ASCI 309 Rectilinear Motion Exercise Select and identify your aircraft. Then provide the following: A. Maximum Takeoff Weight (MTOW) [lbs]: B. Engine Type and Rated Thrust [lbs]: C. Total Available Thrust (sum of all engines for multiengine aircraft) [lbs]: D. Maximum Rate of Climb [ft/min]: E. Take-off distance at MTOW [ft]: Uniformly Accelerated Rectilinear Motion and Newton’s Law of Momentum Equations: F = ma m = W/g A=F/M g = 32.2 ft/sec2 Takeoff distance (s) = VF 2 /2a KE = ½ mV2 PE = Wh HP= T*Vkts /325 1 kt = 1.69 ft/sec * Remember to keep track of units, convert as required, and express answers in the requested unit. Next complete the following: 1. Find the mass of your aircraft. (m = W/g) 2. Find the Acceleration of your aircraft using the total thrust you found. (A=F/Mass. Note in this case F=Force of Total Thrust of your engines) 3. If your aircraft lifted off the ground at 150kts, what would be the length of the takeoff run (in feet)? (Takeoff distance (s) = VF 2 /2a. Watch for unit conversions.) 4. The time t [S] it took for this Takeoff. Similar to detailing assumptions and conditions at the onset, any quantitative result of our theoretical work also requires a qualitative discussion of applicability. The important question to discuss is how accurate our result will depict the real world. Possible errors College of Aeronautics | worldwide.erau.edu All rights are reserved. The material contained herein is the copyright property of Embry-Riddle Aeronautical University, Daytona Beach, Florida, 32114. No part of this material may be reproduced, stored in a retrieval system or transmitted in any form, electronic, mechanical, photocopying, recording or otherwise without the prior written consent of the University. should be identified, our certainty about results evaluated, and additional recommendations for further improvement provided. Therefore, comment on your findings in Questions #1 through #3. Compare your calculated takeoff distance in #3 with your research above in item E. What elements did we neglect in the acceleration computed in Question #1? How did it affect our further work in #2 and #3? 5. What is the power [HP] of the aircraft engines after takeoff at the total available thrust from item B (found above) if flying at 200kts? (HP= T*Vkts /325 – (T is Total Thrust). Remember, this formula already has unit conversions included.) 6. What is the Kinetic Energy [ft-lb] of the aircraft at 200kts and Maximum Takeoff Weight (KE = ½ mV2 - from item B above)? 7. What is the Potential Energy [ft-lb] of the aircraft after climbing out to 10,000ft above sea level at Maximum Takeoff Weight (PE = Wh W is WT and H Is Height from item B)? 8. What is the Total Energy of the aircraft using questions 5 & 6 above? (TE=KE +PE) Page 2 of 3 Page 3 of 3 CONVERSION FACTORS multiply / divide by 150 6 6 144 psf psi 2.036 Hg" psf 144 psi psf 70.726 Hg" Hg" 2.036 psi Hg" 70.726 psf knots 1.69 fps knots 1.15 mph knots 101.3 fpm fps 0.5925 knots fps 0.6818 mph mph 1.467 fps mph 0.869 knots nautical mile (nm) 6076 ft nautical mile (nm) 1.15 statue mile (sm) ft 0.00016458 ft 0.00018939 statue mile (sm) statute mile (sm) 0.869 nautical mile (nm) statue mile (sm) 5280 ft slug 14.594 kg kg 14.594 slug (°F) (F-32)*5/9 (°C) (°C) (C*9/5)+32 (°F) add / subtract Fahrenheit (°F) 47.6 nautical mile (nm) 460 Rankine (°R) -460 Fahrenheit (°F) Celsius (°C) 273.15 Kelvin (K) Kelvin (K) -273.15 Celsius (°C) Statute mile (sm) = 5280 ft Velocity (knots(kt) or nm/hr) 1 kt = 1.69 ft/s Velocity (mph) 1 kt = 1.15 mph Horsepower = 550 ft-lb/s Foot = 0.305 meters Nautical mile = 1851 meters Statue mile = 1609 meters 1 kg = 2.2 lbmass 1 Newton = 0.225 lbforce 0.0 0.000 0.00 0.000 0.00 0.0 253.50 6.90 607.80 0.00 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.0 0.0 0.00 -17.8 32.0 to get by Rankine (°R) Nautical mile (nm) = 6076 ft Fundamental Units to get psi 507.6 -460.0 273.2 -273.2 British Grav. Sys (BGS) Term BGS/English Unit Aviation Terms US Unit ICAO Unit Internat'l System (SI) Term SI Unit Distance feet ft meter m Time second s second s Temperature Fahrenheit °F Celsius °C Altitude and Vertical distance feet (ft) feet Absolute Temp Rankine °R Kelvin °K Air Distance nautical mile (nm) nautical mile (nm) Force Pound-force (pounds x g) Airspeed knots (kt) = nm/hr knots ft-lb/s 2 Mass kilogram kg Derived Units British Grav. Sys (BGS) Term BGS/English Unit Force Internat'l System (SI) Term SI Unit Newton (N) kg-m/s 2 lb-s 2 /ft ft/s meters/second m/s ft/s 2 meters/second squared m/s 2 ft 2 Square meters m2 liters Mass Slug or Poundmass (W / g) Velocity feet/second (fps) Acceleration feet/second squared Area Square feet Volume Cubic feet ft 3 Pressure pound/square foot (psf) Pascal (Pa) Energy foot-pounds lb/ft ft-lb l or m 3 N/m2 Joules(J) N-m Work foot-pounds