We next need to examine our stock suspension and steering component layout (geometry) to determine the bumpsteer potential of each component and the design as a whole. To determine how much bumpsteer might/will occur due to the geometry would require a lot of geometric math to calculate, and it's been too long ago and way too time consuming/boring for me to go back to school on the math, so I will not talk in exact numbers, degrees or angular displacements, but rather in terms of severity from none to minimal to slight to moderate to "hang on we're going for a ride". If anyone else is so inclined, please feel free to do the math for us.

Our suspension/steering is pretty basic. any/all bumpsteer is the result of angular displacement (Change in effective length of an arm due to it pivoting/swinging about a point).


note that as the moving end pivots a certain vertical distance the effective length changes. That change is far smaller when the arm is nearer horizontal and increases dramatically the further the end of the arm is moved.
Also note that the effective length change is much more for the shorter arm than the longer arm for the same vertical change.

 

Sorry I have to post this in installments.
Two equal length pivoting arms parallel to each other will maintain the same effective length relative to each other as they swing the same vertical amount.

Now lets examine the OEM steering geometry and identify the various swing arms, their geometric relationships to each other and the affect their effective length changes might have on bump steer.
Pitman arm: fixed at one end, installed vertical when steering wheel is straight ahead, relatively short arm. The change in effective length is largest when the arm is vertical and least at maximum turning angle. The net result is you get more turning of the wheels near straight ahead than at full turn, a positive affect.
Drag link: can pivot at either or both ends. When steering the pitman end moves up and down as the pitman arm connection changes vertical position. Since this also results in turning input to the steering arm, that swing is negligable unless the neutral poisition of the pitman arm is not vertical. if the steering arm end of the drag link swings (such as when the wheel moves vertically over a bump then the effective length change could cause steering input. However Ford anticipated that affect by putting in a neutralizing parallel arm, the rear half of the leaf spring. If you examine the relationship you will see that the end of the pitman arm/draglink connection is horizontally and vertically aligned with each other and the draglink/steering arm connection is directly over the center of the axle and only slightly above the leaf spring axle connection. The leaf spring change in length due to flexing is designed to keep the effective length change equal so the two arms stay parallel and equal length. The net result is negligable bump steer. One end of the axle rising or lowering compared to the other tries to twist the springs which is resisted forcing the axle back to level much like a swaybar.

 

Next installment: chassis mounted R&P issues.
Here's where the whole geometry business goes down the tubes
A R&P steering box is designed to work with the geometry of an IFS. There are basically 4 pivot points across the vehicle the two points where the control arms attach to the crossmember and the steering arm pivots. For the sake of simplifying the discussion lets assume first that the chassis does not move. When a wheel(s) move up and down the control arms pivot at the crossmember and (since most IFS have unequal length contol arms and non parallel angles) the steering arm transcribes a designed arc length around a theoretical pivot point somewhere in between the control arm attachment points, other than that of either control arm, but a relatively short one none the less. The steering rack is attached to the chassis crossmember at a height ~ equal to the theoretical pivot point, and has pivoting end sections the length of the steering arm arc. Therefore when the wheel moves up and down the section of the chassis that include the control arms and steering arms as well as the end of the R&P swing in a parallel arc so there is no effective arm length change and we keep steering straight ahead. In a recirculating ball steering box IFS, the three piece tie rod and idler ams set up the same geometric movement relationships.
Now, the trouble starts when you start defining the swing arms and arcs of the beam axle- parallel leaf spring suspension. Since the axle is solid kingpin to kingpin, wheel movement is in an arc pivoting someplace past the opposite wheel. The axle also transcribes an arc parallel to the frame pivoting at the rear spring mount pivot, due to the spring acting as an arm. So you have the steering arm pivot moving in two arcs in perpendicular planes when a wheel moves, one quite long, the other moderately long.
If you mount the R&P box to the chassis, you will have two short arms unable to length match and/or remain parallel to either of those arms. This mismatch of effective arm lengths during suspension movement will cause unwanted steering inputs resulting in severe bump steer. That is why the R&P conversions for the straight axle currently mount the R&P on the axle, it eliminates the axle moment arms matching issues, the only problem now is matching a chassis mounted column to a steering box that is moving in two planes...

 

Are you running flathead or SBF ? If you are running SBF how did you get your header around the toy gear box ? thanks