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Tests Prep WiSe2022 > Flight Mechanics and Control > Flashcards

Flight Mechanics and Control Flashcards

1
Q

Aircraft Components

A

Horizontal Tail (Elevator), Aileron, Trailing edge flaps, Engines, Fuselage, Vertical Tail (Rudder), Landing Gear, Wing

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2
Q

Main Control Surfaces and Axis name + symbol

A

Aileron (Roll Axis πœ‰ / p), Rudder (Yaw Axis 𝜁 / r), Elevator (Pitch Axis πœ‚ / q)

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3
Q

Additional Control Surfaces + Function

A

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

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4
Q

What are the Different Reference Frames Used in this lecture?

A

Kinematic, Aerodynamic, NED (North East Down, O), WGS 84 ( World Geodetic System, Used in GPS), Body Fixed, ECEF (Earth Centered Earth Fixed).

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5
Q

Difference between old and modern control systems?

A

Old: Airplane Control through Mechanical Systems, Additional controls through controller

Modern: Pilot doesn’t command surface positions, commands values. Calculation of surface positions is done by the controller

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6
Q

What is β€œFly by wire”?

A

The control surfaces are no longer mechanically linked to the pilot’s actuators (pedals, etc.). They are linked through electronic sensors that detect the pilot’s inputs.

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7
Q

What are the 3 different ways to transform the NED frame into Body-Frame?

A

NED -> Kinematic -> Rot. Kinematic -> Body Frame
NED -> Body Frame
NED -> Aerodynamic Frame -> Body Frame

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8
Q

How to transform directly from the NED-frame to the Body fixed Frame?

A

By rotating the frame using the Euler angles in the following order (Yaw, Pitch, Roll)

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9
Q

How to transform from the WGS-84 to the ECEF frame?

A

x = (N + h) cos(πœ‡) cos(πœ†)
y = (N + h) cos(πœ‡) sin(πœ†)
z = [N ( 1-e2) + h] sin (πœ‡)

where
πœ‡ = Geodetic Latitude
πœ† = Geodetic Longitude
h = GPS height

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10
Q

What are the 3 rotation matrices for a 3-D rotation from NED to Body Fixed Frames?

A

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)]

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11
Q

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?

A

NED -> Kinematic: πœ’πΎ (course), 𝛾𝐾 (climb)

Kinematic -> Rotated Kinematic: πœ‡πΎ

Rotated Kinematic -> Body-Fixed: βˆ’π›½πΎ, 𝛼𝐾

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12
Q

What is and how to calculate Geopotential Height?

A

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

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13
Q

What are the Mean Sea Level conditions (T, 𝜌, p)?

A

Ts = 288.15 K
𝜌s = 1.225 Kg/m3
ps = 101325 Pa

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14
Q

How to calculate Temperature in the Troposphere?

A

@ Troposphere T(HG) = TR + 𝛾 (HG - HGR)

where 𝛾 = -[(n-1)/n] * [g/ R] β‰ˆ -0.0065

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15
Q

What is the Relation between pressure and temperature?

A

p(HG) / pR= [ T(HG-(g/𝛾R))/TR]

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16
Q

What is the relation between Density and Temperature?

A

𝜌(HG)/𝜌R = T(HG-(g/𝛾R + 1)/TR or
𝜌(HG) = 𝜌MSL (1 + HG * 𝛾TR/TMSL)1/(n-1)

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17
Q

How does the temperature behave between 11 and 20 km of height?

A

It is constant with a value of 216.65 K

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18
Q

What are the different air speeds used in aviation? How can they be calculated?

A

VCAS = sqrt[2(pT -p)/𝜌MSL] CAS corrected for instrument errors in IAS

VEAS = VCAS Corrected for compressibility effects

VTAS = VEAS sqrt[𝜌MSL/𝜌] EAS with compensation for density variation at altitude

VIAS = Indicated Airspeed (measured in plane)

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18
Q

What relationship is there between the different Airspeeds? (which one is larger)

A

EAS < CAS < IAS < TAS

@ MSL: EAS = CAS = TAS

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18
Q

What is the Center of Pressure?

A

Point at which all the aerodynamic forces act due to the pressure distribution around the profile. Ξ£M = 0
This point changes with AoA.

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18
Q

What is the Neutral Point?

A

Point at which the Pitching Moment does not change with the angle of attack. Also called Aerodynamic Center. Ξ£M β‰  0; CM𝛼 = 0
Located @ around 1/4 c in subsonic. @ around 1/2 c in supersonic

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19
Q

Aerodynamic Force Coefficients in Aerodynamic Frame A?

A

(FAA)A = [-D ; Q ; -L ]A = qS [ -CD ; CQ ; -CL]A

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20
Q

Aerodynamics Moment Coefficients in Body-Fixed Frame B?

