Spindle kingpin
- Thread starter Sjg22
- Start date
Ted Hamilton
Helmet Painter / Racer
The only way the LF can be "pulled down" into the racing surface and the RF "pushed down" is if we're talking about an independently suspended vehicle with front a-arms that are engineered with precisely calculated roll center paths. They will be non-parallel a-arms. They may also be completely asymetrical to accomplish anti-squat or anti-dive also... With an effective "beam axle" like a kart, that's not possible. Assuming the roll center of a kart is above ground, the LF gets "pulled" up and the RF gets pushed down as the kart tries to roll about it's Y axis roll center.
Paul, I highly recommend you read Paul Van Valkenburgh's classic motorsports book on the topic:
http://www.amazon.com/Race-Engineer...=sr_1_1?s=books&ie=UTF8&qid=1420656260&sr=1-1
Milliken's treatment of the subject is even more comprehensive, but collegiate engineering level, so not for light reading:
http://www.amazon.com/Race-Car-Vehi...1420656420&sr=1-1&keywords=miliken+suspension
The caster split will, however, cause different corner weights to be applied, affecting chassis dynamics by shifting the roll center laterally. It would be somewhat the same effect as taking a movable weight and sliding it to driver's left as the turn was initiated.
Paul, I highly recommend you read Paul Van Valkenburgh's classic motorsports book on the topic:
http://www.amazon.com/Race-Engineer...=sr_1_1?s=books&ie=UTF8&qid=1420656260&sr=1-1
Milliken's treatment of the subject is even more comprehensive, but collegiate engineering level, so not for light reading:
http://www.amazon.com/Race-Car-Vehi...1420656420&sr=1-1&keywords=miliken+suspension
The caster split will, however, cause different corner weights to be applied, affecting chassis dynamics by shifting the roll center laterally. It would be somewhat the same effect as taking a movable weight and sliding it to driver's left as the turn was initiated.
paulkish
old fart
"Assuming the roll center of a kart is above ground"
They are not all above the ground. If they were, indoor kart racing would be impossible.
And the books you pointed out deal with "Real Race Cars" which turn both left and right, though most of it applies, most on this site do not race "Real Race Cars". The in addition too, information needed for LTO(left turn only), is not covered in the books you mentioned.
edit: IMHO, on a kart you can leverage to push both the left and right tires into the ground, without rolling about a roll center. Think of it as the direct application of force in a straight line. and... I ain't sure because I ain't no engineer and am just winging it. ...
They are not all above the ground. If they were, indoor kart racing would be impossible.
And the books you pointed out deal with "Real Race Cars" which turn both left and right, though most of it applies, most on this site do not race "Real Race Cars". The in addition too, information needed for LTO(left turn only), is not covered in the books you mentioned.
edit: IMHO, on a kart you can leverage to push both the left and right tires into the ground, without rolling about a roll center. Think of it as the direct application of force in a straight line. and... I ain't sure because I ain't no engineer and am just winging it. ...
ABR #69
Member
Only way I see the LF being pulled down is through steering input. As weight is pushing the RF down, we've essentially designed the steering geometry to pull the left front tire down as the chassis tries to move up. Thus pushing the RF down with weight and the jacking effect of the castor, allowing the kart to begin rotating on entry. Then the castor pulls the LF back down to equalize some load from the RF tire to keep it from over loading it and create more side bite for the front to keep it on track.
Maybe that's what you are getting at, Paul?
Maybe that's what you are getting at, Paul?
Ted Hamilton
Helmet Painter / Racer
The whole reason a kart bicycles is because its' roll center is above ground....it's just usually low enough that the lateral grip of the tire is exceeded before the kart can lever itself up and over. Indoors, the traction is artificially raised, and so unless more weight is transferred left, and/or grip removed from tires, the kart will bicycle more easily.
When the wheels are turned, the positive caster pushes the left tire down, or more accurately, pushes the left of the chassis up, and as a consequence, it has the same effect as if you took the rear axle and moved the carriers one hole lower -- weight is transferred to the corner that's closest to the chassis rail via mechanical means, and transferred to the right of the kart via dynamic means.
I won't bother doing a free-body-diagram, but rest assured, a kart's roll center is above ground all the time, otherwise both tires would indeed get pulled into the ground and a kart could never naturally flip on its' own.
