We are searching data for your request:
Upon completion, a link will appear to access the found materials.
I was wondering how I could get the sun's azimuth and elevation values to shade a particular window with a roller shutter.
At first I thought azimuth is good enough; of course, it wasn't, as I found out in practice. While there are calculators to find a and e for a specific location at a certain date, I lack the maths to figure out when the sun will hit a western window.
The window faces 270 deg, I know how far the eaves stick out, and the top and bottom edges of the window (and of course location).
I get the idea the maths will be complicated… however, (it won't matter much) as I want to program this into a controller to operate the shutter.
Any hints appreciated.
You can use a package such as the pyephem package for python. It can calculate the position of any astronomical object.
However for the sun since it moves along the ecliptic, roughly at a uniform rate, you can approximate the position by doing coordinate transformations. The sun's longitude moves by 365.24/360 degrees a day from 0 at the vernal equinox and has an ecliptic latitude of 90 degrees. This can be converted into equatorial coordinates (right ascension and declension), and then, given the hour, the alt and az positions can be found. The formulae can all be found on https://en.wikipedia.org/wiki/Celestial_coordinate_system
Determine sun azimuth and elevation for shading a window throughout the year - Astronomy
In the tropical climates, the designer should keep the solar radiation off the opaque solid elements of the building's envelope where possible. Special care should be taken to shade the windows to reduce the incoming heat and the risk of overheating.
The design of shading devices can be quite complex. Computer programs exist to accurately shape shades for very specific purposes. However, in their absence, and with a little understanding of the mechanics of sun position and sun-path diagrams, manual methods can be used.
External shading devices are preferable and more effective than internal ones. This includes devices fixed to the outside of the window or attached to building envelope. Among the operable units are louvers made of wood or metal, exterior venetian blinds, shutters, awnings and fixed or movable overhangs.
As you should know from your own personal experience, the most important characteristic of solar position is its seasonal variation. At the height of summer in the southern-hemisphere the sun rises slightly south-east and sets slightly south-west. In winter it rises slightly north east and sets slightly north-west. It also rises much earlier and sets much later in summer than in winter. In the northern hemisphere, north and south are reversed.
The aim of good shading design is to utilise these characteristics to best advantage, usually complete exclusion in summer and maximum exposure in winter.
Rules of the thumb
Shading devices should be selected according to the orientation of the window. Whilst some orientations are easy to shade, others are much more difficult as the sun can shine almost straight in at times. The table below indicates the most appropriate type of shading device to use for each orientation in the southern hemisphere. These are guidelines and, of course, there are many variations to these basic types.
|North (equator-facing)||Fixed horizontal device|
|East or West||Vertical device/louvres (moveable)|
|South (pole-facing)||Not required|
When attempting to shade a window, the absolute azimuth and altitude of the Sun are not as important as the horizontal and vertical shadow angles relative to the window plane. These can be calculated for any time if the azimuth and altitude of the Sun are known.
Horizontal Shadow Angle (HSA)
This is the horizontal angle between the normal of the window pane or the wall surface and the current Sun azimuth. The normal to a surface is basically the direction that surface is facing its orientation. If the orientation is known,
The vertical shadow angle is more difficult to describe. It is best explained as the angle a plane containing the bottom two points of the wall/window and the centre of the Sun, makes with the ground when measured normal to the surface. It is therefore given by:
It is the VSA that determines the depth of the required shade. The diagram more adequately describes the derivation of the VSA
These two angles, HSA and VSA, can then be used to determine the size of the shading device required for a window. If the height value refers to the vertical distance between the shade and the window sill, then the depth of the shade and its width from each side of the window can be determined using relatively simple trigonometry.
The depth of the shade is given by:
The width simply refers to the additional projection from the side of the window. Exactly which side is a matter of the time of day and which side of the window the Sun is on.
The design requirements for a shading device depend entirely on a building's use and local climatic conditions. In a multi storey open plan office building, the occupancy and equipment gains are such that heating is rarely required. In this situation, to avoid unnecessary loads, shading may be designed to completely protect the windows all year-round.
In a domestic building or one that is occupied 24 hours, the release of stored heat during cold nights in winter can be important. In this case, the shading would be designed to fully protect the windows during the summer months, but to expose them as much as possible to direct sun in winter so that they have a chance to absorb heat during the day. In climates where summers are also relatively cold, the requirement may be to allow full solar access all year round.
If you look at outdoor air temperature and the intensity of solar radiation at different times of the year for Perth, Western Australia, it is clear that the transition to colder weather really begins in mid to late March. Thus, in order to take advantage of solar heating, the transition from shaded to exposed should really begin at the same time. This means that the window should remain completely shaded up until mid to late March, with maximum exposure occurring at the winter solstice in mid June.
A convenient date, by happenstance, is the 21st of March. This has the advantage of being the autumn equinox. One characteristic of the equinox is that, for a north-facing wall, the VSA is exactly the same throughout the day. This is an important piece of information as, in summer, the lowest daily VSA occurs at noon, whereas in winter noon sees the highest VSA.
Thus, if the cut-off date for a north-facing shade occurs on or before the autumn equinox, its depth will be defined by the noon VSA. If the cut off date occurs after the 21st of March, the VSA at either the start or end times will determine its depth.
To design a horizontal shading device, simply following the following steps.
- Determine cut-off date. This is the date before which the window is to be completely shaded and after which the window will be only partially shaded.
- Determine Start and End Times. These represent the times of day between which full shading is required. Keep in mind that the closer to sunrise and sunset these times are, the exponentially larger the required shade.
- Look up Sun Position. Use solar tables or a sun-path diagram to obtain the azimuth and altitude of the sun at each time on the cut-off date.
- Calculate HSA and VSA. Using the formulae given above, calculate the HSA and VSA at each time.
- Calculate Required Depth and Width. Once again, using the formulae above, calculate the depth and width of the required shade on each side of the window.
The above method will provide a precisely shaped shade that will provide full protection over the time period selected. However, we have not yet looked at how much Sun we will get in winter, when some penetration is usually desirable. Unfortunately, a shading device will not suddenly stop working after a certain date (unless it is retractable). It will usually partially obscure the window year round, more so in summer and less so in winter.
This is where the trade-off begins the amount of which depends on the relative heating and cooling stresses in the environment. In a very hot climate you may not actually need solar gains in winter, whereas in a very cold climate solar gains even in summer may be desirable.
