A B757-200 FLT CREW GOT A HUNG START BECAUSE THEY SHUT DOWN THE APU PREMATURELY; THEN SHEARED THE STARTER SHAFT WHEN THEY ENGAGED THE STARTER TO MOTOR THE ENG BEFORE IT HAD SPOOLED DOWN.

Narrative

I LEFT HOME (PHX) THE DAY BEFORE I WAS TO BEGIN MY PC. THE PLAN WAS TO FERRY AN ACFT FROM ZZZ TO LAX; THEN DEADHEAD BACK TO ZZZ FOR MY PC. I HAD PULLED THE PAPERWORK IN PHX. I DID MY FLT PLANNING IN THE AIRPLANE ON THE WAY TO ZZZ. UPON ARR AT ZZZ; I WENT TO THE ACFT; MET THE FO AND BEGAN THE PROCESS OF READYING THE PLANE FOR DEP. THE FO MENTIONED THAT HE HAD A TIGHT CONNECTION IN LAX TO GET HIM BACK TO ORD AND CATCH THE LAST FLT TO HIS HOME. I NORMALLY DO NOT LET MYSELF BECOME RUSHED; BUT THIS MAY BE A CONTRIBUTING FACTOR. WE COMPLETED THE PREFLT AND PUSHED BACK FROM THE GATE. AFTER RECEIVING CLRNC; I ASKED THE FO TO START BOTH ENGS. THE L ENG WAS STARTED NORMALLY; AND HE ASKED IF I WANTED TO START THE R. I SAID YES THAT IT WOULD BE A SHORT TAXI. AS HE WAS IN THE PROCESS OF STARTING THE R ENG; I WAS COMMUNICATING WITH THE PUSHBACK CREW. WITH EVERYTHING DONE; I RECEIVED A SALUTE AND RELEASE FROM GUIDANCE. THEN; AND I DON'T KNOW WHY; I GLANCED AT THE ENG INSTS AND BELIEVING THE R ENG WAS STABLE; SHUT DOWN THE APU. THE ENG WAS NOT FULLY STARTED AND WE GOT A HUNG START. THE FO TOOK OUT THE QRC AND WE AGREED THAT ENG SHOULD BE SHUT DOWN. MAX TEMP WAS ABOUT 350 DEGS; WAY BELOW MAX START TEMP. UP TO NOW; NO HARM; NO FOUL. AS THE ENG WAS SPOOLING DOWN; THE FO ASKED IF WE SHOULD MOTOR THE ENG TO KEEP THE TEMP COMING DOWN. THE RIGHT ANSWER WAS 'WHAT DOES THE QRC SAY?' MY ANSWER WAS 'OK.' FO OPENS THE BLEED VALVE AND IT DID NOT TAKE US LONG TO REALIZE WE SHEARED THE STARTER SHAFT. MY HEART JUST SANK. NEVER DONE SOMETHING THAT DUMB IN 35 YRS OF FLYING BIG AIRPLANES. MAINT CHANGED THE STARTER AND WE GOT TO LAX ABOUT 50 MINS LATE. SHUTTING DOWN THE APU DURING A SENIOR MOMENT WAS; HOWEVER STUPID; A RECOVERABLE ERROR. ALL WE NEEDED TO DO WAS COMPLETE THE 'ABNORMAL ENG START' QRC! THE VERY NEXT STATEMENT IS 'CAUTION: IF STARTER CUTOUT HAS OCCURRED; DO NOT SELECT GND UNTIL N2 IS 20% OR LESS. READ ALSO; DO NOT OPEN BLEED VALVE ON RUNNING ENG TILL BELOW 20%.' I FEEL AWFUL; STARTERS ARE EXPENSIVE; AND IT DID NOT NEED TO HAPPEN. LESSONS LEARNED: ALWAYS; ALWAYS; ALWAYS USE THE CHKLIST.