Solar Angle Calculator

7-18aLocal Solar Time INPUT CELL Intermediate Calculation Output Cell

DST = LST-1 Longitude Latitude MeridianDate (mm/dd/yyyy) LST/LST-1 (hh:mm:ss/dec hr) (+N/-S)(deg/rad) (+W/-E) (deg/rad)

04/21/2011 12:00:00 85.73 38.18 75111 12 1.4963 0.6664 1.3090

n (Day of Year) N (deg/rad) EOT (min) Apparent Solar Time (hh:mm:ss/dec hr)111 108.4932 1.2175 11:18:17 AM

1.8936 11.3050

Local Solar Angle

h, Hour Angle (deg/rad) δ, Declination (deg/rad) EST - 75 deg-10.4256 11.8514 CST - 90 deg

-0.1820 0.2068 MST - 105 degPST - 120 deg

β, Solar Altitude (deg/rad)62.0754 157.7795 202.2205

1.0834 2.7538 3.5294

ψ, Surface Azimuth (deg/rad) γ, Surface Solar Azimuth (deg/rad) α, Tilt Angle (deg/rad)180 22.2205 45

3.1416 0.3878 0.7854

θ, Angle of Incidence (deg/rad)21.3574

0.3728

(+W/-E) (deg/rad)

φ, Solar Azimuth (deg/rad) AM φ, Solar Azimuth (deg/rad) PM

Solar Irradiation INPUT CELL Intermediate Calculation Output Cell

0.96 0.2

0.8536 0.1464 1.2285

*Interpolated from Table below

Day of the year B C111 358.000 0.164 0.120

285.4592 265.8559

29.2386 42.0816

7.3874 1.0033 8.3907

303.4851

CN, Clearness Number ρg, Ground Reflectance

Fws, Sky View Factor Fwg, Ground View Factor GdV/GdH, Vert./Horiz Factor

A (Btu/hr-ft2)

GND, Normal Direct (Btu/hr-ft2) GDθ, Direct (Btu/hr-ft2)

Gdθ, Diffuse (Btu/hr-ft2) Gdθ, Diffuse Vertical (Btu/hr-ft2)

GR,ND, Reflected Direct (Btu/hr-ft2) GR,d, Reflected Diffuse (Btu/hr-ft2) GR, Reflected Total (Btu/hr-ft2)

Gt, Total Irradiance (Btu/hr-ft2)

Fenestration Shading INPUT CELL Intermediate Calculation Output Cell

Depth of Opening (ft)2

γ, Surface Solar Azimuth (deg/rad) β, Solar Altitude (deg/rad) Ω, Threshold Altitude (deg/rad)22.2205 62.0754 63.8646

0.3878 1.0834 1.1146

X, Vertical Shade (ft) Y, Horizontal Shade (ft)0.8170 4.0761

Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C111 358.000 0.164 0.120

A (Btu/hr-ft2)

A (Btu/hr-ft2)

7-18bLocal Solar Time INPUT CELL Intermediate Calculation Output Cell


04/21/2011 15:00:00 85.73 38.18 75111 15 1.4963 0.6664 1.3090

n (Day of Year) N (deg/rad) EOT (min) Apparent Solar Time (hh:mm:ss/dec hr)111 108.4932 1.2175 2:18:17 PM

1.8936 14.3050

Local Solar Angle

h, Hour Angle (deg/rad) δ, Declination (deg/rad) EST - 75 deg34.5744 11.8514 CST - 90 deg

0.6034 0.2068 MST - 105 degPST - 120 deg


0.8639 2.1158 4.1674


3.1416 1.0258 0.7854


0.6829

(+W/-E) (deg/rad)



1 0.2

0.8536 0.1464 1.0774


Day of the year B C111 358.000 0.164 0.120

288.5465 223.8394

29.5548 37.3042

6.4264 1.0142 7.4405

260.8347



A (Btu/hr-ft2)








1.0258 0.8639 1.1540


Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C111 358.000 0.164 0.120

A (Btu/hr-ft2)

A (Btu/hr-ft2)

