!PROIECT-P1

Equations

Program de calcul a sarcinii termice de racire ptr un perete cu fereastra - C Iosifescu

Programul calculeaza sarcina termica a unui perete plan multistrat, orizontal, vertical sau inclinat, cu o fereastra,in fct de pozitia geografica (localitate), orientare, si moment (data, ora)Datele de calcul (localitate, dimensiuni, structura pereti, tip fereastra, etc.) se vor modifica in fct de tema deproiect

Functii si proceduri diverse pentru calculul instalatiilor de climatizare

procedure Ziuadin,an(l, zl : nz) (1)

Calculul numarului din an al unei zile in fct de data (zi si luna)

zil,0..12 = [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]; (2)

i = 0; nz = 0; (3)

repeat (4)

nz = nz + zil,i; (5)

i = i+ 1; (6)

until (i ≥ l) (7)

nz = nz + zl; (8)

end (9)

procedure Unghiurisolare,1(long, φ, nz, LT , ∆TGMT : δ, α, azim); (10)

IVC - Niculescu, Duta, Stoenescu, Colda - EDP, pg 93

δ = −23.45 [deg] · Cos(0.986 [deg] · (nz + 10.5)); declinatie (11)

αcalc = arcsin (sin (δ) · sin (φ) + Cos(δ) · Cos(φ) · Cos(15 [deg] · (LT − 12))); elevatie/inaltime (3.106)(12)

α = max (αcalc, 0 [deg]); (13)

a = arcsin

(Cos(δ) · sin (15 [deg] · (LT − 12))

Cos(α)

); (3.110) (14)

azim = 180 [deg] + a; azimut (3.108) (15)

1

end (16)

procedure Radsol(rdrad,sol, ora : Idir, Idif ) (17)

Nu# exista radiatie solara noaptea: 18<ora<6

If(ora < 6)or (18 < ora) then (18)

Idir = 0; Idif = 0; (19)

else (20)

Idir = Lookup(‘Rad sol’ , rdrad,sol, max (2, ora− 4)); (21)

Idif = Lookup(‘Rad sol’ , 10, max (2, ora− 4)); (22)

endif (23)

end (24)

$Bookmark Date_intrare

Marimi de intrare

ziua = 23; luna = 7; (25)

$IfNot ParametricTable= ’Ora’

ora = 13; Ora locala / Local time (26)

Orient$ = ‘E’ ; (27)

$EndIf

∆TGMT = 2; diferenta de fus orar fata de meridianul 0 (28)

Cladire

Oras$ = ‘Galati’ ; (29)

grdasig = 90/100; grad asigurare (30)

φint = 50/100; umiditate relativa interior (31)

αint = 8[W/m2 ·C

]; αext = 17.5

[W/m2 ·C

]; (32)

Perete/terasa - structura se va modifica cf temei de proiect. Calculul se va face de 5 ori: ptr cei 4 pereti si terasa.Terasa NU# are fereastra!

Bper = 3 [m] ; Hper = 3 [m] ; (33)

Tipper$ = ‘P 6’ (34)

Caracteristi straturi (de la interior la exterior)

2

$If Tip_per$=’P_i’

Peretetip$ = ‘Problema initiala’ ; (35)

mat$1 = ‘Beton armat’ ; deltaper,1 = 6×10−2 [m] ; rho1 = 2500[kg/m3

]; lambdaper,1 = 1.74 [W/m ·C] ; s1 = 16.24

[W/m2 ·C

]; (36)

mat$2 = ‘BCA’ ; deltaper,2 = 7.5×10−2 [m] ; rho2 = 600[kg/m3

]; lambdaper,2 = .21 [W/m ·C] ; s2 = 2.73

[W/m2 ·C

]; (37)

mat$3 = ‘Beton armat’ ; deltaper,3 = 11×10−2 [m] ; rho3 = 2500[kg/m3

]; lambdaper,3 = 1.74 [W/m ·C] ; s3 = 16.24

[W/m2 ·C

]; (38)

mat$4 = ‘————-’ ; deltaper,4 = 0.0 [m] ; rho4 = 2500[kg/m3

]; lambdaper,4 = 1.74 [W/m ·C] ; s4 = 16.24

[W/m2 ·C

]; (39)

mat$5 = ‘————-’ ; deltaper,5 = 0.0 [m] ; rho5 = 20[kg/m3

]; lambdaper,5 = 0.044 [W/m ·C] ; cp,5 = 1460 [J/kg ·C] ; (40)

mat$6 = ‘————-’ ; deltaper,6 = 0.0 [m] ; rho6 = 1800[kg/m3

]; lambdaper,6 = 0.93 [W/m ·C] ; cp,6 = 840 [J/kg ·C] ; (41)

mat$7 = ‘Aer ext’ ; (42)

