Presentation title: Solar Radiation

Solar Radiation

Lecture 16.

A refresher: Solar Geometry variables

Angle of Incidence (Θ) Angle of sun to a line normal to the surface in question (time and orientation specific)

Solar-Surface Azimuth (γ) Angle in plan between the sun and a line normal to the Angle in plan between the sun and a line normal to the surface in question (time and orientation specific)

Profile Angle (Ω) Angle in the sun’s position in a two-dimensional section and a line normal to the surface in question (time and orientation specific)

Surface Tilt (Σ)Tilt of a surface relative to the ground plane (orientation specific)

Schema for

Equidistant

Sun Path Diagram

Solar Surface Azimuth diagramSolar-Surface Azimuth (γ) Angle in plan between the sun and a line normal to the surface in question (time and orientation specific)

Angle of incidence diagramAngle of Incidence (Θ) Angle of sun to a line normal to the surface in question (time and orientation specific)

Angle of incidence diagramProfile Angle (Ω)Position of sun translated into a two-dimensional vertical plane (as in section)

Recall that a profile is

the view of a person or

an object from the side

SITE SOLAR ANALYSIS

Tools of the Trade

Using Profile Angles (Ω)

Using Profile Angles (Ω)

A

A

Using Profile Angles (Ω)

Solar

Altitude (β)

Using Profile Angles (Ω)

Solar

Surface

Azimuth (γ)

Using Profile Angles (Ω)

This is the sun’s position in three dimensions,

now let’s consider its representation in section.

Using Profile Angles (Ω)

Cut a section perpendicular to the back wall

Using Profile Angles (Ω)

B

B

Section perpendicular to back wall

Using Profile Angles (Ω)

Profile Angle (Ω) for

section perpendicular

to back wall

Using Profile Angles (Ω)

Cut a section parallel to the back wall

Using Profile Angles (Ω)

C

Section parallel to back wall

C

C

Using Profile Angles (Ω)

Profile Angle (Ω) for

section parallel to back wall

Profile Angle (Ω)

Profile Angle (Ω)

Profile Angle (Ω)

Profile Angle (Ω)

An example problem:

Let’s cast some shadows for

an declined vertical dial. A

two-foot horizontal gnomon

is placed in a southwest-

facing wall at 36º NL. Cast

the shadow for 3 pm on 21 the shadow for 3 pm on 21

May.

Southwest

Note that this vertical gnomon could easily be the corner of

an awning or other shading device.

Southwest

I confess a deep

and continuing

fondness for

renderings in

the Beaux Arts

tradition

Our familiar LOFSAC

– a Sun Path Diagram

in the equidistant

polar form

3 PM, 21 May

We will use our

LOFSAC overlay

for calculating

1. Profile Angle

2. Angle of

Incidence

3. Solar- Surface

Azimuth

Let’s look at the development of

this overlay. We begin with a wall

of random orientation.

The wall can only ‘see’ the half of the

sky vault that lies in front of it.

One can map positions in that quarter

sphere using coordinates relative to

the wallΘ = 60º

This fix set of relative positions can be translated

into several variables that are dependant on

position – e.g., angle of incidence, profile angle,

radiation

Overlay for

calculating Profile

Angle, Angle of

Incidence, and

Solar- Surface

Azimuth

Overlay for

calculating Profile

Angle

Overlay for

calculating Angle of

Incidence

Overlay for

calculating Solar-

Surface Azimuth

3 pm,

21 May

Back to our

sample

calculation

problem: our

southwest-facing

wall ‘sees’ this

half of the sky

vault21 May

Start with a wall elevation.

What do we have to work with?

The Beaux Arts

rendering wizards

used orthographic

projections – our

familiar plans,

elevations, and

sections

We can project plan and

section to provide three views

of the same object.

Since sunpath diagrams are projections of the sun’s path onto a

plan diagram let’s focus on plan for a moment.

Here is the

sunpath diagram

placed in position

relative to our

wall in plan

And the profile And the profile

angle overlay in

position relative to

our wall in plan.

Note the normal to

window line. This

will yield a profile

angle in a section

perpendicular to

the wall

Problem setup for Profile

Angle (Ω), section

perpendicular to wall

3 PM, 21 May

The two

diagrams

combined.

Now we can

derive a value

for Ω for a

southwest –

facing surface

3 pm

21 May

facing surface

at 3 PM, 21

May

21 May

Ω = 54°

Find the intersection of

the 3 pm and 21 May

lines. This is the

absolute position of

the sun in the sky.

Read a value for

profile angle

from the

contours of

the profile

3 pm

the profile

angle overlay.

This overlay is

positioned relative

to the wall.

The result is profile angle equals 54°

OK, what do

we do with our 54°profile

angle value?

Ω = 54º

Problem setup for

Profile Angle (Ω),

section parallel to

wall

3 PM, 21 May

Problem setup for

Profile Angle (Ω),

section parallel to

wall

3 PM, 21 May

Profile angle

overlay in place

for normal parallel

to wall

21 May

Read the value for

profile angle parallel

to the wall from

the contours of

the profile

angle overlay.

