Test Prep Flashcards
Aspect Ratio Formula
AR=b2/Sref
Taper Ratio Formula
λ=Ctip/Croot
Mean Aerodynamic Chord Formula
CMAC=(2/3)Croot(1+λ+λ2) / (1+λ)
Lift Formula
L=(1/2)𝜌V2CLSref
Drag Formula
D=(1/2)𝜌V2CDSref
Moment Fomula
M=(1/2)𝜌V2CMCMACSref
Lifting Line Theory Formula for Lift-AoA Coefficient
CL𝛼=(2𝜋AR)/(2+AR)
Polhamus Method Formula &
𝛽 value for subsonic
CL𝛼=(2𝜋AR)/(2+sqrt((AR2𝛽2/K2)(1+(tan2Λ50%/𝛽2))+4))
𝛽=sqrt(1-M2)
Slender Body Theory Formula
CL𝛼=𝜋AR/2
Components of 0-Lift Drag Coefficient Formula and Meanings?
CD0=Cf+CDfi+CDw
Where:
Cf=Friction Drag
CDfi=Form & Interference Drag
CDw=Wave Drag (M>0.8)
Equivalent Aircraft & Component Parasite Drag Area Formula D0
𝐷0 = (1/2) 𝜌 𝑉2 𝑆𝑟𝑒𝑓𝐶𝐷0
= (1/2) 𝜌 𝑉2SUMj=1n(SjCD0,j)
Reynolds Number Formula
𝑅𝑒=𝜌𝑉𝑙/𝜇
Component’s Zero Lift Drag Coefficient &
Parasite Drag Area Formulas
𝐶𝐷0,𝑗=𝑐𝑓,𝑗𝐹𝑗
𝑓𝑗=𝑐𝑓,𝑗𝐹𝑗𝑆𝑗
Lift-Induced Drag Coefficient Formula
𝐶𝐷𝑖=𝑘𝐶𝐿2
K-Factors formula
k=1/C𝐿𝛼 when CL >= C Lmax (k0%)
k=1/𝜋𝐴𝑅𝑒
Stability Measure Definition
The offset distance of the neutral point to the acual center of gravity, referring to the aerodynamic reference chord of the wing [%].
Usually -5%…-10% on civil transport aircraft
Stability Measure Definition
The offset distance of the neutral point to the acual center of gravity, referring to the aerodynamic reference chord of the wing [%].
Usually -5%…-10% on civil transport aircraft
Stability measure Formula
𝜕𝐶𝑀/𝜕𝐶𝐿= 𝑥𝐶𝐺/𝑐𝑀𝐴𝐶,𝑊− 𝑥𝐴𝐶/𝑐𝑀𝐴𝐶,𝑊= (𝑥̅𝐶𝐺 − 𝑥̅𝐴𝐶 ) [%]
Neutral Point Fomula
𝑥̅𝐴𝐶 =(𝐶𝐿𝛼,𝑊𝑥̅𝐴𝐶,𝑊 − 𝐶𝑀𝛼,𝑓𝑢𝑠 + ((𝑞𝐻𝑇/𝑞)(𝜕𝛼𝐻𝑇/𝜕𝛼)(𝑆𝐻𝑇/𝑆𝑟𝑒𝑓)𝐶′𝐿𝛼,𝐻𝑇) 𝑥̅𝐴𝐶,𝐻𝑇)/
(𝐶𝐿𝛼,𝑊 + ((𝑞𝐻𝑇/𝑞)(𝜕𝛼𝐻𝑇/𝜕𝛼)(𝑆𝐻𝑇/𝑆𝑟𝑒𝑓 𝐶′𝐿𝛼,𝐻𝑇)))
Trim around Lateral Axis Calculation
𝐶𝑀(𝑥=0) = 𝐶𝑀(𝐶𝐿=0) + (𝜕𝐶𝑀/𝜕𝐶𝐿)𝐶𝐿
Definition of Trim
Balancing of pitching moments. Usually achieved through the horizontal stabilizer. Basically trim is what maintains the aircraft at a certain altitud (and angle of attack) without any other control input.
