ackerman III (the payoff)

Now that we have some mathematical expressions to describe ackerman in terms of steering geometry I was able to look at how different steering system ideas affect ackerman. First, here is the tool I made for excel:





This has all the variables I defined yesterday. I use the convention to put all user inputs as blue cells. So this describes a car turning left with rear steer. The whole idea of this is that the angle alpha would be different magnitude if the rack moves left 0.5 inch vs right 0.5 inch. So the second group of rows are negative rack position for the other side of the car.

The corresponding left and right side instant center differences are used to calculate ackerman %. Just for reference I threw in what ackerman percentage corresponds to parallel steering. I think that this is sort of the limit of remotely acceptable.

I also made a few plots to help visualize what is going on:

  

Left: shows how two variables are related.  Right: gives a visual representation of of the steering components and their positions based for each row on the left side.

The plots above go with the first spreadsheet and are close to my stock Ford Focus steering geometry. So as the rack moves up (top point in plot) you can see the angle of the wheel changes (segment from 0,0 to about 4.6,0). When we look at the spreadsheet we can see that the factory set up is for slight anti-ackerman (slightly negative). This is what we would predict for a street car. Now we can look at what happens with each of the solutions being considered:

Option 1:  Moving the rear steer rack forward

Several days ago I posted an image showing that the rack on the stock setup can not stay where it is. What happens if we still let it rear steer the knuckle, but move it way forward like this:







Notice that rack movement is 0.6 inch for all rows, bot that turn radius increases for the negative rack positions. So we can concluded that the steering gets less sensitive as the rack moves forward.  We can also see that things deteriorate nonlinearly in terms of ackerman.  By the time we are 8 inches ahead of the axle we are way more anti than parallel steering and although not shown this gets worse for tighter turn radii.

Option 2:  Swap left and right knuckles and front steer.

The shown geometry actually describes this already. Only the ackerman calc changes, and left and right change for forward steer.  As a result we end up with slightly pro ackerman, but nothing that dramatic.  Which was a surprise to me.
Here are plots looking at what happens if we vary front steer rack position

Above we can see that the further forward we move the rack the tamer everything gets.  This is the equivalent on a rear steer car of moving the rack further back.  Only here we diminish pro-ackerman instead of diminishing anti ackerman.  To see how it behaves over the range of steering I plotted + 8 inch offset:

This looks as close to perfect as anyone would need.

Conclusions:

It appears that moving the rack to the opposite side of the axle for either front or rear steer is a bad move.  Things start to head downhill quickly.  The surprise win is that if I swap left and right knuckles, I don't need to correct for ackerman if I can locate a front steer rack far enough forward.  If this works out spacewise, then it will be a low effort and low cost solution to a major hurdle in this build.