SOLAR CALCULATIONS (2)


 Kristina Bishop
 5 years ago
 Views:
Transcription
1 OLAR CALCULATON The orbit of the Earth is an ellise not a circle, hence the distance between the Earth and un varies over the year, leading to aarent solar irradiation values throughout the year aroximated by [1]: N = C cos (1) 365 the solar constant, C = 49.5 Btu/hr ft² (1353 W/m²). The Earth s closest oint (about 146 million km) to the sun is called the erihelion and occurs around January 3; the Earth s farthest oint (about 156 million km) to the sun is called the ahelion and occurs around July 4. The Earth is tilted on its axis at an angle of As the Earth annually travels around the sun, the tilting manifests itself as our seasons of the year. The sun crosses the equator around March 1 (vernal equinox) and etember 1 (autumnal equinox). The sun reaches its northernmost latitude about June 1 (summer solstice) and its southernmost latitude near December 1 (winter solstice). The declination is the angular distance of the sun north or south of the earth's equator. The declination angle, δ, for the Northern Hemishere (reverse the declination angle's sign for the outhern Hemishere) is [] N + 84 δ = 3.45 sin 365 () N is the day number of the year, with January 1 equal to 1. The Earth is divided into latitudes (horizontal divisions) and longitudes (N divisions). The equator is at a latitude of ; the north and south oles are at +9 and 9, resectively; the Troic of Cancer and Troic of Caricorn are located at and 3.45, resectively. For longitudes, the global community has defined as the rime meridian which is located at Greenwich, England. The longitudes are described in terms of how many degrees they lie to the east or west of the rime meridian. A 4hr day has 144 mins, which when divided by 36, means that it takes 4 mins to move each degree of longitude. The aarent solar time, AT (or local solar time) in the western longitudes is calculated from AT = LT + ( 4 min/ deg)( LTM Long) + ET (3) LT = Local standard time or clock time for that time zone (may need to adjust for daylight savings time, DT, that is LT = DT 1 hr), Long = local longitude at the osition of interest, and LTM = local longitude of standard time meridian Long LTM = 15 (4) 15 round to integer olarcalcs.doc 7, K. E. Holbert Page 1
2 The difference between the true solar time and the mean solar time changes continuously daytoday with an annual cycle. This quantity is known as the equation of time. The equation of time, ET in minutes, is aroximated by [3] ET = 9.87 sin( D) 7.53 cos( D) 1.5 sin( D) D = 36 ( N 81) 365 Examle 1: Find the AT for 8: a.m. MT on July 1 in Phoenix, AZ, which is located at 11 W longitude and a northern latitude of olution: ince Phoenix does not observe daylight savings time, it is unnecessary to make any change to the local clock time. Using Table, July 1 is the nd day of the year. From Equation (5), the equation of time is ( N 81) ( 81) D = 36 = 36 = ET = 9.87 sin( D) 7.53 cos( D) 1.5 sin( D) = 9.87 sin( ) 7.53 cos(119.3 ) 1.5 sin(119.3 ) = 6.5 min From Equation (4), the local standard meridian for Phoenix is Long 11 LTM = 15 = 15 = 15 7 = round to integer 15 round to integer Using Equation (3), the aarent solar time (AT) is AT = LT + (4 mins)( LTM Long) + ET = 8 : + (4 mins)(15 11 ) + ( 6.5 min) = 7 : 6 a.m. (5) The hour angle, H, is the azimuth angle of the sun's rays caused by the earth's rotation, and H can be comuted from [4] ( No. of minutes ast midnight, AT) 7 mins H = (6) 4 min / deg The hour angle as defined here is negative in the morning and ositive in the afternoon (H = at noon). The solar altitude angle ( 1 ) is the aarent angular height of the sun in the sky if you are facing it. The zenith angle (θ z ) and its comlement the altitude angle ( 1 ) are given by cos( θ ) = sin( 1) = cos( L)cos( δ )cos( H ) sin( L)sin( δ ) (7) z + L = latitude (ositive in either hemishere) [ to +9 ], δ = declination angle (negative for outhern Hemishere) [ 3.45 to ], and H = hour angle. olarcalcs.doc 7, K. E. Holbert Page
