I can assure that angela is right. There are nonbroke castles that can't be taken without siegemachines. I am very long playing and experienced player, beleie me if not her
It depends on fortification level and I can assure you that you can find same solution with the calculator too if to put in right options and try it. You need really only one try of calculation, because if you already see moral below 50 you can lose even with moral 49. And like I assume you know, every castle has its limit of attacking footmen. In my era level 4 castle has limit of 1200 attacking footman. You can try it on your calculator. In my case, there is no different what so ever (without castle own attacks when there will be little difference in number and moral drop) if you send to attack 4tk level castle 1 200 footman or 1 200 000 footman, result is same, because only 1 200 can attack castle in the same time, and if castle is too strong for 1 200 footman, then there is no other way than use siege machine too - or risk to lose battle