Ok, party time.
Basically, I hope you understand the concept of force/moment balance, in the sense that as you apply force on the front brake, it causes the pitching moment of the bike.
The way to solve the weight over the front and rear tire, is by a system of 2 equations. First equation is that the sum of the above forces, must equal the weight of the bike. Secondly, for steady braking, the sum of moments must be zero.
If you read this article, it lists that the good approximation to the cg location of the bike + rider is half of the wheelbase both vertically, and horizontally. In braking however, the horizontal value shifts forward by about 5% because the rider braces against the handlebars as the bike slows down.
Another variable is the max break force. Modern tires have a peak friction coefficient of 1.2, but lets assume a conservative one of .95.
So we do the math, and we solve for the normal forces as a function of brake force (since the brake force affects the pitch down moment and thus puts more weight over the front tire), and we get the resulting plot, assuming a bike weights 450 lb.
You can see as the brake force is applied, the weight over the front wheel goes up, the weight over the rear wheel goes down. Likewise, the maximum braking force increases, since its the product of the weight over the front wheel and the friction coefficient (and I know that the tire behaviour is non linear, but for the region of interest, the linear approximation is rather accurate).
The particular points of interest are when the rear wheel weight goes to zero, and when the front brake force reaches the maximum value. Note how the former happens before the latter.
What does it mean? That means that the bike will stoppie before the front tire lets go. Which means that the max brake force is achieved with the front only.
However, since the front fork is not a rigid system, care must be taken to not jam the front brakes brakes. Jamming the brakes doesn't let the rest of the bike come down and compress the spring, which puts the described weight over the front wheel. And this is not that hard to do - apply the brakes progressively, and keep squeezing, the weight will come down on the front nice and hard and cause it to bite. You can try this for yourself - find a parking lot, do your best shot as you know it now with both brakes in terms of the shortest distance. Then just do the above and don't be afraid of squeezing harder, and you will likely stop in a shorter distance than before.
This is most clearly seen at the track, when people don't really use the rear brake because all of the braking on sporbikes comes from the front. You can see pros hover the rear wheel above the ground.
When does this not apply? Couple of cases. The first one is the weight distribution does not follow the approximations - cruisers are a great example, the vertical cg is lower, about .3 times the wheelbase distance, and rearward of the centerline of the bike due to the further back sitting position. Doing the same math results in this. Hopefully you can see the difference.
Another case is when the friction coefficient is low, like when riding offroad or on very wet roads. This is the result.
What does that mean to you as a rider? If you are on anything except a cruiser or offroad on a dirtbike, you should practice stopping hard using the front brake, and overall avoid the rear brake use for any straight line stops. Getting used to the front brake and its braking power through repeated use is what is going to lead you to using it properly in an emergency situation.
So given that, and the fact that my original comment is being downvoted, you now understand why I call the people on here retarded. I have explained this in way less detail then before, and people just argue with me without any real basis.
