Sorry, that second link was supposed to be:
http://www.stoptech.com/whitepapers/brake_systems_and_upgrade_selections_122701.htm
First, I would like to comment that I do not think that your ABS unit is not causing your problems with underbraking the rear axle. I think that there are other fundamental problems with the braking system. Of course I could be wrong. The best way to tell this is to shut off the power to the ABS unit and re-test. You can do this by pulling the ABS fuse or pulling off the connector at the ABS unit. When a ABS unit has no power, it does nothing to limit pressure in the system, it is pass through. If you still have poor braking from the rear axle, it is some other fundamental problem.
The math to calculate your brake proportioning is really simple, but it just takes some serious thinking and data to do the calculation. It is all just simple geometry and statics. You don't have to do the whole calculation, you just need to understand how your changes are going to affect the end result. I'll go through it in some detail:
First you need to know your center of gravity to figure out what the weight transfer is under braking. You will also need the static weight bias of your truck. The weight is transfered to the front under braking, which means that you now have less normal force on the rear tires. This is why you need to have proportioning. If your weight bias was 50/50 and the COG was very low, you could run the same m/c diameter and calipers on the front and rear w/o proportioning. Trucks obviously have high COGs, so hence the need for heavy proportioning. BTW - you change your brake proportioning when you lift your vehicle (Higher COG = more frontal weight transfer under braking).
Second you need to look at the pressure in the front and rear system. You take the force that you apply on the brake pedal and multiply that by the pedal ratio and that then is the force into the m/c. You take this force divided by the area of the m/c piston and that is the pressure in the line. The pressure in the line is then converted back to force at the caliper. This is calculated by taking the pressure and multiplying it by the area of the caliper piston. That is then the force on the rotor. As you can see then, if you increase the size of the caliper, or wheel cylinder piston (at the wheel), you increase the force at the rotor or drum.... HOWEVER (this is a big misconception) if you DECREASE the size of the m/c piston you INCREASE the force at the rotor (assuming the caliper diameter stays the same). If you are having problems with the rear axle being too heavily biased, you could increase the size of the m/c piston going to the rear axle and vice-versa.
The rest of the picture is just torques, but this is the most complicated step. (Calculations with drum brakes are really complicated, so I will ignore them for now) You need to know coefficients of frictions between the friction pads and rotor (which is HIGHLY temperature dependant) and the coefficient of friction between the tire and road. The caliper creates a torque which is the rotor radius times the caliper force (from the pressure) times the coef of the pads. This torque divided by the tire radius is the force at the tire-road interface. If this force exceeds the force that the tire can support, the wheel starts sliding. Ice can support much less force than dry pavement can. Normal force (weight on that tire) changes the force that the tire can support also.
Basically, you need to balance all of these components to have a well-designed braking system. A prop valve in the rear circut is going to LIMIT pressure at the rear axle, which will not help your poor braking performance at the rear axle. What you need to do is change system components to fix your problem. You could do something simple like put really high coef pads or shoes on the rear axle (less pressure will give more torque) or even put crappy pads on the front. You could even change m/c bores, or wheel cylinder bores.
I am not trying to be a know-it-all. I just think that there should be more written on this subject because there is a general lack of knowledge about brakes. One of these days I will do a complete write up and post it on a web page somewhere. I could even generate a web based calculator for braking... I just need more hours in the day!
BTW - I wrote this up pretty fast, so it may be confusing. Ask questions if you don't understand a part of it.
Later-
Ed