ft-lb Joules(J) N-m Power foot-pounds/second ft-lb/s Watts (W) Moment foot-pounds ft-lb Newton meters N-m Momentum (p ) Mass x Velocity (lb- s /ft) x (ft/s) = lb-s Mass*Velocity kg-m/s 2 2 J/s Term Runway Length Temperature Atmospheric Pressure feet (ft) Remarks Meters (m) Celsius Celsius Pounds/square inch (PSI) or Hg" Hectopascals Old Soviet bloc use meters Old Soviet bloc use meters/s Table 2.1, Standard A Altitude (ft) 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 20,000 25,000 30,000 35,000 36,089 40,000 45,000 50,000 60,000 70,000 80,000 90,000 100,000 150,000 200,000 250,000 Density Ratio, σ 𝜎 1.0000 0.9711 0.9428 0.9151 0.8881 0.8617 0.8359 0.8106 0.7860 0.7620 0.7385 0.6292 0.5328 0.4481 0.3741 0.3099 0.2971 0.2462 0.1936 0.1522 1.0000 0.9854 0.9710 0.9566 0.9424 0.9283 0.9143 0.9004 0.8866 0.8729 0.8593 0.7932 0.7299 0.6694 0.6117 0.5567 0.5450 0.4962 0.4400 0.3901 Table 2.1, Standard Atmosphere Table (pg 16) Pressure Ratio, δ Temperature (°F) Temperature (°R) Temperature Ratio, θ Speed of Sound (knots) 1.0000 0.9644 0.9298 0.8962 0.8637 0.8320 0.8014 0.7716 0.7428 0.7148 0.6877 0.5643 0.4595 0.3711 0.2970 0.2353 0.2234 0.1851 0.1455 0.1145 59.00 55.43 51.87 48.30 44.74 41.17 37.60 34.04 30.47 26.90 23.34 5.51 -12.32 -30.15 -47.98 -65.82 -69.70 -69.70 -69.70 -69.70 519.00 515.43 511.87 508.30 504.74 501.17 497.60 494.04 490.47 486.90 483.34 465.51 447.68 429.85 412.02 394.18 390.30 390.30 390.30 390.30 1.0000 0.9931 0.9862 0.9794 0.9725 0.9656 0.9587 0.9519 0.9450 0.9381 0.9312 0.8969 0.8625 0.8281 0.7937 0.7594 0.7519 0.7519 0.7519 0.7519 661.7 659.5 657.2 654.9 652.6 650.3 647.9 645.6 643.3 640.9 638.6 626.7 614.6 602.2 589.5 576.6 573.8 573.8 573.8 573.8 Kinematic Viscosity, v 2 (ft /s) 0.000158 0.000161 0.000165 0.000169 0.000174 0.000178 0.000182 0.000187 0.000192 0.000197 0.000202 0.000229 0.000262 0.000302 0.000349 0.000405 0.000419 0.000506 0.000643 0.000818 Acceleration due to gravity, g (ft/s2) 32.189 32.159 32.143 32.128 32.112 32.097 32.082 32.066 32.051 32.036 32.020 31.990 31.959 31.929 31.897 31.868 31.717 31.566 31.415 Links (to find:) MASS / Weight Mass / Weight W = m * g // m = W/g Find Acceleration (when Velocities and Time are known) Find Acceleration (when Velocities and distance known) Weight Find Velocity (given time & acceleration) Mass Find Takeoff Velocity (given accel, distance, & initial Velocity) Gravity Accel Find Time (given Vel & Accel) Find distance (given Vel & Accel) Find distance (given initial Velocity, Time & Accel) PE KE TE (total mechanical energy) Work Power Finding Ground Speed V h = V a/c (Cos λ) Horsepower, when Velocity is in ft/s Horsepower, when Velocity is in Knots Friction Ground Speed Acft TAS Climb Angle Ground Speed Rate of Climb Finding Rate of Climb Speed (R V v = V a/c (Sin λ) Acft TAS Climb Angle Rate of Climb Find Acceleration (when Velocities an known) a = (V 2 - V 0 2 ) / 2s Initial Velocity Final Velocity Distance traveled a MASS / Weight W = m * g // m = W/g W m = = 32.2 0.03 lbs slugs nm/hr degrees nm/hr Vh = 173.2 nm/hr W 1 lbs m 1 (lb-s )/ft g 32.2 2 ft/s2 Finding Ground Speed V h = V a/c (Cos λ) Va/c 200 30 ? λ Vh Finding Rate of Climb Speed (ROC) V v = V a/c (Sin λ) Va/c 200 nm/hr Vv = 100.0 nm/hr λ 30 degrees Vv = 10,140.0 ft/min Vv ? nm/hr nd Acceleration (when Velocities and distance known) a = (V 2 - V 0 2 ) / 2s V0 V s 0 219.7 500 ft/s ft/s ft = 48.3 ft/s2 Find Acceleration (when V & Time known) a = ΔV / Δt = (V - V 0 ) / (t - t 0 ) Initial Vel V0 0 fps Meas Vel V 219.7 fps Initial Time t0 0 sec Meas Time t 5 sec Find Velocity (given ti V=V0 +a a a a = = = 43.9 158,184.0 107,852.7 ft/s2 Initial Vel 2 Acceleration 2 Initial Time ft/min mi/hr Meas Time V Vh Ground Speed Va/c True Airspeed Vv Rate of Climb λ Climb Angle Find Velocity (given time & acceleration) V = V 0 + a(t - t 0 ) Find Takeoff Velocity (given accel, distance, & initial Velocity) V f = √(V 0 2 +2as) V0 5 fps a 24 ft/s2 Initial Vel t0 1 sec t 5 sec = 101.0 fps V0 50 fps Acceleration a 10 ft/s Distance s 500 ft Vf = 111.8 2 fps Find Time (given Vel & Accel) t = [(V - V 0 ) / a]+ t 0 Find distance (given Vel & Accel) s = (V 2 - V 0 2 ) / 2a Initial Vel V0 0 fps Initial Vel V0 0 fps Meas Vel V 219.7 fps Final Vel V 24 fps Initial Time t0 0 sec Accel a 5 ft/s Acceleration a 12.88 ft/s2 Distance s ? ft Time t ? sec = 1440.0 = 17.1 t s sec 2 ft Find distance (given initial Vel, Time & Accel) s = V 0 t + (at 2 / 2) Potential Energy (PE) PE = W * h V0 0 fps Weight W Time t 10 sec Height h Accel a 5 ft/s Pot. Energy PE Distance s ? ft PE = = 250.0 Initial Vel s 2 ft Potential Energy (PE) PE = W * h Kinetic Energy (KE) KE = (mV 2 ) / 2 (lb-s2)/ft ft/s 10000 lbs Mass m 310.56 10000 ft Velocity V 422.5 ft-lbs Kin. Energy KE ? KE = 27,718,450.50 ft-lbs 2.772E+07 ft-lbs ? 