In order to understand the full effect of a shading device, we really need to turn again to the sun-path diagram and a percentage overshadowing graph. It may be that, whilst we want 100% shading throughout most of summer, we could probably live with only 80 to 85% shading in early Autumn in order to gain extra solar gains in winter. You will notice that the shading patterns displayed in the diagram below all display "fuzzy" edges. This is because we are dealing with a large window surface, not a single point.
The golden hours of peak sunlight lie between the dotted lines of the two solstice suns, and between 9 a.m. and 3 p.m daily. This is known as the solar window. If any object -- be it on the roof or in the nearby surroundings -- should eclipse the sun where it shines on the array, the electricity output may decrease substantially.
How to Measure a Year's Worth of Shade by Hand
To predict shading over an array, the site assessor takes into account any obstruction, near or far, that can get between the sun and the array some time during the year. Naturally, obstructions located to the north of the array are of no concern. Also, shading that occurs outside the solar window of 9 a.m. to 3 p.m. daily is typically not counted against the potential kilowatt hour estimate. (It's common practice, however, to widen the window for the summer months.)
In a nutshell, a shadow will be cast across an array if an object's elevation or altitude angle is the same or greater than the sun's when they share the same compass bearing -- that is, from the perspective of the array. This bearing is called an azimuth angle .
Two measurements are necessary to find out if a tree or other potential obstruction will cast shade over your array at some point during the year. One is the elevation or altitude angle of the object. The second is it's compass bearing (factoring in magnetic declination).
Nearly all solar contractors use an expensive shading assessment device to determine the best placement for an array. A software app is included with both the Solar Pathfinder and Solmetric Suneye to help quantify shading, along with providing an estimate of annual insolation and sun hours.
You can, of course, compile the same intel using a few simple tools and data sets available for free on the internet. This is a useful skill to learn, not only for solar power applications, but for wilderness navigation, planning a farm or garden, astronomy, forestry management, surveying. Just keep in mind that many solar rebates and tax credits require you to submit a Pathfinder or Sun-eye report, so you may still need to rent or borrow one of these devices.
Here's a six-step guide to help you to get the job done for free:
Step 1: Generate a sunpath diagram online for your latitude.
A sun path diagram provides the track of the sun over a year's time for your local latitude and time zone. On the order form provided by the Univ. of Oregon online, you'll find several options to choose from. The first one to pick is "Look up location with a U.S. zip code." Next, select your time zone. Most of the default options that follow are OK, but to get a printout that's easier to read, select "Crop azimuth axis to fit plotted data," and "Crop elevation axis to fit plotted data."Also, in Step 5 you can add two title lines to identify your chart.
Diagram adapted from solardat.uoregon.edu.
The solid curving lines on the graph represent the sun's path on one day for each two months out of the year (e.g. April and August), except on the solstices, which represent one day. Although there's a white space between each curved line, it's assumed that the sun will gradually track through these spaces over the course of 30 days. The horizontal axis of the graph charts the azimuth angle (compass orientation), while the vertical axis charts the altitude angle.
The vertical dotted lines plot the time of day in relation to the azimuth and altitude angles. Remember, it's only between the hours of 9 a.m. and 3 p.m. that shading across an array is counted. For this particular chart, any obstruction located outside the compass range of 100 degrees (close to due east) and 265 degrees (close to due west) does not even need to be measured. The top azimuth scale, incidentally, uses the reference-to-due-south system.
Step 2: Next, go outside to the site of your potential solar aray and take compass bearing to determine the azimuth angle and width of each potential obstruction. Create a table with five columns before you start. The first column is for listing each of the obstructions by name. The second column is for the first bearing, the left side of the object. The third column is for the second bearing , the right side of the object. Don't forget to factor in declination in your readins, a process explained on Page 2 of this section.
As you size up potential obstructions, be on the lookout for deciduous trees. Since they lose their leaves in the fall, they'll have less shade impact between December and April. Make a note of this on your table, so you can shave off some of the tree's girth (graph-wise) in Step 4.
Step 3: Record the altitude angle of all the same obstructions.
Altitude or elevation angles are measured with an inclinometer (aka clinometer, theodolite, angle finder). The device is used for astronomy, surveying, and to measure trees. Several videos on Youtube (like this one) demonstrate how to quickly construct the device from simple materials. (Or you can try these online instructions.) After that, you can watch the next in the series to see how it's used. Remember, you don't need to find out the height of the obstruction, just the angle shown in the image on the left above. That's the altitude or elevation angle.
With your clinometer, stand or squat on the side (or at a corner) of your planned array, a few feet ahead of the nearest side facing the object. Let the rock dangle straight down so that it's exactly plumb to the ground. Sight the straight edge of the instrument so that one end is pointed at the top of the obstruction, the other end pointed down at the array. The idea here is create an invisible line running from the array to the top of the object, as the photo above left demonstrates.
With the protractor's rock plumb (dangling straight down), the string should now be lined up across the correct altitude angle on the curved ruler. Press a finger down on the string near the scale without moving it, and hold it taught while you turn the protractor to where you can read the angle. Record the result in the fifth column of your table. Then repeat the process for all the other potential obstructions.
Note: If you plan to rely solely on this data collection method to assess shading, you should repeat the entire series of measurements in each corner of the array, and at the center point as well. Create a separate table for each measuring location, then label them for easy reference -- e.g. "NE, SE, NW, SW, CENTER".
If you know the height of an obstruction, and it's on level ground with your array location, you may be able to use the Pythagorean Theorum to compute its altitude angle. (The obstruction must likewise be perpendicular to the ground, rather than pitching forward or backward.) In addition to its height, you'll need to know the distance from its base to the array. Also, you'll need to know how much higher the array location is off the ground versus the object.
With this data in hand, first subtract the height of the array (off the ground) from the height of the object. If you look at the diagram below, you'll see why it's important to do this. For example, if you have a 40-foot-high obstruction and your array is 10 feet off the ground, your object height should be adjusted to 30 feet.
Using the Pythagorean Theorem to measure an altitude angle requires the height of the object, distance from the array, and a scientific calculator.
Now, divide the object's adjusted height by the distance on your calculator, then use the ArcTan key to get the altitude angle. Be sure to perform the division first, save the result in memory, then recall it after hitting Arc Tan. (You may need to hit "shift-tan" or "tan-1" keys if there's no arc tan option.)
Step 4: On the sun path diagram, plot the coordinates for each potential obstacle.
The chart will tell you if an obstruction will eclipse the sun as it shines on the array. It will also tell you how long the shade will occur. As you can see, a sun path diagram is a simple line graph with X and Y axes. Plot each set of coordinates in pencil (i.e. the two azimuth measurements and one altitude angle), one by one. Mark the points near the axes lines on the chart. Now draw and fill in a vertical bar shooting up from the Azimuth axis. Once that's done, you can erase the horizontal line emanating from the Altitude axis.
