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• SLAM_N SAM’S QUIK-N-DIRTY AERO NOTES •• PART 1 •• Why a pilot might want to read these notes • Definitions • Properties of Air • Aerodynamic Forces • Laws of Thermodynamics• States of Air • Bernoulli’s Equation • Myths of Flight •• WHY A PILOT MIGHT WANT TO READ THESE NOTES

⁃ Pilots and scientist describe flight differently.⁃ You can tell a pilot, but you can’t tell him much. Pilots are probably not

QUITE as smart as Newton and Bernoulli. After all, Newton invented calculus just to make sense of his new laws of motion. But if you ask pilots, we’ll tell you Newton was just thinking too hard, and the explanation is really very simple. For example, ask pilots about force and they’ll tell you with authority “force is mass times acceleration”, and that’s a good explanation, as far as it goes. But Newton’s law actually says force is a derivative (rate of change) of the momentum of a body in motion, which is its mass times its velocity. Momentum is an important property of moving air and it is used frequently in aerodynamics. So, even if scientific and pilot descriptions are only subtly different, pilots must understand that difference to know why airplanes fly and engines produce thrust.

⁃ These notes help pilots review aerodynamics quickly ⁃ but avoid thinking too hard.

⁃ These notes are split into two parts: ⁃ the pilot part, aero in pilot-speak, then ⁃ the science part, the technical stuff

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• DEFINITIONS ⁃ Crash (first things first)

⁃ a landing in which the vertical acceleration is so great and the time spent reducing it to zero is so brief that the acceleration, and hence the forces acting, result in structural failure. ⁃ USAF Academy Contrails 1974)

⁃ Acceleration (A) ⁃ Pilot

⁃ change of either direction or speed usually measured in velocity change over time (ft/sec/sec, ft/sec2)

⁃ Science ⁃ from the verb accelerate, to apply a force for some time ⁃ Acceleration is not used very much in dynamics (aero or hydro),

momentum change over time is more applicable. ⁃ Aerodynamics

⁃ Pilot ⁃ science of how air, and objects moving through air, affect each other.

The first thing pilots need to understand about aerodynamics is: aerodynamics is NOT the study of air moving around stationary objects, though every Aero 343 textbook gives us that impression. It is the study of objects moving though stationary air, causing the air to move. The air doesn’t move itself except in wind tunnels!

⁃ Science ⁃ aero (air, from the Greek aerios), dynamics (motion forces, from the

Greek dynamis, powerful) ⁃ Atoms

⁃ Pilot ⁃ little bits of stuff too small to see that everything we CAN see is

made of ⁃ Science

⁃ numbers on a blackboard that predict the cause and effect of matter/energy (remember E=MC2) that we can then observe. (Weird note here: the observation and the observer are part of the equation, so don’t go there) Sometimes matter/energy acts like waves, and sometimes like particles (quanta). When they act like particles, we slap a label on them (protons or neutrons or some such).

⁃ Force (F) ⁃ Pilot

⁃ mass x acceleration ⁃ weight, lift, drag, and thrust are forces. ⁃ usually measured in slugs (mass) times ft/sec2 (acceleration)

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• Definitions, Force

⁃ ⁃ Science ⁃ first derivative (change) of momentum (mass x velocity) over time⁃ change of momentum of mass⁃ since momentum is mass x velocity, it is measured by the amount of

change of the velocity vector (speed or direction) of mass ⁃ Molecules

⁃ Pilot ⁃ combinations of elements (grouped atoms) that form substances

⁃ Science ⁃ defined groups of atomic particles. ⁃ The formulas of atoms imply that as particles, atoms have mass and

inertia (momentum and energy) and other properties that are not as important in macro (meaning looking at the gas, not its molecules) sciences like aerodynamics.

⁃ The kinetic theory of gasses assumes that molecules, existing in a state of matter called a gas, are very small compared to the distance between them and their movements are constant, random, and unordered.

⁃ Mass (M) ⁃ Pilot

⁃ an amount of air ⁃ weight is mass accelerated by force, usually gravity

⁃ usually measured in slugs ⁃ Science

⁃ quantity of matter/energy. ⁃ When used in formulas for particles (as opposed to waves), it defines

momentum⁃ Momentum (m*)

⁃ Pilot⁃ inertia

⁃ Science ⁃ the mass times the velocity of air ⁃ The integral sum of momentum is kinetic energy.

⁃ Velocity (v) ⁃ Pilot

⁃ direction and speed usually measures in distance/time (ft/sec or fps) ⁃ Science

⁃ vector consisting of speed (distance over time) and direction. ⁃ Speed and direction imply Newtonian physics, the physics where

things happen at a small percentage of the speed of light.

