Badger
Joined: 05 Jan 2007 Posts: 8

Posted: Sun Apr 22, 2007 7:17 am Post subject: lat/lon projection methods 


I was recently asked by a 214th member if there was a way of determining the Latitude and Longitude of an unknown steerpoint, when given the bearing and distance FROM a known steerpoint.
For instance, using the Recon function you have determined the Latitude and Longitude of a target point. For example, the end of a runway you have tasked an OCA strike against. However, you want to begin your ingress to the target steerpoint some distance from it. You have also determined the heading you want to ingress on. In this case, the runways magnetic heading.
A simple diagram should help explain...
X180 degs.36 _________________18
X3 miles
Since you know the lat/lon of the target point, for example between the VASI lights, and you know the reciprocal of the ingress heading (180 in the example above) as well as the ingress distance, you can calculate the Latitude and Longitude of X, the unknown steerpoint.
In this way you can place a steerpoint there! Upon reaching that steerpoint you turn to the ingress heading and you should be lined up with the runway.
This is beneficial, especially when at low altitude and you don't want to fly up in order to acquire the correct ingress heading visually. In this case, the runway itself.
There are several ways of performing this calculation depending on how precise you need to be. However, since the Earth is not a perfect sphere the math can be daunting for some as it requires a sound understanding of Trigonometry. Specifically, Spherical Trigonometry, etc. But fear not, there are easier ways. After all, if I can do it, it can't be too hard, right?
In Falcon 4 and/or Allied Force one can assume the Earth is flat and therefore, given the relatively short distances involved, we can use a "Flat Earth" model to perform the calculations. See, I keep it simple.
Here are several ways you can perform the calculation and determine the Latitude and Longitude of X as depicted above:
Method 1:
The manual method for you geeks out there...
lat2 = lat1 + cos(hdg) * dist * (360/40000)
lon2 = lon1 + sin(hdg) * dist * (360/40000) / cos(lat1)
Note: you will need to convert the lat/lon values into the units required by your calculators trigonometry functions. For example: convert degrees to radians.
Again, this formula is based on a "flat Earth" model and assumes the lines of longitude are parallel to one another. It isn't perfect, but it's simpler than performing great circle calculations which are not needed for our purposes in Falcon 4 or Allied Force. Why not you ask? Because the distances involved are too short to be affected by the Earth's curvature. Assuming Falcon 4 even models it.
Method 2:
If you have a handheld GPS unit with a waypoint projection feature you can use it, as it will do precisely what is needed. Refer to your units instruction manual.
Method 3. No calculator wristwatch needed.
(Is cheating and if I catch anyone using it!...)
Use a small program called GeoCalc. It can be found here:
http://www.fizzymagic.net/Geocaching/GeoCalc/GeoCalc.html
 Click on the Projection tab
 Set distance unit to Nautical Miles
 Select the Rhumb Line option button
Here's an example:
Enter the following exactly as shown. You must use this format so you'll need to convert from the Falcon 4 or Allied Force lat/lon as displayed on the recon screen or in the DED to this one.
Point = 71 45 23 N 67 45 23 E
Distance = 10
Bearing = 145
Result = N 71 37.192, E 68 03.640
Compare with the other methods shown above.
 Badger 
