Determine Target Distance Given Depression Angle and Altitude

[Skylar289]

Ok, I'm not a programmer and my excel skills are stretched to the max at this point.

Problem

I am in an aircraft with a camera, on a gimbal. I know my altitude, I know my depression angle of my camera, should be simple enough to find my distance. Unfortunately I have no idea how to calculate degrees to radians, then input said radians into my formula and solve for distance.

400 ft Height
20 degrees downward angle
x is my distance variable

Eventually I would also like to use my current gps coordinates, my aircraft heading, my camera starepoint heading, and my distance....solved by the above problem, and determine the coordinates of what I am looking at.

Please help. I'm not even sure excel can even handle this, but if its possible, please let me know!!!

 

[davesweep]

Hi,

You want to know the distance from the camera to the ground?

=height / cos(90-angle of depression in degrees)

to convert from degrees to radians, multiply by pi/180

So, if the height is in A1 and the depression angle in A2,

=A1/COS((90-A2)*PI()/180)

 

[bertie]

Hi, and welcome to the forum.

You can use the Radians() function to convert degrees to radians, see the help file.

It has been many moons since I last used trigonometry, so apologies if my formula is wrong, for example:

Excel Workbook
	A	B	C
1	Height	Angle	Distance
2	4000	20	11695.22
Sheet1

NB
I haven't taken into account if you need to convert feet to metres, etc.

 

[MikeWx]

With your height above the ground as 400 feet and the angle below horizontal as 20 degrees, the following formula gives the distance to what the camera is looking at as 1,099 feet away from the point the plane is currently located at. It looks correct on the diagram I drew, but the diagram doesn't load to the forum.

Sheet1

<TABLE style="BACKGROUND-COLOR: #ffffff; PADDING-LEFT: 2pt; PADDING-RIGHT: 2pt; FONT-FAMILY: Calibri,Arial; FONT-SIZE: 11pt" border=1 cellSpacing=0 cellPadding=0><COLGROUP><COL style="WIDTH: 30px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"></COLGROUP><TBODY><TR style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt"><TD> </TD><TD>A</TD><TD>B</TD><TD>C</TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">1</TD><TD>Height</TD><TD>Angle</TD><TD>Distance</TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">2</TD><TD style="TEXT-ALIGN: right">400</TD><TD style="TEXT-ALIGN: right">20</TD><TD style="TEXT-ALIGN: right">1098.991</TD></TR></TBODY></TABLE>
<TABLE style="BORDER-BOTTOM-STYLE: groove; BORDER-BOTTOM-COLOR: #00ff00; BORDER-RIGHT-STYLE: groove; BACKGROUND-COLOR: #fffcf9; BORDER-TOP-COLOR: #00ff00; FONT-FAMILY: Arial; BORDER-TOP-STYLE: groove; COLOR: #000000; BORDER-RIGHT-COLOR: #00ff00; FONT-SIZE: 10pt; BORDER-LEFT-STYLE: groove; BORDER-LEFT-COLOR: #00ff00"><TBODY><TR><TD>Spreadsheet Formulas</TD></TR><TR><TD><TABLE style="FONT-FAMILY: Arial; FONT-SIZE: 9pt" border=1 cellSpacing=0 cellPadding=2><TBODY><TR style="BACKGROUND-COLOR: #cacaca; FONT-SIZE: 10pt"><TD>Cell</TD><TD>Formula</TD></TR><TR><TD>C2</TD><TD>=A2/TAN(RADIANS(B2))</TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE>

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Mike

 

[Skylar289]

With your height above the ground as 400 feet and the angle below horizontal as 20 degrees, the following formula gives the distance to what the camera is looking at as 1,099 feet away from the point the plane is currently located at. It looks correct on the diagram I drew, but the diagram doesn't load to the forum.

Sheet1

<TABLE style="BACKGROUND-COLOR: #ffffff; PADDING-LEFT: 2pt; PADDING-RIGHT: 2pt; FONT-FAMILY: Calibri,Arial; FONT-SIZE: 11pt" border=1 cellSpacing=0 cellPadding=0><COLGROUP><COL style="WIDTH: 30px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"><COL style="WIDTH: 64px"></COLGROUP><TBODY><TR style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt"><TD> </TD><TD>A</TD><TD>B</TD><TD>C</TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">1</TD><TD>Height</TD><TD>Angle</TD><TD>Distance</TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">2</TD><TD style="TEXT-ALIGN: right">400</TD><TD style="TEXT-ALIGN: right">20</TD><TD style="TEXT-ALIGN: right">1098.991</TD></TR></TBODY></TABLE>
<TABLE style="BORDER-BOTTOM-STYLE: groove; BORDER-BOTTOM-COLOR: #00ff00; BORDER-RIGHT-STYLE: groove; BACKGROUND-COLOR: #fffcf9; BORDER-TOP-COLOR: #00ff00; FONT-FAMILY: Arial; BORDER-TOP-STYLE: groove; COLOR: #000000; BORDER-RIGHT-COLOR: #00ff00; FONT-SIZE: 10pt; BORDER-LEFT-STYLE: groove; BORDER-LEFT-COLOR: #00ff00"><TBODY><TR><TD>Spreadsheet Formulas</TD></TR><TR><TD><TABLE style="FONT-FAMILY: Arial; FONT-SIZE: 9pt" border=1 cellSpacing=0 cellPadding=2><TBODY><TR style="BACKGROUND-COLOR: #cacaca; FONT-SIZE: 10pt"><TD>Cell</TD><TD>Formula</TD></TR><TR><TD>C2</TD><TD>=A2/TAN(RADIANS(B2))</TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE>

Excel tables to the web >> http://www.excel-jeanie-html.de/index.php?f=1" target="_blank"> Excel Jeanie HTML 4


Mike

AWESOME!!! That did it! all of your equations worked, I chose Mike's using Tan. Thanks everyone!

 

[shg]

That assumes that the world is flat with no terrain relief ...