Repeat the process for all the other objects you measured. And if you took readings from more than one location, repeat the tasks -- one sun path chart per location.
Each vertical bar represents a shading obstruction drawn onto a downloaded sunpath diagram. The altitude angle and compass bearings taken of the left and right edge of the obstruction are used to plot the top (vertical axis) and sides (horizontal axis). At the same time, the numbers written inside the squares are a rough estimate of the percentage of insolation dispersed around the course of the year. (They should total 100.) By adding the numbers where shade falls inside a square, you can get an idea of the shade impact at the array site. Note the negative numbers recorded at the bottom of the sheet. These represent the insolation cancelled out by each bar and add up to 21%. Clearly, it's the third obstruction from the right that's the big showstopper for this array placement. If it could be eliminated or reduced in some way (e.g. a tree pruning or removal), the location might otherwise be deemed a good one.
Step 5: Analyze the data to determine how much shading will occur.
First you'll need to hone in on the data that pertains to the solar window. To do this, draw a border along the following lines: the 9 a.m and 3 p.m. dotted lines between the uppermost and lowermost curved sun path line and the curved sun path upper and lower lines, stopping at the 9 a.m. and 3 p.m. borders. Now you can use the graph paper squares to help you approximate a percentage of the solar window that's shaded.
You could start by taking the number of squares within the borders and dividing by 100 to allocate roughly the same percentage of insolation (i.e. sunlight on your array) to each square. For example, if you count 30 squares in the solar window, you could assign 3% to each one. Then you can add an extra 1% to the ten boxes closest to noontime, since that's when insolation peaks. Once you've allocated percentage values to the squares, you can make a tally of the shaded portion. Often, the bars you draw will only cover part of a square, which means that a 3% square that's half-covered translates into 1.5% worth of shading. Add up all the shaded percentages when you're done.
Next, if you made separate charts for multiple locations, you'll need to average the shading sums of all the charts. For example, if your percentage sums are 14 for NE, 5.5 for CENTER, 7 for NW, 8 for SE, and 10.5 and SW, first add them up (45), then divide by 5 (the number of charts) to get an averaged shade tally of 9%. That, in turn, indicates a 91% insolation value for your array.
Array shading is an aspect of system sizing that must be factored in to get a realistic expectation of system performance. It can be included as a derate when sizing the array. (Check here for a list of standard derate factors and how they're used.) More often, designers use the adjusted insolation value generated on a Solar Pathfinder or Sun-Eye report when it's time to count the modules needed.
The chart is exerpted from a report by the Solar Pathfinder software and provides the month by month impact of shading on a proposed solar array. The photo on the right shows another module placement scheme designed to avoid a yearround obstruction - the chimney.
Step 6: Use one or more of the following remedies to correct and/or mitigate the problem of shading.
If your assessment produces more than 10% shading, you can take a variety of steps to improve that number. Moreover, any amount of shade -- even one percent! -- can cause a loss of voltage that affects all modules wired in the same series string. In addition to changing the placement or orientation of an array, you can and should try to mitigate its impact within the electric circuit . Here are the most common adjustments solar designers employ to address shading over an array site:
- Move the site farther down the roof (or off the roof).
- Use a non-rectangular configuration.
- Leave an empty space within the array to avoid an obstruction.
- If possible, arrange for a tree removal or seasonal pruning.
- Raise the array's height so that the object altitude angle is lower than the sun's altitude/elevation.
- Use a module model with extra shade mitigation features.
- Use several microverters instead of one central inverter, or some form ofDC optimization, so that shaded modules won't affect the production of non-shaded modules.
- Run separate cables to the central inverter for each module string so that a lower voltage in one string won't affect the voltage of the others.
- Use a tracking system instead of a fixed mount.
A single-axis tracking system called SunSeeker is manufactured by Thompson Technology Industries. This solar solution is normally implemented where there's plenty of space to install scores of PV panels, like an apartment building, big-box retailer or college.Single and dual-axis tracking mechanisms are activated by sunlight, which change PV panel orientation so they'll follow the sun throughout the year. Tracking generally increases output by about one-thrid. A single axis rotates the azimuth direction, while dual-axis tracking does that and adjusts the array's upward tilt. Unfortunately, the extra components and required maintenance make tracking an expensive option for homeowners. And they may or may not effectively get around the shading.
If you're a homeowner considering a solar electric system, ask a professional contractor to help you figure out the most economical solution to the problem of shading. Sometimes an obstruction turns out to be not such a big deal -- for instance, a deciduous tree that loses all its leaves in the fall. If your chimney is in a bad spot, you may be able to avoid its shade by staggering your modules to avoid the shadow it casts, as shown in an earlier photo. Always consider creative ways to get around obstructions before abandoning a good spot with an ideal due south orientation and lots of space for modules.
The Solar Pathfinder, retailing at $260, comes with sun path charts covering a range of latitudes in both hemispheres. The curved lines are separated into 12 months, and crossed perpendicularly by hour lines. This makes it easier to allocate insolation. The device chart allows you to tally shading for each month, with the percentages divided by hour of the day. You can photograph the reading in the field, then load it into the software app (which costs an extra $190) for data crunching. Here's a sample report with the results. Alternatively, you can skip the app and add the numbers manually, then average the results of the different readings in the same manner described earlier in this section. To look it at a larger image of the photo above, see Page 8 of the user manual. Photo: SolarPathfinder.com.
Regardless, lost kilowatt hours due to shading cuts right to the heart of a solar PV investment and can extend payback time by a year or more. That's why it's essential to ask your contractor for copies of the data collected from a Solar Pathfinder or Sun-Eye survey. After reading this section, you'll be able to analyze the data yourself and suggest an alternative approach, if necessary.
For a look at a variety of photovoltaic simulators, calculators and software available to predict array performance, click here or here. You might also like to try a new Android mobile app called ScanTheSun.
Next: Solar Inverters
Send any feedback or suggestions to info [at] thesolarplanner dot com .
The use of sun control and shading devices is an important aspect of many energy-efficient building design strategies. In particular, buildings that employ passive solar heating or daylighting often depend on well-designed sun control and shading devices.
During cooling seasons, external window shading is an excellent way to prevent unwanted solar heat gain from entering a conditioned space. Shading can be provided by natural landscaping or by building elements such as awnings, overhangs, and trellises. Some shading devices can also function as reflectors, called light shelves, which bounce natural light for daylighting deep into building interiors.
