Britannia performance - take off run required
The difficulty here is that the Take Off Distance Available (TODA - paved run plus clearway over which to climb to a screen height) and the Take Off Run Available (TORA - paved surface alone) are different beasts, as is the Emergency Distance Available (EMDA - paved surface plus stopway on which to bring the aircraft to a halt). I do not remember ever having to calculate a Take Off Run Required as such in 30-odd years of wrestling with Group A performance on various types. The aim was to input the TORA, TODA and EMDA plus the density altitude, temperature, wind, slope etc in order to determine the maximum weight allowable to get the aircraft to the screen height (eg 35 or 50 ft above the first obstacle at the end of the TODA), having suffered an engine failure at V1 (decision speed). And the answer was always a weight and a speed, never a distance or the amount of tarmac from brakes-off to airborne. TORA and EMDA came into it certainly but you had to input them to the graphs, not calculate them from the graphs. Excuse my rusty memory; it's about 50 years since I studied Britannia 252/253 variant performance but I still have occasional access to a Vol 1 ODM courtesy of the XM496 Preservation Society should there be questions.