Small Aircraft
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 3
Situational Awareness
ATC Issue All Types; Airspace Violation All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Airspace Structure; Human Factors; Procedure
Aircraft X was enroute from TOA..HHR about 5 miles south of HHR airport and level at 3000 feet when I took over the LAKR position from the previous controller.  The previous controller had issued the aircraft a heading that would not have provided sufficient separation of 1.5 miles from the adjacent airspace to the east (Harbor sector) and so I initially issued a heading of 040 to maintain this airspace separation. This particular operation of putting HHR arrivals on the downwind to runway 25 requires very precise timing to both remain clear of Harbor sector's airspace as well as remain 3 miles south of the LAX final for runway 25L.  There is only about 1/8 mile - 1/4 mile wide margin of error in which an aircraft being vectored for the downwind at HHR will remain clear of both.When Aircraft X was in the appropriate position I turned the aircraft from the 040 heading to a 070 heading for the downwind and issued a frequency change to the next sector (Downey).  The pilot's hesitated and responded with multiple incorrect read backs; meanwhile tracking a heading of roughly 090 or 080.  It appeared to me at the time that the track could have been erroneous radar returns as they looked a bit erratic or that the pilot was correcting to the appropriate assigned heading as I did reissue the heading of 070 multiple times because of the incorrect read backs.  After the aircraft changed frequencies to the next controller; it was evident that the aircraft was still not heading 070 as instructed and therefore ended up not maintaining 1.5 miles lateral separation from Harbor sector's airspace. Around the time I was issuing the frequency change to Aircraft X; Aircraft Y; departed off runway 30 at LGB on the SENIC departure.  This aircraft climbed out at a very high speed and ended up taking a wide turn to the south as a result (to me it appeared that Aircraft Y did not comply with the SID as he should have begun a southbound turnout of 1500 feet but did not).  Because of the speed on departure this aircraft also did not remain at least 1.5 miles away from my airspace boundary and therefore I believe lost separation with Aircraft X.  I am unaware if LGB tower or the Harbor sector controller were able to achieve visual separation between the two aircraft.I could have called LGB tower to stop departures.  This was a consideration I had when I took over the position but considering Aircraft X was a small aircraft indicating 100 knots; if LGB did have any departures they would have had to wait for at least 5 minutes; possibly longer.I could have pointed Aircraft X out to Harbor sector before putting the aircraft of the downwind so that the Harbor controller would at least be aware of my traffic.  If Harbor denied the point out; I would have had time to either spin my aircraft or Approval Requested (APREQ) something different with the Downey controller.As mentioned above; this handoff only has at most a 1/4 mile margin of error within which the handoff from Laker to Downey maintains 3 miles separation from the LAX final and 1.5 miles separation from the Harbor sector airspace boundary.  If an aircraft either tracks a heading just 10 or 20 degrees off the handoff heading of 070 or has a crosswind that pushes an aircraft even a little to the north or south an airspace deviation or loss of separation can happen almost immediately.  With the LGB departures initially climbing to 3000 feet and the Laker handoff altitude for HHR arrivals to Downey at 3000 feet; a loss of separation can occur very easily.  I feel that changing the handoff altitude from Laker to Downey to 4000 feet would dramatically improve safety with regards to mitigating an event like the one I experienced from recurring.
A Southern California TRACON Controller reports of a loss of separation with an aircraft he was vectoring to an airport while another faster aircraft departed a different airport. The departing aircraft speed was too fast and the aircraft was wide in turning leading to the loss of separation.