The design of effective shading devices will depend on the solar orientation of a particular building facade. For example, simple fixed overhangs are very effective at shading south-facing windows in the summer when sun angles are high. However, the same horizontal device is ineffective at blocking low afternoon sun from entering west-facing windows during peak heat gain periods in the summer.
Exterior shading devices are particularly effective in conjunction with clear glass facades. However, high-performance glazings are now available that have very low shading coefficients (SC). When specified, these new glass products reduce the need for exterior shading devices.
Thus, solar control and shading can be provided by a wide range of building components including:
- Landscape features such as mature trees or hedge rows
- Exterior elements such as overhangs or vertical fins
- Horizontal reflecting surfaces called light shelves
- Low shading coefficient (SC) glass and,
- Interior glare control devices such as Venetian blinds or adjustable louvers.
Aluminum architectural sun shade, horizontal sun control device, vertical fins
Fixed exterior shading devices such as overhangs are generally most practical for small commercial buildings. The optimal length of an overhang depends on the size of the window and the relative importance of heating and cooling in the building.
In the summer, peak sun angles occur at the solstice on June 21, but peak temperature and humidity are more likely to occur in August. Remember that an overhang sized to fully shade a south-facing window in August will also shade the window in April when some solar heat may be desirable.
To properly design shading devices it is necessary to understand the position of the sun in the sky during the cooling season. The position of the sun is expressed in terms of altitude and azimuth angles.
- The altitude angle is the angle of the sun above the horizon, achieving its maximum on a given day at solar noon.
- The azimuth angle, also known as the bearing angle, is the angle of the sun's projection onto the ground plane relative to south.
- An easily accessed source of information on sun angles and solar path diagrams is Architectural Graphic Standards, 12th Edition, available from John Wiley & Sons, Inc. Publishers.
See pveducation.org for more information.
Shading devices can have a dramatic impact on building appearance. This impact can be for the better or for the worse. The earlier in the design process that shading devices are considered they more likely they are to be attractive and well-integrated in the overall architecture of a project.
In ANSI/ASHRAE/IES Standard 90.1 Energy Efficient Design of New Buildings Except Low-Rise Residential Buildings (on which the Federal equivalent 10 C.F.R. § 435 is based), the degree of window shading is a major consideration. Both the projection factor (PF) for exterior shading and the shading coefficient (SC) of glass must be evaluated when using the Alternate Component Packages envelope design approach.
Designing Shading Systems
Given the wide variety of buildings and the range of climates in which they can be found, it is difficult to make sweeping generalizations about the design of shading devices. However, the following design recommendations generally hold true:
Use fixed overhangs on south-facing glass to control direct beam solar radiation. Indirect (diffuse) radiation should be controlled by other measures, such as low-e glazing.
To the greatest extent possible, limit the amount of east and west glass since it is harder to shade than south glass. Consider the use of landscaping to shade east and west exposures.
Do not worry about shading north-facing glass in the continental United States latitudes since it receives very little direct solar gain. In the tropics, disregard this rule-of-thumb since the north side of a building will receive more direct solar gain. Also, in the tropics consider shading the roof even if there are no skylights since the roof is a major source of transmitted solar gain into the building.
Remember that shading effects daylighting consider both simultaneously. For example, a light shelf bounces natural light deeply into a room through high windows while shading lower windows.
Do not expect interior shading devices such as Venetian blinds or vertical louvers to reduce cooling loads since the solar gain has already been admitted into the work space. However, these interior devices do offer glare control and can contribute to visual acuity and visual comfort in the work place.
Study sun angles. An understanding of sun angles is critical to various aspects of design including determining basic building orientation, selecting shading devices, and placing Building Integrated Photovoltaic (BIPV) panels or solar collectors.
Carefully consider the durability of shading devices. Over time, operable shading devices can require a considerable amount of maintenance and repair.
When relying on landscape elements for shading, be sure to consider the cost of landscape maintenance and upkeep on life-cycle cost.
Shading strategies that work well at one latitude, may be completely inappropriate for other sites at different latitudes. Be careful when applying shading ideas from one project to another.
Examples of side landscape features that help to conserve energy
For more information see: greenglobes.com
Curtain wall and a light shelf in a second-floor library space
Materials and Methods of Construction
In recent years, there has been a dramatic increase in the variety of shading devices and glazing available for use in buildings. A wide range of adjustable shading products is commercially available from canvas awnings to solar screens, roll-down blinds, shutters, and vertical louvers. While they often perform well, their practicality is limited by the need for manual or mechanical manipulation. Durability and maintenance issues are also a concern.
Require A&E professionals to fully specify all glass. They should be prepared to specify glass U-value, SC, and Tvis and net window U-value for all fenestration systems. The shading coefficient (SC) of a glazing indicates the amount of solar heat gain that is admitted into a building relative to a single-glazed reference glass. Thus, a lower shading coefficient means less solar heat gain. The visible transmittance (Tvis) of a glazing material indicates the percentage of the light available in the visible portion of the spectrum admitted into a building. See also WBDG Windows and Glazing.
When designing shading devices, carefully evaluate all operations and maintenance (O&M) and safety implications. In some locations, hazards such as nesting birds or earthquakes may reduce the viability of incorporating exterior shading devices in the design. The need to maintain and clean shading devices, particularly operable ones, must be factored into any life-cycle cost analysis of their use.
2.15 Applying Shading to a Solar Chart
Here, we are going to work through a problem of plotting critical points of shading onto an existing sun path diagram. Keep in mind that we will use the plots that you developed from the University of Oregon Solar Radiation Monitoring Laboratory in the "Try This" section on the previous page.
Here, I am using a program called Skitch to draw over the top of my PDF files. There is a 30-day free trial of the editing software if you would like to use it to digitally mark up your documents. Otherwise, I recommend that you print out your work, draw on the print directly with a pen, and then take a snapshot of the edited image with your phone or scanner to upload.
Quick review of the Charts:
First, we will go over the key features of the orthographic plots with the arcs of six days plotted out for the first half of the year.
All right, so, here we have a sun path diagram of State College, Pennsylvania. We've developed this in the University of Oregon's website for our local latitude and local longitude, time zone UTC minus 5 hours. That's Daylight Standard Time, not Daylight Savings Time. And I've done a little bit of modification to this to give it the green background. So, this is not something that normally you would see inside of your normal program.
But, I want to point out a few things. One is that we see that, as discussed before, the sun rises in the east. And the sun sets in the west, right?
