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Aviation & Aeronautics

Aerodynamics, flight performance, navigation and atmospheric formulas used in aviation

True Airspeed (rule of thumb)

Basic
TASIAS+(IAS×0.02×alt1000)TAS \approx IAS + (IAS \times 0.02 \times \tfrac{alt}{1000})

Quick estimate: true airspeed increases about 2% per 1000 ft of altitude above indicated airspeed.

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Ground Speed

Basic
GS=TAS±WGS = TAS \pm W

Ground speed is true airspeed adjusted for the headwind/tailwind component.

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Flight Time

Basic
t=dGSt = \dfrac{d}{GS}

Time en route equals distance divided by ground speed.

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Fuel Required

Basic
F=f˙×tF = \dot{f} \times t

Total fuel needed is the fuel-burn rate multiplied by flight time.

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Rate of Climb

Basic
ROC=ΔhtROC = \dfrac{\Delta h}{t}

Vertical speed is the altitude gained per unit time (ft per minute).

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3-Degree Descent Rate

Basic
RODGS×5ROD \approx GS \times 5

On a standard 3° glide path, required descent rate (fpm) is roughly ground speed (kt) times 5.

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Wind Components

Basic
HW=Wcosθ,  XW=WsinθHW = W\cos\theta,\; XW = W\sin\theta

Resolve wind into headwind and crosswind components relative to runway/track.

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Pressure Altitude

Basic
PA=(29.92QNH)×1000+hPA = (29.92 - QNH)\times 1000 + h

Altitude referenced to standard pressure; correct field elevation for the altimeter setting.

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Fuel Uplift

Basic
Vup=FreqFOBρV_{up} = \dfrac{F_{req} - F_{OB}}{\rho}

Fuel to be loaded: the required ramp/block fuel minus fuel already on board, converted from mass to volume using fuel density.

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MEL Rectification Interval

Basic
Ddue=Ddisc+IcatD_{due} = D_{disc} + I_{cat}

Latest date a deferred defect must be fixed: the discovery date plus the Minimum Equipment List category interval. The day of discovery is “day zero” and is not counted.

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Lift Equation

Intermediate
L=12ρv2SCLL = \tfrac{1}{2}\rho v^2 S C_L

Aerodynamic lift produced by a wing depends on air density, speed squared, area and lift coefficient.

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Drag Equation

Intermediate
D=12ρv2SCDD = \tfrac{1}{2}\rho v^2 S C_D

Aerodynamic drag force on the aircraft, analogous to lift with a drag coefficient.

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Stall Speed

Intermediate
Vs=2WρSCL,maxV_s = \sqrt{\dfrac{2W}{\rho S C_{L,max}}}

Minimum speed for level flight, set by maximum lift coefficient.

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Load Factor in a Turn

Intermediate
n=1cosϕn = \dfrac{1}{\cos\phi}

The g-load in a level, coordinated turn depends only on the bank angle.

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Stall Speed vs Load Factor

Intermediate
Vs,n=VsnV_{s,n} = V_s\sqrt{n}

Accelerated stall speed rises with the square root of the load factor.

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Turn Radius

Intermediate
r=v2gtanϕr = \dfrac{v^2}{g\tan\phi}

Radius of a level coordinated turn from speed and bank angle.

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Rate of Turn

Intermediate
ω=gtanϕv\omega = \dfrac{g\tan\phi}{v}

Angular rate of a coordinated turn (radians/s; a standard rate turn is 3°/s).

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Crosswind Component

Intermediate
XW=VwsinθXW = V_w\sin\theta

Crosswind component determines whether landing is within aircraft limits.

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Density Altitude

Intermediate
DA=PA+120(OATISAtemp)DA = PA + 120(OAT - ISA_{temp})

Pressure altitude corrected for non-standard temperature; higher DA reduces performance.

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Glide Ratio

Intermediate
GR=dh=LDGR = \dfrac{d}{h} = \dfrac{L}{D}

Horizontal distance traveled per unit of altitude lost equals the lift-to-drag ratio.

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Mach Number

Intermediate
M=vaM = \dfrac{v}{a}

Ratio of true airspeed to the local speed of sound.

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Speed of Sound

Intermediate
a=38.94Ta = 38.94\sqrt{T}

Local speed of sound (kt) as a function of absolute air temperature (Kelvin).

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Specific Range

Intermediate
SR=GSf˙SR = \dfrac{GS}{\dot{f}}

Distance flown per unit of fuel; maximizing it gives best fuel economy.