7-18cLocal Solar Time INPUT CELL Intermediate Calculation Output Cell


04/21/2011 18:00:00 85.73 38.18 75111 18 1.4963 0.6664 1.3090


1.8936 17.3050

Local Solar Angle


1.3888 0.2068 MST - 105 degPST - 120 deg


0.2694 1.5169 4.7663


3.1416 1.6247 0.7854


1.4188

(+W/-E) (deg/rad)



1 0.2

0.8536 0.1464 0.6234


Day of the year B C111 358.000 0.164 0.120

193.3247 29.2810

19.8016 14.4615

1.5071 0.6795 2.1866

51.2692



A (Btu/hr-ft2)







γ, Surface Solar Azimuth (deg/rad) β, Solar Altitude (deg/rad) Ω, Threshold Altitude (deg/rad)93.0904 15.4361 -78.9524

1.6247 0.2694 -1.3780

X, Vertical Shade (ft) Y, Horizontal Shade (ft)-37.0439 -10.2436

Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C111 358.000 0.164 0.120

A (Btu/hr-ft2)

A (Btu/hr-ft2)

7-18c_2

Local Solar Time6:00 AM -2.14 9.78 0.68 8.327:00 AM 49.46 22.08 2.80 74.348:00 AM 120.36 26.57 4.78 151.719:00 AM 186.36 28.69 6.47 221.52

10:00 AM 238.48 29.80 7.76 276.0411:00 AM 271.61 30.35 8.57 310.5312:00 PM 282.89 30.52 8.84 322.25

1:00 PM 271.38 30.35 8.56 310.292:00 PM 238.05 29.79 7.75 275.593:00 PM 185.76 28.68 6.45 220.894:00 PM 119.66 26.54 4.76 150.965:00 PM 48.79 22.02 2.78 73.596:00 PM -2.33 9.57 0.66 7.90

GDθ, Direct (Btu/hr-ft2) Gdθ, Diffuse (Btu/hr-ft2) GR, Reflected (Btu/hr-ft2) Gt, Total (Btu/hr-ft2)

4:48 AM 7:12 AM 9:36 AM 12:00 PM 2:24 PM 4:48 PM 7:12 PM-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

R² = 0.999994916636765

TotalPolynomial (Total)DirectPolynomial (Direct)DiffusePolynomial (Diffuse)ReflectedPolynomial (Reflected)

Time (HH:MM)

Irrad

ianc

e, (B

tu/h

r-ft2

)

Total Radiation

2570.76Energy per Area per Day (Btu/ft2)

4:48 AM 7:12 AM 9:36 AM 12:00 PM 2:24 PM 4:48 PM 7:12 PM-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

R² = 0.999994916636765


Time (HH:MM)

Irrad

ianc

e, (B

tu/h

r-ft2

)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = 0.00106454 x⁶ − 0.0382709 x⁵ + 0.61652 x⁴ − 5.617511 x³ + 18.26117 x² + 53.09897 x + 8.270656R² = 0.999994916636765


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

Direct Radiation


0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = 0.00156409 x⁶ − 0.0562304 x⁵ + 0.875044 x⁴ − 7.515271 x³ + 26.20014 x² + 32.50327 x − 2.206728R² = 0.999988788984361


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

Diffuse Radiation


0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = 0.00156409 x⁶ − 0.0562304 x⁵ + 0.875044 x⁴ − 7.515271 x³ + 26.20014 x² + 32.50327 x − 2.206728R² = 0.999988788984361


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = − 0.000498431 x⁶ + 0.0179202 x⁵ − 0.259383 x⁴ + 1.927609 x³ − 7.950347 x² + 18.45711 x + 9.797555R² = 0.999836214120607


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

Reflected Radiation


0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = − 0.000498431 x⁶ + 0.0179202 x⁵ − 0.259383 x⁴ + 1.927609 x³ − 7.950347 x² + 18.45711 x + 9.797555R² = 0.999836214120607


