A C650 DEPARTING RWY 36L WAS RELEASED BEHIND A DH8 AND QUICKLY GAINED ON THE LEAD ACFT. THE C650 TURNED TO A HDG OF 300 DEGS INSTEAD OF 330 DEGS; WHICH COMPOUNDED THE SEPARATION PROB. THE RPTR STATES THAT THEY WERE DISTR WATCHING THE DH8 AND MISSED THE TURN.

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I BRIEFED THE FO (TKOF BRIEFING) BEFORE WE LEFT THE RAMP AREA; EXPECTING TO GET RWY 36R. HOWEVER; GND ASSIGNED US RWY 36C. DURING THE TAXI I RESTATED THE TKOF HDG AND ALT FOR THE SID GLANCING AT THE SID AS WE TAXIED; ONLY BRIEFLY AS WE HAVE USED IT MANY TIMES. WHEN WE WERE #2 FOR TKOF THE TWR CLRED A DASH 8 WHO WAS #1 FOR TKOF AND IMMEDIATELY CLRED US INTO POS AND HOLD. I ASKED THE FO WHAT WAS THE WIND DIRECTION ON THE ATIS (WIND SOCK WAS NOT IN SIGHT). HE SAID WIND 300 DEGS AT 9 KTS. AS SOON AS THE DASH 8 BROKE GND THE TWR CLRED US FOR TKOF. I REMEMBER TELLING THE FO THAT WE WOULD SURELY OVERTAKE THIS DASH 8 QUICKLY AS SOON AS WE BECAME AIRBORNE. BOTH MYSELF AND THE FO BEGAN TO WATCH THE DASH 8 AND STARTED THE NOISE ABATEMENT TURN ON THE SID. AS WE WATCHED THE DASH 8 I STATED TO THE FO WE'RE GAINING ON HIM; AND I DIDN'T ALLOW US TO ACCELERATE; KEEPING THE SPD TO ABOUT 180-190 KTS AND SLOWED OUR RATE OF CLB. WE WERE BOTH 'OUTSIDE' WATCHING OUR SEPARATION GETTING CLOSER. I EXPECTED DEP CTL TO TURN US TO INTERCEPT THE TRANSITION; HOWEVER; THEY DIDN'T. AS WE WERE ABOUT TO CALL AND ASK ABOUT THE DASH 8 (DEP CTL WAS VERY BUSY); HE CALLED US AND ASKED WHAT WAS OUR HDG. THE FO LOOKED AT ME AND SAID WE'RE ON 300 DEGS WHICH SHOULD HAVE BEEN 330 DEGS. WE TOLD ATC 300 DEGS. THEY TURNED US AND TOLD US TO STOP OUR CLB AT 3500 FT MSL; AT WHICH TIME WE WERE APPROX 1 MI AND 500 FT FROM THE DASH 8. WE HAD BEEN DISTR BY WATCHING THE DASH 8 AND HAD OVERSHOT OUR 330 DEG HDG AND NOT READ THE HSI HDG CORRECTLY IN RELATION TO THE DESIRED HDG. WHEN ATC ASKED WHY WE WERE ON THE 300 DEG HDG; WE SAID WE MISREAD THE HDG TO KEEP THE EXPLANATION SHORT. WE HAD TOTAL VISUAL CONTACT AT ALL TIMES WITH DASH 8 AND IT DISTR US TO AN ALMOST TOTAL OUTSIDE THE ACFT CONCENTRATION.