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Environmental Control

Systems I- Temperature and

Humidity, Arch 353

Lecture # 9

Dr. Hussain Alzoubi

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-Solar radiation and buildings

-The solar radiation is not more intense in

summer than in winter.

the earth is closest to the sun in January, and

for the northern hemisphere the solar

insolation I0 is about 6 % greater in January

than it is in July,

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Sun angles calculations

To calculate solar altitude and azimuth at a certain

local time, you should know the following

information:

1- Latitude of the city

2-Longitude of the city(use negative sign for cities located west of Greenwich)

3-Solar time

4-Equation of time (from graphs)

5-Declination

5-Hour angle(difference between 12 pm and the time

at which you need to find the altitude)

6-Lloc: longitude of the place

7-Lst:standard meridian for time zone (Amman: +30)

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The solar altitude () and azimuth()could be found

by applying the following equations:

Where

: solar altitude (Beta)

L : latitude, degrees

: declination (delta)

H: hour angle

: solar azimuth (phi)

: altitude

: azimuth

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Steps to calculate solar altitude:

1-Make sure the latitude, longitude, Lst of the site are available

2-Find the equation of time for the given date(from figure 4-16 below)

3-Calculate the local solar time as follows:

Solar time = Standard Time + 4(Lloc-Lst)+ ET

(east of Greenwich Lloc is positive +, and west is Lloc negative -)

4-Find the hour angle as follows:

H= 60 *(solar time – 12 pm)/4

5-Find the declination value (from figure 4-15 below)

6-If you have daylight saving, then

Standard time = Daylight saving time – 1

7-Apply the following equation:

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Example1:

Oklahoma city is located at 97.5 W in the central

standard time zone (meridian at 90 W).

Find the local solar time Lsot at 3pm (local time) on August 15th.

(daylight saving is applied).

Solution:

Local standard time Lt = daylight saving time-1

Lt = 3 pm – 1 = 2 pm

From figure 4-16, ET = -5

Local solar time Lsot = local Time + 4(Lloc-Lst)+ ET= 2pm + 4(-97.5 – (-90))+ (-5)

= 2 pm + (-35 minute)

= 1:25 pm

Example2:

Amman city is located at 36 E in (meridian at 30 E).

Find the local solar time Lsot at 12:38 pm (local time) on June 21st .

(daylight saving is applied).

Solution:

Local standard time Lt = daylight saving time-1

Lt = 12:38 pm – 1 = 11:38 am

From figure 4-16, ET = -1.7

Local solar time Lsot = local Time + 4(Lloc-Lst)+ ET= 11:38 am + 4(36 – 30) + (-1.7)

= 11:38 am + (22 minute)

Local solar time= 12 pm

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Example 3

Find the solar altitude and azimuth at 12:38 pm (

Local time) in Amman city on June 21st. ( lat = 32

Long= 36). (daylight saving is applied).

Solution:

Local standard time Lt = daylight saving time-1

Lt = 12:38 pm – 1 = 11:38 am

From figure 4-16, ET = -1.7

Local solar time Lsot = local Time + 4(Lloc-Lst)+ ET= 11:38 am + 4(36 – 30) + (-1.7)

= 11:38 am + (22 minute)

Local solar time = 12 pm

-Hour angle , H = 60*(12-12)/4 = 0.00

- from figure 4-15, declination = 23.45

-apply the following equation:

sin = cos 32 *cos23.45 * cos 0 + sin 32 * sin23.45

sin = 0.778 + 0.2108

sin = 0.98888

= sin-1 0.98888 = 81.45

Continue to find the solar azimuth

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sin = cos 23.45 * sin 0.00/cos 81.45

sin = 0.00

The azimuth at 12 pm ( solar time) is

zero

= 0.00

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Example 4

Find the solar altitude and azimuth at 11:34 am (

Local time) in Amman city on Dec 21st. ( lat = 32

Long= 36).

Solution:

From figure 4-16, ET = +2

Local solar time Lsot = local Time + 4(Lloc-Lst)+ ET= 11:34 am + 4(36 – 30) + 2

= 11:34 am + (26 minute)

Local solar time = 12 pm

-Hour angle , H = 60*(12-12)/4 = 0.00

- from figure 4-15, declination = -23.45

-apply the following equation:

sin = cos 32 *cos-23.45 * cos 0 + sin 32 * sin-23.45

sin = 0.778 + (- 0.2108)

sin = 0.5671

= sin-1 0.5671 = 34.55

Continue to find the solar azimuth

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sin = cos -23.45 * sin 0.00/cos 34.55

sin = 0.00

The azimuth at 12 pm ( solar time) is

zero

= 0.00

Special cases for maximum minimum altitudes:

-On June 21st at 12 pm (solar time):

= 90 – latitude + 23.45(declination)

= 0.00

-On December 21st at 12 pm (solar time):

= 90 – latitude - 23.45 (declination)

= 0.00

-On March 21st at 12 pm (solar time):

= 90 – latitude + 0.00

= 0.00

-On September 21st at 12 pm (solar time):

= 90 – latitude + 0.00

= 0.00

Example: what is the maximum solar altitude in Detroit city

during the year.(latitude = 42

Solution: = 90 – latitude + 23.45 = 90-42+23.45=71.45 Note: you do not need city longitude, if you use solar time in your

calculations.

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Because of the elliptical orbit of the earth and axis tilt,

there should be a correction factors for the solar time

with respect to local time called equation of time. the

Following curve gives the value of the equation of time:

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Declination curve