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = − 0.00000111799 x⁶ + 0.000039305 x⁵ + 0.000859216 x⁴ − 0.0298493 x³ + 0.0113747 x² + 2.138585 x + 0.679829R² = 0.999999794015328


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00-5.00

45.00

95.00

145.00

195.00

245.00

295.00

345.00

f(x) = − 0.00000111799 x⁶ + 0.000039305 x⁵ + 0.000859216 x⁴ − 0.0298493 x³ + 0.0113747 x² + 2.138585 x + 0.679829R² = 0.999999794015328


Time (hours)

Irrad

ianc

e, (B

tu/h

r-ft2

)

Time (Hours)0.00 4.161.00 41.332.00 113.033.00 186.624.00 248.785.00 293.286.00 316.397.00 316.278.00 292.949.00 248.24

10.00 185.9311.00 112.2812.00 40.75

3.95

2403.93

Area (Btu/ft2)

Total (Btu/ft2)

7-20aLocal Solar Time INPUT CELL Intermediate Calculation Output Cell


04/21/2011 9:00:00 93.747373 32.5136 90111 9.0000 1.6362 0.5675 1.5708

n (Day of Year) N (deg/rad) EOT (min) Apparent Solar Time (hh:mm:ss/dec hr)111 108.4932 1.2175 8:46:13 AM

1.8936 8.7705

Local Solar Angle

h, Hour Angle (deg/rad) δ, Declination (deg/rad) EST - 75 deg-48.4430 11.8514 CST - 90 deg

-0.8455 0.2068 MST - 105 degPST - 120 deg


0.7180 1.8064 4.4768


3.1416 1.3352 1.5708


1.3941

(+W/-E) (deg/rad)



0.91 0.2

0.5000 0.5000 0.6365


Day of the year B C111 358.000 0.164 0.120

253.8967 44.6282

15.2338 19.3921

16.7027 3.0468 19.7495

83.7698



A (Btu/hr-ft2)








1.3352 0.7180 1.3097


Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C111 358.000 0.164 0.120

A (Btu/hr-ft2)

A (Btu/hr-ft2)

7-20bLocal Solar Time INPUT CELL Intermediate Calculation Output Cell


07/21/2011 12:00:00 93.747373 32.5136 90202 12.0000 1.6362 0.5675 1.5708

n (Day of Year) N (deg/rad) EOT (min) Apparent Solar Time (hh:mm:ss/dec hr)202 198.2466 -6.3486 11:38:39 AM

3.4601 11.6444

Local Solar Angle

h, Hour Angle (deg/rad) δ, Declination (deg/rad) EST - 75 deg-5.3345 20.4825 CST - 90 deg-0.0931 0.3575 MST - 105 deg

PST - 120 degβ, Solar Altitude (deg/rad)

77.0621 157.1084 202.89161.3450 2.7421 3.5411


3.1416 0.3995 1.5708


1.3630

(+W/-E) (deg/rad)



0.91 0.2

0.5000 0.5000 0.6535


Day of the year B C202 346.000 0.186 0.138

260.1564 53.6603

17.9508 23.4600

25.3552 3.5902 28.9454

106.0656



A (Btu/hr-ft2)








0.3995 1.3450 1.3622


Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C202 346.000 0.186 0.138

A (Btu/hr-ft2)

A (Btu/hr-ft2)

7-20cLocal Solar Time INPUT CELL Intermediate Calculation Output Cell


09/21/2011 17:00:00 93.747373 32.5136 90264 17.0000 1.6362 0.5675 1.5708


4.5273 16.8652

Local Solar Angle


1.2737 0.0126 MST - 105 degPST - 120 deg


0.2564 1.7231 4.5601


3.1416 1.4185 1.5708


1.4235

(+W/-E) (deg/rad)



0.91 0.2

0.5000 0.5000 0.6209


Day of the year B C264 360.000 0.165 0.121

170.9130 25.0781

10.3402 12.8397

4.3343 2.0680 6.4023

44.3201



A (Btu/hr-ft2)








1.4185 0.2564 1.0463


Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C264 360.000 0.165 0.121

A (Btu/hr-ft2)

A (Btu/hr-ft2)

