Gradients and Weak Field

Off topic but I really want to know, how fast can a D stock go on the level on those long sections east of Barking? Can they exceed 45 mph?

Very nice

I went on the District line the other day and it did not feel that fast the C stocks seem to have more power lets hope the S7 stock wont be preformance limited lower than the C stock?

Don't know what D stock you got on the District line... the C stocks have no power IMO and are falling apart as well!

The field weakening comes in after the equipment has notched up fully in full field, thus acceleration does not diminish as quickly as if it had been in full field.
On D78, the notching current up to full parallel is not affected by the flag switch. So the train will get to full parallel - about 18 mph - the same flag up or down. As Dstock 7080 states, the train will be quicker up the climb from Bow Road flag up, because it continues to accelerate above 18mph and take advantage of the weak field setting.
The difference on A stock is that with the flag up, the notching up to full parallel is at a lower notching relay setting. A stock is the only LU stock configured that way. It was done to help minimise peak current demand in the outer London sections and hence minimise the number of sub-stations needed in the 1958-1960 upgrade project.

I think the reason for Flag Switch changeover being at Bow Road both ways is mostly human factors related. The driver only needs to learn a few changeover places. The signalling is designed accordingly (overlaps). Even though there is a speed limit on the descent to Bow Road, there is a small run time benefit before slowing for the speed limit area, coming from Bromley-by-Bow.

Yes, S7 performance is matched to C stock flag down (which is virtually the same as D stock flag down) and D stock flag up, capped to just over 40mph and 45mph respectively to suit the present line limits. Initial acceleration from stand just as C and D stock, not the A stock equivalent. Controlled automatic changeover at the usual places, Bow Road, Turnham Green and Putney Bridge.
Plenty more performance when ATC is implemented later.

@notatraindriver, Im guessing that the 378's arnt capped because the maximum line speed iirc on the North London line is 60mph. But also mainline stock doesnt seem to have the same sort of regulations tube stock has to do with overlaps etc.