A reference to Harry Potter series.
ah ... that would explain why it meant naught to me ..
Surely the climb performance and Weight, Altitude, Temperature are vitally important to V1 choice?
Unrelated.
Climb to screen will depend on weight etc., and that is wrapped up in the TOD calculations.
WAT limits are certification Design Standard lines in the sand to limit maximum weights to values at which the aircraft can demonstrate a modest OEI climb gradient capability in the various segments .. nothing to do with runway considerations.
V1 looks at handling (Vmcg, Vmu), ASD (higher V1), TOR (lower V1), and TOD (lower V1).
This highlights the need for the takeoff calculation to go through all the various limiting calculations to determine which is the most limiting and that limit then determines the RTOW on the day.
As an anecdotal tale to illustrate this need .. I was involved in an audit on an operator some years ago and, sitting in a little terminal in the middle of nowhere waiting for a flight from A to B, I idly did some back-of-a-fag-packet calculations to compare their RTOW tables to the AFM charts. It rapidly became apparent that they had based all their calculations (for a runway which was particularly critical for the company paying for the audit) on ASD limits. Unfortunately, TOD1 was the limiting animal and they were operating significantly above the limiting RTOW day in day out. The client rapidly suggested that I take off my auditor hat and put on my ops engineer version and fix the problem pronto .. which we could do only to a limited extent. Of interest, some years later, I had to train a number of pilots from that operator onto the 737 and the management folk recognised me straight away from the previous encounter ... appears I had acquired a bit of a cult respect within the flight operations group for picking up the error (which was, in fact, quite obvious after a few minutes work while sitting in the aforementioned terminal).
the certified Flight Envelope is an envelope of sharp lines and corners drawn across a picture of shades of gray
The man wins the $64 ... you got it in one ... where the sharpness relates to an idealised world ... and the greys relate to the real world.