The result is

3 pm

The result is

profile angle equals 62°

Ω = 62°

Ω = 54º

54ºΩ = 62º

Add the new Add the new

profile angle

value to the

elevation. The

intersection of

these two lines is

the end of the

shadow.

We can now run a

check on the

shadow position

using solar-surface

azimuth.

Solar surface azimuth

protractor in place for

normal parallel to wall

Problem setup for

Solar-Surface

Azimuth (γ)

3 PM, 21 May

Determining

solar surface

azimuth

value

Find the intersection of

the 3 pm and 21 May

lines. Then draw a

straight line from

the zenith (center

of sunpath diagram)

through the

month/time

intersection to the

perimeter.

γ = 36º

Read a value for

solar-surface azimuth on

the perimeter scale of the

overlay.

The result is solar-surface azimuth equals 36°

54ºΩ = 62º

54º62º

Shadow position for

3 pm, 21 Mayγ = 36º

Problem setup for

Angle of Incidence (Φ)

3 PM, 21 May

Angle of Incidence

21 May

Find the intersection of

the 3 pm and 21 May

lines. This is the

absolute position of

the sun in the sky.

Read a value for

angle of incidence

from the

contours of

the angle of

incidence overlay.

Θ = 57º

Shadow length = gnomon height x tan Θ

= 3.1’

incidence overlay.

This overlay is

positioned relative

to the wall.

The result is angle of incidence equals 57°

54º62º

Shadow position for

3 pm, 21 Mayγ = 36º

54º62º

Θ = 57º

3.1’

Angle of incidence

yields a shadow

length of 3.1 feet

Penumbral shadows – go ponder a flagpole

Penumbral shadows – go ponder a flagpole

But wait -- it is time for the 7th inning stretch

PEC Monthly Solar Geometry Spreadsheet

PEC Annual Solar

Geometry

Spreadsheet

Annual Version

Benton’s Solar

Geometry

Spreadsheet

Annual Version

1. The Solar Constant

The earth receives a relatively

constant flux of solar radiation

at the edge of its atmosphere.

This value will vary about 7%

during the year and is taken to during the year and is taken to

average 429.2 BTU/Ft2 Hr.

Values for each month can be

found in ASHRAE Handbook of

Fundamentals.

2. Earth’s Movement

The orbit of the sun about the

earth (declination) and the

earth's rotation on its axis.

(hour) establish the seasonal

and diurnal cycles of solar and diurnal cycles of solar

radiation at the earths surface.

Declination and hour are

fundamental inputs to all

methods of calculating solar

geometry.

3. Location on Earth

The location of a site on the

earth's sphere will determine

the range and limits of seasonal

and diurnal solar variation.

Latitude will affect solar Latitude will affect solar

altitude, azimuth and day

length Longitude will establish

the relationship between solar

time and standard time.

Altitude will establish

atmospheric attention.

4. Surface Tilt & Orientation

At a given location, the

relationship of a target plane

to the earth's surface and to

south will establish the angle of

incidence between the surface incidence between the surface

and the sun at any given time.

The angle of incidence will

indicate if the surface is shade

or in the sun. If the surface is

in the sun, the impact will vary

with angle of incidence.

5. Weather / Climate Patterns

Solar radiation impact at the

earth's surface will vary

according to the weather

patterns characteristic to a

given region. This variation, given region. This variation,

primarily due to shading by

clouds, can be established

using calculation procedures

(see article by S.A. Klein in

Solar Energy Journal, Vol. 19,

pp. 325) or referring to climatic

data.

6. Microclimatic Shading

Topography and vegetation

establish site specific radiation

patterns that vary through the

year. These shading effects can

be examined using horizon be examined using horizon

shading diagrams sunpath

projections or using three-

dimensional models for scale

simulation

7. Surface Shading Devices

The three-dimensional

character of a surface will

establish the extent of self

shading that occurs with hour

and seasonal changes. This may and seasonal changes. This may

be studied graphically using

profile angle projections or sun

path shading mask. Three-

dimensional models provide an

accurate analysis method.

8. Transmission through Glazing

The transmitted component of

radiation striking a glazing

material will vary with the

physical properties of the

glazing, the assembly of glazing

components, and the angle of components, and the angle of

incidence. Consult glazing

manufacturers or Duffie and

Beckman, Solar Energy Thermal

Processes, p. 108.

9. Surface Absorption

The conversion of radiation t

heat and the transfer of heat

from the surface to storage, or

to the air, will vary with

surface absorptance, angle of surface absorptance, angle of

incidence, target mass, target

temperature, and air

temperature.

A radiation

overlay for

the sun

Diffuse radiation only

when sun is behind

the surface

the sun

path

diagram

Direct and diffuse

radiation when sun is

in front of the surface

The radiation

overlay applied to

our SW-facing

wall example

The radiation

overlay applied to

a SW-facing wall

example

Solar Geometry

Spreadsheet

Annual Version

The radiation

overlay applied to

our SW-facing

wall example

21 May

Find the intersection of

the 3 pm and 21 May

lines.

Read a value for solar

3 pm

Read a value for solar

radiation from the

contours of the solar

radiation overlay.

The result is 180 Btu/Hr

for a clear sky.