Originally Posted by
conspiratemus1
Your drawing and explanation confuses force with power. Power (rate of dissipation of kinetic energy of bike + riders into heat) is what determines how fast the bike will stop, regardless of how much force or distance you have to pull on the brake lever. I don't want to hijack this thread and won't say any more about this. Hydraulic brakes are not on the OP's menu and we should leave it at that.
You're correct on the semantics but in this case it appears the lack of braking power was due to insufficient mechanical advantage provided by the cable disc brake. Using a hydraulic setup allows one to exert maximum force and dissipate maximum power with one finger.
Cable brakes can also be designed with sufficient mechanical advantage but then they will have more lever travel and require more frequent adjustment.
If you're running discs I hope they're bigger than 160mm. Discs will likely get smoking hot going down a 9% hill.