Ahhh.....if only we still had FEs,
OK...back to the present, Boeing (B737NG) recommends that rolling takeoffs are better, less chance of compressor stalls due to crosswinds.
If the rolling takeoff is carried out correctly, there is no appreciable difference in t/o distance required.
That means, advancing the thrust to approximately 40% N1 to stabilize both engines, is limited to a maximum of 2 seconds at that setting, before TOGA is selected, otherwise takeoff performance may be affected.
Simple and easy,
Cheers, FD