$EndIf

$If Tip_per$=’P_6’

Peretetip$ = ‘Perete Tip 6’ ; (43)

mat$1 = ‘Int tencuiala ipsos’ ; deltaper,1 = 0.02 [m] ; lambdaper,1 = 0.37 [W/m ·C] ; cp,1 = 840 [J/kg ·C] ; rho1 = 1000[kg/m3

]; (44)

mat$2 = ‘Caramida tip 1’ ; deltaper,2 = 0.29 [m] ; lambdaper,2 = 0.7 [W/m ·C] ; cp,2 = 870 [J/kg ·C] ; rho2 = 1550[kg/m3

]; (45)

mat$3 = ‘Polistiren’ ; deltaper,3 = 0.05 [m] ; lambdaper,3 = 0.044 [W/m ·C] ; cp,3 = 1460 [J/kg ·C] ; rho3 = 20[kg/m3

]; (46)

mat$4 = ‘Ext tencuiala ciment’ ; deltaper,4 = 0.02 [m] ; lambdaper,4 = 0.93 [W/m ·C] ; cp,4 = 840 [J/kg ·C] ; rho4 = 1800[kg/m3

]; (47)

mat$5 = ‘————-’ ; deltaper,5 = 0.0 [m] ; lambdaper,5 = 0.044 [W/m ·C] ; cp,5 = 1460 [J/kg ·C] ; rho5 = 20[kg/m3

]; (48)

mat$6 = ‘————-’ ; deltaper,6 = 0.0 [m] ; lambdaper,6 = 0.93 [W/m ·C] ; cp,6 = 840 [J/kg ·C] ; rho6 = 1800[kg/m3

]; (49)

mat$7 = ‘Aer ext’ ; (50)

ηper = 1/140; Coeficientul de amortizare a oscilatiilor de temperatura: etaper - calculat/adoptat ! (51)

εper = 15; Coeficientul de defazare a oscilatiilor de temperatura: epsilonper - calculat/adoptat ! (52)

3

$EndIf

$If Tip_per$=’P_11’

Peretetip$ = ‘Perete Tip 11’ ; (53)

mat$1 = ‘Caramida eficienta’ ; deltaper,1 = 0.25 [m] ; lambdaper,1 = 0.7 [W/m ·C] ; cp,1 = 870 [J/kg ·C] ; rho1 = 1550[kg/m3

]; (54)

mat$2 = ‘Polistiren tip 1’ ; deltaper,2 = 0.05 [m] ; lambdaper,2 = 0.044 [W/m ·C] ; cp,2 = 1460 [J/kg ·C] ; rho2 = 20[kg/m3

]; (55)

mat$3 = ‘Ext. tencuiala ciment’ ; deltaper,3 = 0.01 [m] ; lambdaper,3 = 0.93 [W/m ·C] ; cp,3 = 840 [J/kg ·C] ; rho3 = 1800[kg/m3

]; (56)

mat$4 = ‘Tabla de otel’ ; deltaper,4 = 0.001 [m] ; lambdaper,4 = 58 [W/m ·C] ; cp,4 = 480 [J/kg ·C] ; rho4 = 7850[kg/m3

]; (57)

mat$5 = ‘————-’ ; deltaper,5 = 0.0 [m] ; lambdaper,5 = 0.044 [W/m ·C] ; cp,5 = 1460 [J/kg ·C] ; rho5 = 20[kg/m3

]; (58)

mat$6 = ‘————-’ ; deltaper,6 = 0.0 [m] ; lambdaper,6 = 0.93 [W/m ·C] ; cp,6 = 840 [J/kg ·C] ; rho6 = 1800[kg/m3

]; (59)

mat$7 = ‘Aer ext’ ; (60)

ηper = 1/80; εper = 9; (61)

$EndIf

$If Tip_per$=’T_1’