100,000,000.00 ft-lbs 1.00E+08 ft-lbs ft-lbs Mechanical Energy (TE) TE = PE + KE TE = Work w=F*D Force F 100 lbs ft 127,718,450.50 ft-lbs Distance D 150 1.277E+08 ft-lbs Work w ? = 15,000.00 ft-lbs 1.500E+04 ft-lbs w ft-lbs Power P = [(F * D) / time] OR P = F * V or P = W/t Horsepower (when V is in ft/s) HP = (F * V) / 550 Force F 1500 lbs Force F 1500 Distance D 10 ft Distance D 10 time t 1 sec Velocity V 10 Power P ? ft-lbs/s time t 1 P = 15,000.0 ft-lbs/s = 27.3 1.500E+04 ft-lbs/s → HP Manually, from values above HP HP = = 27.3 27.3 when V is in ft/s) V) / 550 Horsepower (when V is in knots) P (HP) = (TV k ) / 325 lbs Thrust T 32000 ft Velocity V 450 Friction (runway) Fb = μ*N lbs Braking Force Fb nm/hr Normal Force N Coef of Friction μ (mu) Fb = μ (mu) = ft/s sec ft-lbs/s m values above ft-lbs/s ft-lbs/s P (HP) = 44,307.7 = 2.4336E+07 HP ft-lb/s Friction (runway) Fb = μ*N 1500 lbs 500 lbs 0.53 unitless 265.0 3.0 lbs unitless Density (ρ-rho) / Mass (m) / Volume (V) ρ=m/V Links to Find: Density (ρ-rho) / Mass (m) / Volume (V) Mass m 0.15 slugs Pressure Alt (PA), given Altimeter Setting Volume V 3 Ambient Pressure P, given δ (Press Ratio) Air Density ρ (rho) 0.05 0.05 0.15 slugs/ft3 3.00 ft3 ft 3 slugs/ft3 Pressure Ratio (δ - delta) Density Ratio (σ - sigma), given density m = = Find Density (ρ -rho), given Density Ratio V = Temperature Ratio (θ - theta) Density Ratio (σ - sigma) , given Press. & Temp. Density Ratio (when δ is Interpolated from table) Dynamic Pressure (q), when V is in ft/s Dynamic Pressure (q), when V is in knots "ICE-T" (acronym for airspeeds) True Airspeed (TAS) Density (ρ) slugs Altitude Pressure Ratio (δ - delta) Temperature Ratio (θ - th δ=P/P0 Ambient Static Press Std SL Static Press Press Ratio ( δ delta) θ=T/T0 P P0 13.75 psi or Hg" Ambient Air Temp 29.92 psi or Hg" Std SL Air Temp = 0.45956 unitless Temp Ratio ( θ theta) Find Ambient Pressure P , given δ P= δ*P0 Press Ratio Std SL Static Press Ambient Pressure (P) δ P0 0.4595 unitless 29.92 psi or Hg" = 13.75 psi or Hg" Find Pressure Alt (PA), given Altimeter Setting 1) 29.92" Hg - Alt Setting = ΔP 2) ΔP / .001" = Δalt 3) Elevation + Δalt. = Pressure Alt. (PA) Elevation 5,000 ft Altimeter Setting 28.92 Hg" Std Sea Level Pressure 29.92 Hg" Change in Pressure ΔP 1.00 Hg" Change in Altitude Δ Alt 1000 ft Pressure Alt. (PA) = 6,000 Pressure Altitude (PA) Density Altitude (DA) ft Standard Day Parameters Temperature Ratio (θ - theta) Density Ratio (σ - sigma), given density θ=T/T0 σ=ρ/ρ0 T T0 507.6 °R / °K Density 519 °R / °K SL Density = 0.97803 unitless ρ (rho) ρ 0 (rho) Density Ratio ( σ) 0.0012468 slugs/ft3 0.002378 slugs/ft3 = 0.5243 unitless Find Density, given Density Ratio ρ=σρ0 Density Ratio Density (ρ) σ (sigma) = 0.5243 unitless 0.0012468 slugs/ft3 1.2468E-03 slugs/ft3 is altitude in the standard atmosphere corresponding to a certain static pressure. Used to determine True Airspeed (TAS), Density Altitude (DA) and takeoff/landing data PA is the vertical disance above a std datum plane where atmospheric pressure is 29.92" PA, corrected for nonstandard temperature Standard Day Parameters (σ - sigma) Density Ratio (given Press. & Temp.) σ = δ /θ = (P / P 0 ) / (T / T 0 ) Static Press E2.10 Dynamic Pressure (q), when 2 q = .5(ρV ) 6.754 psi or Hg" Velocity Std Sea Lvl Press P P0 14.70 psi or Hg" Density ratio Absolute Temp T 437.7 °R Density (air) Std Sea Lvl Temp T0 519 °R Press Ratio δ (delta) 0.4595 unitless Temp Ratio θ (theta) 0.8434 unitless = 0.5448 Density Ratio ( σ) Dynamic Press (q) unitless Find Density Ratio (when δ is Interpolated from table) σ = δ /θ Pressure Ratio δ (delta) 0.8014 unitless E2.10 Dynamic Pressure (q), when q = ( σV k 2 ) / 295 Velocity Temperature Ratio θ (theta) 0.9780 unitless Density ratio = 0.8194 Altitude (from chart) 20,000 ft Indicated Temp 507.6 °R Density Ratio ( σ) unitless Dynamic Press (q) 10 Dynamic Pressure (q), when V is ft/s 2 ICE-T (airspeeds) q = .5(ρV ) V 338 σ 0.7385 ρ = ft/s unitless I Indicated Airspeed (IAS) C Calibrated Airspeed (CAS) the actual reading off of the AS Indicator Dial 0.00175615 slugs/ft3 100.31 lb/ft2 IAS corrected for installation error and instrument error EAS = CAS + ΔVc 10 Dynamic Pressure (q), when V is Knots q = ( σV k 2 ) / 295 Vk 200.3 knots σ 0.7385 E Equivalent Airspeed (EAS) T True Airspeed (TAS) (see chart below) CAS corrected for compressibility effects (high flight speeds) EAS corrected for Density Ratio (σ) unitless TAS = EAS / √σ = 100.44 lb/ft2 Equivelant Airspeed EAS Square root of Density ratio √σ True Airspeed (TAS) = use this table for computing EAS airspeeds) the actual reading off of the AS Indicator Dial IAS corrected for installation error and instrument error KIAS KCAS CAS + ΔVc CAS corrected for compressibility effects (high flight speeds) KEAS EAS corrected for Density Ratio (σ) KTAS EAS / √σ 220.5 knots 0.5328 unitless 302.1 knots Links to Find: E4.1 Reynolds Number R g = Vx / v Reynolds Number Stream Velocity V Lift Equation (basic) aq x Lift Equation (when dealing with velocity) Coefficient of Lift (when dealing with acft weight) Stall Velocity-to-Weight Relationship in lift Kinematic Viscosity v Reynolds # (R g ) = Stall Speed Equation AIRFOIL TERMINOLOGY NACA AIRFOIL SERIES #DIV/0! mber E4.2 Lift Equation (basic) v L = C L qS ft/s Coefficient of Lift CL ft Dynamic Pressure Planform Area q lb/ft2 S ft2 ft2/s unitless Lift (L) = 0.5945 0.0 unitless lbs E4.2 Lift Equation (when dealing with velocity) L =C L ( σV 2 /295) S CL Coefficient of Lift 0.8 unitless Density Ratio Velocity (airflow) Planform Area Lift (L) σ V S 0.8617 200 150 = 14,020.9 unitless knots ft2 lbs E4.2 Coefficient of Lift (when dealing with acft weight) C L = (295W / σV 2 S) Weight (gross) W 1,974 lb Density Ratio σ 1.0000 unitless Velocity (airflow) V 46 knots Planform Area S 174 ft2 Coefficient of Lift (CL) = 1.5816 unitless E4.3 Stall Velocity-to-Weight Relationship in lift AIRFOIL V 2 = V 1 √(W 2 / W 1 ) Velocity V1 114 Weight (gross) W2 Weight (gross) Stall Speed (V 2 ) knots 1. Chord Line 20,000 lb 2. Chord (C) W1 15,000 lb 3. Mean Camber Line 4. Max. Camber = 131.6 knots 5. Max Thickness 6. Leading Edge Radius E4.3 Stall Speed Equation V s = √(295L / C L(max) σS) Lift Lift Coefficient Density Ratio Wing Area L 15000 C L(max) σ S 1.35 1 340 lbs unitless unitless ft2 NACA Stall Speed (V s ) = 98.2 knots Designator Four Digit digit pos. 1st 2nd 3rd/4th Five Digit One Series Six Series 1st 2nd 3rd 4th/5th AIRFOIL TERMINOLOGY NACA AIRFOIL SERIES Description the amount of camber (% C) position of max camber from leading edge (10ths or % C) maximum thickness (% C) indicates the airfoil series location of minimum pressure in 10ths or % C design lift Coefficient (CL) in 10ths maximum thickness (% C) Links to Find: E2.10 Dynamic Pressure (q), when V is ft/s q = .5(ρV 2 ) Dynamic Pressure Aspect Ratio Velocity V 338 Aspect Ratio (when chord avg is not easily calculated) Density ratio σ 0.7385 Wing Surface Area Density (air) ρ 0.00175615 = 100.31 Wing Taper Ratio Basic Drag Equation (simple) Dynamic Press (q) Basic Drag Equation (alternate) Parasite Drag E2.10 Dynamic Pressure (q), when V is Knots q = ( σV k 2 ) / 295 Vk Velocity 200.3 Coefficient of Parasite Drag Density ratio Coefficient of Drag (derived from Basic Drag Eq) Induced Drag Induced Drag Alternate (if dealing with acft weight) Coefficient of Induced Drag Lift to Drag Ratio Dynamic Press (q) σ = 0.7385 100.44 , when V is ft/s Aspect Ratio AR = b/c avg ) ft/s Wingspan unitless slugs/ft 3 b 36 ft Root Chord c root 4.8 ft Tip Chord c tip 4.8 ft Aspect Ratio (AR) = 7.50 unitless lb/ft2 when V is Knots Aspect Ratio, when cavg not easily calculated AR = b 2 / S 295 knots Wingspan b 36 ft unitless Planform Area S 174 ft lb/ft2 Aspect Ratio (AR) = 7.45 2 unitless Wing Surface Area Wing Taper Ratio S = b * c avg λ = ctip / croot b 36 ft Tip Chord ct Root Chord c root 4.832 ft Roort Chord cr Tip Chord c tip 4.832 ft Taper Ratio (λ) = Wingspan Planform (S) = 174.0 ft 2 Wing Taper Ratio BASIC Drag Equation (simple) = ctip / croot D=CD *q*S 4.832 ft Coefficient of Drag CD 4.832 ft Dynamic Pressure q Planform Area S Drag (D) = 1.00 unitless - BASIC Drag Equation (alt) D = (C D σ V 2 S) / 295 CD Coefficient of Drag Density Ratio (sigma) Velocity σ V2 Planform Area S Drag (D) = - Coefficient of Drag (derived from Basic Drag Eq) C D = (295D) / ( σ V 2 S) Drag D Density Ratio (sigma) σ 2 Velocity V Planform Area S Coefficient of Drag (C D ) = #DIV/0! mple) unitless lb/ft ft 2 2 Parasite Drag D P = (C Dp σ V 2 KTAS C Dp Coefficient of Para. Drag Density Ratio Velocity σ V 2 Planform Area S Acft Parasite Drag (D P ) = S) / 295 0.02547 unitless 1 unitless 46 KTAS 174 ft2 lb alt) 31.79 lb Coefficient of Parasite Drag C Dp = 295 D p / σ V 2 KTAS S) Dp Parasite Drag 31.8 lb lb/ft KEAS Density Ratio ft2 295 unitless 2 lb Basic Drag Eq) 2 V S) lb unitless KEAS ft2 unitless σ 1 unitless V2 46 KTAS Planform Area S 174 ft2 Coeff. Of Parasite Drag (C Dp ) = Velocity 0.02548 lb D i = (C L 2 σ Coefficient of Lift Induced Drag V 2 KTAS S) / CL Density Ratio Velocity σ V 2 ( π e AR 295) 1.582 unitless 1 unitless 46 KTAS 174 ft2 Planform Area S PI (constant) π Wing efficiency factor e 0.7 unitless AR 7.4 unitless Wing Aspect Ratio Acft Induced Drag (D i ) = 3.14159265 unitless 191.94 Coefficient of Induced Drag C Di = C L 2 / ( π e AR) CL Coefficient of Lift 1.582 PI (constant) Wing efficiency factor Wing Aspect Ratio Induced Drag Coeff (C Di ) π e AR = lb unitless 3.14159265 unitless 0.7 unitless 7.4 unitless 0.15 unitless Induced Drag Alternate (if dealing with acft weight) D i = (295W 2 ) / ( σ V 2 KTAS S π e AR) Acft Weight