3 The noon altitude is N = 9 L + δ. The sun rises and sets when its altitude is, not necessarily when its hour angle is ±9. The hour angle at sunset or sunrise, H, can be found from using Eq. (7) when 1 = cos( ) = tan( L) tan( δ ) (8) H H is negative for sunrise and ositive for sunset. Absolute values of cos(h ) greater than unity occur in the arctic zones when the sun neither rises nor sets. W Zenith N Altitude Azimuth E The solar azimuth, α 1, is the angle away from south (north in the outhern Hemishere). sin( 1)sin( L) sin( δ ) cos( α1) = (9) cos( ) cos( L) α 1 is ositive toward the west (afternoon), and negative toward the east (morning), and therefore, the sign of α 1 should match that of the hour angle. f δ >, the sun can be north of the eastwest line. The time at which the sun is due east and west can be determined from min tan( δ t E / W = 4 18 m arccos (1) deg tan( L) these times are given in minutes from midnight AT. Examle : For the conditions of Examle 1, determine the solar altitude and azimuth angles. olution: The hour angle is first comuted using Equation (6) ( No. of minutes ast midnight, AT ) 7 mins [6*7 + 6] 7 min H = = = min / deg 4 min / deg The declination angle is found from Equation () N δ = 3.45 sin = 3.45 sin = The altitude angle ( 1 ) of the sun is calculated via Equation (7) sin( ) = cos( L)cos( δ )cos( H ) + sin( L)sin( δ ) 1 1 [ cos(33.43 )cos(.44 )cos( 68.5 ) + sin(33.43 )sin(.44 )] = = arcsin The solar azimuth angle (α 1 ) is found from Equation (9) olarcalcs.doc 7, K. E. Holbert Page 3
4 sin( 1)sin( L) sin( δ α = arccos cos( 1) cos( L) [ sgn( )] 1 H sin(8.6 )sin(33.43 ) sin(.44 = arccos sgn( 68.5 ) = cos(8.6 ) cos(33.43 ) This value indicates that the sun is north of the eastwest line. The time at which the sun is directly east can be comuted using Equation (1) tan( δ tan(.44 t E = 4 min 18 arccos = 4 min 18 arccos = 8 :17.5 a.m. tan( ) tan(33.43 ) L The AT is earlier than t E, thus verifying that the sun is still north the eastwest line. Normal to Earth s surface Normal to inclined surface θ N nclined surface facing southwesterly E 1 W α α 1 Horizontal rojection of normal to inclined surface Figure 1. olar angles [4] Horizontal rojection of sun s rays olarcalcs.doc 7, K. E. Holbert Page 4
5 The collector angle (θ) between the sun and normal to the surface is cos( θ ) = sin( 1)cos( ) + cos( 1)sin( )cos( α1 α ) (11) α is the azimuth angle normal to the collector surface, and is the tilt angle from the ground. f θ is greater than 9, then the sun is behind the collector. ome collector anel angles of interest are given below. Azimuth, α Tilt, θ Orientation n/a 9 1 Horizontal (flat) 9 varies Vertical wall 9 varies outhfacing Vertical 9 9 varies East facing wall +9 9 varies West facing wall α Tracking ystem The sunrise and sunset hours on the collector are different when the collector is shadowed by itself. The collector anel sunrise/sunset hours may be comuted from [1] a b ± a b + 1 H R = m min H,arccos a + 1 (1) cos( L) sin( L) a = + sin( α ) tan( ) tan( α ) cos( L) sin( L) b = tan( δ ) tan( α ) sin( α ) tan( ) (13) Examle 3: For the conditions of Examle 1, find the collector angle for a wall that faces eastsoutheast and is tilted at an angle equal to the location latitude. olution: The latitude is which is also the tilt angle ( ). Referring to Figure 1, the collector azimuth angle (α ) for an eastsoutheast direction is = Finally, the collector angle is comuted from Equation (11) = arccos [ sin( 1)cos( ) + cos( 1)sin( )cos( α1 α )] [ sin(8.6 )cos(33.43 ) + cos(8.6 )sin(33.43 )cos( ( 67.5 ))] = 34.7 θ = arccos Examle 4: Determine the time of sunrise for the conditions of the revious examles. olution: Using Equation (8), we find the (negative) hour angle for sunrise is H [ tan( L) tan( δ )] = arccos[ tan(33.43 ) tan(.44 )] = 14. = arccos To find the corresonding sunrise time in AT, we rearrange Equation (6) min ( unrise, AT ) = 7 mins + H (4 min / deg) = 7 + ( 14. )(4 deg ) = 5 : 3 a.m. olarcalcs.doc 7, K. E. Holbert Page 5
6 The corresonding local time is then found using Equation (3). LT = AT (4 mins)( LTM Long) ET = 5 : 3 a.m. (4 mins)(15 11 ) ( 6.5 min) = 5 : 37 a.m. The direct normal irradiance to the ground is [1] B DN = A ex (14) sin( 1 ) A is the aarent extraterrestrial solar intensity *, B is the atmosheric extinction coefficient (mainly due to changes in atmosheric moisture), and / is the ressure at the location of interest relative to a standard atmoshere, given by = ex(.361 z) (15) z is the altitude in feet above sea level. The direct normal radiation at sealevel then is B DN (ft) = A ex (16) sin( 1 ) Table : Aarent solar irradiation (A), Atmosheric extinction coefficient (B), and Ratio of diffuse radiation on a horizontal surface to the direct normal irradiation (C) [] Date Day of Year A (Btu/hr ft ) B C Jan Feb Mar Ar May June July Aug et Oct Nov Dec Note: 1 W/m =.3173 Btu/hr ft The direct radiation flux onto the collector is = cos(θ ) (17) D DN The diffusescattered radiation flux onto the collector is * Page 69 of Ref. 1 describes the rocedure for finding A for the outhern Hemishere. olarcalcs.doc 7, K. E. Holbert Page 6