Peretetip$ = ‘Terasa cu strat termoizolant pe beton de panta (Tip 1, 2, 3)’ ; (62)

mat$1 = ‘Pietris’ ; deltaper,1 = 0.04 [m] ; lambdaper,1 = 0.70 [W/m ·C] ; cp,1 = 920 [J/kg ·C] ; rho1 = 2000; (63)

mat$2 = ‘Hidroizolatie bituminoasa’ ; deltaper,2 = 0.01 [m] ; lambdaper,2 = 0.17 [W/m ·C] ; cp,2 = 840 [J/kg ·C] ; rho2 = 1050; (64)

mat$3 = ‘Sapa din mortar de ciment’ ; deltaper,3 = 0.025 [m] ; lambdaper,3 = 0.93 [W/m ·C] ; cp,3 = 1000 [J/kg ·C] ; rho3 = 1700; (65)

mat$4 = ‘Polistiren extrudat’ ; deltaper,4 = 0.16 [m] ; lambdaper,4 = 0.044 [W/m ·C] ; cp,4 = 1460 [J/kg ·C] ; rho4 = 20; (66)

mat$5 = ‘Beton de panta’ ; deltaper,5 = 0.10 [m] ; lambdaper,5 = 1.62 [W/m ·C] ; cp,5 = 840 [J/kg ·C] ; rho5 = 2400; (67)

mat$6 = ‘Placa beton armat’ ; deltaper,6 = 0.10 [m] ; lambdaper,6 = 1.74 [W/m ·C] ; cp,6 = 840 [J/kg ·C] ; rho6 = 2500; (68)

mat$7 = ‘Aer ext’ ; (69)

ηper = 1/160; εper = 11; (70)

4

$EndIf

$If Tip_per$=’T_4’

Peretetip$ = ‘Terasa cu strat termoizolant ı̂n trepte (Tip 4)’ ; (71)

mat$1 = ‘Pietris’ ; deltaper,1 = 0.04 [m] ; lambdaper,1 = 0.70 [W/m ·C] ; cp,1 = 920 [J/kg ·C] ; rho1 = 2000; (72)

mat$2 = ‘Hidroizolatie bituminoasa’ ; deltaper,2 = 0.01 [m] ; lambdaper,2 = 0.17 [W/m ·C] ; cp,2 = 840 [J/kg ·C] ; rho2 = 1050; (73)

mat$3 = ‘Sapa din mortar de ciment’ ; deltaper,3 = 0.035 [m] ; lambdaper,3 = 0.93 [W/m ·C] ; cp,3 = 1000 [J/kg ·C] ; rho3 = 1700; (74)

mat$4 = ‘BCA’ ; deltaper,4 = 0.20 [m] ; lambdaper,4 = 0.27 [W/m ·C] ; cp,4 = 877 [J/kg ·C] ; rho4 = 600; (75)

mat$5 = ‘Placa beton armat’ ; deltaper,5 = 0.10 [m] ; lambdaper,5 = 1.74 [W/m ·C] ; cp,5 = 840 [J/kg ·C] ; rho5 = 2500; (76)

mat$6 = ‘Tencuiala tavan’ ; deltaper,6 = 0.01 [m] ; lambdaper,6 = 0.93 [W/m ·C] ; cp,6 = 1000 [J/kg ·C] ; rho6 = 1700; (77)

mat$7 = ‘Aer ext’ ; (78)

ηper = 1/40; εper = 12; (79)

$EndIf

s [W/m2-C] - coeficient de asimilare termica / a caldurii, cf STAS 6472/3-75: s= 8.5e-03[1/s1/2]*sqrt(λ*ρ*cp)

Fereastra - datele se vor modifica cf temei de proiect:

Tipfer$ = ‘dubla’ ; (80)

Bfer = 1 [m] ; Hfer = 1 [m] ; nrfer = 1; (81)

s1 = 0.1 [m] ; latime pervaz exterior - vezi fig 9.1.2 (82)

s2 = 0.2 [m] ; latime streasina (83)

h1 = 0 [m] ; dist pe verticala dintre fereastra si streasina (84)

=====Calcule preliminare=====

Coeficienti/marimi citite din tabele/grafice:

rdloc = Lookuprow(Localit, ‘Localit$’ , Oras$); (85)

longit = Lookup(Localit, rdloc, ‘Longit’ ); latit = Lookup(Localit, rdloc, ‘Latit’ ); (86)

5

Az = Lookup(Localit, rdloc, ‘A z’ ); (87)

tem = Lookup(Localit, rdloc, ‘t em’ ); Anexa 2.2: temperatura medie zilnica, in fct de gradul de asig !!!(88)

xcl = Lookup(Localit, rdloc, ‘x cl’ ); (89)

