NMAC AT 1500 FT WHEN THE LOW TIME PLT OF A PA28 MISUNDERSTANDS HIS TFC PATTERN INSTRUCTIONS AND LATER CONFLICTS WITH A DEP KING AIR; RWY 18 AT CGX; IL.

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I WAS FLYING OVER DOWNTOWN CHICAGO ON A SCENIC FLT; AT 1800 FT; IN CONTACT WITH MEIGS TWR. HALF A MI W OF SEARS TWR AND HEADING S THE CTLR ASKED ME TO 'CROSS OVER THE N SIDE OF THE FIELD AND ENTER THE L DOWNWIND FOR RWY 18.' I ACKNOWLEDGED HIS REQUEST. I BELIEVE I MISINTERPRETED THE REQUEST; AND HEADED TO THE S END OF THE FIELD. ABOUT HALF A MI W OF THE FIELD; I WAS HEADING TO THE SE; APPROX ABEAM THE 3RD QUARTER OF THE RWY. I WAS ABOUT TO TURN TO A HEADING OF 90 DEGS AND CROSS OVER THE RWY; WHEN THE CTLR ASKED ME WHAT I WAS DOING. AT THAT MOMENT; THERE WAS A KING AIR AT THE NORTHERN END OF THE RWY; GETTING READY FOR TKOF. I REALIZED THAT I WAS SUPPOSED TO BE OVER THE S END; AND ANNOUNCED MY INTENTIONS TO THE CTLR; 'I WILL CROSS OVER THE S END OF THE RWY AND ENTER L DOWNWIND FOR RWY 18.' ALMOST INSTANTLY THE CTLR ASKED ME TO MAKE AN IMMEDIATE R TURN. THE KING AIR HAD STARTED ITS ROLL THEN. I ENTERED A R STEEP TURN; GOING FROM THE SE TO THE E. DURING THE TURN; I HAD CROSSED THE RWY TWICE; FROM W TO E; AND E TO W. WHILE HEADING SW; DURING THE TURN; I SAW THE KING AIR HEADING TOWARD US ABOUT 300 FT BELOW; AND PASS BELOW US WHEN I WAS ON THE EXTENDED RWY ALIGNMENT. I WAS THEN INSTRUCTED TO ENTER THE DOWNWIND AND LAND ON RWY 18; WHICH WAS UNEVENTFUL. THE ARPT MGR NEEDED TO SEE ME AFTER THIS AND EXPLAINED HOW CLOSE I WAS TO COLLIDING WITH THE KING AIR. I DID ALSO EXPLAIN MY SIDE OF THE STORY AND ACKNOWLEDGE THE MISTAKE I MADE. HOWEVER; I DON'T THINK I WAS IN A COLLISION COURSE WITH THE KING AIR WHILE HEADING SE ABOUT TO CROSS OVER THE RWY. THE KING AIR WAS STILL ON THE GND AT THE OTHER END OF THE RWY. AT ABOUT 100 KTS; 1/4 MI AWAY FROM THE RWY; I NEEDED AT MOST 10 SECONDS; WHICH IS FAR FROM BEING THE TIME A KING AIR NEEDS TO ACCELERATE TO ITS LIFT-OFF SPD AND REACHING THE S END OF A 3800 FT RWY. IN ADDITION; THERE WAS A NE WIND OF 17 KTS. SO; I COULD HAVE BEEN WAY OVER THE E SIDE OF THE RWY BY THE TIME THE KING AIR REACHED MY POS. THE ONLY TIME I WAS IN A COLLISION COURSE WITH THE KING AIR IS DURING THE TURN I WAS ASKED TO DO.