# How do I calculate the sun's azimuth based on zenith, hour angle, declination, and latitude?

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Wikipedia cites this formula for calculating solar azimuth:

Where:

• $$phi_s$$ is the solar azimuth angle
• $$heta_s$$ is the solar zenith angle
• $$h$$ is the hour angle, in the local solar time
• $$delta$$ is the current sun declination
• $$Phi$$ is the local latitude

I'm implementing this equation in JavaScript, but it doesn't seem correct. Can someone here help me confirm whether or not this equation is correct?

Here's my JS implementation. The only strange thing is at the end: limiting the acos domain to [-1, 1] to prevent NaN values.

const getSolarAzimuth = function( zenithAngle, hourAngle, declination, latitude ) { const cos = Math.cos; const sin = Math.sin; const cos_phi = ( sin(declination) * cos(latitude) - cos(hourAngle) * cos(declination) * sin(latitude)) / sin(zenithAngle); return Math.acos(Math.min(Math.max(cos_phi, -1), 1)); };

I've confirmed that this formula is in fact correct. I did have the wrong units in the code, which @Glorfindel suggested: sun's hour angle was in hours instead of radians.

I did need to adjust the azimuth's angle offset based on the hour angle:

// The angle offset needs to be adjusted based on whether the hour angle // is in the morning or the evening. // https://en.wikipedia.org/wiki/Solar_azimuth_angle#Formulas if (hourAngle < 0 || hourAngle > Math.PI) { return az; } return (Math.PI * 2) - az;

## Solar azimuth angle

The solar azimuth angle is the azimuth angle of the Sun's position. [1] [2] [3] This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent altitude.

There are several conventions for the solar azimuth however, it is traditionally defined as the angle between a line due south and the shadow cast by a vertical rod on Earth. This convention states the angle is positive if the shadow is east of south and negative if it is west of south. [1] [2] For example, due east would be 90° and due west would be -90°. Another convention is the reverse it also has the origin at due south, but measures angles clockwise, so that due east is now negative and west now positive. [3]

However, despite tradition, the most commonly accepted convention for analyzing solar irradiation, e.g. for solar energy applications, is clockwise from due north, so east is 90°, south is 180°, and west is 270°. This is the definition used by NREL in their solar position calculators [4] and is also the convention used in the formulas presented here. However, Landsat photos and other USGS products, while also defining azimuthal angles relative to due north, take counterclockwise angles as negative. [5]

### 2.3.5 Hour angle

The hour angle is one of the coordinates used in the equatorial coordinate system to give the position of a point on the celestial sphere. The hour angle of a point is the angle between two planes: one containing the earth’s axis and the zenith (the meridian plane), and the other containing the earth’s axis and the given point. The angle is negative east of the meridian plane and positive west of the meridian plane or it can be positive westward zero to 360 degrees. The angle may be measured in degrees or in time, with 24 hours equalling 360 degrees exactly. The hour angle is paired with the declination to fully specify the position of a point on the celestial sphere. The hour angle (HA) of an object is equal to the difference between the current local sidereal time (LST) and the right ascension (α) of that object:

Thus, the object’s hour angle indicates how much sidereal time has passed since the object was on the local meridian. It is also the angular distance between the object and the meridian, measured in sidereal hours (1 hour = 15 degrees). For example, if an object has an hour angle of 2.5 hours, it crossed the local meridian 2.5 sidereal hours ago (i.e. hours measured using sidereal time), and is currently 37.5 degrees west of the meridian. Negative hour angles indicate the time until the next transit across the local meridian. Of course, an hour angle of zero means the object is currently on the local meridian.

## Calculating Azimuth And Altitude At The Assumed Position By Spherical Trigonometry.

There are several ways of calculating the azimuth and altitude at the assumed position these include the use of sight reduction methods and software solutions. However, the traditional method is by the use of spherical trigonometry which is demonstrated below.

PZ is the angular distance from the Celestial North Pole to the zenith of the observer and is equal to 90 o – Lat.

PX is the angular distance from the Celestial North Pole to the celestial body and is equal to 90 o – Dec.

ZX is the Zenith Distance and is equal to 90 o – altitude.

Therefore, altitude is equal to 90 o – ZX

The angle ZPX is equal to the Local Hour Angle of the Celestial Body with respect to the observer’s meridian.

The angle PZX is the azimuth of the body with respect to the observer’s meridian.

In order to calculate the azimuth and altitude of a celestial body we must solve the triangle PZX in the diagram above. Specifically, we must calculate the angular distance of side ZX so that we can find the altitude and we must calculate the angle PZX so that we can find the azimuth.

However, because the triangle PZX is on the surface of an imaginary sphere, we cannot solve this triangle by the use of ‘straight line trigonometry’ instead we must resort to the use of ‘spherical trigonometry’ which is explained here.

Examples of the use of spherical trigonometry to calculate the azimuth and altitude of celestial bodies.

Note. Traditionally, the ‘half-haversine’ formula was used for this task but this formula does not lend itself well to solution by electronic calulator therefore, the following solutions involve the cosine formula.

The sign convention is typically that the observer latitude ϕ is 0 at the equator, positive for the Northern Hemisphere and negative for the Southern Hemisphere, and the solar declination δ is 0 at the vernal and autumnal equinoxes when the sun is exactly above the equator, positive during the Northern Hemisphere summer and negative during the Northern Hemisphere winter.

