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Mszazynski
Antenna-Theory.com Newbie

Joined: 26 Dec 2017
Posts: 6

 Posted: Fri Dec 29, 2017 5:40 pm    Post subject: Converting 2D angles to solid angles If I know the beamwidth of my main beam is 2 degrees in the azimuthal and 2 degrees in elevation, how can I determine what solid angle this would create? This article essentially says that the number of steradians in your solid angle would be equal to: (Max_Azimuth-Min_Azimuth)*[sin(Max_Elevation)-Sin(Min_Elevation)] https://math.stackexchange.com/questions/1243540/how-to-calculate-the-solid-angle-of-a-spherical-rectangle-from-astronomical-angl Would you say this is accurate? Is there a better way?
e.fannio
Antenna Theory Regular

Joined: 12 Jul 2018
Posts: 10
Location: Naples, Italy

Posted: Thu Jul 12, 2018 8:22 pm    Post subject: Re: Converting 2D angles to solid angles

 Mszazynski wrote: If I know the beamwidth of my main beam is 2 degrees in the azimuthal and 2 degrees in elevation, how can I determine what solid angle this would create? This article essentially says that the number of steradians in your solid angle would be equal to: (Max_Azimuth-Min_Azimuth)*[sin(Max_Elevation)-Sin(Min_Elevation)] https://math.stackexchange.com/questions/1243540/how-to-calculate-the-solid-angle-of-a-spherical-rectangle-from-astronomical-angl Would you say this is accurate? Is there a better way?

The right formula should be Omega = (Max_az - Min_az)*[cos(min_el) - cos(max_el)]
Here is the demonstration

Joined: 03 Jan 2007
Posts: 210

 Posted: Thu Jul 12, 2018 9:26 pm    Post subject: Yes great proof both answers are correct though....if you define elevation as angle above horizon e.fannio note you are using standard polar coordinates with uses angle measured off z-axis, hence the reason for change between sin and cos
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