7 1+ cos( D = C DN (18) C is the ratio of diffuse radiation on a horizontal surface to the direct normal irradiation. The reflected radiation flux for a nonhorizontal surface may be aroximated by 1 cos( DR = DN ρ ( C + sin( 1) ) (19) ρ is the foreground reflectivity with some values given below ρ urroundings condition. Ordinary ground or vegetation.8 now cover.15 Gravel roof The total radiation flux is then = + + () Tot D D DR Examle 5: Determine the direct and diffusescattered radiation flux to the collector of Examle 3, Phoenix is at an elevation of 111 ft. olution: The ressure ratio is comuted using Equation (15) = ex(.361 z) = ex( ) =.967 Extracting the July 1 values of A and B from Table, and using Equation (14) yields a direct normal radiation of ex B Btu.7 Btu DN = A = 344 ex (.967) = 7 hr ft sin( 1) sin(8.6 ) hr ft From Equation (17), the direct radiation onto the collector is = cos( θ ) = D DN Btu ( 7 ) Btu cos(34.7 ) = Using Equation (18), the diffuse scattered radiation flux to the collector is = C D DN 1+ cos( = (.136) Btu 1+ cos(33.43 Btu ( 7 ) = 8.3 References 1. P. J. Lunde, olar Thermal Engineering: ace Heating and Hot Water ystems, John Wiley & ons, 198, [TH7413.L85]. Chater 3, olar Energy Utilization, AHRAE Handbook, Alications, [TH711.A1] 3. unangle, htt:// 4. A.W. Cul, Princiles of Energy Conversion, nd ed., McGrawHill, 1991, olarcalcs.doc 7, K. E. Holbert Page 7
APPENDIX D: SOLAR RADIATION
APPENDIX D: SOLAR RADIATION The sun is the source of most energy on the earth and is a primary factor in determining the thermal environment of a locality. It is important for engineers to have a working
More informationEarthSun Relationships. The Reasons for the Seasons
EarthSun Relationships The Reasons for the Seasons Solar Radiation The earth intercepts less than one twobillionth of the energy given off by the sun. However, the radiation is sufficient to provide
More informationSun Earth Relationships
1 ESCI61 Introduction to Photovoltaic Technology Sun Earth Relationships Ridha Hamidi, Ph.D. Spring (sun aims directly at equator) Winter (northern hemisphere tilts away from sun) 23.5 2 Solar radiation
More informationFull credit for this chapter to Prof. Leonard Bachman of the University of Houston
Chapter 6: SOLAR GEOMETRY Full credit for this chapter to Prof. Leonard Bachman of the University of Houston SOLAR GEOMETRY AS A DETERMINING FACTOR OF HEAT GAIN, SHADING AND THE POTENTIAL OF DAYLIGHT PENETRATION...
More informationSunlight and its Properties. EE 495/695 Y. Baghzouz
Sunlight and its Properties EE 495/695 Y. Baghzouz The sun is a hot sphere of gas whose internal temperatures reach over 20 million deg. K. Nuclear fusion reaction at the sun's core converts hydrogen to
More informationTropical Horticulture: Lecture 2
Lecture 2 Theory of the Tropics Earth & Solar Geometry, Celestial Mechanics The geometrical relationship between the earth and sun is responsible for the earth s climates. The two principal movements of
More informationRenewable Energy. Solar Power. Courseware Sample 86352F0
Renewable Energy Solar Power Courseware Sample 86352F0 A RENEWABLE ENERGY SOLAR POWER Courseware Sample by the staff of LabVolt Ltd. Copyright 2009 LabVolt Ltd. All rights reserved. No part of this
More informationSolar energy and the Earth s seasons
Solar energy and the Earth s seasons Name: Tilt of the Earth s axis and the seasons We now understand that the tilt of Earth s axis makes it possible for different parts of the Earth to experience different
More informationThe Four Seasons. A Warm Up Exercise. A Warm Up Exercise. A Warm Up Exercise. The Moon s Phases
The Four Seasons A Warm Up Exercise What fraction of the Moon s surface is illuminated by the Sun (except during a lunar eclipse)? a) Between zero and onehalf b) The whole surface c) Always half d) Depends
More informationPHSC 3033: Meteorology Seasons
PHSC 3033: Meteorology Seasons Changing Aspect Angle Direct Sunlight is more intense and concentrated. Solar Incidence Angle is Latitude and Time/Date Dependent Daily and Seasonal Variation Zenith There
More informationChapter 3 Earth  Sun Relations
3.1 Introduction We saw in the last chapter that the short wave radiation from the sun passes through the atmosphere and heats the earth, which in turn radiates energy in the infrared portion of the electromagnetic
More informationCelestial Observations
Celestial Observations Earth experiences two basic motions: Rotation WesttoEast spinning of Earth on its axis (v rot = 1770 km/hr) (v rot Revolution orbit of Earth around the Sun (v orb = 108,000 km/hr)
More informationWhere on Earth are the daily solar altitudes higher and lower than Endicott?