So, we're going to have a progression of the sun across the day from left to right. In this particular case, we start out with east on the left, west on the right. South is denoted by 180 degrees, right?
And so, the thing that I wanted to point out here is that here we have December at the bottom and June 21 at the top. So, this December 21 is the winter solstice. June 21 is the summer solstice. And, in between, we have right about March 21 through the 23 is going to be one of the equinoxes. The other equinox, of course, is going to happen in September.
Only half of the year is shown. The arcs that you're seeing here are all the hours of the day interpreted as solar time. So, this is going to be 10 o'clock solar time. We're using a 24-hour system here. So, this is going to be 2 o'clock solar time, right?
And when I look at this, I see that I have two key points-- 90 degrees and 270 degrees. 90 degrees, of course, is going to be due east. And 270 degrees is due west, in this particular meteorological standard for the azimuth directions.
We see that on the left side, we have the altitude angle. That would be alpha. And we're counting down for the zenith angle, the complement to the altitude angle.
Let's go back to this east and west. So, when does east happen? East happens at due east, is 90 degrees. Due west is 270 degrees.
What's really important here is when does that happen? You see that there's an arc right along here for March 21. And that's really close to the equinox. So, during the equinox, we have the sun-- that's the only time of the year-- so, two times during the year when the sun rises due east and sets due west.
And if we count the hours, we have-- one, two, three, four, five, six-- exactly six hours in the morning-- one, two, three, four, five, six-- exactly six hours in the afternoon, so, a 12-hour day, our only 12-hour day that's going to happen. Otherwise, all of the rest of this time if we're looking at-- let's grab a color here. If we're looking at all of this time of the year from December to February and after March, so, before March is down here. After March is up here. So we're going to have short days, shorter than 12. And we're going to have longer than 12 hours up in the summertime.
Gives you a brief breakdown of what's happening on orthographic projection. This is for State College, of course. As we go further north, we're going to see that our sun charts are going to get lower to the ground.
If we were to choose a latitude location that is closer to the equator, we're going to have plots that start to look like this, actually. They're going to look really kind of funny because they're going to spread out up into the 90 degree space because once you're within the tropics, you're going to find that the sun can be to the north or to the south. It's not always in the south as it is when you're beyond the tropics. Anyway, I hope that's a helpful explanation and--
Second, we can compare the key features of the orthographic plots to the polar plots, again with the arcs of six days plotted out for the first half of the year. You should notice the similarities (East is on the left, solar time is represented, the same location is plotted), as well as the distinct differences (the June and December arcs are "flipped").
All right, and now we got the same location. Again, the location is going to be State College Pennsylvania. Solar time is going to be minus 5 hours, relative to UTC. And latitude longitude is the same.
Again, this is a polar plot of the same data that you just saw in the previous video. And the north of this plot is right down at the bottom. The south is up at the top. And I do this in this particular case, just to keep the arcs in the same general direction. But you're going to notice some differences here.
One is that the June arc is at the bottom. Whereas the December arc is at the top. So, this polar projection is what you would get if you were effectively lying on the ground and looking at the sky with a fisheye lens. And then trying to project that flat.
So, we see here that we've got the arcs of the day the morning begins over here. The evening ends over here, right in June time. And the progression of the day is going to be across the arc, again, from left to right, the same thing as we had before. Left to right in the winter months as well.
But here, you're really seeing the differences in the length of the day. It's probably a lot more apparent here that the length of the December 21st day is much shorter of an arc then the summer solstice on June 21st. Again, our arrows just pointing out, these green arcs are days. And the red lines are the hours of the day in solar time.
So that this top location here at 90 degrees, is going to be the top of the sky, the zenith. So, the zenith angle is basically any angle down from here to one of these circles. Whereas the altitude angle is going to be the angle up from the ground, which is going to be in our case the edge of the ring up.
So, we're going to see in a zenith angle going down or going outward, two rings. An altitude angle coming up or inward, basically coming along the edge of that skydome. And any one of these points of these green arcs are going to be a combination of an altitude angle and a azimuth angle.
And here, the azimuth angles are going to rotate from North which is zero degrees. North right here, is zero degrees. Rotating along to plus 30, plus 60, to finally when we're due east we are at 90 degrees. When we are due west, we're at 270 degrees. South in this case, is going to be 180 degrees. So, the azimuth rotates around clockwise and 180 degrees is in the meteorological standard going to the south.
Again, I want you to pay attention to the one day of the year when the sun rises due east and sets due west. And that's going to be around this, March 21st through the 23rd. It's kind of a flexible date depending on the year.
But it basically is defined as the day when within which the equinox occurs. And so, it's going to be one of the few days, or the only official day that you're going to have twelve hours of sunlight. So, we can count again one, two, three, four, five, six hours in the morning that's going to mirror to the six hours in the evening making it a 12 hour day.
And again, that means that we're going to have everything in the summer is going to be longer, whereas everything in the winter months is going to be shorter. And that's the flip that I'm talking about in the notes, that the arcs flip back and forth. So, long days are on the bottom, short days are on the top, or short days are towards the south.
This should make sense when we think about the fact that the sun is low in the sky, low in the sky is going to be closer to the outermost rings. The sun is low in the sky in the winter. The sun is high in the sky, especially around the noon hour, during the summer.
And you're seeing that right here, is that the closer I am to this center ring, the closer I am to right here. Which is 90 degrees, the higher in the sky that I am. And so, in the winter time, I'm close to the perimeter, which is close to zero degrees altitude angle. This up at the top is close to 90 degrees altitude angle.
How to integrate shading as an overlay
Now, we need to add an additional layer of information to the plot. I'm going to talk through the addition of critical points on the sun chart, followed by connecting those points and shading the areas correctly. In each of the following examples, we will use orthographic projections, but there is no reason why you couldn't use polar plots instead.
The first example will come from the textbook. We will be plotting shading relative to a single receiving point: X, with three critical points of shading (A, B, and C).
So now, we want to plot some critical points. And I'm going to go back to what you already encountered in the textbook in Chapter 7, applying the angles to shadows and tracking. So, let's focus on shadows. The first example that we've got here is the example of a wing wall, a wing wall being an extension out from the side of a building that might be blocking the sun. In the case that we've got in the textbook, we've got a wall that is to the west of the site.
And so, in our case, that means that on this plot, it's going to be a shadow that's going to be occurring on the west side in the afternoon sun. And we'd like to plot when is that shading going to happen on our central point, our point of interest, x. In this case, x was in the center of the building. So, we can imagine that this is a window that we wanted to understand-- or a central point in the window-- and we wanted to understand when is it being shaded versus not shaded.