Caracteristici de material:

a1 = 1; a2 = 1; factor de corectie ı̂n functie de altitudine (90)

Aper = 0.91; A - coeficientul de absorbtie a radiatiei solare, conform tabelului 9.1.1 in fct de mat ext al peretelui(91)

Rfer = 0.4[m2 ·C/W

]; Rfer - rezistenta termica a ferestrei conform STAS 1907/1 [m2-C/W] (92)

Afer = 0.12; geamuri duble (93)

c1 = 0.5; c1 - coeficient de calitate (94)

c2 = 0.5; coeficienti Tabelul 9.1.2 (95)

c3 = 0.9; c3 - raportul dintre suprafata sticlei si suprafata totala a ferestrei (96)

m = 0.5; m - coeficientul de acumulare (97)

$Bookmark Calc

=====Calcule=====

$IfNot ParametricTable= ’nr_zi’

call Ziuadin,an(luna, ziua : nrzi); (98)

$EndIf

call Unghiurisolare,1(longit, latit, nrzi, ora, ∆TGMT : declin, elev, azim); ar tb sa fie diferit ptr fereastra si perete datorita defazarii(99)

tev = tem + Az; 2.4.2.2 Climatizare ı̂n scopuri de confort (100)

tint,v = 10 [C] + 0.5 · tev; tint,v,x = tev − 6 [C] ; sau (101)

rdA,z = Lookuprow(‘cA z v’ , ‘A z’ , Az); rand din tab cAz,v coresp valorii lui cAz (102)

rdrad,sol = Lookuprow(‘Rad sol’ , ‘Orientare’ , Orient$); rand din tab Radsol corespunzator orientarii(103)

azimper = Lookup(‘Rad sol’ , rdrad,sol, ‘Azim per’ ); (104)

azimrel = min (89.99 [deg] , Abs (azim− azimper)); Azimutul relativ NU poate fi mai mare de 90 grd !!!(105)

$Bookmark Fer

6

=====Fereastra=====

orafer = max (6, ora); Soarele NU apare mai devreme de ora 6 (106)

colfer = 1 +orafer + 1

2; col/poz din tab 2.4.5 cAz-vara ! coresp Az si orei (107)

cAz,fer = Lookup(‘cA z v’ , rdA,z, colfer); (108)

te,fer = tem + cAz,fer; Temperatura aerului exterior (2.4.2) (109)

call Radsol(rdrad,sol, orafer : Idir,fer, Idif,fer); (110)

Ifer = a1 · a2 · Idir,fer + Idif,fer; (2.4.3) (111)

c1∗ = tan (azimrel); Fig 9.1.2 (112)

bu,fer = min (Bfer, c1∗ · s1); (9.1.11) Latimea umbrei NU poate fi mai mare decat latimea ferestrei !(113)

c2∗ =tan (elev)

Cos(azimrel); (114)

hu,fer = min (Hfer, c2∗ · s2 − h1); (9.1.12) Inaltimea umbrei NU poate fi mai mare decat inaltimea ferestrei !(115)

Si,fer = (Hfer − hu,fer) · (Bfer − bu,fer) ; (9.1.10) (116)

Sfer = Bfer ·Hfer; (117)

Idir,max = Lookup(‘Rad sol’ , rdrad,sol, ‘I max’ ); Idif,max = Lookup(‘Rad sol’ , 10, ‘I max’ ); (118)

ΦI,fer = c1 · c2 · c3 ·m · (Si,fer · Idir,max · a1 · a2 + Sfer · Idif,max) ; (9.1.8) (119)

kfer = 1/Rfer; (120)

$If Tip_fer$= ’dubla’

ts,fer∗ = te,fer +

(2 · Afer · (Afer − 1)

αext

)· Ifer; fer dubla (9.1.13) (121)

$Else

ts,fer∗ = te + (A/αext) · I; fer simpla (9.1.13) (122)

$EndIf

Φt,fer = Sfer · kfer · (ts,fer∗ − tint,v) ; (9.1.9) (123)

Φfer = ΦI,fer + Φt,fer; (124)

$Bookmark Per

7

=====Perete=====

Toti parametrii exteriori tb considerati ptr ora=(ora curenta - εper) !!!