Where on Earth are the daily solar altitudes higher and lower than Endicott? In your notebooks, write RELATIONSHIPS between variables we tested CAUSE FIRST EFFECT SECOND EVIDENCE As you increase the time
More informationThe ecliptic  Earth s orbital plane
The ecliptic  Earth s orbital plane The line of nodes descending node The Moon s orbital plane Moon s orbit inclination 5.45º ascending node celestial declination Zero longitude in the ecliptic The orbit
More informationASTRONOMY 161. Introduction to Solar System Astronomy
ASTRONOMY 161 Introduction to Solar System Astronomy Seasons & Calendars Monday, January 8 Season & Calendars: Key Concepts (1) The cause of the seasons is the tilt of the Earth s rotation axis relative
More informationNoon Sun Angle = 90 Zenith Angle
Noon Sun Angle Worksheet Name Name Date Subsolar Point (Latitude where the sun is overhead at noon) Equinox March 22 nd 0 o Equinox September 22 nd 0 o Solstice June 22 nd 23.5 N Solstice December 22 nd
More informationLab Activity on the Causes of the Seasons
Lab Activity on the Causes of the Seasons 2002 Ann BykerkKauffman, Dept. of Geological and Environmental Sciences, California State University, Chico * Objectives When you have completed this lab you
More informationSolar Energy Systems. Matt Aldeman Senior Energy Analyst Center for Renewable Energy Illinois State University
Solar Energy Solar Energy Systems Matt Aldeman Senior Energy Analyst Center for Renewable Energy Illinois State University 1 SOLAR ENERGY OVERVIEW 1) Types of Solar Power Plants 2) Describing the Solar
More informationCoordinate Systems. Orbits and Rotation
Coordinate Systems Orbits and Rotation Earth orbit. The earth s orbit around the sun is nearly circular but not quite. It s actually an ellipse whose average distance from the sun is one AU (150 million
More informationBasic Coordinates & Seasons Student Guide
Name: Basic Coordinates & Seasons Student Guide There are three main sections to this module: terrestrial coordinates, celestial equatorial coordinates, and understanding how the ecliptic is related to
More informationHeat Transfer. Energy from the Sun. Introduction
Introduction The sun rises in the east and sets in the west, but its exact path changes over the course of the year, which causes the seasons. In order to use the sun s energy in a building, we need to
More informationSolar Radiation. ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Solar Radiation Solar Radiation Outline Properties of radiation: Summary of equations, terms, concepts Solar Spectra Terrestrial Solar Radiation: Effects of atmosphere, angular dependence of radiation,
More informationCHAPTER 3. The sun and the seasons. Locating the position of the sun
zenith 90 summer solstice 75 equinox 52 winter solstice 29 altitude angles observer Figure 3.1: Solar noon altitude angles for Melbourne SOUTH winter midday shadow WEST summer midday shadow summer EAST
More informationSeasonal Temperature Variations
Seasonal and Daily Temperatures Fig. 3CO, p. 54 Seasonal Temperature Variations What causes the seasons What governs the seasons is the amount of solar radiation reaching the ground What two primary factors
More informationShadows and Solar Zenith
Shadows and Solar Zenith Name Lab Partner Section Introduction: The solar zenith angle is defined to be the angle between the sun and a line that goes straight up (to the zenith) In reality the sun is
More informationSolar Angles and Latitude
Solar Angles and Latitude Objectives The student will understand that the sun is not directly overhead at noon in most latitudes. The student will research and discover the latitude ir classroom and calculate
More informationThe following words and their definitions should be addressed before completion of the reading:
Seasons Vocabulary: The following words and their definitions should be addressed before completion of the reading: sphere any round object that has a surface that is the same distance from its center
More informationToday FIRST HOMEWORK DUE NEXT TIME. Seasons/Precession Recap. Phases of the Moon. Eclipses. Lunar, Solar. Ancient Astronomy
Today FIRST HOMEWORK DUE NEXT TIME Seasons/Precession Recap Phases of the Moon Eclipses Lunar, Solar Ancient Astronomy How do we mark the progression of the seasons? We define four special points: summer
More informationThe Celestial Sphere. Questions for Today. The Celestial Sphere 1/18/10
Lecture 3: Constellations and the Distances to the Stars Astro 2010 Prof. Tom Megeath Questions for Today How do the stars move in the sky? What causes the phases of the moon? What causes the seasons?
