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Antisquat And "Up" And "Out"

5K views 12 replies 6 participants last post by  BillyShope 
#1 ·
I've done this before, but it was with equations. Realizing pictures might be more effective, I submit the following:

In Fig. 1, I've drawn a vertical line with arbitrary length. We'll consider this to be a "body" upon which forces can be exerted. At the bottom of the line, I've drawn a horizontal line, again with arbitrary length. This line (arrow) is a force vector. That is, its length is proportional to the magnitude of the force and its direction indicates the force direction. I've also added some "links." One is attached at the top of the vertical link and the other is attached at some arbitrary point on the vertical line. The links are angled (again, arbitrarily), so, if link lines are drawn, they intersect at what we call the "instant center" or "IC."

In Fig. 2, I've replaced the links with force vectors. When we're working with the forces and moments (torques) acting on a body, everything must be "balanced." That is, there must not be an "extra" force or moment which would send the body spinning and/or moving into space. We're not to this point in the diagram, but we're getting there. Those angled forces have both horizontal and vertical components. The difference between the horizontal components must be equal and opposite to the original force at the bottom of the body.
So, the horizontal component of the force attached at B, less the horizontal component of the force attached at C, must be equal in magnitude...but opposite in direction...to the force AK.
In addition, there must be a moment balance. So, taking moments around A, the distance AB times the horizontal component of the force at B must be equal in magnitude, but opposite in direction, to the distance AC times the horizontal component of the force at C.
With these two bits of information, we can determine the force vectors acting at B and C, as also shown in Fig. 2.

To maintain a force balance, the force acting at A must have a vertical component. I could simply say that this is equal in magnitude, but opposite in direction, to the sum of the vertical components acting at B and C, but, to make this clearer, I've added the equal and opposite force vectors in Fig. 3. AT is equal and opposite to HB, TL is equal and opposite to CD, LP is equal and opposite to GH, and PS is equal and opposite to DF. The resultant, as you can see, goes directly to the IC.

Since we have seen this to be true for a completely arbitrary case, it is safe to assume that, for the "real life" case of an axle assembly (Fig. 4), the resultant force at the tire patch (the sum of forward thrust and weight transfer), must also point to the IC. I have labelled this force action line the "no squat/no rise line." This implies that the tangent (slope) of this line also happens to equal the center of gravity height divided by the wheelbase. An IC on this line would further imply, then, that the car would neither squat nor rise on launch. Since a line is comprised of an infinite number of points, it follows that it also contains an infinite number of possible ICs which would yield the same launch performance. The car, in other words, "knows" that a force is acting on it along a certain line, but is unable to determine where, on that line, it is acting. So, rather than define a specific "up" and "out" for an IC, it is far more reasonable to define the slope of the force action line upon which the IC is located. If the slope is greater than the ratio of center of gravity height to wheelbase, the car will rise; if less, it will squat. If we divide a given slope by the neutral slope and then multiply by 100, we have that which is called "percent antisquat."
Since parallel lines intersect at infinity, another 4link design would be one in which the links are parallel to each other and parallel to the desired force action line. Adjustment would be a matter of positioning vertically an end bracket.

As for my reason for posting, I'm trying to make it easier for dragracers to communicate. The use of "ups" and "outs" has caused a great deal of confusion. One racer will recommend one set and another racer recommends a "different" set. But, if they're on the same constant percentage antisquat line, they're NOT different! They're the same, as anyone with CAD software can prove for himself.

Personally, I would find it much easier to use a bubble angle tool and measure the angle of a parallel link setup than to input my link end measurements into software. Art Morrison, for one, offers a parallel link setup, but, as far as I know, it lacks adjustability. If Mr. Morrison...or anyone...would offer an adjustable parallel 4link that could handle high horsepower engines, I'm certain he would find a large number of racers who would gladly opt for the "loosen, tap with a hammer, check with the bubble, and tighten" method of 4link adjustment.
 
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#4 ·
#5 ·
You have to leave Euclidean geometry to understand this. In non-Euclidean geometry, you include situations like a triangle drawn on the surface of a sphere. The interior angles do not add up to 180 degrees.

But, even in Euclidean geometry, you can conclude that parallel lines, for practical purposes, intersect at large distances. Consider three parallel lines and a fourth line not quite parallel. As you proceed along the parallel lines, the fourth line goes further and further away.