When the wheels are turned, the positive caster pushes the left tire down, or more accurately, pushes the left of the chassis up, and as a consequence, it has the same effect as if you took the rear axle and moved the carriers one hole lower -- weight is transferred to the corner that's closest to the chassis rail via mechanical means, and transferred to the right of the kart via dynamic means.
I won't bother doing a free-body-diagram, but rest assured, a kart's roll center is above ground all the time, otherwise both tires would indeed get pulled into the ground and a kart could never naturally flip on its' own.
alvin l nunley
Site Supporter
You can have a role center, it can move up and down, but the pivot point is always where the tire touches the ground. That is, a role center has to have a point around which it pivots. That pivot point is always the tire, where it touches the ground. "Getting the tire into the ground" is just an expression, an expression used, inappropriately, to explain the transfer of weight to one or more tires. If you transfer weight, laterally and down, to a tire, you will increase the traction of that tire with the ground. You can increase, or decrease, that traction, (with a given tire) by moving the role center up and down. You can move the role center up or down by moving the major weight source, (the driver) up or down, or widening, or narrowing, the distance between the wheels on the rear axle. I know there are other techniques, and other variables, for doing this, this is just a couple of them.
Ted Hamilton
Helmet Painter / Racer
Al -- I agree. And if one wishes to understand what's going on from a physics standpoint, one must be committed to using precise and correct terminology. There IS a phenomenon where the inside tire CAN be "pulled" harder into the ground via dynamic weight transfer when the suspension geometry is set up so that body roll translates into a force toward the inside of the turn instead of "rolling outward." This happens when the Cg (roll center) of the car is BELOW the suspension pickup points, so that the constraints of the physical suspension arms are pulling the inside tire down (and to some extent, the outside tire "up"). This causes some of the dynamic weight transfer to be cancelled, resulting in a more stable average loading on the tires. As such, the tires can be loaded at a more optimum weight and slip angle. The more rigid a suspension, the quicker the weight transfer occurs and the less motion there is to change a roll center. The roll center is determined by the line between the contact patch on the tire and the "instantaeneous center". Perhaps this diagram will help clarify:
For a kart, there are no "a arms", just a mishmash of tubing that operates like nearly ridgid parallel a-arms or a beam axle. In such cases, the roll center is on the ground (at rest), but in turning, the beam angles some, raising the roll center slightly. It is so low, however, that karts tend to handle really well. This is because they are loading the tires closer to the angle the tire is trying to resist slip in, therefore less energy is wasted in a greater downward vector.
If you want to see a revolution in karting, start playing with waist behavior and design. Wayne Felch may have a head start...
For a kart, there are no "a arms", just a mishmash of tubing that operates like nearly ridgid parallel a-arms or a beam axle. In such cases, the roll center is on the ground (at rest), but in turning, the beam angles some, raising the roll center slightly. It is so low, however, that karts tend to handle really well. This is because they are loading the tires closer to the angle the tire is trying to resist slip in, therefore less energy is wasted in a greater downward vector.
If you want to see a revolution in karting, start playing with waist behavior and design. Wayne Felch may have a head start...
Al -- I agree. And if one wishes to understand what's going on from a physics standpoint, one must be committed to using precise and correct terminology. There IS a phenomenon where the inside tire CAN be "pulled" harder into the ground via dynamic weight transfer when the suspension geometry is set up so that body roll translates into a force toward the inside of the turn instead of "rolling outward." This happens when the Cg (roll center) of the car is BELOW the suspension pickup points, so that the constraints of the physical suspension arms are pulling the inside tire down (and to some extent, the outside tire "up"). This causes some of the dynamic weight transfer to be cancelled, resulting in a more stable average loading on the tires. As such, the tires can be loaded at a more optimum weight and slip angle. The more rigid a suspension, the quicker the weight transfer occurs and the less motion there is to change a roll center. The roll center is determined by the line between the contact patch on the tire and the "instantaeneous center". Perhaps this diagram will help clarify:
For a kart, there are no "a arms", just a mishmash of tubing that operates like nearly ridgid parallel a-arms or a beam axle. In such cases, the roll center is on the ground (at rest), but in turning, the beam angles some, raising the roll center slightly. It is so low, however, that karts tend to handle really well. This is because they are loading the tires closer to the angle the tire is trying to resist slip in, therefore less energy is wasted in a greater downward vector.
If you want to see a revolution in karting, start playing with waist behavior and design. Wayne Felch may have a head start...
