"Please have a look and check for mistakes/misunderstandings:"
One would start with your terminology. You describe an effect eg:'it makes the kart tip more/less' when that isn't what happens. As a result you may do something expecting one result but actually get another.
For example, for all practical purposes in lifting the inside rear, a narrow track on the rear does not cause the kart to tip more.
If you think of the kart 'tipping' by a constant angle, then widening the track will mean that the inside wheel lifts further. (Think of a triangle, the further one gets from the 'angle' the larger the distance between the lines.)
Why is the difference important? Well, the kart 'grip' is dictated by the shape and size of the contact patches between rubber and road.
A tyre is flexible and when you go round a corner the side walls distort. For a certain amount the tyre stays flat on the road, but the axle is no longer parallel to the road.
At that point you still have maximum grip on one tyre.
To lift the inside tyre, you either have to increase the angle, or move the inside tyre along the axle until it is off the ground.
If you increase the angle you start to reduce the size of the contact patch as the tyre starts to 'peel' off the road.
If you reduce the size of the contact patch you reduce the ability of the kart to counter the sideways forces in the corner, it skids more easily.
So, what you are doing in set up is to combine the twist in the chassis (leverage?) and the length of the lifting arm (not leverage) with the distortion in the tyres (not leverage) so that you have maximum grip for the largest number of corners.
(And Haskenheim looks to have interesting corners, in fact it doesn't seem to have straights).
Varying tyre pressure for example would alter the distortion range of the tyre and appear to give more or less 'lift', but that is complicated by the mechanical and chemical adhesions of the tyre.
At the same time, theory says that you adjust the camber of the tyres so that they maintain negative 0.1 (the angle at which they have maximum grip) in the turn, which again is affected by the driver, the track and the kart. It has nothing to do with 'tipping the kart over'.
Caster creates a larger jacking effect, which doesn't 'tip the kart over' but does increase the force affecting the inside rear wheel (so one could say tipping the kart over in one sense). Caster also affects the forces needed to turn the wheel (trail distance) and one can design or set the kingpin offset (ie the centre of the stub axle does not pass through the kingpin) to make the steering heavier or lighter. If you have adjustable caster, you can feel a difference between having the caster set fully forward top and bottom and fully aft top and bottom. It wont change the caster angle, the amount of jacking, but will change the force needed to steer.
With a cadet that may be important.
Also don't underestimate the value of driving technique. For example, decelerating (braking) in the turn reduces the stability of the kart by about 45%, in other words it is roughly twice as likely to spin.
For a novice or inexperienced driver, the value of teaching them to brake on the straight is that they have taken their foot off the brake by the time they start the turn in.
One has to remember that just changing direction is itself a deceleration, so one increases stability by accelerating in the turn, but not so much that one spins the rear wheel.
One can save far more time by getting this technique right than one can by braking very late and being unstable in the turn. It may feel slower but will be much more predictable and as has been pointed out, you cannot test and improve until the driver can do constant laps, because the changes might be due to driver error rather than kart set-up.
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