Weight breakdown of take-off mass
𝑤𝑇𝑂 = 𝑤𝑂𝐸 + 𝑤𝑓𝑢𝑒𝑙 + 𝑤𝑃𝐿
where w0E is the Operating Empty weight (Wairframe, Wprop, Wsys), Wfuel the weight of the fuel and WPL the Payload.
Growth Factor of Payload Formula, Relation TO mass to PL mass.
𝜕𝑚𝑇𝑂 = (𝑚𝑇𝑂/𝑚𝑃𝐿)%𝜕𝑚𝑃𝐿
Vertical Load Factor Formula
𝑛𝑧 = 𝐿/𝑤
Load Factors during manouvers Formulas
For Pull-Up/ Flare manouver: 𝑛𝑧 = (𝐿0 + Δ𝐿𝑚𝑎𝑛)/𝑤
For Steady Turning Manouver: 𝑛𝑧 = (𝑤/cos(𝜙)) ⁄ 𝑤
Conversion from VTAS to VEAS
𝑉𝐸𝐴𝑆 = √(𝜌𝐻/𝜌 0 )* 𝑉𝑇𝐴𝑆
VTAS Definition
True Airspeed = VCAS adjusted fo derivationds from standard atmosphere conditions (pressure and temp)
VIAS Definition
Indicated Airspeed = The airspeed indicated on instrument panel. Uncorrected airspeed relative to the surrounding air
VCAS Definition
Calibrated Airspeed = VIAS adjusted for installation, positioning and instrumentation errors (e.g. angle of attack, sideslip angles, or flaps and landing gear settings)
VEAS Definition
Equivalent Airspeed: Used for structural calculations, normally converting the True Airspeed at the aircraft height into an equivalent airspeed at sea level.
Engine Thrust Formula
𝑇/𝑇𝑖 = (𝑉/𝑉𝑖) 𝑛𝑉( 𝜌/𝜌𝑖) 𝑛𝜌
Where n𝜌 is the dependency of the thrust on the density (altituda) and nv depends solely on the engine type.
Thrust Specific Fuel Consumption Formula
TSFC = 𝑚̇𝑓𝑢𝑒𝑙/𝑇
Power Specific Fuel Consumption
PSFC = 𝑚̇𝑓𝑢𝑒𝑙/P
Specific Excess Power Formula
𝑆𝐸𝑃 = ((𝑇 cos(𝛼 + 𝜎) − 𝐷) / 𝑚 𝑔) 𝑉
Weight Reduction Rate Formula
𝑑𝑤 = −𝑚̇𝑓𝑢𝑒𝑙 𝑔 𝑑𝑡
Flight Condition I: Duration Formula
Δ𝑡 = ((𝑉𝑛𝑉) / (𝑔 𝑆𝐹𝐶𝑥)) (𝐶𝐿 / 𝐶𝐷)𝑥 ln(𝑤𝑖/𝑤𝑖+1)
During Flight Fase “x”
Flight Condition I: Range Formula
Δs = ((𝑉𝑛𝑉+1) / (𝑔 𝑆𝐹𝐶𝑥)) (𝐶𝐿 / 𝐶𝐷)𝑥 ln(𝑤𝑖/𝑤𝑖+1)
During Flight Fase “x”
Values for SFCx on Flight Condition I
For Turbojet/turbofan:
SFCx = TSFCx ; nv ≈ 0
For Turboprop:
SFCx = PSFCx ; nv ≈ -1
Thrust to Weight Ratio Definition
Thrust to Weight = T/w, Usually indicates the aircraft’s performance, high T/w ratio is usually an indication that the aircraft is highly efficient (usually related to endurance, range, etc.)
Definition of Wing Loading
Wing Loading = w/S = Weight/Surface. Indicates Stalling speed of an aircraft. A low wing loading means low stalling speed, which means take off and landing at lower speeds (or with more load), and faster turning rate.
Lift Coefficient, lift curve slope and angle of attack relation
𝐶𝐿 = 𝐶𝐿(𝛼=0°) + 𝐶𝐿𝛼 𝛼
Mach number formula
M = V / a
Dynamic Pressure Formula (q-)
q-= rho/2 x V2
From 11,000 - 20,000 m above sea level, what’s the temp and the speed of sound?
a = 295 m/s
T = -57 °C = 216.15 K
Constant
What are 3 approaches to estimating aerodynamic drag? What limitations do each have?
