STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! indicatd altitud actual altitud
STANDARD ATMOSHERE indicatd altitud actual altitud
STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! Today s Actual ssu ofil indicatd altitud Standad ssu ofil actual altitud masud
STANDARD ATMOSHERE A STANDARD ATMOSHERE IS A MATH MODEL WHICH, ON AVERAE, AROXIMATES THE REAL ATMOSHERE IT ROVIDES A BASIS FOR AIRCRAFT ERFORMANCE COMARISON IT ALLOWS EXERIMENTAL DATA TO BE ENERALIZED IT ROVIDES A BASIS FOR UNIFORM DESIN T STANDARD ATMOSHERE is basd on masumnts of tmpatus aound t wold, diffnt days, diffnt latituds. HOT DAY Low Tust Low Ciling COLD DAY Incasd Tust Hig Ciling
6 Dfinitions of Altitud
Altituds THERE IS A UNIQUE ABSOLUTE ALT FOR EACH EOMETRIC ALT EOMETRIC ALT IS THE DIFFERENCE BETWEEN a AND E a = + E E 6400 km 4000 mi TWO ALTITUDES ARE EQUAL AT ONE OINT BUT NOWHERE ELSE. WHICH ALTITUDES ARE THESE? CAN AN AIRCRAFT BE AT SEVERAL ALTITUDES AT THE SAME TIME?
STANDARD ATMOSHERE
TEMERATURE ALTITUDE altitud is basd on masu of T & cosponds to t pofil of t std atmosp T IS MULTIVALUED FOR VALUES OF T AVERAE VALUES DO NOT MATCH ACTUAL VALUES
STANDARD ATMOSHERE - ssu gadint (statosp) isotmal (topopaus) gadint (toposp)
STANDARD ATMOSHERE STANDARDIZATION (assum a T vs pofil) Tmpatu vaiation of 2 foms RADIENT (constant slop) ISOTHERMAL (constant T) adint Equations basd upon Isotmal HYDROSTATIC EQUATION EOOTENTIAL ALTITUDE EQUATION OF STATE DEFINED TEMERATURES
a T = T 2 T a is t invs of t slop
DERIVATION OF THE HYDROSTATIC EQUATION (o ao static ) Fom ΣF = ma = 0, sum vtical focs -- wigt of fluid = ρ f g V = ρ f g A -- p A (upwad) -- (p + p) A (downwad) w is t gomtic altitud (p ( + p) A ) A W substituting p A - (p + p) A - ρ f g A = 0 p A = - ρ f g A p A A p = - ρ f g W = ρ g A f in t limit, as t volum vaniss, dp = - ρ f g d (t ydostatic quation) Assuming g = g 0 = constant, dp = - ρ f g 0 d, w is t EOOTENTIAL altt EOOTENTIAL altitud dos not account fo cangs in gavity.
Rcall, Nwton s Law of Univsal (avitational) Attaction Fo t attacting bodis, w M, m = masss of t 2 bodis is t Univsal avitational Constant is t distanc btwn t cnts of t 2 bodis F = Mm 2 at t Eat s Sufac, M = M E, mass of t Eat, m = mass of an objct = R E (Eat s adius) at any altitud, = R E + = distanc fom cnt of Eat F M M = = = "g o " m R E 2 2 E F M M m R E = = = 2 2 ( + ) E "g" T atio lads to a nic qn. btwn g and altitud Wat is g wn on is at = R E? (not, R E = 6365 km = 3955 mi) 2 g RE = g R ( + ) o E 2
T Hydostatic Equation DERIVATION OF THE HYDROSTATIC EQUATION T fom d = - ρ f g 0 d maks intgation asi sinc g 0 = constant, but d = - ρ f g d is t coct fom of t ydostatic quation. W will us bot to find t standad atmosp As an asid, if w want to consid cangs of and wit tim, lts assum ρ f and g 0 a fixd, and lts tak a divativ w..t. tim d dt = ρ g d dt o & = ρ g& allowing us to xamin at of cang of wit at of cang of altitud, o vic vsa. Tis is t basis fo an A/C Rat of Climb Indicato!
RELATIN AND W nd = ( ): Divid ou two vsions of t ydostatic quation SUBSTITUTIN INTERATIN BETWEEN SEA LEVEL AND d d gd g d d g g d = = = 0 0 ρ ρ g g d d 0 2 2 = + = + ( ) ( ) + + + = + + = + = + = + = 2 2 0 2 0 2 2 0 2 0 d d d = +
STANDARD ATMOSHERE Fom d = -ρg d and = ρrt W find ou diffntial qn. FOR ISOTHERMAL LAYERS, Sinc T IS CONSTANT, INTERATION IS SIMLE. d g0 = RT d d g RT 0 = NOW, Raising bot sids to t pow of Tus, wit t constant T ( isotmal ), d 0 0 ( ln ) = ( ) ln = ( ) = g RT g0 RT ( ) ρ RT ρ = = = ρ RT ρ g 0 RT g RT ( )
STANDARD ATMOSHERE Again, t quid diffntial quation is obtaind: (divid t ydostatic quation (t vsion is usd to allow g to b constant) by t quation of stat ) d = ρ g 0 RT d g0 = ρ d RT Now, fo t adint gion, t laps at a is dfind lating to T Substituting d in tms of dt Wit intgation in t gadint gion ( - ) = a (T - T ) d g = 0 ar dt T d a d = dt d g dt g ar T ar a dt T 0 0 T = ln = ln T T T ln g0 T = ln ar T T = T g0 ar
STANDARD ATMOSHERE THE EQUATION OF STATE ALLOWS DEFINITION OF DENSITY IN THE RADIENT REION g0 g0 ar + ρt T ar T = = T ρ = T ρ ρ T VARIATION OF T IS LINEAR WITH T T T a( ) a = = + T T T Tmpatu atio givs and ρ atios as a function of (gopotntial) altitud ρ ρ g T ar = a = + T T T ar = a = + T T g ar 0 0 g0 g0 + ar + call, o = + =
STANDARD ATMOSHERE - ssu 4.46 psf = g RT ( ) 0 T = T g0 ar 26.22 psf
STANDARD ATMOSHERE - Dnsity 0.00000536 slug-ft 2 ρ ρ 0 = g RT ( ) ρ = T ρ T g0 + ar 0.0076 slug/ft 3
RESSURE ALTITUDE THE ATMOSHERIC MODEL LEADS TO = () RESSURE ALTITUDE IS DEFINED AS THE RECIROCAL RELATIONSHI: = () Today s Actual ssu ofil suggstd altitud Standad ssu ofil actual altitud masud Wil flying fom ot to cold, o ig to low, watc out blow!