FWIW Ted, the roll centre is not what creates the inside tires to be loaded more. Its actually the VCG being lower than the roll centre. So you need a really high roll centre. (It however wont stop the dynamic weight shifting outward that's impossible). As you would already know this can be achieved with suspension design.
alvin l nunley
Site Supporter
you are obviously much more educated in this subject than me, but, explain to me how a tire can be "pulled" into the ground? It almost sounds like a vacuum "pulling" air into the engine. lol
alvin l nunley
Site Supporter
I would replace, "achieved" with, "improved" or "enhanced".
Ted Hamilton
Helmet Painter / Racer
Al --The simplest way to say it is this.... Every vehicle has a center of gravity (Cg), which wants to move in the direction of the net force applied ("outward" in cornering.) It also has a roll center, which is geometrically determined by the line between the contact patch and an "instantaneous center" which is the point where the lines of the suspension arms intersect. If you can design the vehicle so that the Cg is at the same vertical height as the roll center, then the vehicle does nothing (body roll-wise) during a corner -- it rides flat and responds to the cornering forces only with yaw (z-axis, straight down through Cg).
If the Cg is ABOVE the roll center, then there is a lever arm created between the distance from roll center, and magnified by the mass of the car. The body will want to roll in the ooutward direction, stopped by the suspension forces. This will have the effect of loading the outside tire even more, and lessening the load on the inside tire. A key example of this is in SCCA Showroom Stock classes where they aren't allowed to optimize the geometry and the inside tire is often off the ground:
If the Cg is BELOW the roll center, then there is a lever arm wants to act so that the bottom of the car rotates "outward"...this "pulls" the inside tire down further into its' suspension travel and lessens the load on the outside tire. This is what I meant when I said that the overall "average" load is more constant. High Cg exaggurates the cornering forces with respect to the wheel, and low Cg minimizes it.
From a suspension standpoint, having Cg at the roll center allows you to use the suspension travel to absorb bumps, rebound, etc. with no outside effect from the car dynamically shifting weight around (side to side). Keep in mind, we're only looking at one axis...
Hope that clarifies. It's really a question of how the mass acts with respect to contact patches....karts end up using the sidewalls of the tires as "shocks", tuned by how distorted they started (wider rim = stiffer sidewall because more air pressure is resisting movement) and what air pressure was selected (more pressure = more resistance to distortion.) All of this to say that since a kart's Cg is always higher than its' roll center, the inside tire will never be mechanically pulled downward from the cornering forces. They are affected by braking and acceleration forces at a rate determines by the caster split, which is closer to the original poster's question...
IF it were up to me, the ideal answer for how much caster would be "as little as possible while still maintaining good turn in." This will depend on driver's style as someone who "throws it in" quick and hard will generate quicker and potentially more dynamic load shift, while a smooth driver will perhaps be able to use more available grip.... If I were tuning the kart, I'd narrow the front until the kart was balanced, then remove caster until turn-in exhibited just a touch of push, then see where things ended up. As far as KPI, I consider KPI "dynamic caster / camber " tied together. Camber is looking at the KPI from left to right, Caster is looking from front to back, and scrub is how far the camber occurs from the center of rotation... It would be more accurate to consider the spindle as a line between 2 stacked squares, where it could be set between any two points. The downside of KPI is that it forces the spindle end to always travel in an arc, forcing both caster and camber to change. With a full-size car you can use KPI to cancel camber change on the outside tire as the suspension compresses...in a kart that is much closer to "rigid", the effect isn't as pronounced unless KPI or static camber is high It makes me wonder if anyone has run a kart with 0 KPI anytime recently.
If the Cg is ABOVE the roll center, then there is a lever arm created between the distance from roll center, and magnified by the mass of the car. The body will want to roll in the ooutward direction, stopped by the suspension forces. This will have the effect of loading the outside tire even more, and lessening the load on the inside tire. A key example of this is in SCCA Showroom Stock classes where they aren't allowed to optimize the geometry and the inside tire is often off the ground:
If the Cg is BELOW the roll center, then there is a lever arm wants to act so that the bottom of the car rotates "outward"...this "pulls" the inside tire down further into its' suspension travel and lessens the load on the outside tire. This is what I meant when I said that the overall "average" load is more constant. High Cg exaggurates the cornering forces with respect to the wheel, and low Cg minimizes it.