-CFD (Computational Fluid Dynamics) : Relatively good quality data, and a lot cheaper than wind tunnel testing.
-Empirical: Bad quality data, not accurate
-Wind tunnel testing: Good data, but expensive, can have some size limitations.
-Flight tests: Can be dangerous and expensive, but can provide some of the best data.
What are the Design Phases and what results do each have?
-Conceptual Design : Cost goals, technology, Estimated L and D., Weight goals, Airfoil Design
-Preliminary Design : Design freeze, External Configuration, Camber and Twist, Loads, Stresses.
-Detail Design : Construction of individual parts, Manufacturing Process, Assembly line, Design Optimization
What is iw?
Incidence angle
What is Єt?
Geometric twist of the wing. (e.g. higher angle of attack at root)
What is ΓW?
The Dihedral Angle of the wing, angle between root chord and tip chord of the wing.
What is t/c?
Relative thickness. Max. Thickness to chord ratio
Which standard has a larger Wing Area? Why?
Boeing has a higher Area. The leading edge imaginary line continues until it coincides with the other wings leading edge line at the middle of the aircraft.
However, airbus defines its wing area differently. The leading edge does not continue, and the imaginary line between root leading edges of the wings are connected by a single straight line between them?
What is Cp? Formula?
The Pressure coefficient. Defined by:
Cp = (p - p∞)/q∞
What are some pressure distribution effects on a 3-D wing?
Flow around wing tips. Interference between components.
What advantages and disadvantages does a high aspect ratio wing have with respect to a lower aspect ratio one.
+ : Coefficient of induced Drag
- : Wing root stress for area, Necessary span at wing cord, Turbulence sensitivity.
What advantages and disadvantages does a untapered wing have with respect to a tapered wing?
+ : Manufacturing cost, Tip stall, Available fuel volume.
- : Wing root Stress
Why are wings swept back?
In order to delay critical conditions, such as cpcrit at higher Mach numbers,
What is Lifting Line Theory?
A basic theory used to calculate CL𝛼 for AR>4 and M<= 0.8 (incompressible flow)
What is the Polhamus equation used for? and what is the value of 𝛽 for its calculation in subsonic?
Calculating CL𝛼, but more complete than lifting line. Used for AR>2 and M<Mcrit (Allows compressible flow)
𝛽 = sqrt(1-M2)
Which represents the compressibility effect.
What are k2 and 𝛽 in the Polhamus equation? What are their values?
k2: Airfoil/Pressure influence
k2 = 1+1.5(t/c) for 3%<(t/c)<8%
k2 = 1+0.75(t/c) for 8%<(t/c)<12%
𝛽 = sqrt(1-M2)
Which represents the compressibility effect.
Whats the Slender Body Theory used for?
Calculating CL𝛼 used only for AR<2 at any M
How is Drag Divided?
-Zero Lift Drag: Skin Friction Drag, Pressure Drag (Interference, Form Drag).
-Lift-dependent Drag: Induced Drag, Lift dependent Form-Drag.
What is Reynolds Number?
It describes fluid flow. It describes the flow conditions around the aircraft.
What Reynolds Number should I use? (Re or Reco)
Always the one that is lower. So both must be calculated and if Reco< Re, then Reco is to be used,
What is the Fj in the equation to calculate CD0?
It is each component’s Form Factor. Depends on Geometry.
What is Interference Drag?
Drag produced at aircraft joints (wing-fus, fus-nac, etc).
It can be estimated by counting the number of interference points. This number is basically the percentage of total drag that is due to interference drag.
What is Wave Drag?
Drag that is produced by supersonic regions on the aircraft, which in turn produce flow separation that reduces Lift.
Why does Lift-Induced Drag exist?
Because the wing is Finite and 3 dimensional.
How to know which k-factor to use?
For small values of CL (CL<CL,PB):
use k = 1/(𝜋 𝐴𝑅 𝑒)
For Large CL (CL>CL,max)
use k = 1/(C𝐿𝛼)
Whats e?
Oswald Efficiency Factor. Depends on type of aircraft.
How to obtain CL/CD max?