And so, we did some basic trigonometry in the textbook to give us critical points between the central point, x, and three other shadowing critical points, A, B, and C. And those points are listed in the textbook. And so, what I'm going to do right now is just start plotting those out. And so, we had our points in that case listed as 0 being the south.
And so, when I had plus 54 degrees, what I was having is in addition of 54 degrees onto the original 180 degrees. And so, we're going to end up with some points at the bottom. And they're going to go up to our critical point of A, which was 0 degrees-- altitude angle-- 0 degrees altitude angle and 54 degrees to the west, to the afternoon azimuth angle.
And then point B was going to be a separate altitude angle upwards of 35 degrees. So, let's grow to approximately 35 degrees. We'll plot a second point right there. And our third point-- so, this was point XA. This point was point XB.
And now we're going to need a third point that's going to be point X relative to the critical point, C. And that was going to be 45 degrees up, so, we count up 45 degrees. And we're going to go up 45 degrees. And we need to go into the west in the azimuth 114 degrees. So, first, we had 100 degrees. And then, we're going to get about 114 degrees across to finally get our critical point, C.
So, if I want to connect these guys together, the first thing I know in an orthographic projection-- and I'm just telling you this-- is that it's a vertical drop down. So, lines connected together vertically will basically just have a vertical line down. The connection for the points here is going to be more like an arc. And so, we make sure that we have a nice arc tying these points together.
And I'm just going to extend continuously out towards the north. And then, I'm going to shade that data in under here. So, all of this region is going to be under shadows or our wing wall. So, we understand that in December, we get shading happening at about 4 o'clock in the afternoon. So, 4 o'clock solar time shading happens for the rest of the day.
On March 21, shading is going to happen at about 2:50. And by the time we get to the other extreme, the summer solstice of June 21, that time is going to be about 3:45. So, from 3:45 on to the end of the day, we're going to have shadowing occurring for this particular point, X in the problem.
And now, if I were to take that same plot and show you what we did inside the textbook, it's going to look just like this. So, it's something very much like what the textbook is just by plotting the points out and connecting those points together.
In the next example, we will look at setting up the problem to assess a PV array shading problem. Our intent is to plot shading relative to multiple receiving points: A, B, and C, with three critical points of shading (1, 2, and 3). The result is nine values for altitude coordinates ( α , no subscript) and nine values for azimuth coordinates ( γ , no subscript).
So, here we have the scenario of an array of photovoltaic that are set up one row behind the next. They're each going to have a certain tilt. That tilt is represented by beta and each one is going to have a common collector azimuth of gamma, represented down here. And that gamma again, is that plane or rotation. In this case, the array that you're seeing is rotated 9 degrees towards the east. So, minus 9 degrees of rotation or 9 minus 180 degrees to give us our azimuth.
The distance between the panels, right now it's just specified as D. And the panels themselves are going to have a shadow. And that shadow is going to change over the course of the year, as the sun is high in the sky, and low in the sky.
And what we'd really like is for these panels to be spaced appropriately. Such that, they do not block each other. Because this is one of our goals, one of our mechanisms for the goal of solar design. You want to maximize the solar utility for the client or stakeholders in a given locale. And in this locale, want to know how far apart we can space these to collect the energy to basically avoid, or remove shading from the spacing of these panels.
So, what you're seeing is a system that we're going to define in terms of critical points. We're going to take those critical points and we're going to plot them on a diagram. So, the first thing is, how do we list these critical points. Well, now, we don't have a central point X.
Now, we actually have three points for each one of the panels across the top and across the bottom. This guy is going to be behind here, you won't see it. But you're going to have three points along the bottom, three points along the top. The points along the top are ultimately going to shade these critical points along the bottom.
So, I'm going to name these critical points A, B, and C. And the points that we will be referring to in terms of what kind of shading are we expecting, we're going to label 1, 2, and 3.
So, now, going into this, you're looking at this from the side and you're seeing a system like this there's going to be a certain tilt beta. The beta is going to be the same from both collectors and they're going to be separated by a certain distance D. That's either going to be the spacing from top to top or from bottom to bottom, that's the same spacing with D.
So, looking at this, we want to basically compare any point 1. And what we really like to see is, how does 1 compare to point C, point C is down here. One to point C, 1 to point B, and 1 to point A. That's one of our first questions.
And then, after we've done that, we're going to look at how this point 2 compares to critical point C, critical point B, and A. And then, we'll finally finish that with 3 C, 3 B, and 3 A. And what we should be able to see is that because of similar geometries, we're going to find some kind of similar responses, in terms of all of these geometric relationships.
And I can show you that, again this is in the textbook, but if I bring this up right here, you're going to see that I've got a table of points 1.A, 2.A, 3.A, just like what we were talking about. And 1.B, 2.B, 3.B, 1.C, 2.C, 3.C. They each have their own set of altitude angles, and you're going to notice that there are certain 21 degree common altitude angles. Just due to common geometries. Similarly, you're going to see common 41 degree angles and two 12 degree angles.
Looking at the azimuth angles, the 0 degree azimuth corresponds to 180 degrees in the meteorological standard, and so on down. So, we're seeing that 76 degrees is equivalent to 250 degrees. And minus 64 degrees is equivalent to 116 degrees.
So, we're going to take these points this 180, 244, 256 for the azimuth angles of the collector. And we're going to plot those in the next block and we'll plot the alpha angles. And what we're going to come up with is basically something that looks like the cross section of a loaf of bread. It's going to have two vertical sides and it's going to have an arc in the middle.
You will notice how the horizontal surfaces of the building that create shadows are transposed to the projection as an arc, not as a horizontal line, while the vertical surfaces remain vertical. This has to do with the manner in which spherical data is distorted in an orthographic projection. Hence, the plot of a building shading a point on a window will look a lot like a slice of bread, flat on the sides with a soft curve across the top. The same will be found for this example, where the receiving points A, B, and C are shaded at different times by critical points 1, 2, and 3.
Now, we transition to plotting those points for the two rays onto our sun path chart. And so, here we have our sun path. It's again, I'm just using it for State College. You could use it for your location, in which case, the times at which you're actually going to be shadowing each other are going to be different.
So, if I go to my table from the textbook and I look at 1a, 2a, 3a-- I'm going to do those in blue first-- I'm going to get alpha values at, first, 180 degrees azimuth. And I'm going to go up 41 degrees for 1a. Then I'm going to go to 244 degrees azimuth, or 64 degrees from the convention in the book, up 21 degrees.