A

(MAA)B = qS [ sCL ; c Cm ; s Cn]B

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21
Q

How to estimate Thrust at different altitudes?

A

T/Ti = (V/Vi)nv (𝜌/𝜌i)n𝜌

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22
Q

What are the values for nv for the different types of engines?

A

Classic propeller engine: nv = -1
Turbojet (subsonic) nv = 0
Turboprop Engine: nv = -0.75
Turbofan engine: nv = -0.25

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23
Q

What are the values for n𝜌 for the different heights?

A

For airbreathing engines at heights 0…11km: n𝜌 = 0.7…0.8
For heights 11…20km: n𝜌 = 1

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24
Q

How is the Engine performance number calculated?

A

Lp = T/Vnv

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25
Q

How is the Engine Throttle Position calculated?

A

𝛿T = Lp/ Lp,max

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26
Q

Which are the Equations of Motion of an Aircraft?

A

V_dot = (T - D) /m - g sin(𝛾)
πœ’_dot = ( L sin(πœ‡) / (m V cos(𝛾))
𝛾_dot = ( L cos(πœ‡) / (m V) - (g/V) cos(𝛾)

where 𝛾 is the climb angle and πœ’_dot is the turn rate

27
Q

What are all the Stationary Flight States?

A

Gliding, Straight Horizontal Flight, Climb and Descent, Steady Turn.

28
Q

What is the Physical definition of Gliding?

A

Straight Flight: πœ’_dot = 0
Stationary: 𝛾_dot = 0 V_dot = 0
No Thrust: T = 0

29
Q

What is the Glide Number?

A

πœ€ = CD / CL = -tan (𝛾)

with tan(𝛾) = Ξ”h/Ξ”x

30
Q

How can one calculate the optimal values of CL, CD, V, and πœ€ ?

A

CL, opt = sqrt ( CD0 / k)

CD, opt = 2 CD0

Vopt = sqrt[ 2 (m g)/ (S 𝜌 sqrt(CD0/k)) ] = VD,min

πœ€opt = 2 sqrt (k CD0)

31
Q

Definition for Straight Horizontal Flight?

A

Straight: πœ’_dot = 0
Stationary: 𝛾_dot = 0, V_dot = 0
Horizontal: 𝛾 = 0

32
Q

What is the aerodynamic efficiency number?

A

The inverse of the optimal glide number

33
Q

What is the definition for Climb and Descent?

A

Straight Flight: πœ’_dot = 0
Stationary: 𝛾_dot = 0 , 𝑉_dot = 0
Constant flight path: 𝛾 = const.

34
Q

How to calculate Specific Excess Power? What does it mean?

A

SEP = V (T - D) /mg = spec. propulsion power - spec. power dissipated by drag

35
Q

Definition of Stable Turn?

A

Stationary: πœ’_dot = const, 𝛾_dot = 0 , V_dot = 0

Horizontal: 𝛾 = 0

36
Q

What is the Load Factor of an aircraft?

A

nz = L / mg

When @ horizontal flight nz = 1
It is a measure of how much G-Force is being felt by the aircraft

37
Q

How can the turn radius be calculated?

A

rt = V/πœ’_dot

38
Q

How is the Load Factor related to Turning Flight?

A

nz = sqrt ( 1+ [ V2/(g rt)]2)

39
Q

How is turn rate related to the Load Factor?

A

πœ’_dot = g/V sqrt(nz2 - 1)

40
Q

What is the minimum turn rate?

A

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.

41
Q

How is turn radius related to load factor?

A

rt = V2 / [g sqrt(nz2 -1)]

42
Q

What are the limits in the Flight Envelope Altitude vs. Mach Number (Doghouse Plot)?

A

Thrust Limit
Cabin Pressure Differential Limit (y)
Lift Limitation
Thrust Limit
Dynamics Pressure Limit
Temperature Limit (for high Ma)

43
Q

Flight Time equation?

A

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)

44
Q

Range equation?

A

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)

45
Q

What are the conditions for Static Stability?

A

SM = - Cm𝛼 /CL𝛼 = xN - xG/ cmac > 0
Cm𝛼 < 0
Neutral Point must be Behind Center of Gravity

46
Q

How is elevator deflection related to CL?

A

CL = CL0 + CL𝛼𝛼 + CLπœ‚πœ‚

with πœ‚ being the elevator deflection

47
Q

How is elevator deflection related to the pitching moment?

A

Cm = Cm0 + Cm𝛼𝛼 + Cmπœ‚πœ‚

48
Q

What are the 4 groups of states used in linearization?

A

Position (x, y, z) / ( Ξ», Ξ¦, h)[WGS84]
Translation (V, 𝛼, 𝛽) / (u, v, w)
Attitude (Φ, Θ, Ψ)
Rotation (p, q, r)

49
Q

What are the primary controls of an aircraft? symbol?