At CL vs CD curve, draw line tangent to the curve that crosses the point (0,0), where this straight line touches the curve is the max CL/CD
What does each number in a NACA airfoil mean?
for a NACA 0123:
-the 0 represents the maximum camber in % (0% in this case)
-1 is the rel location of maximum camber (in this case 10% to the rear)
-2 and 3 represent the relative thickness in % (23% in this case)
Whats Cp,crit?
The point at which supersonic flow regions are formed, also called supercritical flight region.
What happens to Mcrit when angle of attack increases?
It gets lower, which is bad because it means it is easier to reach. (Flow separation can happen at lower speeds)
What are advantages and disadvantages of Trailing Edge Flaps?
+ Higher CL,max, higher C𝐿𝛼, higher CL0
- Higher CD,min, Higher CD0
Some types of Trailing Edge Flaps?
Camper flap (plain flap, slotted flap), Spread flaps (split flap, zap-flap), Junkers flap, Fowler System.
Some types of Leading Edge Flaps?
Slotted, Slat, Droop Nose, Krüger
Some types of Engine-Based High-Lift Devices?
Internally/Extranally blown flaps (IBF / EBF), Upper Surface Blowing (USB), Jet Flaps, etc.
Methods of Drag Reduction?
- Reduction of total wetted area to Wing Ratio (Reduce Fuselage)
- Increase of AR
- Streamlining (Removing external components)
- Laminarization (Remove boundary layer)
- Reduction of Turbulence (Material structures in paint can reduce turbulence)
- Wing Tip Forms (Winglet)
Where should the neutral point be in relation to the center of gravity for a statically stable aircraft?
The neutral point should be BEHIND the center of gravity
Whats the Neutral Point?
Point at which the sum of pitching moments do not depend on the angle of attack
What is Trim?
The adjustment of control surfaces (mostly the elevator) to keep the aircraft at a neutral position through balancing the moments.
What is ηHT?
The Horizontal Tail Deflection
Whats CN?
Yaw Moment Coefficient
What is VD?
Design Dive Speed
What method is the mostly used to estimate wing mass? (Roskam or Torenbeek)
Torenbeek, it is much simpler and gives a good approximation.
What is LG?
Landing Gear
How is Operating Empty mass calculated?
mOE = mTO (1- Cfuel) - mPL
where Cfuel = mfuel/mTO
What types of load must be taken into account when designing an aircraft?
Structural Loads
Vertical Loads (includes Limit Loads and Ultimate Loads)
Maneuver Loads
Gust Loads
What are some examples of structural loads?
Point Forces (Landing gear loads, engine thrust)
Surface Forces (Aerodynamic loads, pressure differences)
Body Forces (Mass inertia, gyroscopic torque)
How are vertical loads varied?
Elevator Deflection
Deflection of high-lift devices
Vertical wind gusts
Horizontal wind gusts
What is the difference between Limit Loads and Ultimate Loads?
Limit Loads are expected during normal flight operation,
while ultimate loads are to be reached at exceptional cases, and must be sustainable for 3 second without structural failure.
What is nz?
Vertical load factor, given by nz = L/w
What are the limits in the maneuver Load Diagram?
In the Positive load factor:
-VS+ (Stall speed at a load of 1.0g)
-VA (Design maneuvering speed), point at which the CL,max speed and the 2.5 g upper load limit connect.
-upper load limit of 2.5g
-VD (Design Dive Speed) (Max speed)
In the Negative Load Factor:
-VS- (Stall speed at a load of -1.0g)
-Lower load limit of -1.0g
-VC (Design Cruise speed)
-VD (Design Dive Speed) (Max speed)
What are the differences between the maneuver Load Diagram and the V-n Diagram?
The V-n Diagram includes VS,flap (The Stall speed at 1.0g with extended flaps), a CL,max curve with extended flaps, and a VB (Design gust speed) which is the point at which the aircraft must withstand a higher load factor than the limit of 2.5g
What are the steps to calculate a new center of gravity using a Loading Chart?
1.- Draw line following the loading chart grid, which crosses the point at which the extra load is.
2.- Draw a parallel line crossing through the initial point (Center of gravity vs Weight).
3.-Draw line crossing the new weight of the aircraft from the parallel line drawn previously.
4.-From the point where these two lines cross, draw a line following the grid to the % of croot.
