Flight Mechanics and Control Flashcards
Aircraft Components
Horizontal Tail (Elevator), Aileron, Trailing edge flaps, Engines, Fuselage, Vertical Tail (Rudder), Landing Gear, Wing
Main Control Surfaces and Axis name + symbol
Aileron (Roll Axis π / p), Rudder (Yaw Axis π / r), Elevator (Pitch Axis π / q)
Additional Control Surfaces + Function
Spoilers (Reduce Lift, Increase Drag, Increase Roll Moment)
High Lift Devices (Flaps/Trailing Edge, Slots/Leading Edge)(Increase Maximum Lift)
Trimmable Horizontal Stabilizer (THS)
Trim Tabs
What are the Different Reference Frames Used in this lecture?
Kinematic, Aerodynamic, NED (North East Down, O), WGS 84 ( World Geodetic System, Used in GPS), Body Fixed, ECEF (Earth Centered Earth Fixed).
Difference between old and modern control systems?
Old: Airplane Control through Mechanical Systems, Additional controls through controller
Modern: Pilot doesnβt command surface positions, commands values. Calculation of surface positions is done by the controller
What is βFly by wireβ?
The control surfaces are no longer mechanically linked to the pilotβs actuators (pedals, etc.). They are linked through electronic sensors that detect the pilotβs inputs.
What are the 3 different ways to transform the NED frame into Body-Frame?
NED -> Kinematic -> Rot. Kinematic -> Body Frame
NED -> Body Frame
NED -> Aerodynamic Frame -> Body Frame
How to transform directly from the NED-frame to the Body fixed Frame?
By rotating the frame using the Euler angles in the following order (Yaw, Pitch, Roll)
How to transform from the WGS-84 to the ECEF frame?
x = (N + h) cos(π) cos(π)
y = (N + h) cos(π) sin(π)
z = [N ( 1-e2) + h] sin (π)
where
π = Geodetic Latitude
π = Geodetic Longitude
h = GPS height
What are the 3 rotation matrices for a 3-D rotation from NED to Body Fixed Frames?
around Yaw Axis:
[cos(yaw) sin(yaw) 0 ]
[-sin(yaw) cos(yaw) 0 ]
[ 0 0 1 ]
Around Pitch Axis:
[cos(pitch) 0 -sin(pitch)]
[ 0 1 0 ]
[sin(pitch) 0 cos(pitch)]
Around Roll Axis:
[ 1 0 0 ]
[ 0 -sin(roll) cos(roll)]
[ 0 cos(roll) sin(roll)]
What angles are needed to transform from the NED frame to the Kinematic Frame? what about the Rotated Kinematic Frame? and What about between the Rotated Kinematic and the Body-Fixed Frame?
NED -> Kinematic: ππΎ (course), πΎπΎ (climb)
Kinematic -> Rotated Kinematic: ππΎ
Rotated Kinematic -> Body-Fixed: βπ½πΎ, πΌπΎ
What is and how to calculate Geopotential Height?
The height that takes changes of gravity with height into account. (gravity decreases as altitude gets higher
HG = rE * h / ( rE + h)
where: rE = 6356766m (radius of the earth) and h is the geodetic height
What are the Mean Sea Level conditions (T, π, p)?
Ts = 288.15 K
πs = 1.225 Kg/m3
ps = 101325 Pa
How to calculate Temperature in the Troposphere?
@ Troposphere T(HG) = TR + πΎ (HG - HGR)
where πΎ = -[(n-1)/n] * [g/ R] β -0.0065
What is the Relation between pressure and temperature?
p(HG) / pR= [ T(HG-(g/πΎR))/TR]
What is the relation between Density and Temperature?
π(HG)/πR = T(HG-(g/πΎR + 1)/TR or
π(HG) = πMSL (1 + HG * πΎTR/TMSL)1/(n-1)
How does the temperature behave between 11 and 20 km of height?
It is constant with a value of 216.65 K
What are the different air speeds used in aviation? How can they be calculated?
VCAS = sqrt[2(pT -p)/πMSL] CAS corrected for instrument errors in IAS
VEAS = VCAS Corrected for compressibility effects
VTAS = VEAS sqrt[πMSL/π] EAS with compensation for density variation at altitude
VIAS = Indicated Airspeed (measured in plane)
What relationship is there between the different Airspeeds? (which one is larger)
EAS < CAS < IAS < TAS
@ MSL: EAS = CAS = TAS
What is the Center of Pressure?
Point at which all the aerodynamic forces act due to the pressure distribution around the profile. Ξ£M = 0
This point changes with AoA.
What is the Neutral Point?
Point at which the Pitching Moment does not change with the angle of attack. Also called Aerodynamic Center. Ξ£M β 0; CMπΌ = 0
Located @ around 1/4 c in subsonic. @ around 1/2 c in supersonic
Aerodynamic Force Coefficients in Aerodynamic Frame A?
