UNSOLVABLE! Find A New Lat Long Given Current Lat Long, Altitude, Bearing, Distance, and Depression Angle

[Skylar289]

If the title didn't say enough, here's the deal.

What I have,

My current aircraft altitude 400ft
the current bearing of the aircraft to target is338 degrees... 5.899212872 in radians

the current depression angle 15 degrees.... .261799388 in radians

the current aircraft Latitude 34º 36‘ 59.922"... 0.604174431 in radians

the current aircraft Longitude 112º 27‘ 11.52"... 1.962678594 in radians

the distance to target solved by Distance= Altitude/TAN of Depression Angle is 1492.820323 Ft


Now, the question is whether or not I take straight line distance from my current position to the next position which is effectively using SIN in my distance formula...or keep using TAN for my slant range distance and somehow determine my new accurate target Lat/Long


Please Help!! Too many brain cells lost so far. I may not have explained it enough, but there are so many variables, I'm starting to get a little lost too.

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[MikeWx]

The following solution is based on information from this link:

http://williams.best.vwh.net/avform.htm#LL

The distance you calculated has to be converted to radians in Cell E5. It represents the angle from the center of the earth that would have an arc equal to your distance.

As you can see, with this short distance, the target latitude is 14 seconds north of the aircraft and the target longitude is 6 seconds west of the aircraft. I assumed the latitude was degrees North and the longitude was degrees North.

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: 121px"><COL style="WIDTH: 64px"><COL style="WIDTH: 84px"><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><TD>D</TD><TD>E</TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">1</TD><TD> </TD><TD>Radians</TD><TD>Degrees</TD><TD>Degrees (dd:mm:ss)</TD><TD> </TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">2</TD><TD>Current Latitude</TD><TD style="TEXT-ALIGN: right; FONT-FAMILY: Verdana; FONT-SIZE: 10pt">0.60417</TD><TD style="TEXT-ALIGN: right">34.61664499</TD><TD style="TEXT-ALIGN: right">34:37:00</TD><TD> </TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">3</TD><TD>Current Longitude</TD><TD style="TEXT-ALIGN: right; FONT-FAMILY: Verdana; FONT-SIZE: 10pt">1.96268</TD><TD style="TEXT-ALIGN: right">112.4532</TD><TD style="TEXT-ALIGN: right">112:27:12</TD><TD> </TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">4</TD><TD>Bearing</TD><TD style="TEXT-ALIGN: right; FONT-FAMILY: Verdana; FONT-SIZE: 10pt">5.89921</TD><TD style="TEXT-ALIGN: right">338</TD><TD style="TEXT-ALIGN: right">338:00:00</TD><TD> </TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">5</TD><TD>Distance</TD><TD style="TEXT-ALIGN: right; FONT-FAMILY: Verdana; FONT-SIZE: 10pt">1493</TD><TD>Distance in radians</TD><TD> </TD><TD style="TEXT-ALIGN: right">7.15E-05</TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">6</TD><TD> </TD><TD> </TD><TD> </TD><TD> </TD><TD> </TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">7</TD><TD>New latitude</TD><TD style="TEXT-ALIGN: right">0.604241</TD><TD style="TEXT-ALIGN: right">34.62044274</TD><TD style="TEXT-ALIGN: right">34:37:14</TD><TD> </TD></TR><TR style="HEIGHT: 18px"><TD style="TEXT-ALIGN: center; BACKGROUND-COLOR: #cacaca; FONT-SIZE: 8pt">8</TD><TD>New longitude</TD><TD style="TEXT-ALIGN: right">1.962711</TD><TD style="TEXT-ALIGN: right">112.4550644</TD><TD style="TEXT-ALIGN: right">112:27:18</TD><TD> </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>=B2*180/PI()</TD></TR><TR><TD>D2</TD><TD>=C2/24</TD></TR><TR><TD>C3</TD><TD>=B3*180/PI()</TD></TR><TR><TD>D3</TD><TD>=C3/24</TD></TR><TR><TD>C4</TD><TD>=B4*180/PI()</TD></TR><TR><TD>D4</TD><TD>=C4/24</TD></TR><TR><TD>E5</TD><TD>=(PI()/(180*60)*(B5/6075))</TD></TR><TR><TD>B7</TD><TD>=ASIN(SIN(B2)*COS(E5)+COS(B2)*SIN(E5)*COS(B4))</TD></TR><TR><TD>C7</TD><TD>=B7*180/PI()</TD></TR><TR><TD>D7</TD><TD>=C7/24</TD></TR><TR><TD>B8</TD><TD>=MOD(B3-ASIN(SIN(B4)*SIN(E5)/COS(B2))+PI(),2*PI())-PI()</TD></TR><TR><TD>C8</TD><TD>=B8*180/PI()</TD></TR><TR><TD>D8</TD><TD>=C8/24</TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE>