A

Aileron Deflection: πœ‰
Elevator Deflection: πœ‚
Rudder Deflection: 𝜁
Thrust Lever Position: 𝛿T

50
Q

What is the Linear state space model?

A

𝛿𝒙_dot = 𝑨𝛿𝒙+ 𝑩 βˆ™ 𝛿𝒖
π›Ώπ’š = π‘ͺ βˆ™ 𝛿𝒙 + 𝑫 βˆ™ 𝛿𝒖

where x = state vector
y = output vector
u = input vector
A = system Matrix
B = input Matrix
C = Output Matrix
D = Feed-through Matrix

51
Q

What are the steps used for Linearization?

A

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œ‘, x2 = πœ‘_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

52
Q

What is the difference between a Short Period and a Phugoid?

A

Both are types of longitudinal Motion (straight)

Short Period: Period is short T = 3 s, frequency is high, contributions comes primarily from 𝛼 and q

Phugoid: Longer Period T = 61 s, frequency is Low, contribution comes primarily from V and 𝛾

53
Q

How to obtain the natural frequency, frequency and period?

A

w02 = 𝜎2 + πœ”2

f = w0/2 πœ‹

T = 1/f

54
Q

How are the damping and frequency properties described?

A

From the eigenvalues:
πœ† = 𝜎 + π‘–πœ”
where 𝜎 is the real part of the graph and πœ” the imaginary

55
Q

What is the reduced space state model simplified for Short Period?

A

[𝛼_dot ; π‘ž_dot] = [Z𝛼 Zπ‘ž+1 ; M𝛼 Mπ‘ž] [𝛼 ; π‘ž] + [Zπœ‚ ; Mπœ‚] πœ‚

where Z = Forces
M = Moments
q = pitching rate
πœ‚ = elevator deflection

56
Q

What is the characteristic equation?

A

It is an equation used to obtain the eigenvalues of a given system

det(πœ†π‘° βˆ’ 𝑨) = 0 where the values of πœ† are the eigenvalues.

For a linear 2nd order system:
s2 - 2 Οƒ s + Ο‰02 = 0

57
Q

What is the generic characteristic equation (For a damping/spring system)?

A

s2 - 2 𝜎 s + πœ”02

58
Q

What is the reduced space state model simplified for a Phugoid?

A

[V_dot ; 𝛾_dot] = [ Xv -g ; -Zv 0] [V ; 𝛾] + [ Xπœ‚ X𝛿𝑇 ; -Zπœ‚ 0] [ πœ‚ ; 𝛿𝑇]

where:
𝛿𝑇 = Thrust Lever Position
πœ‚ = Elevator Deflection
𝛾 = Flight Path Angle

59
Q

How can the natural frequency of a Phugoid be approximated?

A

πœ”0,𝑃𝐻 = sqrt(2) g/ V0

60
Q

What are the 3 types of lateral Motion?

A
  • 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 (𝛽), therefore it is simplified as pure Yaw Oscillation.
  • Spiral Mode: Main contributor is the bank/roll angle (Ξ¦)
61
Q

State Space Model of Dutch-Roll (simplified as Yaw Oscillation)?

A

[r_dot ; 𝛽_dot] = [π‘π‘Ÿ 𝑁𝛽 ; -1 Y𝛽] [r ; 𝛽] + [ N𝜁 ; 0] 𝜁

62
Q

State-Space Model for Roll Mode?

A

[p_dot ; Ξ¦_dot ] = [Lp 0 ; 1 0] [p ; Ξ¦] + [Lπœ‰ 0] πœ‰
OR
p_dot = Lp p + Lπœ‰πœ‰

63
Q

What are the 3 Basic Flight Control Systems?

A

SAS: Stability Augmentation System
CAS: Control Augmentation System
CSAS: Control and Stability Augmentation System (Mix between SAS and CAS)

64
Q

What are some characteristics of SAS (Control system)?

A

SAS: Changes eigenvectors and eigenvalues (damping, frequency) It involves Feedback from some quantities.
——–u–>Aircraft—————–x———–>
↑ β€”Servo<–Controller<–Sensor<-|

65
Q

What are some characteristics of CAS (Control System)?

A

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€”>
↑___________Sensor<_______________|

66
Q

What are the different aircraft Classes?

A

Class 1: Small, Light
Class 2: Medium-weight, Low-Medium maneuverability
Class 3: Large, Heavy, Low-Medium maneuverability. (Passenger)
Class 4: High-Maneuverability

67
Q

What are the different categories of Flight Phases?

A

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]

68
Q

How can one directly calculate the characteristic values in a Short Period?

A

πœ”0,𝑆𝑃2= Mq Z𝛼 - M𝛼 (Zq + 1)

2 𝜎 = (Mq + Z𝛼)

Tests Prep WiSe2022 (6 decks)

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