(FAA)A = [-D ; Q ; -L ]A = qS [ -CD ; CQ ; -CL]A
Aerodynamics Moment Coefficients in Body-Fixed Frame B?
(MAA)B = qS [ sCL ; c Cm ; s Cn]B
How to estimate Thrust at different altitudes?
T/Ti = (V/Vi)nv (π/πi)nπ
What are the values for nv for the different types of engines?
Classic propeller engine: nv = -1
Turbojet (subsonic) nv = 0
Turboprop Engine: nv = -0.75
Turbofan engine: nv = -0.25
What are the values for nπ for the different heights?
For airbreathing engines at heights 0β¦11km: nπ = 0.7β¦0.8
For heights 11β¦20km: nπ = 1
How is the Engine performance number calculated?
Lp = T/Vnv
How is the Engine Throttle Position calculated?
πΏT = Lp/ Lp,max
Which are the Equations of Motion of an Aircraft?
V_dot = (T - D) /m - g sin(πΎ)
π_dot = ( L sin(π) / (m V cos(πΎ))
πΎ_dot = ( L cos(π) / (m V) - (g/V) cos(πΎ)
where πΎ is the climb angle and π_dot is the turn rate
What are all the Stationary Flight States?
Gliding, Straight Horizontal Flight, Climb and Descent, Steady Turn.
What is the Physical definition of Gliding?
Straight Flight: π_dot = 0
Stationary: πΎ_dot = 0 V_dot = 0
No Thrust: T = 0
What is the Glide Number?
π = CD / CL = -tan (πΎ)
with tan(πΎ) = Ξh/Ξx
How can one calculate the optimal values of CL, CD, V, and π ?
CL, opt = sqrt ( CD0 / k)
CD, opt = 2 CD0
Vopt = sqrt[ 2 (m g)/ (S π sqrt(CD0/k)) ] = VD,min
πopt = 2 sqrt (k CD0)
Definition for Straight Horizontal Flight?
Straight: π_dot = 0
Stationary: πΎ_dot = 0, V_dot = 0
Horizontal: πΎ = 0
What is the aerodynamic efficiency number?
The inverse of the optimal glide number
What is the definition for Climb and Descent?
Straight Flight: π_dot = 0
Stationary: πΎ_dot = 0 , π_dot = 0
Constant flight path: πΎ = const.
How to calculate Specific Excess Power? What does it mean?
SEP = V (T - D) /mg = spec. propulsion power - spec. power dissipated by drag
Definition of Stable Turn?
Stationary: π_dot = const, πΎ_dot = 0 , V_dot = 0
Horizontal: πΎ = 0
What is the Load Factor of an aircraft?
nz = L / mg
When @ horizontal flight nz = 1
It is a measure of how much G-Force is being felt by the aircraft
How can the turn radius be calculated?
rt = V/π_dot
How is the Load Factor related to Turning Flight?
nz = sqrt ( 1+ [ V2/(g rt)]2)
How is turn rate related to the Load Factor?
π_dot = g/V sqrt(nz2 - 1)
What is the minimum turn rate?
Turn radius is physically bounded by maximum Load factor, which is either limited by what the structure can withstand or by the Lift required for the load factor.
How is turn radius related to load factor?
rt = V2 / [g sqrt(nz2 -1)]
What are the limits in the Flight Envelope Altitude vs. Mach Number (Doghouse Plot)?
Thrust Limit
Cabin Pressure Differential Limit (y)
Lift Limitation
Thrust Limit
Dynamics Pressure Limit
Temperature Limit (for high Ma)
Flight Time equation?
dt = - Vnv /(g bL) CL/CD dm/m
For type 1 flight (V and CL const):
t = Vnv /(g bL) CL/CD ln(m1/m2)
Range equation?
ds = - Vnv+1 / (g bL) CL/CD dm/m
For type 1 flight (V and CL const):
s = Vnv+1 / (g bL) CL/CD ln(m1/m2)
What are the conditions for Static Stability?
SM = - CmπΌ /CLπΌ = xN - xG/ cmac > 0
CmπΌ < 0
Neutral Point must be Behind Center of Gravity
How is elevator deflection related to CL?
CL = CL0 + CLπΌπΌ + CLππ
with π being the elevator deflection
How is elevator deflection related to the pitching moment?
Cm = Cm0 + CmπΌπΌ + Cmππ
What are the 4 groups of states used in linearization?
Position (x, y, z) / ( Ξ», Ξ¦, h)[WGS84]
Translation (V, πΌ, π½) / (u, v, w)
Attitude (Ξ¦, Ξ, Ξ¨)
Rotation (p, q, r)
What are the primary controls of an aircraft? symbol?
Aileron Deflection: π
Elevator Deflection: π
Rudder Deflection: π
Thrust Lever Position: πΏT
What is the Linear state space model?