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Point of No Return

Intermediate
PNR=EGSoutGSbackGSout+GSbackPNR = \dfrac{E \cdot GS_{out} \cdot GS_{back}}{GS_{out}+GS_{back}}

Farthest distance an aircraft can fly and still return with available endurance.

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Reynolds Number

Advanced
Re=ρvLμRe = \dfrac{\rho v L}{\mu}

Ratio of inertial to viscous forces; characterises airflow over an airfoil.

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Lift Coefficient

Advanced
CL=2Lρv2SC_L = \dfrac{2L}{\rho v^2 S}

Non-dimensional lift, obtained by rearranging the lift equation.

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Induced Drag Coefficient

Advanced
CD,i=CL2πeARC_{D,i} = \dfrac{C_L^2}{\pi e AR}

Drag due to lift, decreasing with higher aspect ratio and span efficiency.

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Aspect Ratio

Advanced
AR=b2SAR = \dfrac{b^2}{S}

Ratio of wingspan squared to wing area; higher AR reduces induced drag.

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Thrust Required (level flight)

Advanced
T=WL/DT = \dfrac{W}{L/D}

In steady level flight, thrust must equal drag, which is weight divided by L/D.

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Breguet Range Equation

Advanced
R=VcLDlnWiWfR = \dfrac{V}{c}\dfrac{L}{D}\ln\dfrac{W_i}{W_f}

Maximum range of a jet aircraft from speed, efficiency, L/D and fuel fraction.

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Maximum Endurance (jet)

Advanced
E=1cLDlnWiWfE = \dfrac{1}{c}\dfrac{L}{D}\ln\dfrac{W_i}{W_f}

Longest time aloft for a jet, maximized at maximum L/D.

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ISA Temperature Lapse

Advanced
T=151.98(h1000)T = 15 - 1.98\left(\dfrac{h}{1000}\right)

Standard atmosphere temperature decreases about 2°C per 1000 ft up to the tropopause.

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Barometric Altitude

Advanced
h=RTglnP0Ph = \dfrac{RT}{g}\ln\dfrac{P_0}{P}

Altitude derived from the ratio of sea-level to measured pressure.

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Takeoff Ground Roll

Advanced
s=VLO22as = \dfrac{V_{LO}^2}{2a}

Approximate ground-roll distance assuming constant acceleration to lift-off speed.

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Climb Gradient

Advanced
γ=TDW\gamma = \dfrac{T - D}{W}

Climb angle (as a fraction) equals excess thrust divided by weight.

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Great Circle Distance

Advanced
d=Rarccos(sinϕ1sinϕ2+cosϕ1cosϕ2cosΔλ)d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Shortest distance between two points on the Earth for long-range navigation.

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Glide Ratio

Intermediate
GR=horizontal distancealtitude lostGR = \frac{\text{horizontal distance}}{\text{altitude lost}}

Distance traveled forward per unit of height lost.

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Load Factor

Intermediate
n=LWn = \frac{L}{W}

Ratio of lift to weight, felt as g-force.

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Turn Radius

Advanced
r=v2gtanϕr = \frac{v^2}{g\tan\phi}

Radius of a coordinated banked turn.

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Stall Speed

Advanced
Vs=2WρSCL,maxV_s = \sqrt{\frac{2W}{\rho S C_{L,max}}}

Minimum speed to maintain lift.

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Mach Number

Intermediate
M=vaM = \frac{v}{a}

Ratio of speed to the local speed of sound.

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Rate of Climb

Intermediate
ROC=excess powerWROC = \frac{\text{excess power}}{W}

Vertical speed from excess engine power.

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Wing Loading

Intermediate
WL=WSWL = \frac{W}{S}

Aircraft weight per unit wing area.

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Crosswind Component

Intermediate
X=VsinθX = V\sin\theta

Sideways wind component during landing.

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Headwind Component

Intermediate
H=VcosθH = V\cos\theta

Wind component along the runway.

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Endurance

Basic
E=fuelfuel flowE = \frac{\text{fuel}}{\text{fuel flow}}

Time an aircraft can stay airborne.

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True Airspeed (approx)

Advanced
TASIAS(1+h60000)TAS \approx IAS\left(1 + \frac{h}{60000}\right)

Airspeed corrected for altitude.

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Density Altitude

Advanced
DA=PA+120(OATISA)DA = PA + 120(OAT - ISA)

Pressure altitude corrected for temperature.

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