### Hemispheric relation Edit

The equation above neglects the influence of atmospheric refraction (which lifts the solar disc — i.e. makes the solar disc appear higher in the sky — by approximately 0.6° when it is on the horizon) and the non-zero angle subtended by the solar disc — i.e. the apparent diameter of the sun — (about 0.5°). The times of the rising and the setting of the upper solar limb as given in astronomical almanacs correct for this by using the more general equation

with the altitude (a) of the center of the solar disc set to about −0.83° (or −50 arcminutes).

The generalized equation relies on a number of other variables which need to be calculated before it can itself be calculated. These equations have the solar-earth constants substituted with angular constants expressed in degrees.

### Calculate current Julian day Edit

n is the number of days since Jan 1st, 2000 12:00. J d a t e > is the Julian date 2451545.0 is the equivalent Julian year of Julian days for Jan-01-2000, 12:00:00. 0.0008 is the fractional Julian Day for leap seconds and terrestrial time. TT was set to 32.184 sec lagging TAI on 1 January 1958. By 1972, when the leap second was introduced, 10 sec were added. By 1 January 2017, 27 more seconds were added coming to a total of 69.184 sec. 0.0008=69.184 / 86400 without DUT1. The ⌈ ⋅ ⌉ operation rounds up to the next integer day number n.

### Solar mean anomaly Edit

M is the solar mean anomaly used in the next three equations.

### Equation of the center Edit

C is the Equation of the center value needed to calculate lambda (see next equation). 1.9148 is the coefficient of the Equation of the Center for the planet the observer is on (in this case, Earth)

### Solar transit Edit

Jtransit is the Julian date for the local true solar transit (or solar noon). 2451545.0 is noon of the equivalent Julian year reference. 0.0053 sin ⁡ M − 0.0069 sin ⁡ ( 2 λ ) is a simplified version of the equation of time. The coefficients are fractional days.

### Declination of the Sun Edit

δ is the declination of the sun. 23.44° is Earth's maximum axial tilt toward the sun [1]

### Hour angle Edit

This is the equation from above with corrections for atmospherical refraction and solar disc diameter.

### Calculate sunrise and sunset Edit

Jrise is the actual Julian date of sunrise Jset is the actual Julian date of sunset.

## Azimuth angle formula

Formulas. The following formulas assume the north-clockwise convention. The solar azimuth angle can be calculated to a good approximation with the following formula, however angles should be interpreted with care because the inverse sine, i.e. x = sin −1 y or x = arcsin y, has multiple solutions, only one of which will be correct. ⁡ = − ⁡ ⁡ ⁡ An azimuth is a special kind of geometric angle used chiefly in land navigation. It is the angle between the vertical (north or 0°) and the line between the starting point and the desired end point. No special azimuth formula is needed, just a map, protractor, pencil and your start and end points The azimuth angle varies throughout the day as shown in the animation below. At the equinoxes, the sun rises directly east and sets directly west regardless of the latitude, thus making the azimuth angles 90° at sunrise and 270° at sunset Solar Azimuth Angle - Formulas Formulas It can be calculated to a good approximation with the following formula, however angles should be interpreted with care due to the inverse sine, i.e. x = sin−1(y) has two solutions (unless y is -1 or +1), only one of which will be correct

Using a combination of trigonometry functions and vector dot products, the calculator determines the azimuth angle and altitude angles. It uses the Pythagorean formula to determine the straight. The angle PZX is the azimuth of the body with respect to the observer's meridian. Summary. PX = 90 o - Dec. PZ = 90 o - Lat. ZX = 90 o - Alt. Alt = 90 o - ZX <PZX = Azimuth. <ZPX = Hour angle. In order to calculate the azimuth and altitude of a celestial body we must solve the triangle PZX in the diagram above Azimut (engelska: azimuth) är i ett horisontellt koordinatsystem vinkeln mellan vertikalplanet genom himmelsobjektet eller satelliten (höjdcirkeln) och observatörens meridian, det vill säga den ena koordinaten för en himlakropp i horisontens system. [1] Azimuten betecknas α.. Azimuten mäts numera i astronomiska sammanhang vanligen från horisontens nordpunkt mot öster (medurs sett. The side c is equal to the difference in longitude, Δλ the side b is equal to the difference in latitude, Δφ the angle A is 90º, so sin A = 1 and cos A = 0. To determine X, we want the value of B given b, c and A. Looking at the problem from first principles, we need the two main spherical trigonometry equations: The Sine Formula

### Solar azimuth angle - Wikipedi

1. Now consider a second geodesic of length s12 starting at A with azimuth alpha1 + dalpha1. The second end of this geodesic is separated from B by a distance m12 * dalpha1 where m12 is the reduced length. On a plane, m12 = s12. For a sphere of radius R, m12 = R * sin(s12/R). For an ellipsoid, Helmert gives a formula. - cffk Jan 1 '14 at 12:2
2. Azimuth Angle: The horizontal orientation of your panels (in relation to the equator, in this case). Solar panels work best when they face directly into the sun. But that task is complicated by the fact that the sun moves across the sky throughout the day
3. Solar altitude angle (h): the angle between the horizontal and the line to the Sun (0° ≤ h ≤ 90°).The complement of this angle is the zenith angle (θ z), that is defined by the vertical and the line to the Sun (i.e., the angle of incidence of beam radiation on a horizontal surface).Solar azimuth angle (A): angular displacement from south of the projection of beam radiation on the.
4. Azimuth and Elevation are measures used to identify the position of a satellite flying overhead. Azimuth tells you what direction to face and Elevation tells you how high up in the sky to look. Both are measured in degrees. Azimuth varies from 0° to 360°. It starts with North at 0°
5. Watch more Intermediate Math Skills videos: http://www.howcast.com/videos/259995-How-to-Calculate-AzimuthYes, it's spherical trigonometry - but it's not rock..
6. The angle of incidence (θ i) of the Sun on a surface tilted at an angle from the horizontal (β) and with any surface azimuth angle (A ZS) (figure 3.2) can be calculated from (when A ZS is measured clockwise from north): (3.11) This horrible equation can be simplified in a number of instances

