline.
• Produces lift at zero angle of attack.

• Airfoils that have the MCL below the chordline.
• Produces negative lift at zero angle of attack

• 
• Airflow that travels along the span of the wing, parallel to the leading edge.
• Normally from the root to the tip.
• Not accelerated over the wing and therefore produces no lift.

• 
• Air flowing at right angles to the leading edge of an airfoil.
• Since it is the only flow that accelerates over a wing, it is the only airflow that produces lift.

• θ
• The angle between an airplane's longitudinal axis and the horizon.

• 
• the path described by its center of gravity as it moves through an air mass.

• 
• the airflow the airplane experiences as it moves through the air.
• It is equal in magnitude and opposite in direction to the flight path.

• 
• α
• the angle between the relative wind and the chordline of an airfoil.
• Abbreviated as AOA

• 
• the angle between the airplane's longitudinal axis and the chordline of the wing.

• 
• the angle between the spanwise inclination of the wing and the lateral axis

• the length of a wing, measured from wingtip to wingtip.
• It always refers to the entire wing, not just the wing on one side.

• the apparent surface area of a wing from wingtip to wingtip
• More precisely, it is the area within the outline of a wing in the plane of its chord, including that are within the fuselage, hull, or nacelles.
• S=bc
• S=wing area
• b=wingspan
• c=average chord

• the ratio of an airplane's weight to the surface are of its wings.
• tends to be an inverse relationship between aspect ratio and wing loading.
• WL=W/S
• WL=Wing Loading
• W=weight
• S=surface area of wing
• Gliders have high aspect ratios and low wing loading
• Fighters have low aspect ratios and high wing loading

• Taper is the reduction in the chord of an airfoil from root to tip.
• Assuming the wing the have straight leading and trailing edges, taper ratio is the ratio of the tip chord to the root chord
• 

• CT = tip chord
• CR = root chord

• 
• Λ
• the angle between the later axis and the line drawn 25% aft of the leading edge.
• It is not parallel to the leading edge.
• Wing sweep affects maximum lift and stall characteristics.

• 
• the ratio of the wingspan to the average chord
• Aircraft with a high aspect ratio, such as a glider, would have a long slender wing.
• Aircraft with a low aspect ratio indicates a short, stubby wing, such as those found on a high performance jet.
• AR = b/c
• AR = Aspect Ratio
• b = wingspan
• c = average chord

• the point at which all weight is considered to be concentrated and about which all forces and moments are measured.
• CG can shift as fuel burns, ordinances or cargo unloads, etc.

• the point along the chordline around which all changes in the aerodynamic force take place.
• On a subsonic airfoil, the aerodynamic center is located approximately one-quarter (between 23% and 27%) of the length of the chord from the leading edge.
• The aerodynamic center will remain essentially stationary unless the airflow over the wings approaches the speed of sound.

• Roll: movement around the longitudinal axis
• Pitch: movement around the lateral axis
• Yaw: movement around the vertical axis