W 1982 lbs Density Ratio Velocity σ V 2 1 unitless 43 KTAS 174 ft2 Planform Area S PI (constant) π Wing efficiency factor e 0.7 unitless AR 7.4 unitless = 221.34 Wing Aspect Ratio Acft Induced Drag (D i ) 3.141593 unitless lb Lift to Drag Ratio L/D = C L / C D Lift (or Weight) L (or W) lb Drag D lb Coefficient of Lift CL 1.582 unitless Coefficient of Drag CD 0.1774 unitless Drag = = = CL = #DIV/0! unitless CD = #DIV/0! unitless Ratio Lift 8.92 - unitless lbs lbs Links to Find: Propulsion Efficiency (jet e n p = (2V 1 ) / (V 2 + Propulsion Efficiency (jet engine) Inlet (flight) velocity Thrust Equation Exit Velocity Specific Fuel Consumption (ct) Fuel Flow (when ct and Thrust known) Angle of Climb (steady velocity) Rate of Climb, when climb angle and velocity known Rate of Climb, when V, W, Ta, Tr are known Specific Range Horsepower (when V is in knots) Equivalent Shaft HP (Turboprop) Thrust HP or Propeller Efficiency Propulsion Efficiency (n p ) opulsion Efficiency (jet engine) p Thrust Equation = (2V 1 ) / (V 2 + V 1 ) T = Q (V 2 - V 1 ) V1 65 ft/s Mass Airflow Q 0.5 slug/s V2 85 ft/s Inlet (flight) velocity V1 65 ft/s Exit Velocity V2 85 ft/s = 10.0 = 0.9 unitless Thrust (T) lb Thrust Equation T = ρAV (V 2 - V 1 ) slugs/ft3 Air Density ρ 0.6 Cross-sectional Area A 5 Velocity (airflow) V 25 ft2 ft/s Inlet (flight) velocity V1 65 ft/s Exit Velocity V2 85 ft/s = 1,500.0 Thrust (T) lb Specific Fuel Consumption (ct) Angle of Climb (steady vel c t = Fuel Flow / Thrust sin γ = (Ta - Tr) / W Fuel Flow FF 850 lb/hr Thrust Available Thrust T 1500 lb Thrust Required Acft Weight SFC (c t ) = 0.567 1/hr sin γ climb angle ( γ) Fuel Flow (when ct and Thrust known) FF = Thrust * c t Specific Fuel Cons. ct 0.567 1/hr Thrust T 1500 lb Fuel Flow = 850.5 lb/hr Angle of Climb (steady velocity) Rate of Climb, when climb angle a sin γ = (Ta - Tr) / W ROC = V k * si Ta 4200 lb climb angle Tr 830 lb Acft Velocity W 12000 lb sin γ = 0.280833 unitless 16.3 ROC degrees Rate of Climb, when V, W, Ta ROC = Vk * [ (Ta - T Acft Velocity Thrust Available Thrust Required Acft Weight ROC f Climb, when climb angle and velocity known Specific Range ROC = V k * sin γ SR = V k / FF γ 19.7 degrees Velocity Vk Vk 240 nm/hr Fuel Flow FF = = 80.9 8,195.5 Specific Range = nm/hr ft/min te of Climb, when V, W, Ta, Tr are known ROC = Vk * [ (Ta - Tr) / W] Vk 150 nm/hr Ta 4200 lb Tr 2000 lb W 10000 lb = = 33.0 3,342.9 nm/hr ft/min ific Range Horsepower (when V is in knots) V k / FF P (HP) = (TV k ) / 325 260 nm/hr Thrust T 32000 900 lb/hr Velocity V 450 P (HP) = 44,307.7 Power = 2.4336E+07 0.3 nm/lb lbs nm/hr HP ft-lb/s BHP SHP THP Brake HP: measured at the engine crankshaft Shaft HP: less than BHP; measured at propleller shaft Thrust HP: (usable HP) less than SHP because of propeller efficiency (η). This is also a type of HP and must be converted to thrust units (ESHP) Equivalent Shaft HP (Turboprop) ESHP = SHP + (TV/325 η) Shaft HP SHP 25 HP Thrust T 3200 lb Velocity V 120 nm/hr Propeller Efficiency η 0.98 unitless ESHP = 1,230.7 HP Thrust HP or Propeller Efficiency THP = η* SHP or η = THP / SHP Thrust HP (usable) THP 25 HP Shaft HP SHP 55 HP Propeller Efficiency η 0.65 Prop Efficiency (η) THP = = 0.4545 35.8 unitless unitless HP Links to Find: 10.1 - Velocity V = V 0 + at Conversion Factors Table Acceleration (thrust, drag, friction & weight) Velocity, when initial Velocity, accel & time known Effect of Weight change on Velocity Distance (when V0, time & accel known) Distance (when velocity and acceleration known) Distance (determining from new accel or velocity) Effect of Weight change on distance Effect of Air Density (altitude) on distance Effect of Headwind on TO distance Effect of Tailwind on TO distance Initial Velocity Vo Acceleration a Time t Velocity = 0.1 - Velocity 10.2 - Distance (V0, a & t known) = V 0 + at s = V 0 t + .5(at 2 ) ft/s ft/s s 0.0 2 ft/s Initial Velocity Vo 0 ft/s Acceleration a 12 Time t 28.5 ft/s2 s Distance (s) = 4,873.5 ft 10.3 - Distance (starting from an initial velocity) s = (V 2 - V 0 2 ) / 2a Vo Initial Velocity 0 ft/s Final Velocity V 253.5 ft/s Acceleration a 6.434 Distance (s) = 4,994.0 ft/s2 ft 10.6 - Distance Ratio derived from Eg 10..3 s 2 = (V 2 /V 1 ) 2 *(a 1 /a 2 )*s 1 Velocity (new) V2 ft/s Velocity (known) V1 ft/s Acceleration (known) a1 ft/s2 Acceleration (new) a2 ft/s2 Distance (known) s1 ft New Distance = #DIV/0! ft 10.5 - Acceleration (from thrust, Drag, Friction & Weight) a = g (T-D-F) / W Gravity's Accel g 32.2 Thrust T 4800 Drag Friction Force Weight D F W 250 450 10000 Accleration = 13.2 ft/s2 lb lb lb lb ft/s2 10.6a - Effect of Weight change on Velocity 10.7 - Effect of Weight change on distanc s 2 = (W 2 /W 1 ) 2 * s 1 V 2 = √(W 2 /W 1 )*V 1 Velocity (known) V1 20 ft/s Takeoff Distance (known) s1 Weight (known) W1 4 Weight (known) W1 Weight (new) W2 16 lb lb Weight (new) W2 New Velocity = 40.0 New Distance = ft/s Weight change on distance W 2 /W 1 ) 2 * s 1 2270 ft 10000 lb lb 11000 2,746.7 10.8 - Effect of air density (altitude) change on distance (non-turbocharged engines) s 2 = (1/ σ2 ) 2 * s 1 ft Distance (known) s1 New Air density ratio σ2 ft 0.8617 lb New Distance = 3,057.1 2270 ft 10.9 - Effect of air density (altitude) change on distance (turbocharged engines) s 2 = (1/ σ2 ) * s 1 Distance (known) s1 2500 New Air density ratio σ2 0.762 New Distance = 3,280.8 ft lb ft 10.10 - Effect of Headwind on takeoff distance s 2 = [1-(V w /V 1 )] 2 * s 1 Distance (known) s1 1200 Takeoff Velocity (VLOF) V1 48 Headwind Velocity Vw 12 = 675.00 New Distance 10.7 - Effect of Tailwind on takeoff distance s 2 = [1+(V w /V 1 )] 2 * s 1 ft Distance (known) s1 ft/s ft/s Takeoff Velocity (VLOF) V1 Headwind Velocity Vw ft New Distance = ailwind on takeoff distance V w /V 1 )] 2 * s 1 1200 48 12 1,875.00 ft ft/s ft/s ft 11.1 - Glide Path Force Equation (Lift) L = W cos γ Acft Weight W 2000 Glide Angle γ 25 Lift = 1,812.6 lb degrees lb 11.2 - Glide Path Force Equation (Drag) L = W sin γ Acft Weight W 2000 Glide Angle γ 25 Drag = 845.2 lb degrees lb 11.3 - Maximum Glide Angle γ = tan -1 (1/LD max ) 12 (L/D)MAX Best Glide Angle ( γ) = 4.8 Calculate Landing Distance s = V 0 2 /2a V0 Landing Velocity Deceleration a Landing Distance = degrees Rate of Sink Equation ROS = 101.3V k (D-T/W) 10.6a - Effect of Weight change on Velocity V 2 = √(W 2 /W 1 )*V 1 Velocity Vk 130 nm/hr Drag (Tr) D 3500 lb Velocity (known) V1 Thrust (Ta) T 3000 Weight (known) W1 Weight (new) W 10000 lb lb Weight (new) W2 Rate of Sink = 658.5 New Velocity = ft/min e Landing Distance = V 0 2 /2a 110 8 ft/s 11.6 - Effect of Headwind on Landing distance s 2 = [1-(V w /V 1 )] 2 * s 1 s1 Distance (known) 1785 ft ft/s2 Landing Velocity V1 100 ft/s Headwind Velocity Vw 10 ft/s = 1,445.9 756.3 ft New Distance Weight change on Velocity ft 11.4- Effect of Weight change on Landing distance (W 2 /W 1 )*V 1 s 2 = (W 2 /W 1 ) * s 1 20 ft/s Distance (known) s1 1785 ft 4 lb lb Weight (known) W1 8000 Weight (new) W2 13000 lb lb New Distance = 2,900.6 16 40.0 ft/s ft 11.7 - Effect of Tailwind on Landing distance s 2 = [1+(V w /V 1 )] 2 * s 1 s1 Distance (known) 1785 ft Landing Velocity V1 100 ft/s Headwind Velocity Vw 10 ft/s = 2,159.9 New Distance 11.8 - Approx. Velocity of Total dynamic Hydroplan V H = 9 √P ft 11.5 - Effect of Altitude on landing distance (for non-thrust reverser acft) s 2 = (1/ σ2 ) * s 1 Distance (known) s1 1785 New Air density ratio σ2 0.8 New Distance = 2,231.3 ft ft Tire Inflation Press P Hydroplaning Velocity = of Total dynamic Hydroplaning H = 9 √P 43 59.0 lb/in2 nm/hr CONVERSION FACTORS multiply / divide by 250 144 psf psi 2.036 Hg" psf 144 psi psf 70.726 Hg" Hg" 2.036 Hg" 70.726 knots 1.69 fps 1.15 mph psi psf knots knots 101.3 fpm fps 422.5 0.5925 knots fps 0.6818 mph mph 1.467 fps mph 0.869 knots nautical mile (nm) 6076 ft nautical mile (nm) 1.15 statue mile (sm) ft 0.00016458 nautical mile (nm) ft 0.00018939 statue mile (sm) 0.869 nautical mile (nm) statute mile (sm) statue mile (sm) 5280 slug 14.594 kg kg 14.594 slug (°F) (F-32)*5/9 (°C) (C*9/5)+32 59 add / subtract Fahrenheit (°F) -22.32 Rankine (°R) 445.9 Celsius (°C) 15 Kelvin (K) Nautical mile (nm) = 6076 ft Statute mile (sm) = 5280 ft Velocity (knots(kt) or nm/hr) 1 kt = 1.69 ft/s Velocity (mph) 1 kt = 1.15 mph Horsepower = 550 ft-lb/s Foot = 0.305 meters Nautical mile = 1851 meters Statue mile = 1609 meters 1 kg = 2.2 lbmass 1 Newton = 0.225 lbforce ft (°C) (°F) 0.0 0.000 0.00 0.000 0.00 0.0 422.50 0.00 0.00 250.33 0.00 0.00 0.00 0.00 0.00 0.0000 0.00 0.00 0.0 0.0 0.00 15.0 32.0 to get by 460 Fundamental Units to get psi -460 Rankine (°R) Fahrenheit (°F) 273.15 Kelvin (K) -273.15 Celsius (°C) 437.7 -14.1 288.2 -273.2 British Grav. Sys (BGS) Term Distance feet Time second Temperature Fahrenheit Absolute Temp Rankine Force Pound-force (pounds x g) BGS/English Unit ft Internat'l System (SI) Term meter SI Unit Term m second s Runway Length feet (ft) Meters (m) Celsius °C Altitude and Vertical distance feet (ft) feet Kelvin °K Air Distance nautical mile (nm) nautical mile (nm) kilogram kg °R ft-lb/s 2 Mass Airspeed Temperature Derived Units British Grav. Sys (BGS) Term BGS/English Unit Force Mass Internat'l System (SI) Term SI Unit Newton (N) kg-m/s 2 2 Velocity Slug or Poundmass feet/second (fps) lb-s /ft ft/s meters/second m/s Acceleration feet/second squared ft/s 2 meters/second squared m/s 2 Area Square feet ft 2 Square meters m2 Volume Cubic feet liters Pressure pound/square foot (psf) Pascal (Pa) l or m N/m2 Energy foot-pounds Joules(J) N-m Work foot-pounds Power foot-pounds/second Moment foot-pounds Momentum (p ) Mass x Velocity ft 