From a suspension standpoint, having Cg at the roll center allows you to use the suspension travel to absorb bumps, rebound, etc. with no outside effect from the car dynamically shifting weight around (side to side). Keep in mind, we're only looking at one axis...
Hope that clarifies. It's really a question of how the mass acts with respect to contact patches....karts end up using the sidewalls of the tires as "shocks", tuned by how distorted they started (wider rim = stiffer sidewall because more air pressure is resisting movement) and what air pressure was selected (more pressure = more resistance to distortion.) All of this to say that since a kart's Cg is always higher than its' roll center, the inside tire will never be mechanically pulled downward from the cornering forces. They are affected by braking and acceleration forces at a rate determines by the caster split, which is closer to the original poster's question...
IF it were up to me, the ideal answer for how much caster would be "as little as possible while still maintaining good turn in." This will depend on driver's style as someone who "throws it in" quick and hard will generate quicker and potentially more dynamic load shift, while a smooth driver will perhaps be able to use more available grip.... If I were tuning the kart, I'd narrow the front until the kart was balanced, then remove caster until turn-in exhibited just a touch of push, then see where things ended up. As far as KPI, I consider KPI "dynamic caster / camber " tied together. Camber is looking at the KPI from left to right, Caster is looking from front to back, and scrub is how far the camber occurs from the center of rotation... It would be more accurate to consider the spindle as a line between 2 stacked squares, where it could be set between any two points. The downside of KPI is that it forces the spindle end to always travel in an arc, forcing both caster and camber to change. With a full-size car you can use KPI to cancel camber change on the outside tire as the suspension compresses...in a kart that is much closer to "rigid", the effect isn't as pronounced unless KPI or static camber is high It makes me wonder if anyone has run a kart with 0 KPI anytime recently.
IF it were up to me, the ideal answer for how much caster would be "as little as possible while still maintaining good turn in." This will depend on driver's style as someone who "throws it in" quick and hard will generate quicker and potentially more dynamic load shift, while a smooth driver will perhaps be able to use more available grip.... If I were tuning the kart, I'd narrow the front until the kart was balanced, then remove caster until turn-in exhibited just a touch of push, then see where things ended up. As far as KPI, I consider KPI "dynamic caster / camber " tied together. Camber is looking at the KPI from left to right,
So Ted what about steering wheel feed back ?
So Ted what about steering wheel feed back ?
Ted Hamilton
Helmet Painter / Racer
Stephen -- what manner of feedback are you referring to? More caster / more KPI will make the kart more "self-centering" so the steering will feel progressively heavier as you design in more of each...But toe-in will also accomplish straight-line stability... Are you looking to gain "feel" or responsiveness or ??
By achieved I mean you design roll centre to create outwards or inwards body roll along the roll couple, the efficiency or workings of the roll was not at question. Not improving or enhancing anything. Just saying the suspension design or setup will create the body roll characteristics either above or below the roll centre.
paulkish
old fart
It's really pretty simple.
If you have limited hp, you direct forces either beyond the tire contact patch, at the tire contact patch or inside the tire contact patch. What you do is what you need and beyond that it's about how you lay the tire on the track and how you need the height of the corner set, while doing the above.
And as far as the front end goes when using a staggered solid axle, you only need enough work out of the front end, to provide needed turning you don't get from the back end.
If you have more hp, then to you need more work out of the fronts from turn in to the apex, to be able to apply hp in that area, to carry speed in addition to entry momentum.
It's that simple.
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roll centers, instant centers, and all that other stuff; IMHO, arc100 explained it just fine. I think he just pointed out, how it's all about roll couple and the direction of forces.
__________________
Ted, I have one question. What is the direction of roll?
no hints, arc100. ...
___________________
Just sitting here thunkin about the RF and discussions on here years ago, maybe even ten+ years ago. I have another question Ted. OK, there's all this fancy suspension. What equates to unequal length control arms, on a LTO kart?
sad thing is it's so long ago, I'm proly remembering it wrong and worse yet didn't understand it then and don't understand it now. ...
If you have limited hp, you direct forces either beyond the tire contact patch, at the tire contact patch or inside the tire contact patch. What you do is what you need and beyond that it's about how you lay the tire on the track and how you need the height of the corner set, while doing the above.
And as far as the front end goes when using a staggered solid axle, you only need enough work out of the front end, to provide needed turning you don't get from the back end.