Angle Measurement and Azimuth Calculations Azimuth Computation (Section 7.9) (don't worry about bearing calcs in 7.10) For a closed polygon we often wish to determine the azimuths of line from the interior angles. Once we verify the sum of the interior angles = 180(n-2), we start from a known azimuth and proceed in a clockwise o I've confirmed that this formula is in fact correct. I did have the wrong units in the code, which @Glorfindel suggested: sun's hour angle was in hours instead of radians. I did need to adjust the azimuth's angle offset based on the hour angle I am confused as to which formula I should use to calculate the angle of incidence for a tilted surface. I have 2 possibilities but I don't know if they will end up calculating the same angle Solar azimuth angle (γ s): The solar azimuth angle (γ s) is the angular displacement from south of the projection of beam radiation on the horizontal plane.Displacements east of south are negative and west of south are positive the solar azimuth angle changes in the range of −180 to 180 degrees

### How to Calculate Azimuth Sciencin

Azimuth is simply the angle of an object in the sky along the horizon. Yes, it's spherical trigonometry but it's not difficult! Check out this video and in just a few minutes you will be able to solve azimuth problems on your own. You Will Need A small development of the article Azimuth and solar elevation angle.. Inspired by the calculator request /3004/: There is an excellent, in my understanding, calculator that helps to calculate sun azimuth for each point on the globe and its angle to the horizon at a given time. A calculator able to show time when the sun is at given point would be a great addition If latitude is 55 o N, LHA is 145 o and azimuth angle is 120 o then true azimuth is 360 o - Z i.e. 360 o - 120 o = 240 o. If latitude is 25 o S, LHA is 245 o, and azimuth angle is 075 o then true azimuth is 180 o - Z i.e. 180 o - 075 o = 105 o. Where to buy books of the Astro Navigation Demystified series: Astro Navigation Demystified. Relative to the diagram of the which angles are given in the table, the Azimuth and Elevation angles do not make any sense. How can the midday sun be only on a bearing (Azimuth) between 39 and 67 degrees? I could understand these angles if they are given from the East axis If you want to find Azimuth by a given Coordinates just watch this Video. Khaled Al Najjar , Pen&Paper لاستفساراتكم واقتراحاتكم : Email: [email protected]

4.1) Basic Concepts: In Figure 3, it can be seen that the azimuth of the star equals the azimuth of the line plus the horizontal angle. Thus the azimuth of the line equals the azimuth of the star minus the measured horizontal angle, or in equation form is: where Azline is the azimuth of the line at the time the azimuth of the star is determined Azimuth: Solar Elevation: cosine of solar zenith angle: Azimuth is measured in degrees clockwise from north. Elevation is measured in degrees up from the horizon. Az & El both report dark after astronomical twilight Calculate the azimuth and elevation angle to a geostationary satellite One (1st edition) reader provided an alternate distance formula that is better for small angles. I'm not sure who first proposed using this formula, but it seems to work well. dlon = lon2 - lon The azimuth angle Az of the Sun or a celestial body (St) is depending on it's declination Dec and altitude Alt, and on the latitude Lat of the observer (Astronomical/Nautical Triangle): At sunrise (Alt=0°) the formula is more simple Formula to Find Bearing or Heading angle between two points: Latitude Longitude. Bearing can be defined as direction or an angle, between the north-south line of earth or meridian and the line connecting the target and the reference point. While Heading is an angle or direction where you are currently navigating in. This means to reach a particular destination you need to adjust your heading.

The formula from spherical trigonometry for the azimuth angle between two peaks is, for starting points other than the poles: x = acos( / ) IF sin(lon2-lon1) < 0, phi = x IF sin(lon2-lon1) > 0, phi = 2*pi - x See another excellent webpage: Aviation Formulary V1.24 By using the Azimuth Calculator, you get both the angle you need to point your compass to along with the distance between your starting point and your final point. How to Use the Azimuth Calculator The Azimuth Calculator is an incredibly simple tool you can use to determine the azimuth between two specific points on earth There's quite a lot of the necessary spherical trigonometry in the answer to SO 389211.Copying and modifying what I wrote there: Consider a sperical triangle with angles A, B, C at the vertices and sides a, b, c opposite those vertices (that is, side a is from B to C, etc.).Applying this to the problem, we can call the two points given B and C, and we create a right spherical triangle with a. . G is the difference between position of satellite orbit and earth station antenna. The following figure illustrates the azimuth angle