3 lb/ft 2 ft-lb ft-lb Joules(J) 3 N-m ft-lb/s Watts (W) ft-lb Newton meters N-m (lb- s /ft) x (ft/s) = lb-s Mass*Velocity kg-m/s 2 Aviation Terms US Unit ICAO Unit s °F J/s Atmospheric Pressure knots (kt) = nm/hr knots Celsius Celsius Pounds/square inch (PSI) or Hg" Hectopascals Remarks Old Soviet bloc use meters Old Soviet bloc use meters/s Table 2.1, Altitude (ft) 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 20,000 25,000 30,000 35,000 36,089 40,000 45,000 50,000 60,000 70,000 80,000 90,000 100,000 150,000 200,000 250,000 Density Ratio, σ 1.0000 0.9711 0.9428 0.9151 0.8881 0.8617 0.8359 0.8106 0.7860 0.7620 0.7385 0.6292 0.5328 0.4481 0.3741 0.3099 0.2971 0.2462 0.1936 0.1522 DR Difference 0.0289 0.0283 0.0277 0.0270 0.0264 0.0258 0.0253 0.0246 0.0240 0.0235 0.1093 0.0964 0.0847 0.0740 0.0642 0.0128 0.0509 0.0526 0.0414 𝜎 1.0000 0.9854 0.9710 0.9566 0.9424 0.9283 0.9143 0.9004 0.8866 0.8729 0.8593 0.7932 0.7299 0.6694 0.6117 0.5567 0.5450 0.4962 0.4400 0.3901 Table 2.1, Standard Atmosphere Table (pg 16) Pressure Ratio, δ 1.0000 0.9644 0.9298 0.8962 0.8637 0.8320 0.8014 0.7716 0.7428 0.7148 0.6877 0.5643 0.4595 0.3711 0.2970 0.2353 0.2234 0.1851 0.1455 0.1145 PR Difference Temperature (°F) Temperature (°R) Temperature Ratio, θ 0.0356 0.0346 0.0336 0.0325 0.0317 0.0306 0.0298 0.0288 0.0280 0.0271 0.1234 0.1048 0.0884 0.0741 0.0617 0.0119 0.0383 0.0396 0.0310 59.00 55.43 51.87 48.30 44.74 41.17 37.60 34.04 30.47 26.90 23.34 5.51 -12.32 -30.15 -47.98 -65.82 -69.70 -69.70 -69.70 -69.70 519.00 515.43 511.87 508.30 504.74 501.17 497.60 494.04 490.47 486.90 483.34 465.51 447.68 429.85 412.02 394.18 390.30 390.30 390.30 390.30 1.0000 0.9931 0.9862 0.9794 0.9725 0.9656 0.9587 0.9519 0.9450 0.9381 0.9312 0.8969 0.8625 0.8281 0.7937 0.7594 0.7519 0.7519 0.7519 0.7519 Speed of Sound (knots) Kinematic Viscosity, v 2 (ft /s) 661.7 659.5 657.2 654.9 652.6 650.3 647.9 645.6 643.3 640.9 638.6 626.7 614.6 602.2 589.5 576.6 573.8 573.8 573.8 573.8 0.000158 0.000161 0.000165 0.000169 0.000174 0.000178 0.000182 0.000187 0.000192 0.000197 0.000202 0.000229 0.000262 0.000302 0.000349 0.000405 0.000419 0.000506 0.000643 0.000818 Acceleration due to gravity, g (ft/s2) 32.189 32.159 32.143 32.128 32.112 32.097 32.082 32.066 32.051 32.036 32.020 31.990 31.959 31.929 31.897 31.868 31.717 31.566 31.415 Links (to find:) MASS / Weight Mass / Weight W = m * g // m = W/g Find Acceleration (when Velocities and Time are known) Find Acceleration (when Velocities and distance known) Weight Find Velocity (given time & acceleration) Mass Find Takeoff Velocity (given accel, distance, & initial Velocity) Gravity Accel Find Time (given Vel & Accel) Find distance (given Vel & Accel) Find distance (given initial Vel, Time & Accel) PE KE TE Work Power Horsepower Friction Ground Speed Rate of Climb Finding Ground Speed V h = V a/c (Cos λ) Acft TAS Climb Angle Ground Speed Finding Rate of Climb Speed (R V v = V a/c (Sin λ) Acft TAS Climb Angle Rate of Climb Find Acceleration (when Velocities an known) a = (V 2 - V 0 2 ) / 2s Initial Velocity Final Velocity Distance traveled a MASS / Weight W = m * g // m = W/g W 10000 W m = = 0.0 310.56 lbs slugs knots degrees knots Vh = 173.2 knots knots lbs (lb-s2)/ft m g 32.2 ft/s2 Finding Ground Speed V h = V a/c (Cos λ) Va/c 200 30 ? λ Vh Finding Rate of Climb Speed (ROC) V v = V a/c (Sin λ) Va/c 200 knots Vv = 100.0 λ 30 degrees Vv = 10,140.0 Vv ? knots nd Acceleration (when Velocities and distance known) a = (V 2 - V 0 2 ) / 2s V0 V s 0 219.7 500 ft/s ft/s ft = 48.3 ft/s2 fpm Find Acceleration (when V & Time known) a = ΔV / Δt = (V - V 0 ) / (t - t 0 ) Initial Vel V0 0 fps Meas Vel V 219.7 fps Initial Time t0 0 sec Meas Time t 5 sec Acceleration a ? ft/s Find Velocity (given tim V = V 0 + a( a a a = 43.9 ft/s2 = ######## ft/min2 = ######## mi/hr2 Initial Vel Acceleration Initial Time Meas Time 2 Velocity V Vh Ground Speed Va/c True Airspeed Vv Rate of Climb λ Climb Angle Find Velocity (given time & acceleration) V = V 0 + a(t - t 0 ) Find Takeoff Velocity (given accel, distance, & initial Velocity) V f = √(V 0 2 +2as) V0 5 fps a 24 Initial Vel t0 1 ft/s2 sec t 5 sec V ? fps = 101.0 fps V0 50 fps Acceleration a 10 Distance s 500 ft/s2 ft Vf = 111.8 fps Find Time (given Vel & Accel) t = [(V - V 0 ) / a]+ t 0 Find distance (given Vel & Accel) s = (V 2 - V 0 2 ) / 2a Initial Vel V0 0 fps Initial Vel V0 0 fps Meas Vel V 219.7 fps Final Vel V 24 fps Initial Time t0 0 sec Accel a 5 Acceleration a 12.88 Distance s ? Time t ? ft/s2 sec ft/s2 ft = 1440.0 = 17.1 t sec s ft Find distance (given initial Vel, Time & Accel) s = V 0 t + (at 2 / 2) Initial Vel Time V0 0 fps t 10 sec Accel a 5 Distance s ? = 250.0 s ft/s ft 2 ft Potential Energy (PE) PE = W * h Weight W Height h Pot. Energy PE PE = Potential Energy (PE) PE = W * h Kinetic Energy (KE) KE = (mV 2 ) / 2 (lb-s2)/ft ft/s 10000 lbs Mass m 310.56 10000 ft Velocity V 422.5 ft-lbs Kin. Energy KE ? KE = 27,718,450.50 ft-lbs 2.772E+07 ft-lbs ? 