Consider, also, that all the constant percent antisquat lines converge to a point at the tire patch. This is why it's so difficult to tune a conventional 4link for a short IC. It becomes easier and easier for attempts that are further out.

So, this is why I can assure you that, if you keep your links as parallel as possible and aim them at an angle with a tangent (slope) equal to the desired ratio of "up" over "out," you'll have success.

You're thinking and questioning, though, and I appreciate your comment.
 
#6 ·
I like your explanation, using forces to identify the instant center.

All of the other explanations I've seen rely on the center of gravity and wheelbase to identify the instant center.

My question is always "How do I identify the center of gravity without balancing the vehicle on a point?"
 
#7 ·
To identify the center of gravity the way I would do it is to weigh both ends individually then knowing the wheelbase would allow the center of gravity to be calculated. Sorry I have not had to do weight and balance calculations for a long time so I have forgotten the formula for that. We used to do this on aircraft by weighing the aircraft at each landing gear and then calculating where the CG was. Weight and balance is critical in that world..

Sam
 
#9 ·
Any method of finding the CG height takes a lot of time and effort. Perhaps the easiest method is to tabulate components. You know the weight of the battery, for instance, and you can estimate the CG location fairly accurately. Do this for as many components as you can, then use the difference between the total weight and the sum of your component weights as a final "component." Use a reasonable guess for the CG height for this final "component." Add the products of weight and height for all the components and then divide your answer by the total car weight. (If you've over estimated the weight of some components...like fenders and glass, for instance...that final "component" might have a negative weight. Don't let that bother you. Simply subtract its weight/height product.) The more components you include initially, the more accurate will be your CG height.
 
#10 ·
For those who may not know, Billy is one of the original "Ramchargers" race group from Chrysler, and really knows his stuff... a real performance pioneer.

Glad to see you posting again, always look forward to your posts, and have gained much more understanding of suspensions and chassis reaction from your web site pages.
 
#11 ·



Figs. 1,2, and 3 illustrate the large differences in link settings which result in an IC on the same percentage antisquat line. Does this mean the car will behave the same on launch with any of these setups? Absolutely not! This is because the front of the car will always rise and, in this case, the back will also rise "a bunch." This alters the link angles and, of course, changes the IC locations. The only time that it can be said that the performance is the same is when that faint blue line angled up from the tire patch represents the no squat/no rise line. Oh, there's one other stipulation: The front suspension must be chain-limited or have a very high spring rate.
So, what's the sense of talking about different setups having the IC on the same percent antisquat line? I do this to point out the setup trend as you go from a short IC to a very long (or infinite) IC.

Fig. 4 shows that the links of Fig. 2 do, indeed, intersect on that same faint blue line.
But, look again at Figs. 1,2, and 3. In Fig. 1, the lower link is horizontal and the IC is very short. In Fig. 2, the upper link is horizontal and the IC is a bit longer. In Fig. 3, the links are parallel to themselves and to the blue line, which places the IC at infinity. Note that the links are approaching parallelism as you go from Fig. 1 to Fig. 2, so that my comments on parallel links should come as no surprise.
Remember, also, that the blue line represents only one of an infinite number of constant percentage antisquat lines which converge to a point at the tire patch. This means that "finding" it, in Fig. 2, is far easier than in Fig. 1, and is easier yet in Fig. 3.
You wouldn't have to search this forum's archives very far back to find posters saying that the lower link is to be horizontal. Fortunately, I haven't seen this sort of post recently. A horizontal lower link equates to adjustment difficulty. A longer IC means easier adjustment and more repeatable performance.
shopeshop.org
 
#12 ·
So... You're saying no matter where the bar lines intersect the squat/rise line, "hook" will essentially be the same? Now, which side of the squat/rise line is squat and which is rise? That should make it easier for a yokel like me to find a starting point without knowing anything else...

Thanks!

Russ
 
#13 ·
Each of these lines...and there are an infinite number of them...represent a constant value of percent antisquat. All of the lines converge to a point at the tire patch. If an IC is on the line which represents 100% antisquat (otherwise known as the "no squat/no rise line" or the "neutral" line), the car will neither squat nor rise. If it is on a line which lies above, the car will rise; below, it will squat. The 100% line has an angle from the horizontal with a tangent value (slope) equal to the CG height divided by the wheelbase. In attempts to get the pivot point near the 100% antisquat line, some of the very early ladder bar cars had their pivots up at the firewall. With a 3link, 4link, or torque arm, we can now reach the line without any problem.
 
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