DC10 CREW TURNED TOWARD HIGH TERRAIN AFTER TKOF.

Narrative

I WAS FLYING THE PERCH 1 SID FROM HONG KONG INTL TO MUMBAI; INDIA. THE SID CALLED FOR RWY HDG OF 073 DEG TO POINT PORPA; THEN A R TURN TO POINT BREAM. THE TURN WAS TO BE INITIATED AT 5 DME OFF OF HONG KONG LOC FREQ 109.3. SHORTLY AFTER TKOF I ASKED THE CAPT TO ACTIVATE THE FMS FOR THE SID BY SELECTING HEADING SELECT. HE DID AND I FOLLOWED THE COURSE NEEDLE. SHORTLY THEREAFTER I READ 5 DME ON MY VOR AND EXPECTED A R TURN COMMAND FROM THE FMS TO TAKE ME TO POINT BREAM. IT DID NOT GIVE ME THE COMMAND SO I MANUALLY SELECTED BREAM DIRECT. AS I STARTED MY R TURN THE CAPT WAS BUSY CHANGING COM RADIO FREQ TO DEP FREQ. AFTER CONTACT WE WERE GIVEN AN ALT OF 7000 FT WHICH THE CAPT PUT INTO THE FMS AND I CONFIRMED. AT THIS TIME THE CTLR ASKED IF WE WERE STILL ON THE SID. I SAID; 'YES; WE ARE RIGHT ON IT.' THE CTLR THEN SAID; 'YOU ARE R OF COURSE AND APCHING HIGH TERRAIN.' AT THIS POINT THE CAPT TOOK CTL OF THE ACFT AND IMMEDIATELY STARTED A CLBING L TURN. AT THE SAME TIME HE COMMANDED THE ENGINEER TO PUSH THE THROTTLES UP TO TKOF PWR. AT ABOUT THIS TIME; WE GOT A GPWS WARNING. SHORTLY THEREAFTER THE CTLR SAID WE WERE CLR OF THE TERRAIN AND CLRED TO POINT PERCH (NEXT POINT AFTER BREAM). AFTER SAFELY AIRBORNE WE RESEARCHED THE PROB. I DISCOVERED THAT I HAD SET THE WRONG NAVAID ON MY VOR; THAT READ 5 DME MUCH SOONER THAN REQUIRED FOR THE SID. THE PROB WAS DISCUSSED WITH THE CTLR. HE SAID HE HAD NO PROB WITH IT BUT THEY DID RECEIVE SOME NOISE COMPLAINTS. CONTRIBUTING FACTORS: WE WERE ALREADY ON A 12 HR DAY AFTER FLYING 5.5 HRS FROM MUMBAI; THEN HAD A GND DELAY FOR CARGO LOADING; A RWY CHANGE AND AN ATC DELAY FOR OUR RTE OF FLT. SEVERAL TIME ZONE CHANGES THE PREVIOUS DAY; ALSO CONTRIBUTED TO OUR FATIGUE FACTOR. ALL THIS COMBINED WERE ALL FACTORS CONTRIBUTING TO OUR PERFORMANCE.