Steering Box Ratio

oh i think you have been a bit harsh and too quick to dismiss

Point 1 OK i said i didn't know, now i do... more corners than your average city street or stretch of freeway though...i'd guess. they were designed for a job in a car prepped for racing.

linear. as in "not varying" nice straight line on a graph not a curve etc

Point 2
I didn't say the cross link movement was linear. the sector turns by the same number of degrees near center, and off center i.e its movement is linear, as in not varying.
The pitman arm is perpendicular to the cross link at the mid point. At this point any movement of the pitman causes maximum movement of the cross link. As the pitman turns away from the center point, less of the movement at the cross link is side to side and more of it is front to back or indeed back to front, of the car, depending on if it is LHD or RHD ( which way pitman arm faces differs between the two). For a distance turned at the steering wheel, you get a smaller distance moved at the cross link the closer to lock you get. The sector turning is linear, the movement of the cross link across the car decreases the further from centre you go. NOT linear. The sector turns around a point, the pitman arm connected to it scribes an arc.
However so do the levers at the ball joints. If they are the same length pivot to pivot as the pitman arm length, there is some compensation for the arc, the pitman follows. how effective that is, is really dependent on if your pitman faces front or back, the length of the track rods, how parallel they are with the cross link and the compromises in the design. But we are talking here about lengthening one (pitman) and not the other (balljoint). The cross link movement is not linear... and i never said it was. i personally don't think i'm as daft as you think i am..:) but hey, that can be proved wrong, as i find everyday..

5) by extending the pitman arm, the distance from centre of sector, to centre of pitman arm stud is now longer. so the arc it scribes is longer for the same no. of degrees turned by the sector, and the cross link needs to move fore/aft more as the steering approaches the locks. but no change to the length of the balljoint levers. so i still say faster in the middle and faster off centre than it was with the original. Each degree at the sector now scribes a longer arc at the cross link. like a sector of a bigger circle


Nope. Let me be very clear about this, you are 100% wrong about sector steering. This is basic geometry.

The ends of the pitman, idler, and both steering arms all travel in circular arcs. They are all connected by solid rods that do not change length (excepting bump steer, not what we're talking about here).

Because everything is moving in an arc, there is no "center" or "ends" where the geometry changes between the pitman, center link, and tie rods. It's all uniform motion along the arc. Any length difference between the pitman and steering arms is a ratio split evenly over the arc.

That makes everything you said above completely false. There is no "faster" or "slower" depending on how far the wheels have been turned- the center of the box doesn't mean anything to the geometry relationship between the pitman and center link. Not for standard pitmans, not for fast ratio pitmans, none of it.

3) OK not my best use of terms but "what is built into modern steering" covers my sins.
ratio doesn't change... But variable rate racks exist..... maybe i should have said a combination of modern technology conspires to keep us safe. when talking about modern steering. we don't have that in a 50 year old mopar
The modern set up is designed so that the lock to lock turns are low, and the steering is "less lively" in the middle, and nicely tuned to make driving through winding narrow streets and parking at slow speed easier on the arms, less input for a tighter turn to help close quarters maneuvering . You don't get much of that with a steering box and you will make its " dead" point, in the middle smaller when you extend the pitman arm.

Rack and pinions are just a gear and a bunch of teeth. There do not get "less lively" in the middle. That is again 100% false. The stability in the steering on center is an effect of the alignment geometry, not the racks, which are uniform throughout.

If you know of a variable steering ratio rack that's commonly installed in any automotive application, I'd love to see it. Every system in wide production I'm aware of varies the amount of boost or power assist, not the steering ratio. Not saying on doesn't exist, but again, lets see it.

9)you have just put a longer lever on the end of the sector... a longer lever results in a mechanical advantage at the point farthest from the pivot. So feed back from the wheels into the box can apply greater force to the box internals and then from there to the steering wheel. looking at it the other way the forces seen at the sector tooth/ballnut interface will be greater, because from the pivot point at the sector you are now trying to swing a longer pitman arm/lever. the mechanical advantage works against the steering box in this case. The point where you change the direction of the force applied to steer the wheels now see's the end of, and has to try to swing, a longer lever. the steering box is at the "wrong" end of the lever.

The steering box comes off worst. In a system with no steering damper in theory it will wear out faster.

if it takes x ftlb to shove the cross link left 2 inches with a 4 inch pitman arm
it will take 2x ftlb to shove it 2 inches left with an 8 inch pitman. but the distance turned by the sector will be less, half.... its probably 1/2 the degrees.... i'm not gonna work it out, for a made up deliberately simple example, it is less.... and the distance you turn the steering wheel is less.

Work Done, and force are different things. the energy expended by you turning the steering wheel = force x distance
the Work Done at the steering wheel will be the same for both pitman arms.
With the longer one, the steering wheel is harder to turn, but you don't need to turn it as far.
Short one easier to turn, but you turn the wheel much further.
same energy used, but different ratio of "force to turn" and "distance turned" at the steering wheel.

The forces seen in the steering gear will be greater for the long one, covering a smaller rotation of the sector that results in the same 2 inches movement at the cross link.

Doesn't matter how you achieve a ratio, if the ratio stays the same with 2 different configurations the "force" you use to turn the wheel is the same, but the forces across the components of the system between you and the tyres are distributed differently. id rather be a tooth on a sector shaft in a shorter pitman arm equipped box.

You're right, how you achieve the ratio is irrelevant. The force multiplier in the steering system is always the combination of the steering box and the pitman arm, the "standard" pitman arm is included in the ratio calculation for the steering box. If the ratio is the same, the force is the same. Now, a longer pitman arm might put more force on the bottom bearing of the box instead of entirely within the worm and ball? Sure. But the input and output remains the same. The force multiplication always occurs within the box and pitman arm, changing the ratio or length of the arm just changes slightly the components within the box that see the most force.

If a 16:1 box is going to snap your fingers off, then so will a 20:1 box with a fast ratio steering arm resulting in a final 16:1 ratio. Same force, same number of rotations lock to lock.

granted some of the things i said, or the way i said it, are open to interpretation
but i tried to give a layman's terms explanation to illustrate why i think achieving steering ratio with the steering box is better than with a long pitman arm. the long arm seems like a bit of a "hack" for a specific racing purpose.

I feel in some areas you may have been a bit quick to dismiss as wrong, things that are not actually wrong. Not liking the way i put it, is different from it being wrong.

Dave

Everything we're discussing is basic physics and geometry. It's really not up for "interpretation", it happens the way that it happens. It was all designed to work a certain way, and it DOES work in that way. Whether or not you or I understand it correctly doesn't change how it actually works.