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• PROPERTIES OF AIR ⁃ air: the mixture of gases in the atmosphere

⁃ Pressure ⁃ Static pressure (p)

⁃ Pilot ⁃ In flight, the air is just sitting there doing nothing until the airfoil

moves it. Air molecules have energy (momentum, which is mass and velocity) even if the gas is not moving. (I’d love to tell you the molecules are moving, but the quantum physics geeks and some guy named Heisenberg said you can’t be sure where they are or where they’re going, but that’s my NEXT project: Quik-n-Dirty Quantum Mechanics) The energy is all potential energy because when confined, the molecules act like a room full of Union pilots; they all have an independent idea of where to exert their mass and velocity. The total effect is random (nondirectional, thus no motion to create kinetic energy), constant and uniform. The total effect of all this energy, when pushing on a surface (area), is called static pressure.

⁃ Science ⁃ total of the linear momentum of molecules in a gas. As the gas

molecules collide with the walls of a container, the molecules impart momentum to the walls, producing a force, which can be measured. The force divided by the area is defined to be the pressure. It is scalar (non-directional), constant, uniform, and exerted perpendicular to the surface area.

⁃ Dynamic pressure (q) ⁃ Pilot

⁃ the energy of moving air ⁃ When a wing moves the air, the air’s energy becomes kinetic

(moving), like the Union pilots in the room all heading in the direction of a free buffet. The ordered momentum of the moving air is called dynamic pressure, and when it is exerted on an area, like part of the wing surface, it produces force.

⁃ Dynamic pressure is in just about EVERY formula in aerodynamics. When investigating crime, follow the money. When figuring out aerodynamics, follow the little ‘q’.

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⁃ Properties of Air, Pressure, Dynamic pressure⁃ Science

⁃ Moving air is measured as mass flow rate (velocity of mass flow or mass flux) :the amount of mass passing through a given area during some time (mass/time).

⁃ Thus: mass/time (mass flow rate, m*) = mass/volume (density, p) x distance/time (velocity, v) x area, m* = pAV

⁃ Since force is momentum change (mass x velocity) over time and thus the same as mass flux times velocity, then: force of moving air = 1/2pv2

⁃ Total pressure (p+q) ⁃ Pilot

⁃ Ptot (Pitot tube's namesake) = static plus dynamic pressure ⁃ Science

⁃ indicated airspeed (IAS) ⁃ measured by pitot tube comparison of stagnation point

(point of airflow striking an airfoil where local velocity = 0) pressure, thus total pressure = static pressure, versus static pressure measured at max airflow velocity

⁃ calibrated airspeed (CAS)⁃ IAS corrected for instrumentation errors, (angle of port,

tube ligation) ⁃ equivalent airspeed (EAS)

⁃ CAS corrected for compressibility, for the non-linear change of air pressure with altitude (need an air data computer, ADC)

⁃ produces equal dynamic pressure ⁃ true airspeed (TAS)

⁃ EAS corrected for the non-linear change of air density with altitude

⁃ Barometric pressure ⁃ Pilot

⁃ measured by a barometer, weight of inches of Mercury (Hg) in a (area) tube balanced against weight of outside air on the same area, also measured in millibars/hectopascals

⁃ standard day: 29.92 in Hg, 14.7lbs/ft2, 10.13mb,Hpa ⁃ Science

⁃ measured by a barometer, static pressure of the atmosphere exerted on an area

⁃ altitude pressure ratio (d) delta = P/Psl ⁃ about .5 at 18000ft ⁃ about .19 at max airliner altitudes

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⁃ Properties of Air, Pressure⁃ Pressure altitude

⁃ Pilot⁃ what the altimeter reads when set to standard day

⁃ Science ⁃ the standard atmospheric pressure corresponding to the

measured barometric pressure ⁃ Temperature (T)

⁃ Pilot ⁃ heat energy, a measure of total air mass energy ⁃ decreases about 2oC per 1000ft climb to 35000ft

⁃ Science ⁃ measure of the mean kinetic energy of the gas. The molecules are in

constant random motion and there is an energy (mass x square of the velocity) associated with that motion: the higher the temperature, the greater the motion. (see also Thermodynamics)

⁃ adiabatic: no heat interaction (isolation) ⁃ iso-thermic: no change of temperature

⁃ layer at about 35,000ft. Tropopause starts at this level ⁃ altitude temperature ratio (t) theta = T/Tsl ⁃ Degrees:

⁃ Kelvin (Ko) metric, -273 is absolute zero ⁃ Rankin (Ro) English ⁃ Centigrade (Co) metric, 0-100 based on state change of water