Azimuth is a polar angle in the x-y plane, with positive angles indicating counterclockwise rotation of the viewpoint. Elevation is the angle above (positive angle) or below (negative angle) the x-y plane. This diagram illustrates the coordinate system Azimuth and elevation refer to the satellite TV dish pointing angles. Elevation. Elevation refers to the angle between the beam pointing direction, directly towards the satellite, and the local horizontal plane. It is the up-down angle. When your dish is pointed low down near the horizon the elevation angle is only a few degrees Here is the C# solution. Tested for 0, 45, 90, 135, 180, 225, 270 and 315 angles. Edit I replaced my previous ugly solution, by the C# translation of Wouter's solution:. public double GetAzimuth(LatLng destination) < var longitudinalDifference = destination.Lng - this.Lng var latitudinalDifference = destination.Lat - this.Lat var azimuth = (Math.PI * .5d) - Math.Atan(latitudinalDifference. Re: Convert Angle (Azimuth) to Bearing format. Thank you sir JohnTopley. But there's just a little problem, the reference line of your vba formula is from the positive x axis, I would like to have been referred it to the negative Y axis (south) so 225 degrees will result to N 45° 30' E

Azimuth Airline gives you the opportunity to take the flight at affordable prices. Journey in the Sukhoi Superjet 100 airplane integrating the best solutions of modern aircraft construction will allow feeling the advantage of comfortable cabins which are highly competitive with the cabins of high capacity long-haul airplanes .85701421 p1 -> MP: -2.90404662 So the absolute difference between these two azimuths should be the angle you are looking for, 103.76106083. And again, this is the angle between MP and p2 as viewed from p1 Calculate the azimuth and elevation angle to a geostationary satellite One (1st edition) reader provided an alternate distance formula that is better for small angles. I'm not sure who first proposed using this formula, but it seems to work well. dlon = lon2 - lon To help you better understand how the azimuth is represented on PhotoPills, I've drawn North and azimuth angle of the sun for two different moments on the following screenshots. The first one is telling you that on February 11th 2014 at 10:17am the sun was at azimuth 136.5º and the second one that on February 11th 2014 at 3:01pm the sun was at azimuth 214.6º

formula azimuth cotg azimuth = ( cotg ( 90-decllination) * cos latitude * cosec polar angle ) - (sine latitude * cotg polar angle ) Celestial Navigation - exercises boo The azimuth angle is measured clockwise from the zero azimuth. For example, if you're in the Northern Hemisphere and the zero azimuth is set to South, the azimuth angle value will be negative before solar noon, and positive after solar noon. The azimuth angle is calculated as follows: cos (Az) = (sin (Al) * sin (L) - sin (D)) / (cos (Al) * cos (L) . I am confused as to which formula I should use to calculate the angle of incidence for a tilted surface The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between -180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane Thank you for watching the video. If you are trying to prepare yourself for the NCEES FE or PE Exam, I have created this video to help you pass your exam and ta..

### Azimuth Angle PVEducatio

1. This angle, also called the local sidereal time is a measure of time that depends on the stars, and not on the sun and that is why it is a bit touchy to can be calculated using the formula: θg(τ) = θg(0h) + ωe·Δτ (1) The elevation and the azimuth are very important to know as well in order to analyse the satellite link,.
2. // Calculates the local solar azimuth and elevation angles, and // the distance to and angle subtended by the Sun, at a specific // location and time using approximate formulas in The Astronomical // Almanac. Accuracy of angles is 0.01 deg or better (the angular // width of the Sun is about 0.5 deg, so 0.01 deg is more tha
3. Azimuth and Elevation Calculations. The azimuth and elevation angles for our earth station antenna must be calculated so that the correct satellite can be seen. The azimuth is the horizontal pointing angle of the earth station antenna. The elevation is the angle we look up into the sky to see the satellite
4. Angles are approximate values and should not be used to launch new satellites (or in other orbital operations), but are sufficient to setup a satellite dish to see some more TV channels. List of satellites and formulas from Wikipedi
5. angle between the sun and the local horizon directly be-neath the sun. The solar azimuth angle (Φs) is the angle formed between the current east/west position of the sun from true south, where true south is used as the ref-erence in the northern hemisphere and has a 0° relative angle. A positive azimuth angle is before solar noon an
6. Azimuth = Horizontal angular distance from true north measured clockwise from true north (east = 90 degrees, south = 180 degrees, west = 270 degrees, north = 0 degrees) Elevation angle = Number of degrees the beam is transmitted above the horizon. 0 degrees is parallel to horizon while 90 degrees is straight u

DETERMINATION OF LOOK ANGLES TO GEOSTATIONARY COMMUNICATION SATELLITES By Tom,is Soler, 1 Member, ASCE, and David W. Eisemann-' ABSTRACT: Basic geodetic theory is applied to determine the azimuth and geodetic altitude required to point dish antennas to geostationary communi The hillshade formula requires this angle to be in units of radians. First, the azimuth angle is changed from its geographic unit (compass direction) to a mathematic unit (right angle). Next, the azimuth angle is converted to radians. Change azimuth angle measure: (4) Azimuth_math = 360.0 - Azimuth + 90. Note that if Azimuth_math >= 360.0, then The second ideal azimuth angle was found to be at +17°, where the PV system generated yearly energy production in the range of 2443-2436 kWh. The minimum energy production was observed in PV systems installed at an azimuth angle of -87°, with an average annual energy production in the range of 2021-2019 kWh. Conflict of interest statement I tried to solve the formula as your directing also I have got a wrrong results if you can solve it and inform me i will be greatfull because i am trying to find the shortest way to calculate the azimuth and elevation with out using the programes on the internet because most of the installers do not have internet on the field and we can help each other in solving many problems so if you can.

