So I changed my mind on what to work on next. I completed the front end geometry instead. So now I can customize, camber angle, spindle geometry(which includes scrub radius [how far out the wheels are])], king-pin inclination, ride height, (technically I have caster), toe angle, and if I desire (which I will add soon) modify the Ackerman geometry (but honestly that's easy to do).
The primary driver behind doing this now was to complete the weight transfer to and from the rear tires. Karts have a HUGE king-pin inclination. If you have actually read this entire blog (which I'm sure no one has), I had to replace this pin a while back. By having this inclined so steeply, when the steering wheel is turned, the front tires actually move vertically about an entire inch (my ass is only 1.5" off the ground to start). Both tires do this in opposite directions, this twists the chassis and that results in shifting the weight to the outside rear tire. This is all done even without moving. As I mentioned in the last post, it is very important to unload the inside rear tire for stability reasons. This allows the tire to become unload immediately, even before the kart has actually starts to accelerate into the turn. So modeling these effects was critical to this simulation.
Here's the best part about math, if you do your job right, sometimes the math will surprise you by showing you 'features' you hadn't yet anticipated to happen. I was digging around the code for at least 20minutes looking for the error when it dawned on me, that there was no error at all. In the picture below you will see the rather trapezoidal shape to the chassis twist angle. I was wholly expecting this to be a smooth sine wave (like the graphs above and blow it, which are the actual vector components of the wheel spindle going back and forth). Turns out, that something I was going to test next, was already happening. If you will look at the tire-deformation chart on the right, you'll notice the inside rear tires are getting picked-up off the ground completely. So the chassis stops twisting more and just rotates entirely instead.
This is completely realistic if the chassis is stiff enough. I have not actually calculated respectable values for this, I just picked something from intuition. I'm glad to see it wasn't far off at all in the end. I will soften the chassis only a little more until I get some actual test data.
So some conclusions/understanding to apply to your kart
If you want to unload the inside rear tires more, you have a couple of options...
-If you want this to happen more quickly at the start of a turn (i.e. your kart feels heavy to turn-in at the beginning of a turn), then you might want to either increase your scrub radius, increase your king-pin inclination. Each of these options will increase the vertical travel of the tires. If that doesn't work, try to increase the chassis stiffness by using the torsion bars. This allows for the twisting at the front, to more effectively lift the rear tire.
-If the rear tire just doesn't seem to come up during the turn, you can either loosen up the chassis stiffness (front is more effective than rear I believe). This is opposite of above because while in the turn, the dominant force is the actual G-loading pulling your over, while at the start of the turn, these forces really aren't there. So loosening up the stiffness allows the kart to roll over more.
-If your kart seems to skip/hop during a turn (not while starting it) from the rear touching down, most say continue to loosen the stiffness, I say try stiffening it up a little bit if you're already loose. Reducing the stiffness of your chassis too much will decrease your overall grip because you're going to allow the chassis to roll too much and this forces the tires to increase/decrease their camber angles to the point of unloading the inside of the tires. By increasing the stiffness of the chassis you aren't allowing the tires to come up so far that you're losing grip and then slamming down your rear tire in what is known as an LCO (Limit Cycle Oscillation). So give both directions a shot. Hopefully the completion of these simulations will yield some plots that I can post for everyone's reference and remove a bunch of the guess work.
Another note, decreasing the rear tire pressure will allow for greater compliance to changes in camber. The sidewalls are remarkably flexible on our tires, this flexing allows for the tire to remain flat on the ground even when the axial is at an angle. Decreasing the pressure will allow for more sidewall flexing, but be careful when reducing tire pressure, it can blah blah blah blah legal stuff.
I might try to also complete a slightly better tire model today which accounts (to some degree) for the effects of camber.
Until then,
-S
The primary driver behind doing this now was to complete the weight transfer to and from the rear tires. Karts have a HUGE king-pin inclination. If you have actually read this entire blog (which I'm sure no one has), I had to replace this pin a while back. By having this inclined so steeply, when the steering wheel is turned, the front tires actually move vertically about an entire inch (my ass is only 1.5" off the ground to start). Both tires do this in opposite directions, this twists the chassis and that results in shifting the weight to the outside rear tire. This is all done even without moving. As I mentioned in the last post, it is very important to unload the inside rear tire for stability reasons. This allows the tire to become unload immediately, even before the kart has actually starts to accelerate into the turn. So modeling these effects was critical to this simulation.
Here's the best part about math, if you do your job right, sometimes the math will surprise you by showing you 'features' you hadn't yet anticipated to happen. I was digging around the code for at least 20minutes looking for the error when it dawned on me, that there was no error at all. In the picture below you will see the rather trapezoidal shape to the chassis twist angle. I was wholly expecting this to be a smooth sine wave (like the graphs above and blow it, which are the actual vector components of the wheel spindle going back and forth). Turns out, that something I was going to test next, was already happening. If you will look at the tire-deformation chart on the right, you'll notice the inside rear tires are getting picked-up off the ground completely. So the chassis stops twisting more and just rotates entirely instead.
This is completely realistic if the chassis is stiff enough. I have not actually calculated respectable values for this, I just picked something from intuition. I'm glad to see it wasn't far off at all in the end. I will soften the chassis only a little more until I get some actual test data.
So some conclusions/understanding to apply to your kart
If you want to unload the inside rear tires more, you have a couple of options...
-If you want this to happen more quickly at the start of a turn (i.e. your kart feels heavy to turn-in at the beginning of a turn), then you might want to either increase your scrub radius, increase your king-pin inclination. Each of these options will increase the vertical travel of the tires. If that doesn't work, try to increase the chassis stiffness by using the torsion bars. This allows for the twisting at the front, to more effectively lift the rear tire.
-If the rear tire just doesn't seem to come up during the turn, you can either loosen up the chassis stiffness (front is more effective than rear I believe). This is opposite of above because while in the turn, the dominant force is the actual G-loading pulling your over, while at the start of the turn, these forces really aren't there. So loosening up the stiffness allows the kart to roll over more.
-If your kart seems to skip/hop during a turn (not while starting it) from the rear touching down, most say continue to loosen the stiffness, I say try stiffening it up a little bit if you're already loose. Reducing the stiffness of your chassis too much will decrease your overall grip because you're going to allow the chassis to roll too much and this forces the tires to increase/decrease their camber angles to the point of unloading the inside of the tires. By increasing the stiffness of the chassis you aren't allowing the tires to come up so far that you're losing grip and then slamming down your rear tire in what is known as an LCO (Limit Cycle Oscillation). So give both directions a shot. Hopefully the completion of these simulations will yield some plots that I can post for everyone's reference and remove a bunch of the guess work.
Another note, decreasing the rear tire pressure will allow for greater compliance to changes in camber. The sidewalls are remarkably flexible on our tires, this flexing allows for the tire to remain flat on the ground even when the axial is at an angle. Decreasing the pressure will allow for more sidewall flexing, but be careful when reducing tire pressure, it can blah blah blah blah legal stuff.
I might try to also complete a slightly better tire model today which accounts (to some degree) for the effects of camber.
Until then,
-S
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