On a given bike (with usual front fork, let's forget exotic designs), rake angle and trail are linked: if you increase the rake angle you automatically increase the trail (unless you can change the front tyre diameter).
That's obvious. And as we could see above, the offset can help in manipulating the trail without affecting the rake.
Sure, but on most bikes you don't have that freedom on the fly (yes, you can change your triple clamps but that's not really practical).
As long as we have GPB and BikeEd, we're free to explore many different designs.
I didn't like the explanation on the rake, and the trail is an easy subject as it is already.
Judging by the finishing part of the article, I guess the rake angle helps in retaining the original direction of motion of the whole system (shouldn't having two gyros in it be enough as it is?), while the trail is all about keeping the thing upright.
That's why you need the book. There's a part where a linearised model of the whole bike dynamics is extracted (at different forward speeds). The poles of the model are then plot and the local stability of the bike is deduced from the poles position in the complex plane. A sensitivity analysis is also done, varying the bike's basic parameters (e.g. mass, wheelbase, rake, trail, ...) and judging the effect on the bike's stability (as per the linearised model). If you find an easier way to explain that ...
I don't think all that is necessary to answer the question of "what is the significance of rake in isolation from trail; what consequences does increasing one relative to the other leads to and vice versa."
Sure, for coding my own motorcycling simulator, the book is indispensable. But if I haven't started it before, I doubt that I ever will. The time of me being actively interested in programming is in the past for quite a while already.
Also, I suppose that the majority of people checking this thread would expect to find a concise answer to the topic, but not quite as concise as "increasing rake and trail leads to better stability" (since this kind of popular answer doesn't really answer much).
P.S.
I wouldn't say trail is about keeping the bike upright. Even the article linked tells you much more than that.
The combination of rake and trail gives the "self aligning" behavior of the front. That's the easier to understand effect of rake and trail, but it's not the only one.
Well, also trail encourages the front end to follow the general direction of travel of the system (the effect utilized by drift-prepped cars to a great extent).
These parameters called "rake
and trail" for a reason. We can influence them separately. Therefore, there is a need to look at them separately as well. While at that, we can make simple and clear-cut conclusions in the vein of "increasing the shocks settings leads to decreasing the suspension oscillations' both amplitude and frequency" or "increasing the front ride height results in the static CoG being offset more to the aft".
