Standard Atmosphere AE5363
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This 19 page Class Notes was uploaded by Manohar Notetaker on Friday September 9, 2016. The Class Notes belongs to AE5363 at University of Texas at Arlington taught by Dr. Dudley E Smith in Fall 2016. Since its upload, it has received 10 views. For similar materials see introduction to rotarcraft analysis in Aerospace Engineering at University of Texas at Arlington.
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Date Created: 09/09/16
Standard Atmosphere Four Main Regions of Std Atm • Troposphere – region nearest the surface of the earth extends from ~ 5mi at the poles to 10 mi at the equator (clouds and turbulent conditions) • Stratosphere – from the top of the Troposphere to ~50-75 mi above the surface • stratopause – small layer between Stratosphere and Ionosphere • Ionosphere – region of magnetic and electrical phenomena (aurora borealis, etc.) • Exosphere – fringe region 300-600 mi ICAO Std Atm Variation of temperature with altitude – note regions of linear variation and nearly constant value as altitude changes Most “airborne flight” takes place below 100,000’ (~30km) Variation of Gravity • As the earth spins on its axis, centrifugal forces cause it to flatten at the poles and bulge at the equator. • Although the gravity field of the earth is not symmetrical about all axes, it is presumed spherical for the standard atmosphere . 2 g g R e oha where: h h R absolute _altitude _to_earth _center a G e and: hG geometric _altitude _ from _earth's _ surface Hydrostatic Equation p pdp gdh 0 or dp gdh If g is assumed to be constant over the altitude dp g do or dp gdh G yields dh g dh go G 2 hG R eh G or h 0 2 R eh G Forces on a unit of air R h R h (positive upward) h e G hG e ha Reh ICAO Std Atm • Statement of the seal level conditions • Temperature schedule as a function of altitude • Assume the air behaves per the equation of state p g RT o Where g o is taken as a constant and is the absolute temperature ICAO Std Atm Atmospheric definition at 45 32’40” North Latitude po= 760 mm Hg =29.92” hg = 2116.217 lb/ft 2 3 ro= .00237692 slugs/ft o o o o To= 59 F = 518.688 R = 15 C = 288.16 K g = 32.1741 ft/sec 2 o Vao speed of sound = 1116.44372 ft/sec Re= earth radius 3949.9113 mi = 20,855,531.5 ft o R = the gas constant = 53.35 ft/ R ICAO Std Atm Linear variation of temperature in the Troposphere ICAO Std Atm • For isothermal regions (i.e. constant temperature) p2dp h dh 1 p h1RT Subscript “1” refers to the layers at the base of or log p hh 1 h1h ep RT RT 1 h1h p e define RT , then p1 ICAO Std Atm • Thus, at any point, the pressure ratio to standard sea level pressure p 0 is designated as , thus: p p1 p 1 po o p e p1 in terms of pressure ratio becomes 1 ICAO Std Atm Again, at any point, the density ratio to standard sea level density is designated by o T And the temperature ratio is designated by To T To The equation of state becomes ICAO Std Atm Rearranging, the equation of state becomes 1 e For an isothermal region, is constant, thus 1 1 and 1 ICAO Std Atm Thus, for an isothermal region, we have T constant, constant 1 e1 h1h RT ICAO Std Atm • For gradient regions (i.e. linear temperature variation) T T 1a hh 1 • Where the lapse rate is defined by a dT dh dp dT • Rewriting the EOS yields p aRT ICAO Std Atm • Integrating yields p 1 T log e p aR log eT 1 1 1 log T aR eT1 e 1 ICAO Std Atm Or, rewriting in terms of pressure as before 1 1 1 p T aR aR aR or T p1 T1 11 1T 1 1 1 1 aR aR1 T aR1 Since 1 1 1 1 1 1 T 1 T loge 1log e 1 aR T1 1 1 og T e `1 where aR T 1 ICAO Std Atm For any region with a temperature gradient, we have 1 aR 1 T T aR1 e1 1 e `1 1 T 1 T1 1 T where loge aR T1 1 T 1 oge aR T1 ICAO Std Atm In the troposphere, 1 1 1 5.2561 4.2561 10.000006875 h ICAO Standard Atmosphere
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