CTLR CLRED A BA46 OFF ON A SID CLBING TO 4000 FT; THEN SHORTLY THEREAFTER CLRED A B757 OFF ON A SID THAT DIVERGED FROM THE BA46 AFTER THE LAS 211 DEG RADIAL AT 3 NM. BA46 WAS SLOW IN CLBING AND THE B757 OVERTOOK THE BA46 WITH LTSS.

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I CLRED THE BA46 FOR TKOF SBOUND; ON A SOUTHERN DEP SID. THE BA46 BEGAN WHAT APPEARED TO BE A NORMAL CLB ON THE SID; WHICH CALLS FOR A SLIGHT R TURN AT 3 DME TO JOIN THE 211 DEG RADIAL (OFF RWY 19L). WHEN THE BA46 WAS APPROX A MI S OF THE ARPT; I CLRED ACR Y; A B747; FOR TKOF ON THE SAME RWY ON A DIVERGING SID. COURSE DIVERGENCE; HOWEVER; WOULD NOT OCCUR UNTIL ACR Y REACHED 3 DME; THEN TURNED R AND CROSSED THE 211 DEG RADIAL NWBOUND. AT APPROX 4000 FT ALT; THE BA46 SLOWED ITS RATE OF CLB CONSIDERABLY; DUE PROBABLY TO THE TEMP OUTSIDE (OVER 100 DEG F). ACR Y; HOWEVER; CLBED EXTREMELY WELL; AND AT 3 DME; WHEN ACR Y BEGAN HIS R TURN; THEIR ALTS WERE RIGHT AT 1000 FT. AS ACR Y TURNED; THEIR LATERAL SEPARATION DIMINISHED TO 2.5 MI; AND ALTS REACHED 800 FT APART. ONCE ACR Y CROSSED THE 211 DEG RADIAL; DIVERGING COURSES EXISTED. DENSITY ALT PLAYED A SIGNIFICANT ROLE IN THIS OPERATIONAL ERROR. NO DOUBT THE BA46 PLT KNEW HE WAS NOT GOING TO BE ABLE TO CLB WELL. THERE IS A XING RESTR ON THE SID AT 15 DME WHICH REQUIRES APPROX 550 FT PER NM. ONCE ESTABLISHED ON THE 211 DEG RADIAL; THE PLT ASKED FOR AND RECEIVED A VFR CLB REF THE TERRAIN; WHICH WOULD REMOVE THE XING RESTR. THE PLT NEVER LET ATC KNOW; HOWEVER; THAT HE WAS GOING TO BE CLBING AT SUCH AN UNUSUALLY SLOW RATE. IT WAS ANTICIPATED THAT THE CLB WOULD BE NORMAL; AND EVEN THOUGH THE B757 CLBS MUCH BETTER; IF THE BA46 HAD CLBED JUST 550 FT PER NM (THE MINIMUM TO MAKE THE XING RESTR) VERT SEPARATION WOULD HAVE BEEN MAINTAINED BTWN THE 2 ACFT UNTIL ACR Y WAS BEYOND THE 211 DEG RADIAL AND DIVERGING COURSES EXISTED. NORMALLY; THE B757 CLBS AT A RATE TWICE THE BA46; BUT ON THIS OCCASION; THE RATE OF CLB WAS TRIPLE; DUE TO THE B46 REDUCING; EITHER BY CHOICE OR DENSITY ALT EFFECT. CTLRS CAN ONLY PROVIDE ADDITIONAL SEPARATION IF WE KNOW THERE IS GOING TO BE A PROB IN THE CLB. HAD THE BA46 PLT INDICATED PRIOR TO TKOF THAT HE WAS HVY; OR THAT HE WAS UNSURE IF HE'D BE ABLE TO MAKE THE XING RESTR; A FEW MORE MI WOULD HAVE BEEN ADDED TO ENSURE LATERAL SEPARATION; INSTEAD OF DEPENDING ON THE VERT.