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...

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.

4) We are saying the same thing i think... i didn't mention ratio

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

6) well aware of "pump it down".. must have been 20 year ago now, Mr Ebergs killer tech and all that. Find a slant 6 pump or shim the valve, easy with saginaw pumps.... yes I read that...
There were questions in this thread that hinted that 14:1 power steering must be really hard work if 16:1 manual is hard work.. obviously not the case, not comparing like with like.
Shim the valve, change the wheel size add more + castor yeah you can do stuff to alter the feel of power steering, some things easier to do than others.

7) Ok, thanks... would be hard to disagree with keeping it nearly standard... :)

8) we all have an arm and a shoulder, but fine, ok, just a way to illustrate, and i'll agree perhaps not the best one, that you can make things easier or harder for a system where you use a pivot point, and a lever, to apply a force, when altering the length of the lever.

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.

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