If you have more hp, then to you need more work out of the fronts from turn in to the apex, to be able to apply hp in that area, to carry speed in addition to entry momentum.
It's that simple.
___________________
roll centers, instant centers, and all that other stuff; IMHO, arc100 explained it just fine. I think he just pointed out, how it's all about roll couple and the direction of forces.
__________________
Ted, I have one question. What is the direction of roll?
no hints, arc100. ...
___________________
Just sitting here thunkin about the RF and discussions on here years ago, maybe even ten+ years ago. I have another question Ted. OK, there's all this fancy suspension. What equates to unequal length control arms, on a LTO kart?
sad thing is it's so long ago, I'm proly remembering it wrong and worse yet didn't understand it then and don't understand it now. ...
paulkish
old fart
Read what I wrote last night and today it doesn't make any sense. But I'll leave it hoping someone who really knows about how a front end works and is used, will straighten it out or point out the totally wrong stuff.
thanks and sorry for all the miss information, just because I have fun writing
thanks and sorry for all the miss information, just because I have fun writing
Ted Hamilton
Helmet Painter / Racer
Paul -- To answer your question, on a kart, the direction of "body roll" is "outward", ie. the driver's head and body are trying to lever the kart toward the outside of the turn...VCg is higher than roll center. However, karts tend to skid instead of flip because the adhesion of tires is lost before the force vector exceeds the pull of gravity. And with that, I'll sign off unless the OP asks me a question...
paulkish
old fart
Without asking anything of anyone specific and being post #38 was put up while I was writing and I did not see it, until after posting ...
_____________________________________
I have questions after looking more at the green illustration in post #28.
I'm looking at the lines of the drawing and if I 'only' take into consideration the lines in the drawing, without any forces involved, it appears to me it's impossible for a kart to bicycle, as long as the roll center is below the instant center. Am I seeing that correctly?
Assuming I'm seeing it correctly, the drawing without including forces and the direction forces come from is totally meaningless as an explanation of anything except the lines drawn. Without including force it's miss leading and confusing.
The above has me thinking about what physical things we can change on the kart, to make it harder for the LF to lift up. Assuming the lateral force originates at the center of gravity, the first things to come to mind which can be done all involve relocating the c.o.g.. All of those thoughts seem to involve lowering it and moving it to the left. What next jumps in is when racers go indoor racing, they not only lower the c.o.g., they also move it toward the front. ... assuming also moving it toward the front is correct ... I next ask why do they move it toward the front?
The only reason I see now for moving the cog toward the front, is to take advantage of the sudo front end suspension, the back doesn't have.
What I see in that is, unlike the back of the kart, the front has the ability to redirect lateral forces, to help keep the kart from bicycling.
Two things then come to mind. Exactly what adjustments are available on the front end, to allow for redirecting lateral forces and which direction would you adjust each to cause lateral forces to either be directed in a downward direction or more toward the inside of the kart? That instantly takes me to two more things were discussing on here.
The first is to look at the drawing posted in post #28 and see how lines and points can be moved to get either a more downward acting force if it was shown as arc100's post indicates, or a force to act more towards inside of the RF. And second the first post of this thread comes back in and I'm now asking myself, how does king pin angle effect the lines of the drawing, to cause split to help direct forces both more in a downward direction and towards the inside of the RF?
I really don't see the RF kingpin angle having anything at all to do with things. If I see it right, split is not really a split, but all about the LF kingpin and redirecting forces.
The only thing I see involved with the RF and split is how changing kingpin angle effects camber gain and in turn the change in RF ride height. Again if correct, then all split considerations should be thrown out the window and you make changes to the LF for specific reasons and changes to the RF for specific reasons. Instead of trying to think in 'complicated' terms of split, which combine the activities of both the RF and the LF, we need to learn what LF changes do and what RF changes do.
Next it takes me way back on here to previous discussions about why the front tires are staggered. This all ends up with my thinking, split because it considers combined complex actions of both the RF and the LF, is meaningless except for noting what particular split has worked on your kart. If what has worked on your kart, works on another kart, it's only because ... just because.
Talking about what split you should use is as fruitful as talking about what stagger up front you should use, or what gear ratio and size gear you should use.
It's all about what you and most find works best, for specific track conditions.
Put your best guess on the track and after that it's about fixing on track problems.
