I have a hydraulic disc road bike with a 160mm rotor on the front and a 140mm on the rear. The setup is exactly the same front to rear, except for rotor size. I'd like to know the disparity between the force I would have to apply at the brake lever for the total friction or stopping power to be equal front to rear, for a given speed over a given distance, to a complete stop, i.e. total work done by each to be exactly equal. Since the 140mm rotor is 7/8th's the size of the 160mm, I'd be tempted to say that an equal lever pull would produce 7/8th's the friction on the rear, but I'm sure there is more to it than that.
So, for example, If I'm riding at 10mph and come to a stop over 100ft, how hard would I have to pull each lever (as a ratio of front brake/rear brake) to ensure that my momentum is converted to exactly the same amount of heat by each rotor respectively?