Steering Box Ratio

It is basic geometry and i shouldn't have tried to respond to a range of NOs and Ughs without asking why :) I just succeeded in trying to dispute things that took us away from the original point..
and yes i shouldn't use flippant throw away comments like busted fingers.
I won't use quick steering to mean fewer turns of the wheel or greater turn in of the road wheel, in respect to the same input at the steering wheel or slow to mean more turns, it seems to drag us off into other things

But do me one last service and give me your view. if i'm wrong i wanna know how wrong

V
if this represents the position of a LONG pitman arm at left lock and right lock, Pitman length and the 2 positions represented by the arms of the v, the arc between the tips of the V is long, It took 4.5 turns of the wheel to swing from left lock position to right lock position.

v if this represents the position of a short pitman arm that has been swung through the same angle. The arc between the tips of the V is much shorter and the wheels didn't reach left or right lock

so in the second case i've changed the ratio of my steering by going long pitman arm to short. If i want to turn the driving wheels as far to the left, and as far to the right as i did previously its going to take more than 4.5 turns of the steering wheel to swing from 1 lock to the other, as you would expect. its probably going to be 5.5 or 6.5 turns of the wheel. i've basically gone from say 16:1 steering to 20: or 24:1 and my v is not splayed wide enough to represent lock to lock

as i approach the fullest extent of travel of the centre link in either direction the angle between the pitman arm and the cross link gets more extreme and my V angle would need to get wider if it has to represent left lock and right lock with the shorter pitman

angle swept by long pitman when viewed from the sector shaft is say 30* angle swept by smaller pitman is 45*

the full travel from lock to lock with the long pitman takes place whilst the angle between it and the cross link is still favoring predominantly sideways motion of the cross link

The full travel lock to lock with the shorter pitman arm tends towards a situation near each lock where the angle between the pitman and cross link is veering towards a situation where the biggest component of the movement of the cross link will be fore or aft rather than side to side

this has to have an impact on delivery of turn in/ out at the wheels in respect to input at the steering wheel.

you explained it away with "Its all arcs and simple geometry" and said no impact.

i'm interested in why no impact? I can't see how there couldn't be an impact

if i made the pitman much longer , Long enough to get a ratio of 4:1 steering much like a Kart

1 full turn of the steering wheel now gives me a steering from one lock to the other.
My V in this case is very very narrow. The sector turns only a few degrees to make a big ark with my long pitman and the movement at the cross link was all created by a pitman arm that was a damn sight closer to perpendicular to the cross link for the whole of its travel than either of the previous two

i can't see how this change in interaction between cross link and pitman in respect to the angles between, can be dismissed as irrelevant.

the delivery of the steering request that the driver makes has to change its "profile" as far as i can see
how am i wrong here? i just can't see it.

the cross link is constrained by the arc it follows at the idler, otherwise long pitman arms in extreme cases would have tyres or brake calipers hitting inner fenders i'd guess. but how is that relevant to a situation that plays out only in terms of the angle scribed between pitman arm and cross link
this relationship changes as you extend the pitman arm

this was my only point, i made it in a bad way and ive tried to make it in a good way but either way if its wrong thats not good and i'd like to understand why.

if you change ratio in the steering box from 20:1 to 16:1 you have to turn the wheel fewer turns, but the delivery of you steering request is the same, the turn-in of the car into a hard right will be the same, apart from the fact that you moved the steering wheel a shorter distance. the effect should be much the same at the wheels

if you change ratio to 16:1 by adding longer pitman to a 20:1 steering box you have to turn the wheel fewer turns in this area its the same as the 16:1 box. but delivery of your steering requests out side of straight on will be different. for the same steering wheel input the turn in of the car will be different.
the long arm stays closer to perpendicular with the cross link throughout its travel than the short arm, therefore the reaction of cross link to steering input has to change in all areas that are not straight ahead.

in seat of the pants terms i guess you might not notice but in simple geometry terms all i can see.... is a difference

Dave