To what degree should I set the course box on the G1000 screen? Runway heading or SID course? Because although the runway heading is 044 degrees in the SID chart I shared below, the SID departure course is 057 degrees. I know I will set 044 for the heading but I don't know what to set for the course. I also know that I will take off at heading 044 runway, but I do not know when I will intercept course 057 after takeoff. Should I intercept course 057 after safety altitude? I would be glad if you help.
The G1000 avionics are RNAV capable, or in Garmin jargon "GPS navigation". Even though this SID is the conventional type and does not require RNAV equipment, you can use GPS navigation as a substitute for the VOR.
Rather than fumbling around with the VOR course, the BIG 1R or the EKI 1R SID should be loaded from the navigation database.
The NAV source should be set to GPS and the HSI needle should be magenta.
If for some reason you wanted to fly VOR only, the initial course selection is 057 as explained multiple times on that chart.
but I do not know when I will intercept course 057 after takeoff.
The VOR is located past the runway, which means the radial is intercepted upon passing the VOR. On the G1000 HSI, the green arrow would switch from "up" to "down".
You will NOT intercept "course 057," that is to say, a 057° track across the ground with no underlying reference. That kind of instruction is only found in Area Navigation (RNAV) procedures. The Biga 1R and Tekirdag 1R procedures are "conventional" procedures, not RNAV. This means you will fly according to prescribed headings and NAVAID radials rather than flying unsupported courses. (The CRL057 radial might in truth be a 057° course across the ground but this is by no means guaranteed.)
This procedure tells you to use your VOR receiver for lateral guidance. Before takeoff, tune 114.8 in your NAV radio. Then use your Omni-Bearing Selector knob to set radial 057 on your CDI.
On takeoff, watch the needle on your CDI and maneuver your aircraft so the needle centers on the 057 radial of Corlu VOR. Stay on that radial as you climb to 2000, then turn left back toward the VOR. As you cross the VOR at 3000, set your OBS knob to the 202 radial and fly that one outbound from the VOR.