All right, 244 and 21. And I'm going to go down to 256. So, 256 is 76 degrees, and down to 12. So, somewhere right around here is where I'm looking at.
That plots the three points for 1a, 2a, and 3a. If I go over to 1b, 2b, 3b, I'm going to need to go to 116 degrees and then up 21 degrees. That's going to be for 1b. I'm going to need to go 180 degrees and up to 41 degrees, the same point as 2a. And then, my final point is going to be 21 degrees up and 244 degrees over.
So, again, we've got common overlap there. We're going to see this a couple of times. So, now, let's go to our last set of points. And that was going to be the 1c, 2c, and 3c. We're going to do those in green. And that's going to be 12 degrees up at 104.
So, that's probably going to be the mirror image of this point right over here, point 3a. And we're going to also look at 116 degrees 21 degrees up. That's an equivalent point, also.
And finally, our third point is going to be 180 degrees and 41 degrees up, which again, as we saw, is a common point for all of these. And so, when I connect these together, I'm going to go to my farthest point on each edge and drop a vertical line down. This is vertical, should be vertical. And then, I'm going to draw this loaf of bread arc between all of them.
It might not be pretty. In fact, I might do that one again. Let me just connect these points. Oops. Like this, back down. And then, finally, connect it together.
So, everything under this curve is going to be in shadow. And so, what we are seeing is that the months for this particular array, the way that it was designed, you're going to see that-- if I just look at the analysis of this-- you're going to see that even up to March in the winter months, definitely throughout the entire month of December, you're going to have the photovoltaic array shaded, which is not a good sign. And, again, into the afternoon of March, we're going to have shading.
So, we're going to see some distinct shading possibilities for this array, suggesting that when we actually want to develop this array, we'd want to space the array further apart. And to what degree would we want to space it further apart, we'd effectively want to look into how do we get this array spacing to be far enough apart so that the loaf of bread top fits underneath this area where it's not blocking any of the months in the hours of the day. And we can do that with effective design.
So, right now, as it's designed, the front array is going to shade the rear array. And that's going to create a problem. And we can count the number of hours that shading is occurring in that period. And we could enter that data into our system adviser model into SAM and then run the simulation to find out what the losses would be relative to no shading in that system. And we're going to do that in the next page.
Next, we will be interpreting our results, and inputting the shadow data into SAM.
Site Obstacle Survey
Not surprisingly, the sun must actually shine on a solar collector in order for it to collect useful energy. More surprisingly, some solar projects are built that never meet expectations because obstacles block the sun.
Even if you think you get good sun, do the survey. You may find some surprises (I did).
Path of Sun Across the Sky
Note: If you never liked "Science Time", you may want to skip the next few paragraphs, and go right to "Obstacle Survey".
The path of the sun across the sky changes with the time of year. This is why its important to do this obstacle survey, and not just stick your head out the window and see what the sun is shining on today.
At the two equinoxes, the sun rises due east and sets due west. At solar noon on the equinoxes, the altitude of the sun is 90 minus the local latitude. For example, if you live in Denver with a latitude of 40 degrees, the altitude of the sun at noon on the equinoxes will be 90 - 40 = 50 deg. The length of the day on the equinox everywhere on the earth is 12 hours. The spring equinox occurs on Mar 21, and the fall equinox on Sept 21.
The winter solstice is the shortest day of the year and occurs on Dec 21 in the northern hemisphere. On this day the sun will rise well to the south of east, and will set well to the south of west. The altitude of the sun at solar noon will be 23.5 degrees less than it was on the equinox -- or, 50 -23.5 = 26.5 degrees in our Denver example. This will be the lowest that the noon sun will be in the sky all year.
The summer solstice is the longest day of the year and occurs on June 21 in the northern hemisphere. On this day the sun will rise well to the north of east, and will set well to the north of west. The altitude of the sun at solar noon will be 23.5 degrees more than it was on the equinox -- or, 50 + 23.5 = 73.5 degrees in our Denver example. This will be the highest that the noon sun will be in the sky all year.
The 23.5 degrees referred to above is the tilt of the earth axis of rotation relative to the plane of the earths orbit. The summer solstice in the northern hemisphere occurs when the north pole is tilted toward the sun, and the winter solstice when the north pole is tilted away from the sun.
In planning a solar collector location, it is important to make sure that the sun will shine on the collector during all the parts of the year that you want it to. That's what the following site survey will tell you.
The horizon represents the terrain skyline around the selected location and it is generated from digital elevation model. The relevant shading of the modules throughout the year is calculated from this horizon. It is usually sufficient for PV systems, which are placed in the open landscape. However, typically in urban areas other objects (like high buildings, trees, etc.) may influence the real horizon on the particular location. Therefore the applications like pvPlanner or pvSpot support the manual adaptation of the horizon using interactive horizon editor.
Editing the horizon can be done in a pop-up window (example below):
- while editing, Undo and Redo functions can be used anytime
- tools for uploading and mastering background photos or horizon maps
- reset all changes and get the initial horizon
- text editor allows you to change the horizon by (re)typing the values
- sun-paths throughout the year (the upper and lower line represent sun paths during the solstice days, central line during the equinox days)
- actual horizon
- a) mouse cursor, b) position of the cursor on the sun path graph
- click Apply button to restart pvPlanner simulation with the alternated horizon or Cancel to leave the editor without applying any changes
The horizon can be modified by
- (re)typing the numeric values in the text editor (box 4) in format azimuth:elevation, where azimuth: 0 = North = 360, 90 = East, 180 = South, 270 = West
- (re)drawing a new horizon using the mouse or touchpad directly in the graph (click left mouse button down and hold → move the mouse → release mouse button → repeat the process to modify the horizon) the numbers in the text editor (box 4) are updated automatically according to the actual changes) the values of the actual cursor position in the bottom-left corner (Azimuth, Elevation, Horizon elevation) might be helpful for better navigation
If the horizon of your location is documented on photos, graphs or horizon maps, upload them (1) and resize and displace in the graph (2) as precisely as possible (see the example on the scheme below). If not, simple geometric estimation with goniometer can be used.
Then in the upper menu switch to Edit horizon mode and continue with modifying the horizon (3). The functions hide/show photos or undo, redo might be helpful during this process. When done (4), click Apply button and pvPlanner will start the simulation process with a new horizon. The results should be noted in PV conversion losses and performance ratio table in the line informing about shading losses.