### Solar Azimuth Angle - Formulas

1. e there is a missing element, and I have not been able to complete it so as to give a formula equivalent to
2. Representing the direction of a line with bearings is a long-standing tradition that continues today on plats, legal descriptions, site plans, and other documents. Calculating the direction of a line by using bearings is also a longstanding tradition. However, some surveyors have realized that calculating the direction of a line is much easier when using azimuths and then converting the.
3. e the arcsine of the result, which will give you the azimuth angle. FACT: The distance between Earth and our moon is, on average, 238,900 miles
4. The symmetrical formula for solar elevation at noon for points in the Southern hemisphere is given by: α = 90° + ( ϕ A knowledge of the angle of solar elevation, α, and the azimuth, Α, allows us to calculate the length and the location of a simple shadow
5. Definition azimuth angle: The azimuth is counted starting from the north on the east, so that a star in the north has an azimuth of 0 °, a star in the east has an azimuth of 90 °. Definition zenith angle: The Zenith is starting to be counted from the horizontal to the perpendicular. If the sun is directly above the observer, the zenith has an.
6. COMPARISON OF AZIMUTH AND BEARING Because bearings and azimuths are encountered in so many surveying operations, there is important to know the conversion of these two. Example 1 The azimuth of a boundary line is 128° 13' 46. onvert this into bearing. The azimuth places the line in the southeast quadrant. Thus the bearing angle is
7. The following formulas assume the north-clockwise convention. The solar azimuth angle can be calculated to a good approximation with the following formula, however angles should be interpreted with care because the inverse sine, i.e. x = sin −1 y or x = arcsin y, has multiple solutions, only one of which will be correct

where [[theta].sub.s] is the squint angle of the monopulse beam, [[theta].sub.el] and [[theta].sub.az] are the differences of elevation angles and azimuth angles between the tracking axis and target, respectively, and [[theta].sub.A] is the angle difference between the beam maximum of quadrant 1 and target Here it is the page of satellite ground station look angles calculator look angle calculator i.E azimuth and elevation angles calculator

### Calculating Azimuth, Distance, and Altitude from a Pair of

Calculates a table of changes in the solar elevation and azimuth angles for a day and draws the chart. Input negative degree for west longtitude and south latitude. If your local time is on Daylight Saving time, select 'ON' from DST mode Excel Formula for determining azimuth relative to true north between two sets of geographic coordinates? Using the geographic coordinates for each, I've translated the FCC procedure for determining the distance between two transmitters ( per FCC 73.208) into Excel formulas azimuth definition: 1. the position of an object in the sky, expressed as an angle related to a distance on the horizon. Learn more

This MATLAB function computes the elevation angle, slant range, and azimuth angle of point 2 (with geodetic coordinates lat2, lon2, and alt2) as viewed from point 1 (with geodetic coordinates lat1, lon1, and alt1) The azimuth of a line is defined as the horizontal angle, measured clockwise, from a base direction to the given line. They are usually measured from the north and vary from 0° to 360° and so they do not require letters to categorize their quadrant Your grid azimuth is 199 degrees. 4. The G-M angle depends on where you are in the world. 5. Convert azimuths when given an easterly G-M angle (figure C-32). Figure C-32. Converting azimuths with easterly G-M angle. a. To convert a magnetic azimuth to a grid azimuth, add the value of the G-M angle to the magnetic azimuth. b. To convert a grid. Illustration 2: The altitude is the angle an object makes with the horizon. ©timeanddate.com. Altitude and Azimuth. Just as the geographic coordinate system uses latitude and longitude to define any location on Earth, the horizontal coordinate system provides altitude and azimuth angles to locate objects in the sky

### Tilt & Azimuth Angle: Find the Optimal Angle to Mount Your

In an azimuth thruster the propeller rotates 360° around the vertical axis so the unit provides propulsion, steering and positioning thrust for superior manoeuvrability. Designs have been developed for propulsion and dynamic positioning in response to market requirements. As a result there is a design available to suit virtually any application The terminal coordinates program may be used to find the coordinates on the Earth at some distance, given an azimuth and the starting coordinates. The shortest distance between two points on the surface of a sphere is an arc, not a line. (Try this with a string on a globe.) In addition, the azimuth looking from Point B to Point A will not be the converse (90 degrees minus th Descrizione. L'azimut è la coordinata orizzontale angolare espressa dall'arco d'ortodromia della sfera celeste che si forma partendo convenzionalmente dal punto cardinale nord fino all'oggetto di osservazione, muovendosi in senso orario verso est, quindi a sud e a ovest, fino a tornare al punto di inizio a nord (cioè un angolo giro, 360° sessagesimali) la coordinata azimutale quindi.

### Solar Azimuth Angle - an overview ScienceDirect Topic

• An Azimuth is a clockwise (Angle increases to the right) angle, either from North or South and always has a value between 0° to 360°. These formulas assume azimuths are measured from North. Bearings are directions broken down into the 4 quadrants northeast, southeast, southwest, and northwest
• the azimuth and elevation angle are: coordinates of the observer + coordinates of the object that is observed, both in a geocentric system. For your information, below I appended a fortran subroutine to compute the azimuth and zenith angles given the observer coordinates (here called station coordinates) and the object coordinates. >
• The angles of the triangle: The angle at P is H, the local Hour Angle of X. The angle at Z is 360°-A, where A is the azimuth of X. The angle at X is q, the parallactic angle. We assume we know the observer's latitude φ and the Local Sidereal Time LST. (LST may be obtained, if necessary, from Greenwich Sidereal Time and observer's longitude.
• Calculation of azimuth and elevation of the sun above the horizon for a given position and time. Table with one hour increments. person_outline Timur schedule 2015-10-27 21:16:2
• Altitude and azimuth, in astronomy, gunnery, navigation, and other fields, two coordinates describing the position of an object above the Earth.Altitude in this sense is expressed as angular elevation (up to 90°) above the horizon. Azimuth is the number of degrees clockwise from due north (usually) to the object's vertical circle (i.e., a great circle through the object and the zenith)