More informationExploring Solar Energy Variations on Earth: Changes in the Length of Day and Solar Insolation Through the Year
Exploring Solar Energy Variations on Earth: Changes in the Length of Day and Solar Insolation Through the Year Purpose To help students understand how solar radiation varies (duration and intensity) during
More informationESCI 107/109 The Atmosphere Lesson 2 Solar and Terrestrial Radiation
ESCI 107/109 The Atmosphere Lesson 2 Solar and Terrestrial Radiation Reading: Meteorology Today, Chapters 2 and 3 EARTHSUN GEOMETRY The Earth has an elliptical orbit around the sun The average EarthSun
More informationLECTURE N 3.  Solar Energy and Solar Radiation IDESEDU
LECTURE N 3  Solar Energy and Solar Radiation Lecture contributions Coordinator & contributor of the lecture: Prof. Marco Perino, DENERG Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino,
More informationChapter 2. Mission Analysis. 2.1 Mission Geometry
Chapter 2 Mission Analysis As noted in Chapter 1, orbital and attitude dynamics must be considered as coupled. That is to say, the orbital motion of a spacecraft affects the attitude motion, and the attitude
More informationToday. Solstices & Equinoxes Precession Phases of the Moon Eclipses. Ancient Astronomy. Lunar, Solar FIRST HOMEWORK DUE NEXT TIME
Today Solstices & Equinoxes Precession Phases of the Moon Eclipses Lunar, Solar Ancient Astronomy FIRST HOMEWORK DUE NEXT TIME The Reason for Seasons Hypothesis check: How would seasons in the northern
More informationSiting of Active Solar Collectors and Photovoltaic Modules
SOLAR CENTER INFORMATION NCSU Box 7401 Raleigh, NC 27695 (919) 5153480 Toll Free 180033NC SUN Siting of Active Solar Collectors and Photovoltaic Modules To install a solar energy system properly, it
More information1. In the diagram below, the direct rays of the Sun are striking the Earth's surface at 23 º N. What is the date shown in the diagram?
1. In the diagram below, the direct rays of the Sun are striking the Earth's surface at 23 º N. What is the date shown in the diagram? 5. During how many days of a calendar year is the Sun directly overhead
More informationOk, so if the Earth weren't tilted, we'd have a picture like the one shown below: 12 hours of daylight at all latitudes more insolation in the
Ok, so if the Earth weren't tilted, we'd have a picture like the one shown below: 12 hours of daylight at all latitudes more insolation in the tropics, less at higher latitudes Ok, so if the Earth weren't
More informationDEPLOSUN REFLECTORS. Carrer dels Vergós, 11 08017 Barcelona Spain Tel: (+34) 934.090.359 Fx: (+34) 934.090.358 info@espaciosolar.
DEPLOSUN REFLECTORS DEPLOSUN REFLECTORS DEPLOSUN REFLECTORS is an innovative reflector system which captures the sun rays in the upper part of the atria and redirects them downwards, increasing daylight
More informationThe Sun. Solar radiation (Sun EarthRelationships) The Sun. The Sun. Our Sun
The Sun Solar Factoids (I) The sun, a mediumsize star in the milky way galaxy, consisting of about 300 billion stars. (Sun EarthRelationships) A gaseous sphere of radius about 695 500 km (about 109 times
More informationFor millennia people have known about the sun s energy potential, using it in passive
Introduction For millennia people have known about the sun s energy potential, using it in passive applications like heating homes and drying laundry. In the last century and a half, however, it was discovered
More informationDouglas Adams The Hitchhikers Guide to the Galaxy
There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.
More informationUse WITH Investigation 4, Part 2, Step 2
INVESTIGATION 4 : The Sundial Project Use WITH Investigation 4, Part 2, Step 2 EALR 4: Earth and Space Science Big Idea: Earth in Space (ES1) Projects: Tether Ball Pole Sundial Globe and a Light Indoors
More informationCELESTIAL MOTIONS. In Charlottesville we see Polaris 38 0 above the Northern horizon. Earth. Starry Vault
CELESTIAL MOTIONS Stars appear to move counterclockwise on the surface of a huge sphere the Starry Vault, in their daily motions about Earth Polaris remains stationary. In Charlottesville we see Polaris
More informationSeasonal & Daily Temperatures. Seasons & Sun's Distance. Solstice & Equinox. Seasons & Solar Intensity
Seasonal & Daily Temperatures Seasons & Sun's Distance The role of Earth's tilt, revolution, & rotation in causing spatial, seasonal, & daily temperature variations Please read Chapter 3 in Ahrens Figure
More informationTime of Year  Based onMeasurement by NASA
Solar Sun System: The sun changes its eastwest orientation throughout the day. It also changes its northsouth position throughout the year. The sun reaches its highest position in the sky at noon during
More informationSOLAR ENERGY CONVERSION AND PHOTOENERGY SYSTEMS Vol. I  Solar Radiation Energy (Fundamentals)  L. Wald SOLAR RADIATION ENERGY (FUNDAMENTALS)
SOLAR RADIATION ENERGY (FUNDAMENTALS) L. Centre for Energy and Processes, Ecole des Mines de Paris, France Keywords: Sun, earth, astronomy, radiation, solar constant, energy, irradiance, irradiation, extraterrestrial
