OK then try this, lock your back brake as hard as you like, will it flip the bike, nope, it locks the rear wheel and it slides.It cannot flip because the point of greatest friction with the road is behind the behind the point of greatest mass.The only way you can go over the top of the bars is if under that braking load you fail to brace yourself enough whereby the bike stops but you keep on going.
This latter happened to me when I was riding fixed wheel once and a length of barbed wire somehow managed to get between sprocket and chain.
The bike tries to rotate around the back axle but cannot because there is a point of contact in from of the brake, its almost like having hyper-extended trail, which I’ll explain in a moment.
Yes the weight does transfer toward the front but this is decelaration not rotation around the front wheel(there is a rotation around the back axle but the directions of forces are such as to be near enough in line in this case) which is why suspension forks will dip but they also stiffen as the springs take up, this together with front tyre spread, allows greater brake effort to be applied to the front. Talk to any motorcycle instructor and they will tell you that failure to use the back brake first in an emergency stop will result in failure of a motorcycle test.
I’d dig out the UK highway code book on this which specifically states why the rear brake should be applied first but that means rummaging around cupboards and things to find it.
The effects of trail and rake makes a large differance to the way a bicycle handles under braking.
The first point of call is the adhesion of the tyre, the greater the contact area the greater is the potential grip, by applying the rear brake first the weight transfer will spread the front tyre, even if you are talking about 16mm sew-ups it will spread significantly enough to increase the contact area.
Next is the rake, this makes the steering more skittish as it steepens and also usually transmits more shock through the forks, which can make handling an adventure on bumpy roads.
Trail is the differance between a line drawn down through the steering head to the floor and the vertical drop down from the front axle.
The greater the trail the slower steering a machine is but braking flexes forks, wether suspension or solid and this tends to reduce trail.You would be surprised at just how much solid forks do flex.
Trail is what keeps a bike stable, a good example to look at is a shoppng trolley when wheels get bent away from their intended position after bashing curbstones. What happens is that the steering angle is set backwards and moves closer to the vertical wheel axle drop, result is that is flaps around.
If the steering head is very steep and the trail very short along with the short wheelbase you find on time-trial cycles you have more chance of being flipped over, but if you increase trail so that the axle is well in front of the steering head the rotational effect has a greater inertia to overcome before you go over the top.
Think of it like a flywheel, increase the diameter and its moment of inertia increases and it takes more force to achieve a given rate of rotation.
You can go too far with trail and rake though, because you get to a point where the adhesion of the tyre is overcome and it slides, this is not a good thing.
The clever part is being able to feel when the tyre is on its limits without going beyond them as you transfer your weight backwards.