I thought that you could get a higher payload if you used a lower level off height. Any thoughts, Mr. Tullamarine?
Not a simple matter of this or that. As so often is the case .. it depends.
When running an RTOW analysis, one needs
(a) as input data .. runway info, obstacle info, met conditions, airspace limitations, etc
(b) as a number crunching tool .. either the AFM run on the drawing board with a calculator of some sort .. lots of graph paper and cups of coffee (ah, tradition) .. or a computer model which either did, or was associated with the software which, generate(d) the AFM data (sourced from the OEM) or is derived from the AFM graphs (lookup tables or regressions for the more elegant).
One then runs a bunch of separate calculations to look at the various limits (sometimes the AFM will provide all of these explicitly, sometimes some are buried transparently with the AFM .. however, they are all addressed in one way or another. Such calculation sets are done for each OAT/wind point of interest for the end data presentation.
Limitations (which address AEO and OEI) include such interesting things as
(a) maximum structural weight
(b) WAT limits for the configuration and ambients
(c) TORR
(e) TODR
(g) ASDR
(h) obstacle limited weight for EACH significant obstacle
(i) BEL
plus whatever else might be pertinent for a particular Type. In addition, one usually re-runs the exercise for a range of V1/VR values.
Normally, downstream limitations such as cruise, approach and landing weights are done separately for obvious reasons.
Done manually, the output is a bunch of lines on a graph of TOW by OAT with W/V as a parameter for a set of V1/VR. The resulting dog's breakfast provides, for each data point, a minimum TOW which becomes the limit for that data point.
The difficulty in generalising is that the "limiting" limit can vary across the graph.
Done electronically, each data point is finished and the final output deposited into the final output file - just a different approach to ending up with the same numbers.
Manually, the answers come out to, say, the nearer 50-100lb. Electronically, the nearer umpteenth decimal point which, when flight test and other error ranges are considered is still accurate to around the nearer 50-100lb (or somewhat more, for the big birds).
Getting back to the original query, if there are no significant obstacles further out, a lower third segment is fine .. if there are significant obstacles further out then pushing up the second segment pushes up the third segment in turn so that it sits atop the critical obstacle in the third segment or, similarly, the fourth segment will be higher at a given distance for fourth segment obstacles.
Do keep in mind that the third segment which we are comparing to for obstacle clearance is NOT the (gross) acceleration height which the pilot is endeavouring to maintain but, rather, a somewhat lower (net) level.
All a case of horse for courses.
Nothing overly difficult but it does need diligent housekeeping, a tolerance for boredom, and an ability to drink vast quantities of coffee.
Getting back to the very original question .. what is a good third segment height ? .. beats me ... it all depends, you see.