What's important is to know what the adjustments on the LF do, what the adjustments on the RF do, what you need the LF to do for you at specific places around the track and what you need the RF to do for you at specific places around the track, so you can fix on track problems. Me, if anything I think I'm about trying to understand what each tire needs to do at specific places around the track, the theory of how to use each tire to turn left. ... and it includes how to use your tires on your staggered solid axle while going straight. ... ... but it's just my bull because it is all just IMHO and ain't necessarily right anyway. ...
if ya got this far, thanks for reading and sorry as usual for wasting your time. ... for me it's just coffee time, fun writing and not a waste.
thanks
paul
ps... started on this fun about 9:00 am and after the last edit it's now 10:45. I think this is going to be a three coffee morning.
ps again... it's now about 11:45 the third cup is gone, editing done and it's out to clear the snow. By the looks of it we got 6+ inches of snow today. brrrrrrrrrrrr
_____________________________________
I have questions after looking more at the green illustration in post #28.
I'm looking at the lines of the drawing and if I 'only' take into consideration the lines in the drawing, without any forces involved, it appears to me it's impossible for a kart to bicycle, as long as the roll center is below the instant center. Am I seeing that correctly?
Assuming I'm seeing it correctly, the drawing without including forces and the direction forces come from is totally meaningless as an explanation of anything except the lines drawn. Without including force it's miss leading and confusing.
The above has me thinking about what physical things we can change on the kart, to make it harder for the LF to lift up. Assuming the lateral force originates at the center of gravity, the first things to come to mind which can be done all involve relocating the c.o.g.. All of those thoughts seem to involve lowering it and moving it to the left. What next jumps in is when racers go indoor racing, they not only lower the c.o.g., they also move it toward the front. ... assuming also moving it toward the front is correct ... I next ask why do they move it toward the front?
The only reason I see now for moving the cog toward the front, is to take advantage of the sudo front end suspension, the back doesn't have.
What I see in that is, unlike the back of the kart, the front has the ability to redirect lateral forces, to help keep the kart from bicycling.
Two things then come to mind. Exactly what adjustments are available on the front end, to allow for redirecting lateral forces and which direction would you adjust each to cause lateral forces to either be directed in a downward direction or more toward the inside of the kart? That instantly takes me to two more things were discussing on here.
The first is to look at the drawing posted in post #28 and see how lines and points can be moved to get either a more downward acting force if it was shown as arc100's post indicates, or a force to act more towards inside of the RF. And second the first post of this thread comes back in and I'm now asking myself, how does king pin angle effect the lines of the drawing, to cause split to help direct forces both more in a downward direction and towards the inside of the RF?
I really don't see the RF kingpin angle having anything at all to do with things. If I see it right, split is not really a split, but all about the LF kingpin and redirecting forces.
The only thing I see involved with the RF and split is how changing kingpin angle effects camber gain and in turn the change in RF ride height. Again if correct, then all split considerations should be thrown out the window and you make changes to the LF for specific reasons and changes to the RF for specific reasons. Instead of trying to think in 'complicated' terms of split, which combine the activities of both the RF and the LF, we need to learn what LF changes do and what RF changes do.
Next it takes me way back on here to previous discussions about why the front tires are staggered. This all ends up with my thinking, split because it considers combined complex actions of both the RF and the LF, is meaningless except for noting what particular split has worked on your kart. If what has worked on your kart, works on another kart, it's only because ... just because.
Talking about what split you should use is as fruitful as talking about what stagger up front you should use, or what gear ratio and size gear you should use.
It's all about what you and most find works best, for specific track conditions.
Put your best guess on the track and after that it's about fixing on track problems.
What's important is to know what the adjustments on the LF do, what the adjustments on the RF do, what you need the LF to do for you at specific places around the track and what you need the RF to do for you at specific places around the track, so you can fix on track problems. Me, if anything I think I'm about trying to understand what each tire needs to do at specific places around the track, the theory of how to use each tire to turn left. ... and it includes how to use your tires on your staggered solid axle while going straight. ...
... but it's just my bull because it is all just IMHO and ain't necessarily right anyway. ... if ya got this far, thanks for reading and sorry as usual for wasting your time. ... for me it's just coffee time, fun writing and not a waste.
thanks
paul
ps... started on this fun about 9:00 am and after the last edit it's now 10:45. I think this is going to be a three coffee morning.
ps again... it's now about 11:45 the third cup is gone, editing done and it's out to clear the snow. By the looks of it we got 6+ inches of snow today. brrrrrrrrrrrr