derby said:
After viewing more illustrations in Tony Foale's book, Motorcycle handling and Chassis Design, and modeling some more, adding CM inertia effect, I now at least semi-understand the "anti-dive/pro-dive" analysis of classic Vehicle Dynamics.
My mistake was that I thought braking force and linked mechanical reaction was greater than any other.
Basically under braking there is no force greater than the CM inertia, which can counteract against the lesser brake force mechanical reaction.
So even though the wheel rotation would always jack the frame in extension when IC is outside of the wheelbase as my test models clearly show in all cases, the greater force of the CM's momentum and it's mechanical reaction can counteract the mechanical brake reaction when they are not complementary.
The friction or wheel traction of rear braking is never more than the force of the inertia in relation to the rear wheel contact point. That inertia force counteracts with a greater strength against the mechanical extension of the outside of wheelbase IC. If there was 100% traction with wheel locked the point of the IC is effectively locked momentarily via the frame with the anti-dive line, from rear contact point though the IC "force center". And the frame rotates about the front wheel contact point. So if the CM is higher than the momentary fixed point where the triangulation of the rear wheel contact point, frame and point crossing the front wheelbase line, then their is net compression, flattening the links of anti-dive lines - counteracting the rear wheel and floating brake link's rotation.
I also see that when the IC is forward of the wheelbase and above ground the anti-dive increases when the suspension is compressed by bumps. This would cause reduction in traction due to the inertia of the CM pushing down the rear wheel in the relative decrease in anti-dive (less compression rate) or increase in pro-dive (increased extension rate).
So in conclusion, IC ahead of the wheelbase above ground is bad geometry for bike handling and reduces braking traction. IC always within the wheelbase, above the ground, and moving rearward during bump compression is far better, which complements bump compliance and traction.
And upon further reflection, the anti-dive rate used by classic vehicle dynamics is an average or net compression or extension percent rate. And it is based upon HORIZONTAL input of CM inertia to the frame and suspension on a flat and smooth surface. The motorcycle examples in Tony Foale's "Motorcycle Handling and Chassis Design" all refer to smooth flat paved surface. When anti-dive is aligned at 50% of the CM height above the front wheel patch, near sag, then applying only the rear brake to decelerate will allow extension and increase frame dive (in addition to weight shift induced dive) at a 50% rate less than 0% anti-dive. Only when there is 100% (or greater) alignment of anti-dive, will there be no dive input from rear brake mechanics on a smooth and flat surface.
The dw-Link has roughly 80 - 90% anti-dive rear braking geometry near sag. So very little net frame dive is induced by the mechanical reactions to the horizontal inertia of the CM. The dw-Link is among the most stable along with monopivots in this factor, considering only net horizontal anti-dive effects.
Horst-links, and monopivot floaters such as the Kona Dope or the Trek Fuel's new Split-Pivot type suspension, have lower percent of anti-dive rear braking, roughly 10 - 15% less anti-dive, allowing more noticeable net frame pitch or fork dive input from rear braking.
But in Foale's book, and any other vehicle dynamics literature I have read, I have never seen any frame pitch or dive reactivity calculation due to bump input reaction to the VERTICAL inertia of the CM.
My cardboard model, pictured in my post just above, clearly shows there is frame pitch (extension or compression) reaction depending if the IC is outside or inside the wheelbase from a forward rolling wheel that is braked or locked with the linkage. The inertia of the rear wheel alone to the linkage is very little, but it is also conditioned by traction with the ground. The inertia of the ground is very high. And the higher the rear wheel traction, the closer the closer the rolling wheel's forward rotation reaction with the links and frame approaches a high factor of input.
So when a bump compresses the suspension there become greater than 100% gravity force input to the CM vertical inertia change with the ground, binding the wheel traction and rolling wheel input affecting the frame reactivity. When the wheel becomes unweighted on the backside of a bump or depression, the traction is reduced or lost so that rolling wheel input effect is reduced.
Overall or net horizontal CM inertia anti-dive is important to weight transfer and stability. The bump-hit reactivity is equally if not a greater factor of the ability of anti-dive geometry to be very effective when bumps affect traction.
So on bumpy terrain the placement of the IC outside or within the wheelbase becomes the most important factor to traction and stability. IC well within the wheelbase to produce compressing reaction during bump-induced compression is best to maintain more consistent traction and stability with bump induced vertical CM inertia change.
The more compatible mechanical frame pitch (extension or compression) reaction from wheel rotation inertia is to produce compressing effects when hitting bump faces, in contrast to extending effects which fight the bump induced compression and bind the suspension into hardtail-like bouncing when hitting bump faces. And the bump backside traction is maintained by stored rebound spring reaction from the more bump compatible more deeply compressed spring.
The dw-link IC is always well within the wheelbase moving rearward during bump induced compression for even greater compatibility and stability and traction. And the high compatibility of bump compliance maintains very consistent traction and so complements its high rate of overall anti-dive stability. The high rates of traction and stability enhance direction change and "flickability" while in bumpy and loose terrain.