how would the factor that's limiting change while on the takeoff?
Reflecting, I probably should have been a little more precise with my words viz., at different locations in the RTOW data set, the limiting case may/will vary.
For a particular takeoff with specific parameters, there will be a particular limiting consideration. Apologies for the needless confusion ...
In the basic method of analysis (ie what we did in the olden days before everyone bought themselves a pocket gadget which rivalled mainframes of old) ..
(a) each particular limit was calculated and the limiting weights plotted on a bit of graph paper .. producing some sort of line(s) defining the weight limit variation against temperature (as the usual presentation).
(b) once all this stuff was done .. and it could take quite a while for a complex runway and AFM ... the graph paper was covered with a bunch of lines.
(c) one then rubbed out all the non-limiting line segments ie ending up with the lowest limiting weight at each temperature point.
(d) it was not unusual to find the limiting case changing several times as one went from cold to hot .... all depended on how the original lines fell to paper.
Unfortunately, the younger set in the Ops Eng fraternity run electronic wizardry these days and don't get to play with the olden days techniques .. which gave a wonderful sense of understanding feel for how an aircraft did this and that.
I really wish the regulations for Air Taxi and Commuter ops in Canada were as restrictive as an airline operation with Transport category airplanes!
Ideally, the rules reflect the reality of what can be achieved considering the feasibility of the communities served being able to afford the service. In a similar manner, Australia (when it had responsibility for PNG) introduced very much lowered standards (compared to Oz) reflecting the very different situation existing in PNG.
Horses for courses is the expression we'd tend to use out in the Colonies.
However, it doesn't preclude a risk aware corporate organisation from adopting higher than minimum standards .. however unlikely that may be in the real world.
It seems good airmanship would dictate that you plan an escape route for departure if you determine you can't clear obstacles with OEI but it seems it'd be legal to takeoff knowing that you would crash into a mountain if you had an engine failure.
I refer you back to my previous statement. No real advantage being legal and dead simultaneously. Hence the reference to sensible corporate risk management.
In a long ago previous life I was responsible for Ops Eng for a jet operator .. the Chief Pilot and I, in the most dreadful collusion, sometimes introduced regulatory conservatism .. the better to allow both of us to sleep well at night. What the bean counters didn't know didn't fuss them. Obviously we didn't do this sort of thing capriciously but we did give due regard to real world commonsense.
"No person shall operate an aircraft in such a reckless or negligent manner as to endanger or be likely to endanger the life or property of any person."
Aye, therein lies the rub .. as in most sets of Aviation Regulatory writings.
It probably would take a comment from Flying Lawyer, or one of his PPRuNe legal colleagues, to clarify just what the words mean precisely at law .. however, I have always found a degree of healthy conservatism to be a reasonable and protective defence against predatory legal activity after the event ..