BE76 DEPARTING SNS EXPERIENCES CLOSE CALL WITH GAR ACFT.

Narrative

THE OTHER TWIN WAS ON A PRACTICE ILS OR LOC APCH TO RWY 31. HE WAS SUPPOSED TO GO MISSED AT 3 MI FROM THE ARPT. HE DIDN'T AND DID A LOW APCH ACROSS THE ENTIRE LENGTH OF RWY 31. WE WERE CLRED FOR TKOF (ANOTHER ACFT DID A TOUCH-AND-GO BEFORE US) AND PROCEEDED TO TAKE OFF. THE ACFT JUST BEFORE US WAS IN L CLOSED TFC AND WE WERE R DOWNWIND SO THE SPD DIFFERENCE WAS NOT A FACTOR (C150 OR C172). THERE WAS AN ACFT ON FINAL BEHIND US. WE SAW THESE OTHER ACFT AND SEPARATION (SO FAR) WAS NOT A PROB. AFTER WE TOOK OFF AND WAS CLBING THROUGH 50-100 FT; I THOUGHT I SAW 2 ACFT; SO I LEVELED OFF AT ABOUT 150 FT AGL AND ASKED MY INSTRUCTOR IF THERE WERE 2 ACFT. I HAD ALSO GLANCED DOWN AND DETERMINED THERE WAS NOT ENOUGH ROOM TO DSND AND LAND ON THE REMAINING RWY WITHOUT THE POSSIBILITY OF GOING OFF THE END -- MAINLY DUE TO SPD. THE OTHER TWIN WENT RIGHT OVER US ABOUT 100 FT. ACCORDING TO THE RADIO CHATTER AFTERWARD; THE TWIN ON THE APCH DID NOT HEAR THE 3 NM TURNOUT INSTRUCTIONS. AT THE TIME HE WAS TOLD ABOUT THESE; I WAS DOING MY RUN-UP AND MY INSTRUCTOR WAS LISTING; SO I DON'T KNOW IF HE READ THEM BACK OR NOT. I DON'T KNOW IF IT IS RELEVANT; BUT WHEN WE CAME IN BEFORE; THE APCH CTLR DIDN'T HAVE IT ALL TOGETHER; MISSING CALLS AND FORGETTING ABOUT ACFT. I DON'T KNOW IF THE TWIN READ BACK THE 3 NM TURNOUT; BUT THE RULE WHERE THE CTLR DOESN'T HAVE TO HEAR THE READBACK CORRECTLY MAY HAVE ALMOST CAUSED A MIDAIR. ALSO; RADAR AT SNS WOULD BE A BIG HELP.