fdr;
Thank you very much for your analysis of these high altitude takeoff events. I may be totally mistaken here (it's a LOOOONG time since I've done any dimensional analyses), but your formula for Rate Of Climb (ROC) seems to be for linear acceleration, not ROC. In my opinion, you are, however, correct in your analysis that the dicey takeoffs in question featured both very low climb rates and low airspeeds. This sounds like inadequate acceleration per your equation. To perhaps over simplify, inadequate acceleration is usually due to either inadequate thrust or too much weight or a combination of both. As I stated, and to help in my understanding by maybe oversimplifying, I have omitted considerations of rolling resistance, aerodynamic resistance, guano accumulations etc. At any rate, your point that perhaps either the aircraft manufacturer or the operator, or both, are overly optimistic in their performance calculations, is valid in my opinion and may be the root cause of the subject incidents.
Which leads me to UltraFan's post. Are the flight crews using all available power, or are they only using partial takeoff power settings for some obscure reason?
At this point, considering both fdr and UltraFan's posts, I tend to agree that there may be inadequate (inaccurate?) performance data being furnished by both the manufacturer and the operator.
Just my relatively uninformed opinion.
Cheers,
Grog