The danger of high speed aborts with burst tyres.

[Centaurus]

http://libraryonline.erau.edu/online-full-text/ntsb/aircraft-accident-reports/AAR72-12.pdf

The danger of a high speed abort following tyre burst. In this case, the crew did not initially recognise several tyres had blown. When the heavy vibration and slowing of acceleration due to drag during the latter part of the take off run became alarming, the decision to abort was made. The resulting event proved fatal. An old accident; but nevertheless, tyre bursts are not unknown today. There are lessons to be learned by today's pilots. .

[Mach E Avelli]

The simulator I use does not replicate the situation that DC 8 crew was faced with. The ' tyre burst' mode is fairly obvious because there is a 'popping' noise and a slight swing towards the blown side. Most crews pick it and reject below 80 knots or continue above 80 knots. The nearest this simulator can get to degraded acceleration approaching V1 with no accompanying vibration or swing (as experienced by the DC 8 crew) is to feed it an increasing tailwind ( windshear model). But of course whichever exercise is intended is briefed, as neither are in a standard pass/fail check scenario. The runway length is tweaked to be accelerate-stop limiting for them to make a cut and dried 'correct' decision - if the runway is several thousand feet longer than the aircraft requires, they could argue success by rejecting at any time - as long as they get it stopped! Better on the ground with an unknown problem than in the air says they - and me too (thinking of those poor buggers in Concorde). So the scene must be set for crews to know when to stop and when to go. If they get it wrong, rinse and repeat - the big T little c.

Given that exact scenario which the DC 8 crew faced I don't think that too many crews would have done things differently - not even the armchair experts who lurk here - despite being legends in their own lunchboxes. In fact the accident report agrees that they did what most would do, yet with two seemingly contradictory statements:

"Although the captain realized that the acceleration was slower than normal after attaining V1 speed his decision to continue the takeoff under the existing conditions is understandable" then:
"The captain's decision to discontinue the takeoff under the existing circumstances was valid"

They got to Vr and pulled back to 9 degrees but it did not want to fly. With no obvious engine failure they could have assumed a number of things - iced up? overloaded? c. of g. outside limits? Whether it would have flown with a more aggressive rotation is moot, they had neither the training, knowledge of aircraft status nor prior experience to react in the time left (zero time at that point).

[Centaurus]

They got to Vr and pulled back to 9 degrees but it did not want to fly.

A similar problem (but not due to tyre failure) ending in a tragic result, was another DC8 that became airborne well before VR caused by an elevator jam. It pitched up steeply and crashed.
Investigators discovered a piece of tarmac that must have been blown by jet blast into the hinge line of the elevator at the start of the take off run.
See: https://www.fss.aero/accident-reports/dvdfiles/US/1970-09-08-2-US.pdf

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[Traffic_Is_Er_Was]

I'm pretty sure this one features in Mac Jobs "Air Disaster" Vol 1.