Range has nothing to do with it, it is the ability to actually get the beast off the ground in the first place. The higher you are, the thinner the air, so the faster you have to go to get enough airflow under the wings to generate enough lift to get airborne. In higher temperatures, this speed increases further.

The problem is that allowances have to be made for an engine failure AFTER V1 (the decision speed) - so the aircraft has to be able to get itself off the ground with one less engine, and this is the problem with flying twins out of hot and high fields like JNB.

Dave