oraper = Mod(ora− εper + 24, 24); (125)

colper = 1 +oraper + 1

2; col/poz din tab 2.4.5 cAz-vara ! coresp Az si orei (126)

cAz,per = Lookup(‘cA z v’ , rdA,z, colper); (127)

te,per = tem + cAz,per; Temperatura aerului exterior (2.4.2) (128)

call Radsol(rdrad,sol, oraper : Idir,per, Idif,per); (129)

Iper = a1 · a2 · Idir,per + Idif,per; (2.4.3) (130)

ts,per = te,per + (Aper/αext) · Iper; ts - temperatura echivalenta de calcul a aerului exterior (9.1.5) (131)

Idir,m = Lookup(‘Rad sol’ , rdrad,sol, ‘I med’ ); (132)

tsm = tem + (Aper/αext) · Idir,m; tsm - temperatura echivalenta medie a aerului exterior (9.1.6) (133)

Rper = 1/αint+δper,1λper,1

+δper,2λper,2

+δper,3λper,3

+δper,4λper,4

+δper,5λper,5

+δper,6λper,6

+1/αext; Rezistenta termica a peretelui(134)

kper = 1/Rper; (135)

Sper = Bper ·Hper − nrfer · Sfer; Suprafata peretelui (136)

qper = kper · (tsm − tint,v) + αint · ηper · (ts,per − tsm) ; (9.1.4) (137)

Φper = Sper · qper; (9.1.3) (138)

Sarcina de racire/vara

Φiv = 0; Incaperi vecine (139)

Φap = Φper + nrfer · Φfer + Φiv; Aporturi de caldura prin elem de constructie (140)

Φdeg = 0; Degajari - se calculeaza ! (141)

Φv = Φdeg + Φap; (142)

$ExportPlot ’E:\Users\Crios\Surse\EES\V&C\PHI.jpg’ ’PHI_ap’ /R=2

Data$ = Date$; (143)

$TabStops 1 2 4 6 8 cm

SolutionVariables in Main program

8

αext = 17.5 [W/m2-C] αint = 8 [W/m2-C] azim = 210.9 [deg] azimper = 90 [deg]

azimrel = 89.99 [deg] a1 = 1 a2 = 1 Afer = 0.12

Aper = 0.91 Az = 6 [C] Bfer = 1 [m] Bper = 3 [m]

bu,fer = 1 [m] cAz,fer = 5.5 [C] cAz,per = −1.95 [C] colfer = 8

colper = 12.5 c1 = 0.5 c∗1 = 5731 c2 = 0.5

c∗2 = 10647 c3 = 0.9 Data$ = ‘2018-10-16’ declin = 20 [deg]

∆TGMT = 2 elev = 61.71 [deg] εper = 15 ηper = 0.007143

grdasig = 0.9 h1 = 0 [m] Hfer = 1 [m] Hper = 3 [m]

hu,fer = 1 [m] Idif,fer = 146 [W/m2] Idif,max = 147 [W/m2] Idif,per = 0 [W/m2]

Idir,fer = 0 [W/m2] Idir,m = 105 [W/m2] Idir,max = 575 [W/m2] Idir,per = 0 [W/m2]

Ifer = 146 [W/m2] Iper = 0 [W/m2] kfer = 2.5 [W/m2-C] kper = 0.553 [W/m2-C]

latit = 45.44 [deg] longit = 28.04 [deg] luna = 7 m = 0.5

nrfer = 1 nrzi = 204 ora = 13 Oras$ = ‘Galati’orafer = 13 oraper = 22 Orient$ = ‘E’ Peretetip$ = ‘Perete Tip 6’Φap = 45.96 [W] Φdeg = 0 [W] Φfer = 25.63 [W] φint = 0.5

Φiv = 0 [W] ΦI,fer = 16.54 [W] Φper = 20.32 [W] Φt,fer = 9.09 [W]

Φv = 45.96 [W] qper = 2.541 [W/m2] rdA,z = 2 rdloc = 1

rdrad,sol = 3 Rfer = 0.4 [m2-C/W] Rper = 1.808 [m2-C/W] s1 = 0.1 [m]

s2 = 0.2 [m] Sfer = 1 [m2] Si,fer = 0 [m2] Sper = 8 [m2]

