1. Introduction: what do we know about visible Sun movement and seasons at the Earth?
2. The simple parametrical model describing visible movement of the Sun
3. Exploring seasons and Sun paths using animated solar map
4. From prediction of Sun position to Solar energy. Some useful applications
5. “Shadow maps” and sundials
6. Conclusions
1. Introduction: what do we know about visible 1. Introduction: what do we know about visible Sun movement and seasons at the Earth? Sun movement and seasons at the Earth?
- Where do happen in Kyiv sunrise and sunset regarding - Where do happen in Kyiv sunrise and sunset regarding cardinal directions South-North, West-East in different cardinal directions South-North, West-East in different periods of year?periods of year?
- - Why do winter and summer (seasons) exist on Earth?Why do winter and summer (seasons) exist on Earth?
Absence answer = Absence application of solar energy
Why is so important Why is so important solar motion geometrysolar motion geometry?
Maximizing absorption of sunlight needs knowledge and prediction
of the Sun position in any moment of time
2. The simple parametrical model2. The simple parametrical model
describing visible movement of the describing visible movement of the
- obliquity, tilt ot the Earth axe regarding direction, which is perpendicular to rotational plane (current value: 23.45o)
- lattitude of fixed (!) observer (51.03o for Dresden; 50.45o for Kyiv)
Celestial (sky) sphereCelestial (sky) sphere
Latitude (Latitude () of place being considered ) of place being considered is the most important!!!is the most important!!!
sin
sin
tan
1440
2coscossinsincos
min1440,...2,1,0,1440
2sincos
...365,...2,1,0,25.365
2sin
yz
ty
tt
x
TT
– – latitude of observerlatitude of observer
-> Prediction of Sun position -> Prediction of Sun position on the sky for any time of year on the sky for any time of year
and point on the Earthand point on the Earth
20th of March: T=021th of March: T=1…30th of March: T=10…
The simple parametrical model describing visible The simple parametrical model describing visible movement of Sunmovement of Sun
3. Exploring seasons at different 3. Exploring seasons at different
points of Earth using animated solar points of Earth using animated solar
mapsmaps
Representation of 3D Sun movement at 2D planeRepresentation of 3D Sun movement at 2D plane
Solar time at the maps! Estimation difference between local Solar time at the maps! Estimation difference between local and solar time at solar noon:and solar time at solar noon:
1.1. The moment of the shortest shadows. They should be The moment of the shortest shadows. They should be directed to the north (for its estimation use the compass)directed to the north (for its estimation use the compass)
2.2. The middle time between sunrise and sunsetThe middle time between sunrise and sunset
Animated solar map of Dresden (Animated solar map of Dresden (=51.03=51.03oo) in different ) in different periods of year periods of year (Solar time! 12:00 (s.t.) corresponds ~13:10 (Solar time! 12:00 (s.t.) corresponds ~13:10
in summer time)in summer time)
Animated solar map of Kyiv (Animated solar map of Kyiv (=50.45=50.45oo) in different periods of ) in different periods of year year (Solar time! 12:00 (s.t.) corresponds ~13:00 in summer (Solar time! 12:00 (s.t.) corresponds ~13:00 in summer
time)time)
Dresden: observed angle between direction to Sun and Dresden: observed angle between direction to Sun and horizontal surface in different periods of yearhorizontal surface in different periods of year
4. From Sun angle to Solar energy. Some 4. From Sun angle to Solar energy. Some applicationsapplications
Insolation (irradiance)
= maxsin
Outside of atmospheremax~1366 W/m2
See level with transparent skymax~1000 W/m2
Weather with cloudsmax~200 W/m2
Average heat power of human bodymax~100 W/m2
What can you get using 1 kW-h of energy?What can you get using 1 kW-h of energy?
1 kW-h = 3600 kJ
* Lighting of energy-saving lamp (P=10 W) during 100 hours
* To raise temperature 40 l of water ~20 oC
* To heat an air in the room with volume 150 m3 (10x5x3) ~20 oC
Trombe wall Solar thermal collector
(efficiency is up to 80%) Solar panel
(efficiency is 15-18%)
Time dependence of ideal daily amount of energy (kW-h/mTime dependence of ideal daily amount of energy (kW-h/m22) which can ) which can harvested at different seasons from each side of “Solar cube”harvested at different seasons from each side of “Solar cube”
Winter timeWinter time: the south side gives : the south side gives the maximal amount of heatthe maximal amount of heat
South-oriented eaves in old Ukraine as elements of South-oriented eaves in old Ukraine as elements of energy-effective housesenergy-effective houses
Advantages:1. Protection of south windows of house in summer time against solar light.
Coolness in summer
2. Windows open to Sun in winter time. Barrier from the heat convection at the south wall
Novel GreenhouseNovel GreenhouseSunrise and sunset at winter solstice
(declination =-=-23.45o)
= arcsin(sin/cos)
Sunrise and sunset at winter solstice in Dresden
~ 39~ 39oo
Optimal distances between houses of solar Optimal distances between houses of solar panels? What is the length of shadows in panels? What is the length of shadows in
different seasons?different seasons?
55. “Shadow maps” and Sundials. “Shadow maps” and Sundials
HorizontalHorizontal sundial for Dresden sundial for Dresden
It is possible to calculate the main properties of any kind of sundials using the model
presented here
Sundial at the wall of ancient palace in the Pillnitz Sundial at the wall of ancient palace in the Pillnitz
(Dresden)(Dresden)
Horizontal sundial for KyivHorizontal sundial for Kyiv
Experimental tests performed in Kirovohrad Experimental tests performed in Kirovohrad region of Ukraine using unsophisticated region of Ukraine using unsophisticated
horizontal sundialhorizontal sundial
66. . Summary and outlooks Summary and outlooks based on the proposed model:based on the proposed model:
* always estimate at the sky the sector of the Sun shining!
* optimise position of thermal collector or solar panels in dependence on latitude;
* consider shadow areas
* sundials as useful and simple tools for popularization solar energy applications
Thank you for your attention!
Supplementary materials
Solar maps of different point of the Earth at summer Solar maps of different point of the Earth at summer solsticesolstice
Animated solar map of Murmansk (Animated solar map of Murmansk (=68.97=68.97oo) – the ) – the largest city beyond the polar circle (66.56largest city beyond the polar circle (66.56oo))
Animated solar map of Sohag (Animated solar map of Sohag (=26.55=26.55oo) in different periods ) in different periods of yearof year