⁃ Density (p) rho ⁃ Pilot

⁃ mass of air in a certain volume ⁃ Science

⁃ mass of static air divided by the volume. ⁃ measured in mass (slugs) per volume (cubic feet)⁃ When a mass of air is blown (accelerated) through an engine,

volume is undefined and is measured as mass flux: mass flow rate ⁃ Since pound (lbs) = slugs x acceleration, density (mass

(slugs)/volume (ft3)) x acceleration (ft/sec2) becomes mass flow rate (lbs/ft3)

⁃ standard day density: .0765 lbs/ft3, .002378 slugs/ft3, sometimes called an atmosphere

⁃ density altitude: the standard atmospheric density corresponding to the measured density

⁃ altitude density ratio (s) sigma = p/psl

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⁃ Properties of Air⁃ Viscosity (m) mu

⁃ Pilot ⁃ stickyness, like molasses or oil ⁃ counter intuitive, because it increases as temperature increases ⁃ greater viscosity means objects slow air flow more ⁃ viscosity causes air to changes direction, producing lift

⁃ Science ⁃ rate of change of friction effect over distance ⁃ measured as a ratio (shear stress) vs. distance from object ⁃ viscosity’s friction effect dissipates airflow energy and it’s ‘stickyness’

turns the airflow as it passes over the surface boundary layer, the layer of airflow over airfoil retarded by friction

⁃ starts laminar and thin, transitions to random and thick ⁃ less friction in laminar flow, more lift in turbulent flow ⁃ boundary layer separation: boundary layer airflow energy decreases

due to friction to the point on the airfoil where it cannot overcome the increasing static pressure at the aft of airfoil, and it separates from the surface. If the point of separation is a small enough percentage of chord length, a stall occurs, lift generated cannot sustain the wing load in level flight.

⁃ inviscid: no viscosity ⁃ kinematic viscosity (v) nu: viscosity per amount of density

⁃ Compressibility ⁃ Pilot

⁃ change of density ⁃ airflow doesn't compress much until near mach

⁃ Science ⁃ measured in mass flux per volume ⁃ sound, small compression and decompression of air propagated

over distance ⁃ rate of propagation based on air temperature and medium only

⁃ Internal Energy (U) ⁃ Pilot

⁃ the amount of work the heat in an amount of gas can do ⁃ Science

⁃ the difference of the heat flow (Q) into a system and the work (W) done by the system. Internal energy of a thermodynamic system can be converted to either kinetic or potential energy.

⁃ Like potential energy, the internal energy can be stored in the system. Heat and work cannot be stored or conserved independently since they depend on the process.

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• AERODYNAMIC FORCES⁃ Pilot

⁃ All external forces on surfaces are caused by dynamic pressure, or friction.

⁃ When we add up ALL of the effects of the air on all of the surfaces of the wing, we find the amount and direction of the force on the wing. We then separate this force vector into the part that is moving the wing perpendicular to the direction of the wings’ movement through the air (see lift ) and the part that is forcing the wing in the opposite direction of its movement through the air (see drag).

⁃⁃ Lift (L)

⁃ Pilot ⁃ that part of the total effect of airflow on the wing that is moving the

wing perpendicular to the direction of the wings’ movement through the air

⁃ If there is one thing a pilot needs to know about what makes an airplane fly, it is: lift is a definition we use to describe force created by an airfoil section and the laws of aerodynamics, but a wing lifts an airplane upward by deflecting the air it contacts downward. The wing pushes the free stream of air up ahead of it (upwash), bound vortices created by the decreasing pressure draw the upwashed air across its surface and the airs’ viscosity bends it over the camber as far as its energy will take it, then the vortices and wing tip vortices combine to drive the air downwards (downwash).

⁃ The downwash created by a wing changes the average relative wind the airfoil sections of a wing encounter. Thus the angle of attack of one airfoil section differs from total wing angle of attack.

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⁃ Aerodynamic Forces, Lift⁃ Streamlines: separate homogenous states of airflow

⁃ Wind tunnel smoke streams denote airflow direction and approximate streamlines. ⁃ streams show airflow downwash and velocity changes ⁃ closer streamlines mean higher velocity

⁃ without friction, no streamlines due to no change in velocity, thus no variation, thus no lift

⁃ Science⁃ L = S(1/2 pv2)CL thus L = CL x dynamic pressure x area ⁃ Lift is dependent on airfoil size, area presented to the relative wind =

area (S) x Lift Coefficient (CL), air density (p), and airspeed (V). ⁃ vector portion of the force (integral sum of all derivatives of changes

of airflow momentum) generated by the airfoil directed perpendicular to the relative wind