Tipfer$ = ‘dubla’ Tipper$ = ‘P 6’ tem = 25.8 [C] tev = 31.8 [C]

te,fer = 31.3 [C] te,per = 23.85 [C] tint,v = 25.9 [C] tint,v,x = 25.8 [C]

tsm = 31.26 [C] t∗s,fer = 29.54 [C] ts,per = 23.85 [C] xcl = 11.35

ziua = 23

Variables in Procedure Ziuadinan

l = 7 zl = 23 nz = 204 zil,0 = 0zil,1 = 31 zil,2 = 28 zil,3 = 31 zil,4 = 30zil,5 = 31 zil,6 = 30 zil,7 = 31 zil,8 = 31zil,9 = 30 zil,10 = 31 zil,11 = 30 zil,12 = 31i = 7

Variables in Procedure Unghiurisolare1long = 28.04 [deg] φ = 45.44 [deg] nz = 204 LT = 13∆TGMT = 2 δ = 20 [deg] α = 61.71 [deg] azim = 210.9 [deg]αcalc = 61.71 [deg] a = 30.87 [deg]

Variables in Procedure Radsol

rdrad,sol = 3 ora = 22 Idir = 0 [W/m2] Idif = 0 [W/m2]

Arrays Table: Main

Row mat$i δper,i λper,i ρi cp,i

9

[m] [W/m-C] [kg/m3] [J/kg-C]1 Int tencuiala ipsos 0.02 0.37 1000 8402 Caramida tip 1 0.29 0.7 1550 8703 Polistiren 0.05 0.044 20 14604 Ext tencuiala ciment 0.02 0.93 1800 8405 ————- 0 0.044 20 14606 ————- 0 0.93 1800 8407 Aer ext

Lookup Table: Localit

Row Localit$ Latit Longit Az tem xcl te,i[deg] [deg] [C] [C] [C]

1 Galati 45.44 28.04 6 25.8 11.35 02 Constanta 44.18 28.63 4 24.8 12.65 03 Brasov 45.66 25.61 7 20.7 10.3 04 Iasi 47.17 27.57 6 24.1 11.2 0

Lookup Table: Radsol

Row Orientare 6 7 8 9 10 11 12[W/m2] [W/m2] [W/m2] [W/m2] [W/m2] [W/m2] [W/m2]

1 N 53 3 0 0 0 0 02 NE 333 402 301 130 4 0 03 E 383 568 575 498 338 144 04 SE 188 370 468 514 485 393 2415 s 0 0 41 159 316 354 3946 SV 0 0 0 0 0 58 2417 V 0 0 0 0 0 0 08 NV 0 0 0 0 0 0 09 O 89 41 381 532 647 711 734

10 I dif 53 80 103 123 136 146 147

Row 13 14 15 16 17 18 Imed Imax

[W/m2] [W/m2] [W/m2] [W/m2] [W/m2] [W/m2] [W/m2] [W/m2]1 0 0 0 0 3 53 5 532 0 0 0 0 0 0 49 4023 0 0 0 0 0 0 105 5754 58 0 0 0 0 0 113 5145 354 316 159 41 0 0 89 3946 393 485 514 468 370 188 113 5147 144 338 498 575 568 383 105 5758 0 4 130 301 402 333 49 4029 711 647 532 381 241 89 247 734

10 146 136 123 103 80 53 60 147

10

Row Azimper

[deg]1 02 453 904 1355 1806 2257 2708 3159 0

10

Lookup Table: cAzv

Row Az 1 3 5 7 9 11 13[C] [C] [C] [C] [C] [C] [C] [C]

1 4 -2.8 -3.6 -4 -3 0.4 2.7 3.62 6 -4.2 -5.4 -6 -4.5 0.6 4.1 5.53 7 -4.9 -6.3 -7 -5.2 0.7 4.8 6.4

Row 15 17 19 21 23[C] [C] [C] [C] [C]

1 4 3.5 1.7 -0.7 -1.92 6 5.2 2.6 -1 -2.93 7 6.1 3 -1.2 -3.4

Lookup Table: cAzi

Row Az 1 3 5 7 9 11 13[C] [C] [C] [C] [C] [C] [C] [C]

1 3 -1.8 -2.4 -2.9 -3 -2.3 0.5 2.42 4 -2.4 -3.2 -3.8 -4 -3 0.7 3.23 5 -3 -4 -4.8 -5 -3.8 0.9 44 6 -3.5 -4.7 -5.8 -6 -4.5 1 4.8

Row 15 17 19 21 23[C] [C] [C] [C] [C]

1 3 2.8 2 0.7 -0.72 4 3.7 2.6 1 -0.93 5 4.7 3.3 1.2 -1.14 6 5.6 3.9 1.4 -1.3

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Plot Window 5: PHIap

12