HAWKER 700 FLT CREW HAS HEADING DEV WHILE DEP FROM ILG.

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IFR CLRNC WAS: AFTER TKOF MAINTAIN RWY HEADING; 2000 FT VECTORS TO DO 306 DEG RADIAL TO INTERCEPT J110 LARRI INTXN AS FILED. EXPECT FL310 IN 10 MINS. AFTER TKOF WE SWITCHED TO PHL DEP. THEY ADVISED WE WERE RADAR CONTACT. WE WERE THEN TOLD TO CLB TO 6000 FT AND TURN R HEADING 330 DEGS. NOTHING ELSE WAS SAID TO US. A COUPLE OF MINS LATER AN OBVIOUSLY UPSET CTLR INQUIRED AS TO WHAT OUR CLRNC WAS. WE READ IT TO HIM AND HE SAID TO TURN L TO A HEADING OF 230 DEGS AND SAID WE HAD 'BLOWN' THROUGH THE AIRWAY. WE THEN TOLD HIM THAT WE WERE FLYING HIS ASSIGNED HEADING OF 330 DEGS. NOTHING MORE WAS SAID BY HIM. HE THEN GAVE US A FREQ CHANGE. I FEEL THAT HE THOUGHT THAT HE HAD TOLD US TO INTERCEPT THE AIRWAY WHEN IN FACT HE HAD NOT. WHEN ISSUED A HEADING TO FLY WITH NO ADDITIONAL INFO; THAT HEADING IS EXPECTED TO BE MAINTAINED UNTIL A NEW CLRNC IS ISSUED. TO OUR KNOWLEDGE AT NO TIME WAS THERE A CONFLICT WITH ANOTHER ACFT. I DON'T KNOW OF ANYTHING WE COULD HAVE DONE TO PREVENT THIS MISUNDERSTANDING BY ATC. MAYBE WE; THE CREW; SHOULD QUERY THE CTLRS ANYTIME WHEN ON A HEADING AND ASK WHAT CAN BE EXPECTED NEXT.