⁃ Stall speed Vs: minimum speed needed generate lift to sustain level flight (see boundary layer separation) ⁃ function of wing load (w/S), lift at a (CLmax), density (p) ⁃ vs = sqrt( 2w/ pCLmaxS)

⁃ Coefficient of Lift (CL) ⁃ the ratio of lift force to dynamic pressure coefficient and

dynamic pressure independent of surface area⁃ thus CL = L/qS⁃ coefficient: a description of force independent of surface

area (span-wise flow etc.) ⁃ function of angle of attack (a): the angle between the

relative wind and the airfoil chord line, and wing shape⁃ CL with flaps

⁃ extend aft and down, increasing camber ⁃ greater lift at each a⁃ stall at lower a⁃ less CL max

⁃ CL with slats (slotted flaps) (leading edge)⁃ introduces hi energy air into the boundary layer

delaying boundary layer separation without increasing camber

⁃ delays stall to higher a CL max

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⁃ Aerodynamic Forces, Lift, Coefficient of lift

⁃ CL max maximum coefficient of lift versus a

⁃ thicker airfoils have greater CL max ⁃ symmetric airfoils generate no lift at a=0, (CL=0) ⁃ positive camber airfoils generate lift at a=0

⁃ Drag ⁃ Pilot

⁃ that part of the total effect of airflow on the wing that is moving the wing opposite to the direction of the wings’ movement through the air

⁃ Science ⁃ vector portion of the force (integral sum of all derivatives of changes

of airflow momentum) generated by the airfoil directed opposite and parallel to the relative wind caused by: ⁃ Zero lift drag CDo

⁃ skin friction, parasite drag ⁃ increases with free stream velocity, and

⁃ Pressure distribution drag KCL2

⁃ form friction, drag due to lift, induced drag ⁃ decreases with free stream velocity

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⁃ Aerodynamic Forces, Drag

⁃ Coefficient of Drag (CD) (D/qS) ⁃ the ratio of drag force to dynamic pressure ⁃ function of angle of attack (a), and airfoil shape⁃ independent of surface area (span-wise flow etc.)

⁃ Lift-Drag Ratio ⁃ primary factor of airplane performance ⁃ can be computed for every a based on coefficients of lift and

drag ⁃ L/Dmax maximum lift to drag ratio

⁃ If jet is operating in steady flight, drag is at minimum and enables ⁃ Maximum endurance ⁃ Maximum climb angle ⁃ Minimum descent angle⁃ Maximum glide distance ⁃ Maximum excess thrust

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⁃ Aerodynamic Forces, Drag,L/D max

⁃ Thrust (Ta) ⁃ Pilot

⁃ Suck, Squeeze, Glow, and Blow ⁃ Science

⁃ Thrust results from the acceleration of the mass of air through the jet engine. (see mass flux)⁃ The amount of thrust (force) is the rate of change of air

momentum over time. ⁃ Rockets create lots of rate of change of small amounts of

propellants. ⁃ Propellers create small rate of change of a large amount of

air. ⁃ Turbines are in between.

⁃ Kinetic energy is added to the mass of air by adding heat of burning fuel. (see Laws of Thermodynamics) When the increased energy is converted to velocity (see State of Air) the air retains this energy and some is wasted.

⁃ Ta = mass flow (Q) x (air velocity out, V2 – air velocity in, V1) ⁃ This chart follows the work (see Laws of Thermodynamics) done on

the air mass by a turbojet engine. During steady state operation, turbine work extracted during combustion and acceleration equals compressor work.

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⁃ Aerodynamic Forces, Thrust

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• LAWS OF THERMODYNAMICS ⁃ Thermodynamics: branch of physics, study of energy and work of

systems ⁃ Pilot

⁃ Temperature⁃ a way of measuring the energy of air: its ability to do work. ⁃ Air loses energy when it changes states (pressure, velocity).⁃ It changes states when it does work on objects.⁃ Some of the energy loss is work done by the object vibrating

the air. The propagation of this recurring change in pressure is sound.

⁃ Air through a turbine changes states (pressure, velocity) (see States of Air) and so its energy changes, producing work, losing some in the process.

⁃ Work ⁃ the product of force acting through a distance ⁃ For a gas, work is pressure x volume during a change of

volume. ⁃ pressure (force / area) times volume = units of force times

length ⁃ units of work (Joules or foot-pounds)

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⁃ Laws of Thermodynamics⁃ Science

⁃ Zeroth law ⁃ Thermodynamic equilibrium. When two systems are

separately in equilibrium with a third, the two are also in equilibrium. Also, systems in thermodynamic equilibrium have the same temperature.