The hour angle, H, is the azimuth angle of the sun's rays caused by the earth's rotation, and H can be computed from [4] 4 min/deg ( . , ) −720 mins = No of minutes past midnight AST H (6) The hour angle as defined here is negative in the morning and positive in the afternoon (H = 0° at noon) Azimuth and altitude. are usually used together to give the direction of an object in the topocentric coordinate system. Sometimes, south is used as the starting point for azimuth angles instead of north, but on the Heavens-Above web site, north is always the origin Sun and Moon Azimuth & Elevation. Search Gazetteer for Location. Place Name: * Place Type: All State/Authority: All Clear Search. Search for Events by Location. Name of Location: Located in Australia? * Yes No

### What are the azimuth and elevation of a satellite

• optimum azimuth angle, the tilt was kept constant at latitude and only the azimuth was varied until the maximum possible annual energy yield was obtained. This was repeated for all the points indicated in the map shown in Fig. 2. Once the optimum azimuth angles were obtained, the process was repeated to find the optimum tilt angles. Using the.
• This calculator is designed to give the approximate satellite communications angle for your ground antenna. If you wish to establish communications with a given satellite, then you can obtain the azimuth and elevation for that satellite, based on your Earth location. Enter the geosat orbit location in degrees in the Satellite Longitude field
• The azimuth is angle is referenced from north, and is positive clockwise: North = 0 East = π/2 South = π West = 3π/2. For the geography type, the forward azimuth is solved as part of the inverse geodesic problem. The azimuth is mathematical concept defined as the angle between a reference plane and a point, with angular units in radians
• Average Angle Method assumes one straight line defined by averaging inclination and azimuth at both survey stations, intersects both upper and lower survey stations. Radius of Curvature Method assumes that well path is not a straight line but a circular arc tangential to inclination and azimuth at each survey station

Define azimuth. azimuth synonyms, azimuth pronunciation, azimuth translation, English dictionary definition of azimuth. n. 1. azimuth - the azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridian. AZ The solar azimuth angle is the azimuth angle of the Sun's position. This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent altitude Demo code to compute + visualize solar zenith angle and solar azimuth angle in Python - solarzenithazimuthdemo.py. Skip to content. All gists Back to GitHub Sign in Sign up Sign in Sign up << message >> Instantly share code, notes, and snippets. anttilipp / solarzenithazimuthdemo.py. Last active Apr 18, 2020

### How to Calculate Azimuth - YouTub

• utes of arc
• The azimuth will be a true zenith, grid azimuth, magnetic azimuth, or relative azimuth, depending upon which reference datum is used. ii. The arc of the observer's rational horizon or the angle at his zenith contained between the observer's celestial meridian and the vertical circle through that body
• Solar zenith angle The solar zenith angle z is a function of time, day number and latitude. It can be calculated using the relation: in which is the declination of the sun, the latitude (defined as positive in the northern hemisphere) and the hour angle.The latter is a measure of the local time, i.e. it is defined as the angle through which the earth must turn to bring the meridian of the.
• Note that the azimuth and parallactic angle rates must be continuously variable from zero to the maximum rate in order to track a source across the sky. Formulas. Figure 1 shows the relation between the various angles in the equatorial and horizon systems. The symbols are defined as follows: S = the source position, NP = the celestial north pole

### Part 3: Calculating Solar Angles ITAC

• Angle-1 is measured relative to the pole axis. A complete circle of Angle-1 will go through each pole. The other angle (Angle-2) moves around the pole. The size of the circle for Angle-2 is a function of Angle-1. Figure 2 shows the angles for each coordinate system. Table 2 shows the relationship between Angle-1 and Angle-2 fo
• The azimuth is usually specified in degrees with respect to the geographic or magnetic north pole. See: directional drilling, inclination, survey. 3. n. [Reservoir Characterization] The angle that characterizes a direction or vector relative to a reference direction (usually True North) on a horizontal.
• The azimuth is the horizontal angle from true north in a clockwise direction , or bearing of the satellite from the antenna . Obviously, the azimuth of the antenna must match the azimuth of the satellite, or it will not acquire the satellite. This satellite azimuth depends only on the satellite longitude and the position of vessel
• the former being Cosine(Azimuth) = -tan(latitude)*tan(solar height angle) The latter being Cosine(hour angle) = -tan(latitude)*tan(declination angle) Now one way to intuitively think of why the similarity, is I think (correct me if I'm wrong), finding the Azimuth compass angle is conceptually similar to 1) if you were to lie down sideways 2) see half of the viewing sky and not the other half.

