On Saturday 17 September 2005 23:48, Mike Kopack wrote:
Hey gang,
As part of my simulated UAV control system project, I needed to augment the
built in Autopilot system in FG with a module in my own system (which is
written in java) that takes the aircraft's current position, and a desired
position (lat/long/altitude/desired arrival time) and figures out the
proper autopilot heading to lock to and altitude locks etc.
Now, I'd like to figure out how to handle that last variable: Arrival time.
To do it, I need to know how far I have left to travel, and how long I have
to get there. The time isn't a problem, but how do I get the distance from
my current Lat/Long to another Lat/Long? My investigations online show that
there's no real way to directly convert from Lat/Long to meters. I know
that the GPS system in FG calculates this distance. I just need to know
what the formulas are that are used to arrive at this distance.
Hi Mike
Take a look at Aviation Formulary V1.42
http://williams.best.vwh.net/avform.htm
It has everything you'll ever need formula wise for great circle navigation.
Distance, initial course, cross track error, working out an enroute point at x
distance from the origin along the route, etc
It uses a spherical earth model which means there is a maximum error of about
0.2% which should be acceptable if I'm not mistaken.
There is a worked examples section.
Distance between points
d=2*asin(sqrt((sin((lat1-lat2)/2))^2 +
cos(lat1)*cos(lat2)*(sin((lon1-lon2)/2))^2))
The distance from LAX to JFK is
===
d = 2*asin(sqrt((sin((lat1-lat2)/2))^2+
cos(lat1)*cos(lat2)*(sin((lon1-lon2)/2)^2))
= 2*asin(sqrt((sin(0.592539-0.709186)/2))^2+
cos(0.592539)*cos(0.709186)*(sin((2.066470-1.287762)/2)^2))
= 2*asin(sqrt((-0.05829)^2 +0.829525*0.758893*0.379591^2))
= 2*asin(0.306765)
= 0.623585 radians
= 0.623585*180*60/pi=2144nm
or
d = acos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(lon1-lon2))
= acos(sin(0.592539)*sin(0.709186)+
cos(0.592539)*cos(0.709186)*cos(0.778708))
= acos(0.811790)
= 0.623585 radians
= 0.623585*180*60/pi=2144nm
The initial true course out of LAX is:
==
sin(-0.778708)=-0.7020 so
tc1 = acos((sin(lat2)-sin(lat1)*cos(d))/(sin(d)*cos(lat1)))
= acos((sin(0.709186)-sin(0.592539)*cos(0.623585))/
(sin(0.623585)*cos(0.592535))
= acos(0.408455)
= 1.150035 radians
= 66 degrees
Regards
Paul
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