More informationEarth In Space Chapter 3
Earth In Space Chapter 3 Shape of the Earth Ancient Greeks Earth casts a circular shadow on the moon during a lunar eclipse Shape of the Earth Ancient Greeks Ships were observed to disappear below the
More informationFor further information, and additional background on the American Meteorological Society s Education Program, please contact:
Project ATMOSPHERE This guide is one of a series produced by Project ATMOSPHERE, an initiative of the American Meteorological Society. Project ATMOSPHERE has created and trained a network of resource agents
More informationFIRST GRADE 1 WEEK LESSON PLANS AND ACTIVITIES
FIRST GRADE 1 WEEK LESSON PLANS AND ACTIVITIES UNIVERSE CYCLE OVERVIEW OF FIRST GRADE UNIVERSE WEEK 1. PRE: Describing the Universe. LAB: Comparing and contrasting bodies that reflect light. POST: Exploring
More informationDesigning with the Pilkington Sun Angle Calculator
Designing with the Pilkington Sun Angle Calculator 1 In 1951, LibbeyOwensFord introduced the first Sun Angle Calculator, to provide a relatively simple method of determining solar geometry variables
More informationCELESTIAL CLOCK  THE SUN, THE MOON, AND THE STARS
INTRODUCTION CELESTIAL CLOCK  THE SUN, THE MOON, AND THE STARS This is a scientific presentation to provide you with knowledge you can use to understand the sky above in relation to the earth. Before
More informationLATITUDE GNOMON AND QUADRANT FOR THE WHOLE YEAR
LATITUDE GNOMON AND QUADRANT FOR THE WHOLE YEAR Sakari Ekko EAAE Summer School Working Group (Finland) Abstract In this workshop, we examine the correlation between our latitude and the altitude of the
More informationThe impact of high latitudes on the optical design of solar systems
The impact of high latitudes on the optical design of solar systems Mats Rönnelid 1, Björn Karlsson 2 and J M Gordon 3 1 Solar Energy Research Center, Dalarna University, S781 88 Borlänge, Sweden 2 Vattenfall
More informationStellarium a valuable resource for teaching astronomy in the classroom and beyond
Stellarium 1 Stellarium a valuable resource for teaching astronomy in the classroom and beyond Stephen Hughes Department of Physical and Chemical Sciences, Queensland University of Technology, Gardens
More informationSolar Flux and Flux Density. Lecture 3: Global Energy Cycle. Solar Energy Incident On the Earth. Solar Flux Density Reaching Earth
Lecture 3: Global Energy Cycle Solar Flux and Flux Density Planetary energy balance Greenhouse Effect Vertical energy balance Latitudinal energy balance Seasonal and diurnal cycles Solar Luminosity (L)
More informationChapter 2: Solar Radiation and Seasons
Chapter 2: Solar Radiation and Seasons Spectrum of Radiation Intensity and Peak Wavelength of Radiation Solar (shortwave) Radiation Terrestrial (longwave) Radiations How to Change Air Temperature? Add
More informationSOLAR RADIATION AND YIELD. Alessandro Massi Pavan
SOLAR RADIATION AND YIELD Alessandro Massi Pavan Sesto Val Pusteria June 22 nd 26 th, 2015 DEFINITIONS Solar radiation: general meaning Irradiation [Wh/m 2 ]: energy received per unit area Irradiance [W/m
More informationReasons for Seasons. Question: TRUE OR FALSE. Question: TRUE OR FALSE? What causes the seasons? What causes the seasons?
Reasons for Seasons Question: TRUE OR FALSE? Earth is closer to the Sun in summer and farther from the Sun in winter. Question: TRUE OR FALSE? Earth is closer to the Sun in summer and farther from the
More informationDETERMINING SOLAR ALTITUDE USING THE GNOMON. How does the altitude change during the day or from day to day?
Name Partner(s) Section Date DETERMINING SOLAR ALTITUDE USING THE GNOMON Does the Sun ever occur directly overhead in Maryland? If it does, how would you determine or know it was directly overhead? How
More informationThe Globe Latitudes and Longitudes
INDIAN SCHOOL MUSCAT MIDDLE SECTION DEPARTMENT OF SOCIAL SCIENCE The Globe Latitudes and Longitudes NAME: CLASS VI SEC: ROLL NO: DATE:.04.2015 I NAME THE FOLLOWING: 1. A small spherical model of the Earth:
More informationSolar Geometry P L A N E O F S U N
1 Slar Gemetry The Earth s daily rtatin abut the axis thrugh its tw celestial ples (Nrth and Suth) is perpendicular t the equatr, but it is nt perpendicular t the plane f the Earth s rbit. In fact, the
More informationRelationship Between the Earth, Moon and Sun
Relationship Between the Earth, Moon and Sun Rotation A body turning on its axis The Earth rotates once every 24 hours in a counterclockwise direction. Revolution A body traveling around another The Earth
More informationAstromechanics. 1 solar day = 1.002737909350795 sidereal days
Astromechanics 13. Time Considerations Local Sidereal Time The time that is used by most people is that called the mean solar time. It is based on the idea that if the Earth revolved around the Sun at
More informationSOLAR ENERGY How much strikes the earth? How much can my building get? When is it too much?