Azimuth-Altitude Dual Axis Solar Tracker . December 16, 2010 . A Master Qualifying Project: submitted to the faculty of . The angle of the sunlight to the normal is the angle of incidence (θ). Assuming the sunlight is staying at a constant intensity (λ) the availabl angles and distances used The radar needs 3 pieces of information to determine the location of a target. The first piece of information is the angle of the radar beam with respect to north called the azimuth angle

### How do I calculate the sun's azimuth based on zenith, hour

GEOSAT LOOK ANGLE CHARTS. The above formula can be used to plot look angle charts. These show both azimuth and elevation angles as a function of observer latitude and longitudinal difference from the satellite. The chart below is the one to use at mid-latitudes. The azimuth contours are shown in white or red and are plotted every 2 degrees Azimuth has been born from the merger of Astroturista and Ciencialia, two successful pioneering Granada companies in providing touristic stargazing activities and promoting science education in eastern Andalusia.. We provide our customers with quality astronomy tourism and educational activities which while keeping scientific precision bringing science closer to society and make it attractive. Solar Panel Tilt Bracket Ideal Azimuth Formula Strike Angle 08-12-2011, 09:36 PM [B]I have a W facing roof with no shade on a 35 Degree angle. My latitude is 43 Degrees. I have installed my panels on a 15 Degree angle facing S. What is the actual Azimuth to use in my calculations for output? Does anyone. Calculation of azimuth, Angle of elevation formula calculator. Rearrange. Debra. Trainee's. Placidly. Ramp incline calculator | ez-access. Calctool: height of a building calculator. Ebooks on ethical hacking free download. Projectile motion equations formulas calculator range projection

### How to calculate the solar azimuth angle and solar

Azimuth angle på engelska med böjningar och exempel på användning. Synonymer är ett gratislexikon på nätet. Hitta information och översättning här

## How do I calculate the sun's azimuth based on zenith, hour angle, declination, and latitude? - Astronomy

To fully understand how the azimuth angle and the altitude of a celestial body help us to establish our position, we need to consider them in relation to the celestial sphere.

Consider the diagram below:

The celestial sphere is drawn in the plane of the observer’s meridian with the observer’s zenith (Z) at the top.

Point O represents both the observer and the Earth.

The arc PZQSP’ represents the observer’s celestial meridian.

The arc NAS is the celestial horizon and QRQ’ represents the celestial equator.

ZXAZ’ is a vertical circle running through the position of the celestial body (X). (A vertical circle is a great circle that passes through the observer’s zenith and is perpendicular to the celestial horizon).

The Azimuth Angle is the angle PZX (that is, the angle between the observer’s celestial meridian and the vertical circle through the celestial body).

The Altitude is the angle AOX (that is the angle from the celestial horizon to the celestial body measured along the vertical circle).

The Zenith. Point Z in the diagram represents the observer’s zenith which is an imaginary point on the celestial sphere directly above the observer. It is the point where a straight line drawn from the geocentric centre of the Earth, through the observer’s position and onwards, intersects with the celestial sphere.

The Zenith Distance. The Zenith Distance is the angular distance from the zenith to the celestial body measured from the Earth’s centre. In the diagram above, it is the angular distance ZX which is subtended by the angle XOZ.

Relationship between Altitude and Zenith Distance Since the celestial meridian is a vertical circle and is therefore, perpendicular to the celestial horizon, it follows that angle AOZ is a right angle and angles AOX and XOZ are complementary angles. From this we can deduce that:

Zenith Distance = 90 o – Altitude and Altitude = 90 o – Zenith Distance

### Calculating the Zenith Distance.

Consider the next diagram.

The diagram shows that the angular distance AU on the Earth’s surface is equal to the angular distance ZX in the spherical triangle PZX.

X represents the position of a celestial body on the celestial sphere,

Z represents a point on the sphere which coincides with the zenith of the DR position (A),

P represents the projection of the North Pole onto the celestial sphere,

PX = NU = (90 o – the declination of the body),

PZ = NA = (90 o – the latitude of the DR position),

ZX = AU = (90 o – the altitude of the body).

We can see that the triangle NAU on the Earth’s surface can be solved, in effect, by solving the triangle PZX in the celestial sphere.

Local Hour Angle (LHA)

In the PZX triangle diagram, LHA is the angle ZPX that is the angle between the observer’s celestial meridian and the meridian of the celestial body.

Relationship between LHA and Azimuth Angle. Consider the next diagram.

This diagram is drawn in the plane of the celestial horizon. Imagine that you are looking down on the celestial sphere from a position directly above the observer’s zenith which is in the centre of the circle.

The circle WANESW represents the celestial horizon.

NZS represents the observer’s celestial meridian.

WQE represents the celestial equator,

X is the position of the celestial body,

PXR represents part of the meridian of the celestial body which cuts the Equator at R.

When the LHA (ZPX) is less than 180 o , the celestial body lies to the west of the observer’s meridian and when the LHA is greater than 180 o it lies to the east. (Remember LHA is measured westwards from the observer’s meridian from 0 o to 360 o ).

It follows that if the celestial body is to the west of the observer’s meridian, the azimuth angle must be west and when to the east, the azimuth angle must be east.

LHA 0 o to 180 o = Azimuth Angle West

LHA 180 o to 360 o = Azimuth Angle East

In Astro navigation. It can be seen that by measuring the altitude of a celestial body, we are able to easily calculate the zenith distance which will give us the distance in nautical miles from the observer’s position to the geographical position of the body. The azimuth angle will give us the direction of the GP from the observer’s position. This explains why calculating the altitude and azimuth angle are the first steps in determining our position in celestial navigation.

#### Relationship Between Azimuth Angle and Azimuth.

Azimuth is a specific type of bearing which measures the direction of an object in relation to true north, in the horizontal plane, clockwise from 0 o to 360 o .

Azimuth Angle. In astro navigation, when we calculate the azimuth of a celestial body, what we actually calculate is the azimuth angle. Azimuth angle is measured from 0 o to 180 o either westwards or eastwards from either north or south. If the observer is in the northern hemisphere, the azimuth is measured from north and if in the southern hemisphere, it is measured from south.