5.- This croot is the new position of the center of gravity
Whats the difference between the different types of air breathing engines?
-Turbojet : Intake, compressor, combustion chamber, turbine, thrust nozzle. (No fan or propeller)
-Turbofan: Turbojet + Fan/low pressure compressor + low pressure turbine
-Turboprop: Turbojet + propeller + reduction gear
-Turbo-shaft: Turbojet + propeller + reduction gear + NO thrust nozzle
What are the different types of thrust that exist? (e.g. Gross Thrust)
-Gross Thrust (Outflowing mass thrust)
-Net Thrust Gross Thrust - inlet Ram drag)
-Installed Net Thrust (Net Thrust - Installation loss - Additional drag)
-Stati Thrust (Thrust of uninstalled engine at ISA day)
What is TSFC?
Thrust Specific Fuel Consumption.
Amount of fuel consumed per unit of thrust generated.
How much gas is created from 1 kg of Kerosene?
4.45 Kg.
Whats SEP?
Specific Excess Power.
The amount of extra energy that can be used for acceleration or climb at a given point in time.
What is H*?
Specific Energy
What is STR? And what about ATR?
Sustained Turn Rate. Turn rate that can be maintained for a long period of time without causing excessive stress on the structure.
Attained Turn Rate. Maximum possible rate of turn for a brief period of time without exceeding structural or aerodynamic limitations.
What are the steps for Take-Off?
Describes the aircraft acceleration on the ground from standstill, until clearing a certain obstacle height.
Acceleration, Rotation, Transition,
What is Rolling Friction Drag?
Drag created by the rolling resistance of an aircraft’s wheels when it is in motion on the ground. Significant for Fuel Consumption and take-off performance,
What is the Rotation step for take-off?
Distance it takes for the aircraft to rotate from its fixed angle of attack during roll, to the take-off angle of attack at approximately constant speed. Moment at which the aircraft’s nose wheel lifts off the ground.
What is the Transition step for take-off?
The distance between Lift-off and where the aircraft reaches the “screen height” (clearance distance), adjusting pitch angle to achieve a certain climb rate and airspeed.
What is Cruise?
Flight condition at which the aircraft travels the longest time, therefore it is the flight condition at which aerodynamics must be optimized, and fuel usage must be taken into account.
What are the 3 flight state options that result in an optimum flight trajectory?
1.- Cruise Climb: Constant Speed, Constant Lift Coefficient, BUT a changing Air Density (Height).
2.- Trimming: Constant Speed, Constant Height, BUT Changing Lift Coefficient.
3.- Throttle Back: Constant Lift Coefficient, Constant Height, BUT changing Speed (Not used)
What is the Optimal Flight State option for optimum flight trajectory?
1 Cruise Climb, as it provides the maximum aerodynamic efficiency and a constant velocity.
When should a Max Flight duration be calculated?
For the Loiter step of the flight mission. It maximizes the time that the aircraft can be flying.
Estimation of weight reduction between mission segments.
Engine Start-up W10 = 99%
Taxi W21 = 99%
Take-off W32 = 99.5%
Climb W43 = 98%
Cruise W54 = Range equation
Descent W65 = 99%
Loiter W76 = Duration equation
Landing, taxi, shut-down W87 = 99.2%
What does the Payload-Range diagram tell us?
It shows how the available payload decreases with an increase in payload and vice-versa. It tells what range is possible for a certain range, but also how much fuel is needed.
How is the landing step defined?
Its the Approach distance + the Landing Roll distance. Distance it takes the aircraft to go from loiter conditions to a complete stop on the runway.
What is Wing Loading? What about Thrust to Wight Ratio?
W/S
Weight of the aircraft divided by the total wing area.
T/W
Total thrust generated by the engines divided by the weight of the aircraft.
What is the Design Chart?
It is graphical representation of design limits of an aircraft which depend on the T/W ratio and Wing Loading. It establishes a feasible design region.
What limits must be taken into account in the Design Process (and are seen in the Design Chart)?
Take-off distance limit
Landing distance limit
Sustained Turn Rate maneuvering limit (these state performance requirements)
Attained Turn Rate maneuvering limit
Gust Load factor limit
Specific Excess Power limit
Maximum Mach number limit
Minimum Speed
What are some considerations for the Design Point Selection?