7-27/7-28Local Solar Time INPUT CELL Intermediate Calculation Output Cell


07/21/2011 15:00:00 116.21269 43.6053 105202 15.0000 2.0283 0.7611 1.8326

n (Day of Year) N (deg/rad) EOT (min) Apparent Solar Time (hh:mm:ss/dec hr)202 198.2466 -6.3486 2:08:48 PM

3.4601 14.1467

Local Solar Angle


0.5620 0.3575 MST - 105 degPST - 120 deg


0.9533 2.1021 4.1811


3.9270 0.2541 1.5708


0.9759

(+W/-E) (deg/rad)



1 0.2

0.5000 0.5000 0.8932


Day of the year B C202 346.000 0.186 0.138

275.4238 154.3464

19.0042 33.9487

22.4562 3.8008 26.2571

214.5522



A (Btu/hr-ft2)








0.2541 0.9533 0.9686


Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C202 346.000 0.186 0.138

A (Btu/hr-ft2)

A (Btu/hr-ft2)

Working SheetLocal Solar Time INPUT CELL Intermediate Calculation Output Cell


07/21/2011 15:00:00 84.391141 33.7441 75202 15 1.4729 0.5889 1.3090

n (Day of Year) N (deg/rad) EOT (min) Apparent Solar Time (hh:mm:ss/dec hr)202 198.2466 -6.3486 2:16:05 PM

3.4601 14.2681

Local Solar Angle


0.5938 0.3575 MST - 105 degPST - 120 deg


0.9973 1.8324 4.4508


3.1416 1.3092 1.5708


1.4300

(+W/-E) (deg/rad)



1 0.2

0.5000 0.5000 0.6175


Day of the year B C

202 346.000 0.186 0.138

cos(θ)

277.2748 38.9083 0.1403

sin(β)19.1320 23.6274 0.839995392212908

23.2910 3.8264 27.1173

89.6530



A (Btu/hr-ft2)






Depth of Opening (ft)

2

γ, Surface Solar Azimuth (deg/rad) β, Solar Altitude (deg/rad) Ω, Threshold Altitude (deg/rad)

75.0120 57.1396 80.5161

1.3092 0.9973 1.4053

X, Vertical Shade (ft) Y, Horizontal Shade (ft)

7.4703 11.9722

Day of the year B C21 381 0.141 0.10352 376 0.142 0.10480 369 0.149 0.109

111 358 0.164 0.120141 351 0.177 0.130172 346 0.185 0.137202 346 0.186 0.138233 351 0.182 0.134264 360 0.165 0.121294 370 0.152 0.111325 377 0.144 0.106355 382 0.141 0.103366 382 0.141 0.103

Day of the year B C

A (Btu/hr-ft2)

A (Btu/hr-ft2)

202 346.000 0.186 0.138

NN = (n-1)*(360/365)N = (202 - 1)*(360/365)

EOTEOT = 229.2*(0.000075 + 0.001868*cos(N) - 0.032077*sin(N) - 0.014615*cos(2N) - 0.040849*sin(2N)EOT = 229.2*(0.000075 + 0.001868*cos(198.247) - 0.032077*sin(198.247) - 0.014615*cos(396.493) - 0.040849*sin(396.493)

AST

AST = 15.000 - (84.391 - 75.000)/15 + -6.349/60

h, Hour Angleh = 15(AST - 12)h = 15(14.268 - 12)

δ, Declination

δ = arcsin[sin(-23.44)*cos(((360/365.24)*(202 + 10))+((360/π)*0.0167*sin((360/365.24)*(202 - 2))))]

β, Solar Altitudeβ = arcsin[cos(l)*cos(h)*cos(δ) + sin(l)*sin(δ)]β = arcsin[cos(33.744)*cos(34.022)*cos(20.483) + sin(33.744)*sin(20.483)]

φ = arccos[(sin(δ)*cos(l)-cos(δ)*sin(l)*cos(h))/cos(β)]φ = arccos[(sin(20.483)*cos(33.744)-cos(20.483)*sin(33.744)*cos(34.022))/cos(57.140)]

