Flyboy 136,
Welcome to the PPRuNe Tech Log sandpit .. just a few comments on your post ..
the take-off distance and the accelerate-stop distance are equal.
Might be better to read "limiting takeoff distance ...[/i]"
No factors such as wet, etc. are taken into account.
It is appropriate to take into consideration whatever factors are relevant to the particular takeoff .. ie, the intent is to balance the particular takeoff .. it is not a generic thing.
This is a general performance calculation which does not care on which runway, or at which temperature your take-off is taking place. (The calculation also assumes dry, sea-level conditions).
I think a quick look at the typical AFM will indicate a dependence on Hp and OAT. Certainly not limited to SL conditions and not a general (ie generic) calculation. I can only presume that you have misread some guidance material along the way somewhere ?
UNbalancing the take-off (ie adjusting V1 within the allowed limits of 1.05 VMCG and Vr) is, in any case, a runway-specific procedure which must take into account all relevant factors. (Also referred to as "scheduled" distance or "factored" distances).
Distance and other factors apply equally whether we are looking at a balanced or unbalanced calculation .. both calculations are made using the same AFM data (although, often, there will be a simplified cut-down chart specifically for BFL calculations .. still based on the main AFM data, though.
1st, 2nd segment obstacle clearance requirements (predetermined by the operator, in rare cases by NOTAM (eg. crane, etc.))
The minimum clearance requirements are specified by regulation. The operator may impose a more conservative clearance profile although most would not for commercial reasons. NOTAM regularly advise changed or temporary obstacle data which must be plugged into the calculations ...
ONLY runway, temperature, obstacle, etc.-specific information will allow an adjusted (earlier) V1
For a specific takeoff on any given runway, there will be a range of usable V1. The lower end will be TOD/Vmcg limited, the higher either ASD/BE limited. You pick which suits your operating philosophy and needs on the day. One of these V1 values will result in a BFL situation if that is important to you. Depending on the runway, the day, and the takeoff weight, the calculated BFL data may or may not be limiting for the particular runway.
I suggest that BFL is only of much value for simplification of data .. general TO charts, typical on board computers etc .. For maximum RTOW, one normally needs to go unbalanced. Some AFMs, of course, don't give you the option, only scheduling balanced data, ... but that's another story.