πΏπ_dot = π¨πΏπ+ π© β πΏπ
πΏπ = πͺ β πΏπ + π« β πΏπ
where x = state vector
y = output vector
u = input vector
A = system Matrix
B = input Matrix
C = Output Matrix
D = Feed-through Matrix
What are the steps used for Linearization?
1.- Identify states x(t) and inputs u = F(t): states are the ones that have more than 1 order of derivation, and inputs are time dependent functions.
2.- Reduce system order: x1 = π, x2 = π_dot
3.- Solve for the state derivatives: f1(x,u) = x1_dot = x2 and f2(x,xdot,u) = x2_dot = something else
4.- Compute input at reference conditions: Solve for uref
5.- Calculate the derivatives of f1 and f2 with respect to x1, x2, and u
6.- Assemble results:
A = [derivative matrix of f1 and f2 with respect to x1 and x2]
B = derivative of f1 and f2 with respect to u
7.- x_dot = A x + B u
What is the difference between a Short Period and a Phugoid?
Both are types of longitudinal Motion (straight)
Short Period: Period is short T = 3 s, frequency is high, contributions comes primarily from πΌ and q
Phugoid: Longer Period T = 61 s, frequency is Low, contribution comes primarily from V and πΎ
How to obtain the natural frequency, frequency and period?
w02 = π2 + π2
f = w0/2 π
T = 1/f
How are the damping and frequency properties described?
From the eigenvalues:
π = π + ππ
where π is the real part of the graph and π the imaginary
What is the reduced space state model simplified for Short Period?
[πΌ_dot ; π_dot] = [ZπΌ Zπ+1 ; MπΌ Mπ] [πΌ ; π] + [Zπ ; Mπ] π
where Z = Forces
M = Moments
q = pitching rate
π = elevator deflection
What is the characteristic equation?
It is an equation used to obtain the eigenvalues of a given system
det(ππ° β π¨) = 0 where the values of π are the eigenvalues.
For a linear 2nd order system:
s2 - 2 Ο s + Ο02 = 0
What is the generic characteristic equation (For a damping/spring system)?
s2 - 2 π s + π02
What is the reduced space state model simplified for a Phugoid?
[V_dot ; πΎ_dot] = [ Xv -g ; -Zv 0] [V ; πΎ] + [ Xπ XπΏπ ; -Zπ 0] [ π ; πΏπ]
where:
πΏπ = Thrust Lever Position
π = Elevator Deflection
πΎ = Flight Path Angle
How can the natural frequency of a Phugoid be approximated?
π0,ππ» = sqrt(2) g/ V0
What are the 3 types of lateral Motion?
- Roll Mode: Main contributors are roll rate (p) and roll angle (Ξ¦). Fast, aperiodic.
- Dutch-Roll: Main contributors are Yaw rate (r) and yaw/sideslip angle (π½), therefore it is simplified as pure Yaw Oscillation.
- Spiral Mode: Main contributor is the bank/roll angle (Ξ¦)
State Space Model of Dutch-Roll (simplified as Yaw Oscillation)?
[r_dot ; π½_dot] = [ππ ππ½ ; -1 Yπ½] [r ; π½] + [ Nπ ; 0] π
State-Space Model for Roll Mode?
[p_dot ; Ξ¦_dot ] = [Lp 0 ; 1 0] [p ; Ξ¦] + [Lπ 0] π
OR
p_dot = Lp p + Lππ
What are the 3 Basic Flight Control Systems?
SAS: Stability Augmentation System
CAS: Control Augmentation System
CSAS: Control and Stability Augmentation System (Mix between SAS and CAS)
What are some characteristics of SAS (Control system)?
SAS: Changes eigenvectors and eigenvalues (damping, frequency) It involves Feedback from some quantities.
βββuβ>Aircraftββββββxββββ>
β βServo<βController<βSensor<-|
What are some characteristics of CAS (Control System)?
CAS: Pilot does not command surfae deflection but desired values for defined quantities (AoA, Pitch Rate, Load Factor Roll Rate, Bank Angle)
β->Controllerβ->Servoβ->Aircraftβ>
β___________Sensor<_______________|
What are the different aircraft Classes?
Class 1: Small, Light
Class 2: Medium-weight, Low-Medium maneuverability
Class 3: Large, Heavy, Low-Medium maneuverability. (Passenger)
Class 4: High-Maneuverability
What are the different categories of Flight Phases?
Category A: (Nonterminal) Require rapid maneuvering, precise path control. [Combat]
Category B: (Nonterminal) Use gradual maneuvers, no precision tracking. [climb, cruise, loiter, descent]
Category C: (Terminal) Use gradual maneuvers and accurate flight-path control [Takeoff, Landing, Approach]
How can one directly calculate the characteristic values in a Short Period?
π0,ππ2= Mq ZπΌ - MπΌ (Zq + 1)
2 π = (Mq + ZπΌ)