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Mike

 

[Skylar289]

the following solution is based on information from this link:

http://williams.best.vwh.net/avform.htm#ll

the distance you calculated has to be converted to radians in cell e5. It represents the angle from the center of the earth that would have an arc equal to your distance.

As you can see, with this short distance, the target latitude is 14 seconds north of the aircraft and the target longitude is 6 seconds west of the aircraft. I assumed the latitude was degrees north and the longitude was degrees north.

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: 121px"><col style="width: 64px"><col style="width: 84px"><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><td>d</td><td>e</td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">1</td><td> </td><td>radians</td><td>degrees</td><td>degrees (dd:mm:ss)</td><td> </td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">2</td><td>current latitude</td><td style="text-align: Right; font-family: Verdana; font-size: 10pt">0.60417</td><td style="text-align: Right">34.61664499</td><td style="text-align: Right">34:37:00</td><td> </td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">3</td><td>current longitude</td><td style="text-align: Right; font-family: Verdana; font-size: 10pt">1.96268</td><td style="text-align: Right">112.4532</td><td style="text-align: Right">112:27:12</td><td> </td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">4</td><td>bearing</td><td style="text-align: Right; font-family: Verdana; font-size: 10pt">5.89921</td><td style="text-align: Right">338</td><td style="text-align: Right">338:00:00</td><td> </td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">5</td><td>distance</td><td style="text-align: Right; font-family: Verdana; font-size: 10pt">1493</td><td>distance in radians</td><td> </td><td style="text-align: Right">7.15e-05</td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">6</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">7</td><td>new latitude</td><td style="text-align: Right">0.604241</td><td style="text-align: Right">34.62044274</td><td style="text-align: Right">34:37:14</td><td> </td></tr><tr style="height: 18px"><td style="text-align: Center; background-color: #cacaca; font-size: 8pt">8</td><td>new longitude</td><td style="text-align: Right">1.962711</td><td style="text-align: Right">112.4550644</td><td style="text-align: Right">112:27:18</td><td> </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>=b2*180/pi()</td></tr><tr><td>d2</td><td>=c2/24</td></tr><tr><td>c3</td><td>=b3*180/pi()</td></tr><tr><td>d3</td><td>=c3/24</td></tr><tr><td>c4</td><td>=b4*180/pi()</td></tr><tr><td>d4</td><td>=c4/24</td></tr><tr><td>e5</td><td>=(pi()/(180*60)*(b5/6075))</td></tr><tr><td>b7</td><td>=asin(sin(b2)*cos(e5)+cos(b2)*sin(e5)*cos(b4))</td></tr><tr><td>c7</td><td>=b7*180/pi()</td></tr><tr><td>d7</td><td>=c7/24</td></tr><tr><td>b8</td><td>=mod(b3-asin(sin(b4)*sin(e5)/cos(b2))+pi(),2*pi())-pi()</td></tr><tr><td>c8</td><td>=b8*180/pi()</td></tr><tr><td>d8</td><td>=c8/24</td></tr></tbody></table></td></tr></tbody></table>

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mike

works perfectly!!!!!! Lifesaver!!!!