Presentation 6: Fundamentals of Aircraft Aerodynamics Flashcards
Perfect Gas Law
p = [rho] R T
R = 1716 ft*lb/slugs*R
R = 287.05 N*m/kg*K
Assumptions of the Standard Atmosphere
That the atmosphere is a homogeneous gas of uniform composition that satisfies the perfect gas law.
Effects of Water Vapor
Affects engine performance and supersonic aerodynamics
Standard Sea-Level Properties
g = 32.17 ft/s^2 = 9.806 m/s^2
p = 2116.2 lb/ft^2 = 1.013 x 10^5 N/m^2
T = 59 deg F = 518.7 deg R = 15 deg C = 288.2 K
rho = 0.002377 slug/ft^3 = 1.225 kg/m^3
Tropopause
Transition between the troposphere (negative temperature gradient) and the stratosphere (isotherm).
At 36,089 ft
Temperature is -69.7 deg F
Temperature Variation w/ Altitude
T = T1 + a(h-h1)
a = -0.00356616 deg F/ft
a is the “temperature lapse rate”
Temperature Ratio to S.L. Temp
(Theta)
Theta = 1-6.875 x 10^-6 (h)
Pressure Ratio to S.L. Pressure
(Delta)
Delta = [Theta]^5.2561
Density Ratio to S.L. Density
(Sigma)
Sigma = [Theta]^4.2561
Kinematic Viscosity
[nu] = [mu] / [rho]
Reynolds Number
Re = V*l / [nu]
Re = [rho]*V*L / [mu]
Indicated Airspeed (IAS)
The direct reading from the airspeed indicator. This represents the airplane’s speed through the air, not necessarily its speed across the ground.
Cailbrated Airspeed (CAS)
The indicated airspeed corrected for instrument position and instrument error.
Different for each uniqure aircraft and its position of the pitot tube.
No direct reading of CAS in the cockpit, pilot must refer to handbook for particular aircraft.
True Airspeed (TAS)
Corrects for the effect of change in altitude on airspeed.
The airspeed indicator is calibrated for sea-level, not altitude.
TAS can be approximated by increasing the IAS by 2% per thousand feet of altitude.
The Anatomy of an Airplane
Flight Mechanics
The study of the motions of bodies (aircraft and rockets) through a fluid.
Four Forces of Flight
Lift, Drag, Weight, Thrust
Lift is always perpendicular to the relative wind
Drag is always parallel to the relative wind
Weight is always towards the center of the Earth
Four Forces in Climbing Flight
Turning, Banking the Aircraft
[phi] = bank (roll) angle
Three Equations of Motion
Assumptions of the Three Equations of Motion
Flat Earth
No yaw component
Free stream velocity is always parallel to the symmetry plane of the aircraft.
Sources of Aerodynamic Force
Pressure: acts perpendicular to the surface
Shear stress: acts parallel to the surface
Derivation of Bernoulli’s Equation
Euler’s Equation
dp = -[rho] V dV
Moment
Rotates a body
An increase in angle of attack is a positive moment, by convention
Parameters of the Aerodynamic Force
density, free-stream velocity, surface area, angle of attack, viscosity, compressibility
Buckingham Pi Theorem
A function with “n” varialbes can be described with “n-k” non-dimensional variables
p = n - k
where:
p = number of dimension-less variables needed
n = number of physical variables in physical relation
k = nubmer of fundamental dimensions required to describe the physical variables
Lift Coefficient
CL = L / qS
where q is the dynamic pressure
Mach Number
M = V / a
where a is the speed of sound
Drag Coefficient
CD = D / qS
where q is the dynamic pressure
Moment Coefficient
CM = M / qS
where q is the dymanic pressure
Dynamic Pressure
q = 1/2 [rho] V^2
Wetted Area
Surfae upon which the pressure and shear distributions act
Meaningful geometric quantity when discussing aerodynamic force
Not common
Planform Area
The projected area we can see when looking down at the wing or aircraft (shadow)
Most common definition of S
Base Area
Most common when analyzing slender bodies (like missiles)
Center of Pressure
The centroid of the distributed load
Aerodynamic Center
The point about which moments are independent of angle of attack
Fixed point on an airfoil
xa.c. / c = -m / a
Anatomy of an Airfoil
NACA Four Digit Airfoils