φ = arccos[-((sin(20.483)*cos(33.744)-cos(20.483)*sin(33.744)*cos(34.022))/cos(57.140))] + 180

AST = Local Standard Time - (LL - LSM)/15 + EOT/60

δ = arcsin[sin(-23.44)*cos(((360/365.24)*(n + 10))+((360/π)*0.0167*sin((360/365.24)*(n - 2))))]

φ, Solar Azimuth AM

φ, Solar Azimuth PMφ = arccos[-((sin(δ)*cos(l)-cos(δ)*sin(l)*cos(h))/cos(β))] + 180

γ = |104.988 - 180.000|

γ = |255.012 - 180.000|

θ, Angle of Incidenceθ = arccos[cos(β)*cos(γ)*sin(α) + sin(β)*cos(α)]θ = arccos[cos(57.140)*cos(75.012)*sin(90.000) + sin(57.140)*cos(90.000)]

Fws = (1 + cos(90.000))/2

Fwg = (1 - cos(90.000))/2

if cos(θ) > -0.2

GdV/GdH = 0.55 + 0.437*cos(81.933) + 0.313*(cos(81.933))^2

if cos(θ) < -0.2

γ, Surface Solar Azimuth AMγ = |φAM - ψ|

γ, Surface Solar Azimuth PMγ = |φPM - ψ|

Fws, Sky View Factor

Fws = (1 + cos(α))/2

Fwg, Ground View FactorFwg = (1 - cos(α))/2

GdV/GdH, Vert./Horiz Factor

GdV/GdH = 0.55 + 0.437*cos(θ) + 0.313*(cos(θ))^2

GdV/GdH = 0.45

GND, Normal Direct

GND = (346.000/exp(.186/sin(57.140))*1.000

if cos(θ) > 0

GDθ = 277.275*cos(81.933)if cos(θ) < 0

Gdθ = (.138)*(277.275)*(.500)

Gdθ = (.617)*(.138)*(277.275)

GR,ND = (277.275)*(sin(57.140))*(.200)*(.500)

GR,d = (277.275)*(.138)*(.200)*(.500)

GND = (A/exp(B/sin(β))*CN

GDθ, Direct

GDθ = GND*cos(θ)

GDθ = 0

Gdθ,NV, Non-Vertical

Gdθ = C*GND*Fws

Gdθ,V, Vertical

Gdθ = (GdV/GdH)*C*GND

GR,ND, Reflected Direct

GR,ND = GND*(sin(β))*ρg*Fwg

GR,d, Reflected DiffuseGR,d = GND*C*ρg*Fwg

GR, Reflected TotalGR = GR,ND + GR,d

GR = 23.291 + 3.826

Non-Vertical Surfaces

Gt = 38.908 + 19.132 + 27.117Vertical Surfaces

Gt = 38.908 + 23.627 + 27.117

Ω, Threshold AltitudeΩ = arctan[tan(β)/cos(γ)]Ω = arctan[tan(57.140)/cos(75.012)]

X, Vertical Shadex = (depth of overhang)*tan(γ)x = (2.000)*tan(75.012)

Y, Horizontal Shadey = (depth of overhang)*tan(Ω)y = (2.000)*tan(80.516)

Gt, Total Irradiance

Gt = GDθ + Gdθ,NV + GR

Gt = GDθ + Gdθ,V + GR

EOT = 229.2*(0.000075 + 0.001868*cos(N) - 0.032077*sin(N) - 0.014615*cos(2N) - 0.040849*sin(2N)EOT = 229.2*(0.000075 + 0.001868*cos(198.247) - 0.032077*sin(198.247) - 0.014615*cos(396.493) - 0.040849*sin(396.493)

δ = arcsin[sin(-23.44)*cos(((360/365.24)*(202 + 10))+((360/π)*0.0167*sin((360/365.24)*(202 - 2))))]π)*0.0167*sin((360/365.24)*(n - 2))))]

Solar Angle Calculator

Documents

Transcript of Solar Angle Calculator