SOLAR ENERGY How much strikes the earth? How much can my building get? When is it too much? The sun: friend of foe? Drawing by Le Corbusier ENGS 44 Sustainable Design Benoit CushmanRoisin 14 April 2015
More informationSolar Energy March 5, 2009. Solar Energy. Larry Caretto Mechanical Engineering 496ALT. Alternative Energy. March 5, 2009
Solar Energy Larry Caretto Mechanical Engineering 496ALT Alternative Energy March 5, 2009 Homework assignment on nuclear power due tonight. Reading for tonight and next Tuesday Chapter 13 on solar energy
More informationShadows, Angles, and the Seasons
Shadows, Angles, and the Seasons If it's cold in winter, why is Earth closer to the Sun? This activity shows the relationship between EarthSun positions and the seasons. From The WSU Fairmount Center
More informationCelestial Sphere. Celestial Coordinates. Lecture 3: Motions of the Sun and Moon. ecliptic (path of Sun) ecliptic (path of Sun)
Lecture 3: Motions of the and Moon ecliptic (path of ) ecliptic (path of ) The 23.5 degree tilt of Earth s spin axis relative to its orbital axis around the causes the seasons Celestial Sphere Celestial
More informationSUPPLEMENT 2. ESTIMATING THE EPOCHS OF THE GCC AND GA
Crucifying the Earth on the Galactic Cross. upplement 2 1 UPPLEMENT 2. ETIMATING THE EPOCH OF THE GCC AND GA 2.1. OLAR YTEM AND GALACTIC PARAMETER Coordinate ystems. In the Equatorial and al coordinate
More informationMaximising the sun 1. Introduction
Maximising the sun 1. Introduction South Africa is blessed with some of the best quality solar radiation in the world (Figure 1). In the light of this many exciting opportunities exist to utilize the sun
More informationASTR 1030 Astronomy Lab 65 Celestial Motions CELESTIAL MOTIONS
ASTR 1030 Astronomy Lab 65 Celestial Motions CELESTIAL MOTIONS SYNOPSIS: The objective of this lab is to become familiar with the apparent motions of the Sun, Moon, and stars in the Boulder sky. EQUIPMENT:
More informationOptimum Orientation of Solar Panels
Optimum Orientation of Solar Panels To get the most from solar panels, point them in the direction that captures the most sun. But there are a number of variables in figuring out the best direction. This
More informationChapter Overview. Seasons. Earth s Seasons. Distribution of Solar Energy. Solar Energy on Earth. CHAPTER 6 AirSea Interaction
Chapter Overview CHAPTER 6 AirSea Interaction The atmosphere and the ocean are one independent system. Earth has seasons because of the tilt on its axis. There are three major wind belts in each hemisphere.
More informationEssential Question. Enduring Understanding
Earth In Space Unit Diagnostic Assessment: Students complete a questionnaire answering questions about their ideas concerning a day, year, the seasons and moon phases: My Ideas About A Day, Year, Seasons
More informationThe Analemma for LatitudinallyChallenged People
The Analemma for LatitudinallyChallenged People Teo Shin Yeow An academic exercise presented in partial fulfillment for the degree of Bachelor of Science with Honours in Mathematics Supervisor : Associate
More informationGeometry and Geography
Geometry and Geography Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles March 12, 2011 1 Pedagogical Advice I have been leading mathematical circles using this topic for many years,
More informationAuburn University s Solar Photovoltaic Array Tilt Angle and Tracking Performance Experiment
Auburn University s Solar Photovoltaic Array Tilt Angle and Tracking Performance Experiment Julie A. Rodiek 1, Steve R. Best 2, and Casey Still 3 Space Research Institute, Auburn University, AL, 36849,
More informationNewton s Law of Gravity
Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has
More informationLesson 1: Phases of the Moon
Lesson 1: Phases of the Moon The moon takes 29.5 days to revolve around the earth. During this time, the moon you see in the sky appears to change shape. These apparent changes, which are called phases,
More informationThe Orbit TelleriumThe Orbit TelleriumThe Orbit Tellerium
The Orbit TelleriumThe Orbit TelleriumThe Orbit Tellerium 16 Appendix 4 Moon Chart: For each day draw the shape of the Moon, record the time and mark the position of the Moon in the sky in relation to
More informationAstrock, t he A stronomical Clock
Astrock, t he A stronomical Clock The astronomical clock is unlike any other clock. At first glance you ll find it has similar functions of a standard clock, however the astronomical clock can offer much
More informationOrientation to the Sky: Apparent Motions
Chapter 2 Orientation to the Sky: Apparent Motions 2.1 Purpose The main goal of this lab is for you to gain an understanding of how the sky changes during the night and over the course of a year. We will
More informationCALCULATION OF ENERGY PRODUCED BY SOLAR COLLECTORS
