Embry–Riddle Aeronautical University
The AtmosphereAbbreviationsSL = sea levelSA = standard atmosphereStatic and Dynamic PressureTotal Pressure Static Pressure P Dynamic Pressure q 29.92” Hg at SL in SA q = V2 / 2Dynamic pressure q = V2 / 2is also called Ram Air Pressureis a major cause of parasite drag (lower case rho) = air density in slugs/ft3; V = true airspeed (TAS) in ft/sec;q = ram air pressure in #/ft2We are unconcerned with units in the dynamic pressure equation. However, every pilot should know the implications of the equation q = V2 / 2: Ram air pressure q is directly proportional to air densitydirectly proportional to TAS squaredStandard Atmosphere“Average” static pressure, absolute temperature, and density (among other parameters) in the atmosphere from SL upwardCompiled from scientific observations at many locations around the earth over a extended period of timeA theoretical concept: no air mass precisely replicates the SATo compare the performance of two aircraft operating in different air masses, must determine their density altitudes in a SAStandard Atmosphere Table—a table listing atmospheric properties in a SAUse ONLY this SA Table in quiz and test calculations!!!Pressure Ratio (small delta) in SA = P / P0P is static pressure at your altitudeP0 is static pressure at SL in SA (29.92” Hg)Lapse rate of P in a standard atmosphere is 1” Hg / 1000’ (this “rule of thumb is an accurate approximation in the lower atmosphere ONLY)Altitude (ft)Calculated Using Rule of ThumbActual 100028.92 / 29/92 = 0.966580.96439500024.92 / 29.92 = 0.832870.832051000019.92 / 29.92 = 0.665760.68770200009.92 / 29.92 = 0.331550.45954299200 / 29.92 = 0.000000.29690Temperature Ratio (theta) in SA = T / T0T is absolute temperature at your altitudeT0 is absolute temperature at SL in SA (288O Kelvin or 519O Rankine)KO = Co + 273O (e.g. 15O C + 273O C = 288O K)RO = FO + 460O ( e.g. 59O F + 460O F = 519O R)Lapse Rate of temperature in SA is about 2O C (3.6O F) /1000’ from SL to the tropopause. This approximation is highly accurate.Altitude (ft)Calculated Using 2O /1000’ Lapse RateActual 10000(-5+273) / (15+273) = 0.930560.9312520000(-25+273) / (15+273) = 0.861110.8624930000(-45+273) / (15+273) = 0.791670.79374Suppose the temperature ratio at your altitude is 0.86249. Find the temperature in degrees F at this altitude in SA.T = T0 = (59 + 460)O R (0.86249) = 447.632O RT = 447.63O R – 460O = -12.367O FDensity Ratio (small sigma) = / 0 is air density at your altitude0 is air density at SL in SANo rule of thumb exists for the lapse rate of air density in SA.Relationship between Pressure, Temperature, and Density in SA = / Example: FL350 / FL350 = 0.23530 / 0.75936 = 0.30987 = FL350( is a mathematical symbol that means “is proportional to”) = / = PP0TT0 ∝PTImportant: The equations = / reflects the fact that air density isDirectly proportional to static air pressureInversely proportional to absolute air temperatureSMOE (Standard Means of Evaluation)SMOE = 1 / Some SA tables have a column for Some SA tables have a column for SMOESpeed of Sound in Air adepends on air temperature T only (counterintuitive?)a = a0 where a0 = 661.74 nm/hr, the speed of sound at SL in SAExample: if = 0.79374, then a = a0 = 661.74 0.79374 = 589.56 nm/hrMach Number Mratio of TAS to the speed of sound at cruise altitudeM = TAS / a = TAS / (a0 )Math Review: Linear vs. Non-Linear and Direct vs. Inverse Functionsy = f(x)—a mapping from a domain x to a range yLinear : y changes at a constant rate with respect to x—results in a straight line plotNon-linear: y changes at a varying rate with respect to x—results in a curved line plotDirect (x, y; x, y))Inverse (x, y; x, y)Examples:Linear, Direct: y = xLinear, Inverse: y = -xNon-Linear: y = x2Direct in1st QuadrantInverse in 2nd QuadrantVariation of SA Parameters with Altitude, , are all inverse, are both non-linear; is linear (and has a discontinuity)a is linear inverse (and has a discontinuity)SMOE = 1 / is non-linear direct0.0 < , , ≤ 1.0 in SA at SL and aboveAltitude MeasurementIndicated Altitude (IA)—read on the altimeter. To find altimeter error:Set field elevation on altimeterRead Kollsman window valueCompare Kollsman value to reported altimeter settingExample: Altimeter setting = 3.12 with field elevation setKollsman window reading = 3.15Altimeter error = 3.15 – 3.12 = + 0.03Set Kollsman window to next reported altimeter setting + 0.03Pressure Altitude (PA)—IA corrected for non-standard static pressure PE6B / Flight Computer or use 1” Hg /1000’ rule of thumbSince P decreases as altitude increases (inverse function)Non-standard high static pressure PA lower than IANon-standard low static pressure PA higher than IA is a mathematical symbol that means “implies”Example 1:IA = 35’ (field elevation); Altimeter setting = 30.1430.14 – 29.92 = 0.22: corresponds to 0.22 (1000) = 220’PA = 35’ – 220’ = -185’ (subtract because pressure is non-standard high, implying PA < IA)Example 2:IA = 35’ (field elevation); Altimeter setting = 28.4029.92 – 28.40 = 1.52: corresponds to 1.52 (1000) = 1520’PA = 35’ + 1520’ = 1555’ (add because pressure is non-standard low, implying PA > IADensity Altitude (DA) – PA corrected for non-standard temperature TUse an aviation computer or chart to make this correctionNote: Since P/T, correcting IA for non-standard P and PA for non-standard T is equivalent to correcting IA for non-standard densityThus, DA = IA corrected for non-standard air densityUse the chart below to find DA by correcting PA for temperature TLocate T on bottom horizontal scaleProceed vertically to intersect the curved PA lineAt the intersection, proceed horizontally to readDA on left vertical scaleSMOE on right vertical scaleNote: each small block on the left vertical-axis = 250’ of altitudeT = -15o C; PA = 6000’ (non-standard low temperature)DA = 5000 – (4.5*250) = 3875’; SMOE = 1.05Required Accuracy: ± 250’ DA, ± 0.01 SMOE ................
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