SDK Question Computing a heading to a base from current position

[JMW]

Can anyone help with this for an autopilot?

Computing a heading to a base from current position.

Searching drew a blank except for this deep examination.

And this:

Course between points

We obtain the initial course, tc1, (at point 1) from point 1 to point 2 by the following. The formula fails if the initial point is a pole. We can special case this with:

IF (cos(lat1) < EPS)   // EPS a small number ~ machine precision
  IF (lat1 > 0)
     tc1= pi        //  starting from N pole
  ELSE
     tc1= 2*pi         //  starting from S pole
  ENDIF
ENDIF
For starting points other than the poles:

IF sin(lon2-lon1)<0       
   tc1=acos((sin(lat2)-sin(lat1)*cos(d))/(sin(d)*cos(lat1)))    
ELSE       
   tc1=2*pi-acos((sin(lat2)-sin(lat1)*cos(d))/(sin(d)*cos(lat1)))    
ENDIF 
An alternative formula, not requiring the pre-computation of d, the distance between the points, is:

   tc1=mod(atan2(sin(lon1-lon2)*cos(lat2),
           cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(lon1-lon2)), 2*pi)

but can't get it to work.

There must be a simple formula, no?:thumbup:

 

[astrosammy]

I once wrote an AP lua script to fly to KSC and land there. Maybe I'll add some comments later...

function getHeading (target_lon, target_lat)
	term.out('#003')
    equ = oapi.get_equpos()
	target_lon_b = -80.707265*RAD
	target_lat_b = 28.634564*RAD
	
	londif = target_lon - equ.lng
	latdif = target_lat - equ.lat
	
	londif_b = target_lon_b - equ.lng
	latdif_b = target_lat_b - equ.lat
	
	alph = math.atan(latdif/londif)
	
	heading = 180*RAD-alph-90*RAD
	
	Om = math.atan2(math.sin(londif)*math.cos(target_lat),math.cos(equ.lat)*math.sin(target_lat)-math.sin(equ.lat)*math.cos(target_lat)*math.cos(londif))
	
	var_a = math.sin(latdif_b/2) * math.sin(latdif_b/2) + math.sin(londif_b/2) * math.sin(londif_b/2) * math.cos(equ.lat) * math.cos(target_lat_b)
	var_c = 2*math.atan2(math.sqrt(var_a),math.sqrt(1-var_a))
	distance = 6371 * var_c
	
	
	if equ.lng > target_lon then
		heading = heading + 180*RAD
	end
	
	if equ.lng > target_lon then
		Om = 360*RAD + Om
	end
	
	sethead = 330*RAD-Om
	
	setHeading(330*RAD-sethead*2)
end

I wanted to fly the ship to KSC at an heading of 330 (to line up with the runway), so ignore the last lines (-- is used for comments in lua). Shouldn't be that hard to get it into C++.

EDIT: Om is the heading from shipt to target.

 

[JMW]

Thanks - I'll give it a try

 

[Tommy]

You may find some useful formulas on this site: http://www.movable-type.co.uk/scripts/latlong.html

Note that these formulas don't consider the Earth's rotation, you'll need to modify a bit - figure out about how long the trip will take and adjust the target's longitude accordingly.

 

[astrosammy]

:hesaid:

That's what I used.
For atmospheric flight, rotation can be ignored.

 

[agentgonzo]

I did some of this about 6 years ago for a Navy training sim. Take a look at the Haversine function and do some google searches on that and 'heading'.

Also, a more accurate (and probably far too accurate) method was created by a dude in the 70s. Google 'Vincenty 1975' (his name and the date of the paper) if you want to go that far.