100,000,000.00 ft-lbs 1.00E+08 ft-lbs ft-lbs Mechanical Energy (TE) TE = PE + KE TE = Work w=F*D Force F 100 127,718,450.50 ft-lbs Distance D 150 1.277E+08 ft-lbs Work w ? = 15,000.00 w 1.500E+04 rk *D Power P = [(F * D) / time] OR P = F * V or P = W/t Horsepower (when V is in ft/s) HP = (F * V) / 550 lbs Force F 1500 lbs Force F ft Distance D 10 ft Distance D ft-lbs time t 1 sec Velocity V ft-lbs Power P ? ft-lbs/s time t ft-lbs P = 15,000.0 ft-lbs/s 1.500E+04 ft-lbs/s → HP = Manually, from values above HP = HP = sepower (when V is in ft/s) HP = (F * V) / 550 Horsepower (when V is in knots) HP = (TV k ) / 325 1500 lbs Thrust T 29000 10 ft Velocity V 10 ft/s HP 1 sec Friction (runwa Fb = μ*N lbs Braking Force 425 knots Normal Force HP ? ft-lbs/s Coef of Friction ft-lbs/s HP = 37,923.1 ft-lb/s Fb anually, from values above 27.3 ft-lbs/s 27.3 ft-lbs/s HP = 3.792E+04 ft-lb/s μ (mu) 27.3 Friction (runway) Fb = μ*N Fb 1500 lbs N 500 lbs μ (mu) 0.53 no value = 265.0 = 3.0 lbs no value Density (ρ-rho) / Mass (m) / Volume (V) ρ=m/V Links to Find: Density (ρ-rho) / Mass (m) / Volume (V) Mass m 0.15 slugs Pressure Alt (PA), given Altimeter Setting Volume V 3 Ambient Pressure P, given δ (Press Ratio) Air Density ρ (rho) 0.05 slugs/ft3 = = = 0.05 0.15 3.00 slugs/ft ft3 Pressure Ratio (δ - delta) Temperature Ratio (θ - theta) Density Ratio (σ - sigma), given density Density Ratio (σ - sigma) , given Press. & Temp. Density Ratio (when δ is Interpolated from table) Dynamic Pressure (q) Density (ρ) m V slugs ft3 3 Altitude Pressure Ratio (δ - delta) Temperature Ratio (θ - th δ=P/P0 Ambient Static Press Std SL Static Press Press Ratio ( δ delta) θ=T/T0 P P0 13.75 psi or Hg" Ambient Air Temp 29.92 psi or Hg" Std SL Air Temp = 0.45956 unitless Find Ambient Pressure P , given δ P= δ*P0 Press Ratio Std SL Static Press Ambient Pressure (P) δ P0 0.4595 29.92 unitless psi or Hg" = 13.75 psi or Hg" Find Pressure Alt (PA), given Altimeter Setting 1) 29.92" Hg - Alt Setting = ΔP 2) ΔP / .001" = Δalt 3) Elevation + Δalt. = Pressure Alt. (PA) Elevation Altimeter Setting Std Sea Level Pressure Change in Pressure Change in Altitude Pressure Alt. (PA) ΔP Δ Alt 20,500 30.42 29.92 -0.50 -500 = 20,000 ft Hg" Hg" Hg" ft ft Temp Ratio ( θ theta) Standard Day Parameters Temperature Ratio (θ - theta) Density Ratio (σ - sigma), given density θ=T/T0 σ=ρ/ρ0 T T0 = 437.7 °R / °K Density 519 °R / °K SL Density ρ (rho) ρ 0 (rho) Density Ratio σ (sigma) 0.84335 0.0012468 slugs/ft3 0.002378 slugs/ft3 unitless unitless Density Ratio ( σ) Density (ρ) = = 0.5243 unitless 0.0000000 slugs/ft3 0.000E+00 slugs/ft3 Standard Day Parameters (σ - sigma) Density Ratio (given Press. & Temp.) Dynamic Pressure (q) 2 σ = δ /θ = (P / P 0 ) / (T / T 0 ) Static Press q = .5(ρV ) P P0 30.42 psi or Hg" Velocity 29.92 psi or Hg" Density ratio T T0 437.7 °R or °F Density (air) 519 °R or °F Dynamic Press Press Ratio δ (delta) 1.0167 unitless Temp Ratio θ (theta) 0.8434 unitless = 1.2056 Std Sea Lvl Press Absolute Temp Std Sea Lvl Temp Density Ratio ( σ) unitless Find Density Ratio (when δ is Interpolated from table) σ = δ /θ Altitude 20,500 ft Indicated Temp 437.7 °R Pressure Ratio δ (delta) 0.4595 unitless Temperature Ratio θ (theta) 0.8434 unitless = 0.5449 Density Ratio ( σ) unitless Dynamic Press (q) Dynamic Pressure (q) 2 Links to Find: q = .5(ρV ) V 338 fps Density (ρ-rho) / Mass (m) / Volume (V) σ 0.7385 unitless Pressure Alt (PA), given Altimeter Setting ρ 0.001756 slugs/ft3 ? lbs/ft2 Ambient Pressure P, given δ (Press Ratio) q Pressure Ratio (δ - delta) Temperature Ratio (θ - theta) = 100.31 lbs/ft 2 Density Ratio (σ - sigma), given density Density Ratio (σ - sigma) , given Press. & Temp. Density Ratio (when δ is Interpolated from table) Dynamic Pressure (q) V (KTAS) 113.3 120 140 160 180 190 200 220 240 260 Weight (W) Wing Area (S) Aspect Ratio (AR) e Temp Sigma (∂) CDP CLmax at Stall q= ∂ x V^2/295 (lb/ft^2) CL = W/qS CDI=[1/ (πeAR)] CL^2 CDp CD= CDP+CDI CL/CD Dp=CDp q S (lb) Di = Cdi q S (lb) 43.48 48.81 66.44 86.78 109.83 122.37 135.59 164.07 195.25 229.15 1.50 1.34 0.98 0.75 0.59 0.53 0.48 0.40 0.33 0.28 0.159 0.126 0.068 0.040 0.025 0.020 0.016 0.011 0.008 0.006 0.021 0.021 0.021 0.021 0.021 0.021 0.021 0.021 0.021 0.021 0.18 0.15 0.09 0.06 0.05 0.04 0.04 0.03 0.03 0.03 8.33 9.08 11.02 12.34 12.93 12.98 12.88 12.36 11.56 10.65 210.00 235.77 320.91 419.15 530.48 591.06 654.92 792.45 943.08 1106.81 1589.8 1416.0 1040.3 796.5 629.3 564.8 509.8 421.3 354.0 301.6 15000 230 5.3 0.85 Standard 1 0.021 1.5 295 Dt = Di + Dp (lb) 1799.8 1651.8 1361.3 1215.7 1159.8 1155.9 1164.7 1213.7 1297.1 1408.4 
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