CALCULATION OF ENERGY PRODUCED BY SOLAR COLLECTORS Imants Ziemelis, Liene Kancevica, Zanis Jesko, Henriks Putans Latvia University of Agriculture, Research Institute of Agricultural Machinery Imants.Ziemelis@llu.lv,
More informationMotions of the Earth. Stuff everyone should know
Motions of the Earth Stuff everyone should know Earth Motions E W N W Noon E Why is there day and night? OR Why do the Sun and stars appear to move through the sky? Because the Earth rotates around its
More informationHEAVENLY MATHEMATICS GEK 1506 Sun and Architecture
HEAVENLY MATHEMATICS GEK 1506 Sun and Architecture Group 66 Lee Jin You, Roger Lee Ji Hao, Theophilus Lim Guang Yong Lim Ghim Hui Lim ShuEn Adele Lim Wee Kee U024711R U024730X U024732W U024718X U024757W
More information3. Shading. V. ENVIRONMENTAL IMPACT ANALYSIS A.3 Aesthetics Shading
3. Shading The effects of shading by one building upon another can be either positive or negative depending upon the sitespecific circumstances of the properties involved. A potential benefit of shading
More informationCELESTIAL EVENTS CALENDAR APRIL 2014 TO MARCH 2015
CELESTIAL EVENTS CALENDAR APRIL 2014 TO MARCH 2015 *** Must See Event 2014 ***April 8  Mars at Opposition. The red planet will be at its closest approach to Earth and its face will be fully illuminated
More informationSolar Heating Basics. 2007 Page 1. a lot on the shape, colour, and texture of the surrounding
2007 Page 1 Solar Heating Basics Reflected radiation is solar energy received by collectorsfrom adjacent surfaces of the building or ground. It depends a lot on the shape, colour, and texture of the surrounding
More informationSolstice and Equinox ( Suntrack ) Season Model
Solstice and Equinox ( Suntrack ) Season Model Philip Scherrer & Deborah Scherrer, Stanford Solar Center Introduction This physical model simulates the Sun s tracks across the sky at summer solstice (longest
More information',ffi.. The Cause of Moon Phases
The Cause of Moon Phases 79 Figure 1 shows Earth, the Sun, and five different possible positions for the Moon during one full orbit (dotted line). lt is important to recall that onehalf of the Moon's
More informationMotions of Earth, Moon, and Sun
Motions of Earth, Moon, and Sun Apparent Motions of Celestial Objects An apparent motion is a motion that an object appears to make. Apparent motions can be real or illusions. When you see a person spinning
More informationMotions of Earth LEARNING GOALS
2 Patterns in the Sky Motions of Earth The stars first found a special place in legend and mythology as the realm of gods and goddesses, holding sway over the lives of humankind. From these legends and
More informationSolar Tracking Application
Solar Tracking Application A Rockwell Automation White Paper Solar trackers are devices used to orient photovoltaic panels, reflectors, lenses or other optical devices toward the sun. Since the sun s position
More informationSolutions to Exercises, Section 5.1
Instructor s Solutions Manual, Section 5.1 Exercise 1 Solutions to Exercises, Section 5.1 1. Find all numbers t such that ( 1 3,t) is a point on the unit circle. For ( 1 3,t)to be a point on the unit circle
More informationWhich month has larger and smaller day time?
ACTIVITY1 Which month has larger and smaller day time? Problem: Which month has larger and smaller day time? Aim: Finding out which month has larger and smaller duration of day in the Year 2006. Format
More informationName Period 4 th Six Weeks Notes 2015 Weather
Name Period 4 th Six Weeks Notes 2015 Weather Radiation Convection Currents Winds Jet Streams Energy from the Sun reaches Earth as electromagnetic waves This energy fuels all life on Earth including the
More informationOptimum Solar Orientation: Miami, Florida
Optimum Solar Orientation: Miami, Florida The orientation of architecture in relation to the sun is likely the most significant connection that we can make to place in regards to energy efficiency. In
More informationES 106 Laboratory # 5 EARTHSUN RELATIONS AND ATMOSPHERIC HEATING
ES 106 Laboratory # 5 EARTHSUN RELATIONS AND ATMOSPHERIC HEATING 51 Introduction Weather is the state of the atmosphere at a particular place for a short period of time. The condition of the atmosphere
More informationActive Solar Thermal Energy Applications in Buildings (Part 1)
Active Solar Thermal Energy Applications in Buildings (Part 1) Yerevan State University of Architecture and Construction INOGATE Programme New ITS Project, Ad Hoc Expert Facility (AHEF) Task AM545556
More informationEARTH'S MOTIONS. 2. The Coriolis effect is a result of Earth's A tilted axis B orbital shape C revolution D rotation
EARTH'S MOTIONS 1. Which hot spot location on Earth's surface usually receives the greatest intensity of insolation on June 21? A Iceland B Hawaii C Easter Island D Yellowstone 2. The Coriolis effect is
More information