While flying from hot to cold, or high to low, watch out below!

Transcription

1 STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! indicatd altitud actual altitud

2 STANDARD ATMOSHERE indicatd altitud actual altitud

3 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

4 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

5 6 Dfinitions of Altitud

6 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?

7 STANDARD ATMOSHERE

8 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

9 STANDARD ATMOSHERE - ssu gadint (statosp) isotmal (topopaus) gadint (toposp)

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12 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

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15 a T = T 2 T a is t invs of t slop

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17 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.

18 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

19 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!

20 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 = + = + ( ) ( ) = + + = + = + = + = d d d = +

21 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 ( )

22 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

23 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 = + =

24 STANDARD ATMOSHERE - ssu 4.46 psf = g RT ( ) 0 T = T g0 ar psf

25 STANDARD ATMOSHERE - Dnsity slug-ft 2 ρ ρ 0 = g RT ( ) ρ = T ρ T g0 + ar slug/ft 3

26 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!