⁃ First law ⁃ Between two states of equilibrium, internal energy (U, a state

of a gas) is equal to the difference of the heat flow (Q) into a system and the work (W) done by the system.

⁃ Uin – Uout = Q-W ⁃ Total energy is always conserved

⁃ Second law ⁃ Perfect energy conversion is impossible. ⁃ During a process of changing states of thermodynamic

equilibrium in the real world, heat energy is lost. ⁃ The heat loss is to due to entropy, the scientific assumption

that the tendency of energy differences is to reach universal thermodynamic equilibrium ⁃ (you know what assuming does). ⁃ isentropic: constant entropy ⁃ Entropy is used to measures efficiency of a process.

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• STATES OF AIR ⁃ State: the observation of properties of a gas (not to be confused with

states of matter: solid, gas, or liquid) ⁃ Boyles Law

⁃ The product of pressure (p) and volume (V) is exactly a constant (R) for an ideal gas (constant mass and temperature). pV=C

⁃ Charles&Gay-Lussac Law ⁃ volume is directly proportional to the temperature (T) for an ideal gas

(constant mass and pressure) V/T=C ⁃ Equation of State

⁃ Pilot ⁃ an equation for the relation of pressure, temperature, and density. If

two are known, the third can be determined ⁃ Science

⁃ combination of Boyles and Charles&Gay-Lussac pV=nRT ⁃ R= 8.31 joules/mole/degrees K, constant for all gases ⁃ n = number of moles

⁃ Aerodynamic Equation of State ⁃ Pilot

⁃ Equation of State for air only ⁃ Science

⁃ pv=RT ⁃ divide by mass per mole: Volume becomes Specific Volume (v)

(inverse of air density) 1/r ⁃ R= .286 kj/kg/Ko specific constant for air

• BERNOULLI’S EQUATION ⁃ Pilot

⁃ what makes airplanes fly (see Myths of Flight) ⁃ equation is useful because it relates changes in velocity to changes

in pressure, but it is only used on simple streamlines. It is used with a known velocity, but since airflow velocity is changing, calculus integrals are used to add up all the pressure variations.

⁃ Science ⁃ ptot = p + q, ptot(total pressure), p(static pressure), q(dynamic

pressure) ⁃ equation used to determine the pressure distribution of a fluid for a

known velocity distribution (streamline). It assumes low velocity, no added energy, no friction, no compressibility, irrotational (no angular momentum) flow.

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• MYTHS OF FLIGHT ⁃ Generation of Lift by “The Longer Path”

⁃ The Theory: ⁃ Lift is created by molecules of air having to travel further over the top

of the airfoil than the bottom to get to the same undisturbed state as they started. Since the top molecules move faster, Bernoulli’s equation states lower pressure is developed on the top of the airfoil and thus lift is created.

⁃ Why it’s wrong: ⁃ Airfoils can be designed with longer bottom surfaces or symmetrical

and can create lift. It’s not the distance but the turning of the airflow that’s important.

⁃ Top and bottom molecules do not meet again at the same spot at the back of the airfoil nor are they undisturbed. The airfoil has changed their momentum, both total and angular, and created downwash. Also, the real lift created is much higher than created with the velocity needed to travel the longer path.

⁃ Generation of Lift by Newton’s Law of Action-Reaction ⁃ The Theory:

⁃ Lift is created by air molecules striking the airfoil, imparting their momentum to the bottom surface, pushing the airfoil up.

⁃ Why it’s wrong: ⁃ If air contacts the upper surface, this theory is wrong because the

upper surface of the airfoil is ignored. Two airfoils with the same bottom and completely different tops would create the same lift. The top could have slabs of ice on it, and lift would occur.

⁃ Note: If air does not contact the upper surface, like on Space Shuttle reentry, this theory is correct.

⁃ Generation of Lift by Bernoulli’s Equation and Venturi Effect ⁃ The Theory:

⁃ Lift is created by the venturi effect of mass continuity, mass flowing past a point is constant, thus with total pressure constant and dynamic pressure increasing due to increasing velocity, static pressure decreases creating a vacuum on the upper surface.

⁃ Why it’s wrong: ⁃ The Venturi Effect is produced in a nozzle, but the airfoil surface has

no such constricting device. The flow field over an airfoil changes gradually with distance until it matches the free stream, as do the pressure and velocity of the flow. The Bernoulli equation does not apply.

⁃ The bottom of the wing is ignored. Ask any fighter pilot if weapons pods have drag.

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PART 2

• Stability and aerodynamic moments • Transonic and supersonic airflow • Performance