For example, if the true azimuth of an object is 225 o , the azimuth angle for an observer in the northern hemisphere will be N135 o W but for an observer in the southern hemisphere, it will be S045 o W.

Summary Of The Discussions Above. The relationships discussed above illustrate the importance of altitude and azimuth angle in position finding at sea. It can be seen that from the altitude of a celestial body, we are able to easily calculate the zenith distance which will give us the distance in nautical miles from the observer’s position to the geographical position of the body. From the calculated azimuth angle we can find the true azimuth and this will give us the direction of the GP from the observer’s position. This explains why determining the altitude and azimuth angle are the first steps in determining our position in astro navigation.

In the next post, we will discuss sight reduction which is the process of reducing the data gathered from an observation of a celestial body down to the information needed to establish an astronomical position line.

## Azimuth: Definition

According to the U.S. Army's definition, an azimuth is the angle between a line pointing toward the North Pole and a second line aimed at the location of interest, such as a hilltop, cell phone tower or just a set of numerical coordinates.

Imagine two lines starting as one and pointing at the top of a circle if one stays fixed while the other traces out a full circle (like one of the "hands" of a clock), the angle between them at any instant represents the azimuth of the moving line. This can vary from 0° (degrees) to 360° (these actually represent the same azimuth, due north).

Therefore, an azimuth of 90° corresponds to a quarter of the way clockwise from 0° or 360°, which is east. Similarly, 180° is south, and 270° is west. You can get azimuths corresponding to NE, SE, SW and NW by adding or subtracting 45° to the appropriate N, E, S or W azimuth.

## How do you calculate the angle of the sun above the horizon?

Find out all about it here. Keeping this in view, what is the sun's angle of inclination?

where &psi1 is the angle of inclination of the spin axis of the Earth with the plane of its orbit, approximately 23.5°. The angle between the sun and the vertical is called the zenith angle. The elevation angle of the sun is 90° minus the zenith angle.

Also Know, how do you find the azimuth angle of the sun? Solar azimuth angle, z This equation is correct, provided that cos(h) > tan(&delta)/tan(L) (ASHRAE, 1975). If not, it means that the sun is behind the E&ndashW line, as shown in Figure 2.4, and the azimuth angle for the morning hours is &minus&pi + |z| and for the afternoon hours is &pi &minus z.

Keeping this in view, how many degrees above the horizon is the sun?

What time is the sun at a 45 degree angle?

Equi-umbra thus refers to the time when the angle (altitude) of the sun is equal to 45 degrees. Each day the sun rises to its highest altitude at Midday. Midday (Solar Noon or Transit) in the Northern hemisphere, North of the Tropic of Cancer, is when the sun is exactly due south .

## A STUDY OF SOLAR WATER PUMPING PARAMETERS FOR BAGHDAD AREA

AHMED M. HASSON , . BASSIM E. AL-SAGIR , in Energy and the Environment , 1990

### CONCLUSIONS

For small power production, the photovoltaic surface facing south tilted by fixed solar azimuth angle at noon time STA may be simple ones using for the power required for irrigation and leaching. This type of photovoltaic (STA) may be employed which needed tilt adjustment only few times per a year ( Tabor, 1966 Winston, 1975 Selcuk, 1976 ). Although the fully tracking photovoltaic surfaces STA is more power produced but it is costly. The another disadvantage with this photovoltaic is the need for automatic tracking and they are not utilizing the diffuse radiation. What is the rule of such photovoltaic?

a- low relative cost. b- low maintanance and high reliability. c- easy regulation. d- no internal lubrication requirements other than the main bearing. e- smaller size with high efficiency.

## Solar azimuth angle and solar panels

The understanding of the solar azimuth angle is a vital aspect of photovoltaic and thermal design. Solar power production is maximum when solar panels are right in front of the sun.

Since the azimuth angle dictates the horizontal coordinates of the sun, our solar panels must be angles at the azimuth angle to get maximum solar power.

The solar panel angled at the solar azimuth angle

The position of the sun in the sky changes continuously. And it is impossible to synchronize the direction of solar panels with the position of the sun unless you are using a solar tracking system. Solar tracking is an unaffordable and uncommon option for homeowners and small projects.

Most times, solar panels are permanently fixed in a particular direction. This optimal direction of solar panels is decided by the solar azimuth angle.

If you have carefully looked at one of the preceding monthly variation graphs, you must have noticed a relationship between the solar azimuth angle and location. For Sydney, which lies in the southern hemisphere, the azimuth angle always remains below 90° at noon over the entire year. Thus, people in Sydney will always see the sun in the northern sky. It is also true for other cities in the southern hemisphere. That means the sun appears in the north for regions in the southern hemisphere, so the best direction for solar panels will be south.

With the same reasoning, solar panels in Austin, Tucson, and Denver must be oriented toward the south direction. The azimuth angle always remains more than 90° for these cities at noon they are in the northern hemisphere. People in the northern hemisphere will see the sun in the southern sky.

### What is the solar azimuth angle?

The solar azimuth angle is the angle between the sun and the reference direction (usually north) with the observer on the local horizon.

### What is the difference between the solar azimuth angle and the solar elevation angle?

The solar azimuth angle defines the horizontal coordinates of the sun, whereas the solar elevation angle decides the vertical position of the sun or its altitude.

### What is the solar azimuth angle for sunrise and sunset?

The solar azimuth angle for sunrise will be close to 90° and for sunset will be close to 270°.