-Always Include Safety Margin for design changes
-The more to the right, the smaller the wing area
-The more to the bottom the smaller required thrust
- Priority 1: Low Engine Weight, Priority 2: Lowest Reasonable Wing area
- Caution with CL variations along the curves. Make sure the High lift systems are able to provide this.
Mounting options of Engines and some advantages and disadvantages?
- Under the wing: +Best for maintainability, +low cabin noise, + no intake interference, - risk of Foreign Object damage, - Landing gear must be taller.
- Over the wing: - Bad maintainability, - High Cabin Noise, - Moderate Intake interference, ++ Low risk of foreign object damage, + Low landing gear.
- Aft-fuselage mount: - Bad maintainability, - Very low cabin noise, - High intake interference, + Low risk of foreign object damage, + Low landing gear.
- Tail: - Bad maintainability, - low cabin noise, + Low risk of foreign object damage, + Low landing gear.
Some types of tail configurations and their Pros and Cons?
*T-Tail: +Short vertical tail, Less downwash, possible powerplant at rear, Low interference drag. - Heavy tail structure, Difficult horizontal tail, Trimmable horizontal stabilizer integration problematic, deep stall risk.
*Twin-Tail: +Short horizontal tail, 2 smaller vertical tails, low blanketing-effect. - Heavy tail structure, High interference Drag, Mechanically complex vertical tail control system.
Conventional Tail: +Light structure, Vertical tail easily adapted, Easy trimmable horizontal stabilizer, Simple structural transmission of tail loads. - Increased downwash, Powerplant at rear not possible, Large vertical tail, Degraded spin properties due to blanketing-effect.
Cruciform Tail: + Powerplant at rear possible, Lighter than T-Tail, Less downwash than conventional. - Heavy tail structure, high interference drag, influence on rudder, Large vertical tail.
V-Tail: + Low interference drag, Light structure, smaller tail area necessary, smaller hangar needed. - Control surface mixing is complex, Pitch and yaw control are performed by 1 surface pair.
Canard-empennage: +High maneuverability, Improved overall lift and trim drag. - Large vertical tail, high induced drag, High wing-loading.
What is “Blanketing-effect”?
The reduction of effectiveness of lift due to close ground, which interferes with the smooth flow of air around wing.
What are the steps to calculate the location of the aerodynamic center of a wing/horizontal tail?
1.-Using the graph (Taper Ratio, AR * tan(Λ0%), tan(Λ0%)/ β) obtain nAC. For this use tan(Λ0%)/ β value between 0 and 1.
2.-Use formula for xAC
Aerodynamic Center Calculation for individual Components.
xAC=(x0,W+(nAC,w * croot,W))/cMAC
How is the minimum speed Constraint Relation obtained?
1.- L= nz * Wman
2.- L= qSrefCL,max
3.-Multiply by MTo/MTo
4.-Organize for MTo/S
How is the Vertical Gust Load constraint relation obtained?
1.-∆nz= ∆Lgust/Wman
2.- ∆Lgust = qS∆CL
3.- Expand for ∆CL=CL𝛼 ∆𝛼
4.-Expand and multiply by WTO/WTO
5.- Use ∆𝛼 = wg/V
5.- Solve for WTO/Sref
How to Obtain SEP Constraint Relation?
1.-SEP = V (Tman - D)/Wman
2.- Use relation nz = L/W and expand to obtain CL
3.- Expand D and substitute CL obtained in step 2 with nz = 1.
4.- Multiply Both sides of Eq by Wman
5.- Solve for Tman
6.- Divide both sides by WTO
7.- Multiply Term containing the k by WTO/WTO
8.- Multiply both sides times T0 and solve for <T0/WTO
How to obtain the Landing Distance Constraint Relation?
1.- Expand the sdec = VTD2 / 2a with VTD = 1.15 Vs
2.- Multiply both sides times WTO
3.- Solve for WTO / S
Whats the difference between the Sustained Turn Rate Maneuvering Limit, the Climb Gradient Limit, and the Service Ceiling Limit Relations?
-For STR Maneuvering Limit SEP=0 nz <>1
-For Climb Gradient SEP <> 0, nz = 1
-For Service Ceiling SEP = 0, nz = 1
