No, you have it wrong.
What you have called shortening the track rods is actually increasing the Ackermann angle (if you mean moving from one Ackermann hole to another)
The ackermann angle is the angle between the track line (90 degrees to the rear axle, through the kingpin, effectively straight ahead) and the Ackermann line, (the line throrough the king pin and the Ackermann position on the steering arm.).
Increasing the Ackermann angle will tend to increase the amount the inside wheel turns in comparison to the outside wheel. So what you may get is the inside wheel trying to turn inside the inner circle and the outside wheel trying to turn on the outer circle.
Depending on the width of the rear track in relation to the front track, the amount the contact patch deforms (tyre slip) and the amount the tyre walls deform (tyre pressure) and whether you have front and or rear bars installed and how you are transferring weight not only rear to front but also inside to outside, the inside front wheel may have greater authority(for a while) and thus increase the amount of turn in.
But, if the kart is set up so that the weight transfers very quickly to the outside wheel, then you won't see any effect from the greater turn in of the inside front wheel.
Think about it, it is actually possible to set up the kart so that the inside front wheel 'floats' over the kerb (the old 'Esses' at Dunkeswell, for example, you approached the first Ess almost straight and floated into the second Ess with the inside front in the air), so you aren't going to get any effect from the inside front no matter how much Ackermann angle it is given.
The bit that you are missing is " in some circumstances". What itpro etc are saying is that you have to decide if those circumstances occur on any given track on any given day for any given driver and whether the advantages of any given ackermann angle outweigh the disadvantages.
Or, if shorter track rods means 'increasing the ackermann angle" and gives more turn in means "increases the angular difference between the inner and outer front wheels compared to a lesser ackermann angle", then you are more or less right!
Sorry we can't make it simple!
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