Nigel, if you are referring to NW 255 in Detroit on Aug 16, 87 your facts are incorrect.
From the NTSB accident brief:
NORTHWEST FLT 255 (NW255) CRASHED AFTER TAKEOFF FM RWY 3C AT DETROIT METRO AIRPORT. WITNESSES SAID NW255 ROTATED FOR TAKEOFF 1200-1500 FT FROM THE END AND LIFTED OFF NR THE END OF THE 8500 FT RWY. AFTER LIFTOFF, THE WINGS ROCKED LT AND RT AND THE ACFT FAILED TO CLIMB NORMALLY. 18 FEET OF THE LT WING SEPARATED WHEN THE WING CONTACTED A LIGHT POLE 2760 FT BEYOND THE RWY END. THE ACFT ROLLED STEEPLY TO THE LEFT AND STRUCK POLES, A BLDG, AND AUTOMOBILES BEFORE CRASHING INTO A RAILROAD EMBANKMENT. THE ACFT WAS DESTROYED. THE EVIDENCE INDICATED THAT THE FLAPS AND SLATS WERE IN THE UP/RETRACT POSITION AND HAD NOT BEEN DEPLOYED FOR TKOF. NEITHER PLT RECITED THE ITEMS OF THE TAXI CKLIST. STALL WARNINGS WERE ANNUNCIATED BUT AN AURAL TKOF WARNING WAS NOT ANNUNCIATED BY THE CENTRAL AURAL WARNING SYSTEM (CAWS). IT WAS CONFIRMED THAT 28 VOLT DC PWR WAS NOT PROVIDED TO THE CAWS PWR SUPPLY #2. THE REASON FOR THE LOSS OF ELECTRICAL PWR WAS TRACED TO A CIRCUIT BRKR BUT NO MALF OF THE CB WAS FND. FOR FURTHER INFORMATION, SEE NTSB/AAR-88/05
So the airplane flew for 2,760 feet (1/2 mile) no higher than a light pole, not 4,000 feet as you said.