Thanks for the comments. The basic idea is this:
The chart is an attempt to represent the sum of all the downforces at the forks as one line and sum of all the upforces as another line, both plotted against fork extension.
The intersection of the two lines is the point in the forks extension beyond which instability can arise.
Trying to create this chart imposes a discipline in thinking about ALL the forces in play and how they are likely to vary with fork extension.
It then becomes a little easier to understand and describe how changing any factor might make things better or worse.
(For clarity I should mention that I have categorised anything that tends to cause the forks to extend as an “up force” and anything that tends to compress the forks as a “downforce”).
When the bike is being ridden at steady speed, the weight of the bike plus rider creates a downforce which is balanced by the upforce provided by the springs.
And when the front brake is applied, forward weight transfer creates an additional downforce.
But as we know from experience, the same braking force acting upon the Girdraulics links also creates an upforce.
And as we also know, when the sum of all the upforces exceeds the sum of the all downforces we get problems.
If the forks extend even fractionally past the point where the forces are just balanced, the changed link angles create increased lift. We then have a positive feedback loop which is unstable. The forks either extend and lock at full extension or go into a vertical oscillation. I have twice experienced this.
The upforces that need to be taken into account.
Spring preload creates a constant upforce throughout the suspension range and therefore adds to the upforces. So the higher the preload, the closer the forks instability point is to the ride height point and the greater the probability of problems.
In the past it has been assumed that provided the bottom link is always pointed upwards at the front, there will be no upforce. But it cannot be that simple. Under braking the top link is in tension, so when it is pointed upwards at the front it creates an upforce in the same way as the lower link under compression does when it is pointing downwards. Admittedly, upper link forces are always less than lower link forces but they are still significant. And when the lower link is horizontal and supposedly incapable of creating any vertical force, the upper link is pointing up, so net link forces are still creating an upforce.
There is another possible complication. When I tried to calculate the forces I came unstuck when I tried to resolve the forces acting at the end of each link.
Put simply, is the net vertical force zero when a link is horizontal, or is it when the link is at 90 degrees to the fork blades? I am embarrassed because I used to be able to do these calculations.
I have a suspicion all leading link forks can create some uplift. Provided it never exceeds total downforce nothing dramatic happens. But it may explain the apparently unsatisfactory feel of the new Brough under braking.
For completeness, I should also mention that aerodynamic drag (and lift?) on the bike and especially the rider also creates an upforce. It can perhaps be ignored as it is not a function of fork design, but it may be significant for a bike with a marginal fork geometry ridden at high speed.