HINTS with positioning the pictures correctly:
- if you try to take panorama photo(s) for this purpose by yourself, we recommend you to use the tripod with level bubble (or alternative device) and take the picture with the leveled camera
- some modern cameras save the azimuth and angle with the taken pictures check the meta information of such pictures
- many freeware or shareware software support the creation of panorama view from more pictures automatically or semi-automatically
- iMaps can help you to determine the azimuths. Find your location on the satellite map, identify few objects common with your panorama pictures (e.g. the corner of significant building, solitary tree, crossroads, etc.) and calculate the right azimuth between the object and your location. Alternatively use a compass to mark the main directions (East, South, West) when taking the pictures
- don't worry if you cannot reach a very high level of precision in the example presented above it is always more accurate to modify the default horizon with some data than do nothing small imprecisions are often acceptable
In order to extract data from pvPlanner without horizon shading, one just needs to set the horizon values to zero from the 'Horizon Editor' first. You can easily do that by deleting the values on the right side and typing the data pairs 0:0 and 359:0. Then click on apply (please see image below). Then download the new XLS or CSV files from the pvPlanner section 'report'.
This handy tool provides a relatively simple method of determining solar geometry variables for architectural design, such as designing shading devices or locating the position of the sun relative to a particular latitude and time. The Sun Angle Calculator is a quick and accurate tool and has been used extensively by educators, researchers, and design professionals for the past 50 years.
Solar Angle Calculator. This solar angle calculator tells you the optimum angle to get the best out of your system. To get the best out of your photovoltaic panels, you need to angle them towards the sun. The optimum angle varies throughout the year, depending on the seasons and your location and this calculator shows the difference in sun height on a month-by-month basis.
The Direction to the Sun vs the Position of the Sun
If we were to observe the direction to the Sun over the entire course of the day, on multiple locations on Earth’s surface, and then plot the results on the so-called flat-Earth map then they would not consistently point to the position of the Sun that is calculated from its location on such map.
This fact happens because the flat-Earth map is not the correct description of the real Earth.
These discrepancies are evident in sunrises and sunsets. The observed directions to the sun almost never point to the correct location of the Sun on the flat-Earth model.
Around solstices, we can see extreme cases of such discrepancies: the directions to the Sun, at some point, would point to the opposite from the location of the Sun according to such map.
The flat-Earth model fails to describe simple facts we encounter every day, like the position of the Sun. On the other hand, the globe model of the Earth is 100% consistent with observation.
Overhang for shading and sun. pretty neat calculator.
I've been toying with the amount of overhang that I'm going to shoot for and thought that some of you might enjoy checking this calculator that figures an "Overhang Annual Analysis ". This helps you determine the amount of overhang you need above your window for either shading the window at specific times or allowing sun to shine in at specific times. This graphs out the entire year focusing on the 15th of each month and for each hour of the day.
You'll need to input your latitude which can be found by using this google map app. Google Maps Latitude, Longitude Popup This starts in Europe so you'll have to drag back to the USA. Simple clicking on a location gives the exact longitude/latitude. With the satellite overlay you can easily get really close to your location.
The overhang calculator is pretty easy to use. You can click on each label and a description of that value is explained. It's a really neat application.
Using the calculator I'm going to shoot for southern windows that are 4' tall and 2' below the lowest part of a 2' overhang. This will give me complete shade from May to August, 24% shading in March, 41% in September, and less than 10% shading in October. From November through Februrary the southern windows will receive full sun.
I'm still toying with my west window. trying to figure out a compromise between cool shade in the hot south Alabama summer and getting some warm afternoon sun coming in in the winter.
How can I determine sun's altitude & azmiuth at a given time?
I would like to do some starbursts (or sunbursts) at, say, Turret Arch in Arches NP from the South Window in the late afternoon on September 10 and get the sun just "touching" Turret Arch and I'd like to know within a 30 minute window what time to be there. I realize I can walk around some to get the shot, but I don't want to wait several hours for the right time. I'd appreciate any suggestions and/or links or software so I can determine the altitude and azimuth of the sun. September 10 is only a reference and not the date I'll be there.
I have access to Google Earth, The Photographer's Ephemeris and Photo Sundial (a software program I got thru Rick Sammon).
If there's a better forum to ask this question, please tell me.
The photographer's ephemeris gives you the Azimuth and Elevation angle for any place on earth on any date at any time, give it a try.
I you have an iPhone, you might also want to try PhotoPills. It's similar to The Photographer's Ephemeris, but with some extra features.
Baring use of an astrolabe, there are free (and paid) apps for astronomy that give you the Sun's position (in addition to the planets and stars of course), and would permit you to know its position at any time and date from any location.
There are two sorts of people in this world those who can extrapolate from data
Thanks! I've used Photographer's Ephemeris before but only for sunrise/sunset info. The info I need is right there.
I'll try PhotoPills. I do have an iPhone.
Kent, I have been using this one fore many years. Be careful with time entry, day savings and such. This is a recently updated version, but should work fine:
I have used wunderground.com, a weather program with an astronomy link that tells you where the moon and planets and maybe galaxies are relative to where you are located.
See this link and put in your zip and time, etc.
Using Photographer's Ephemeris on my iPhone with the red pin on the Turret Arch, the date set to 9/10/16, and moving the time slider at the bottom so that the light yellow line looking into the sun lines up with the South Window at 4:45 pm MDT the altitude is about 32 degrees and at 5:15 pm the altitude is about 26 degrees which is kind of high since the Turret Arch is only 65 feet tall.
If you want the altitude at 10 degrees or less you will have to wait until after 6:30 pm and move about 250 feet to the south. Just guessing the shot that you want with the sunburst kissing the top of Turret Arch and framed by the South Window will not be 'celestially' possible. If you can give up the framing by the South Window you might still get a great shot if the weather cooperates. Sunset that day is 7:33 pm.
Looks like mid-October(16th) has the sun lining up the way I think you want: 5:45 pm altitude 9 degrees and lined up with the South Window over Turret Arch.
Another good iOS app is LightTrac, which I have used with satisfaction for several years.
Another good iOS app is LightTrac, which I have used with satisfaction for several years.
Another vote here for LightTrac. I have three iOS apps for tracking the sun and moon -- LightTrac, The Photographer's Ephemeris, and PhotoPills --- and LightTrac is my go-to most of the time. It's the easiest to use, and it gives me what I need about 90% of the time. When I need elevation information or augmented reality or I am dealing with a really tricky situation, I turn to PhotoPills. The Photographer's Ephemeris is always the odd one out for me, although a lot of people swear by it.