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Car suspensions

  1. Nov 18, 2008 #1
    I am trying to model all the forces a car suspension could undergo, for this car game of mine.

    I am using the pacejka model to model the tyre, so that's not important, but I do need to understand how a car would transfer its weight under load.

    I am using the following to calculate the load on one tyre:

    n = normal force for the full car
    l_c = load due to roll on the y axis (y axis points perpendicular to the direction of the car)
    l_s = load due to roll on the x axis (x axis points in the direction of the car)
    h = 1.0m (height of the CG from the ground)
    L = length from front to back wheel (positive)
    W = width from left to right wheel (positive)
    m = mass of car
    a_x = instantaneous x acceleration
    a_y = instantaneous y acceleration (well both of these are not perfectly instantaneous when simulated, they are integrated over time).

    The CG for simplicity is assumed to be at exactly halfway between both wheels in both directions.

    (tyre load on front left tyre)

    l_c + l_s = n/4.0 - ((h * mass * a_x)/L)/2.0 + ((h * mass * a_y)/W)/2.0

    I think there's something wrong here, but I'm not well versed enough to figure it out. I'm also having the problem of getting lateral acceleration of like 100 (almost 10G's), but this is likely a problem with my tyre model giving too much grip.

    If anyone could tell me how to determine the amount of roll a car experiences when it turns that would be great! I got the idea for the above from this website:

    http://www.dur.ac.uk/r.g.bower/PoM/pom/node16.html [Broken]

    which probably explains it better, but doesn't add the term that deals with lateral roll.

    I am using SAE coordinates, so z is up, y is right, and x is forward.

    If someone could point me to another place which also describes the physics of a car's suspension in depth, that would be helpful also. I am currently simulating just a spring at each wheel, but I have the feeling this is wrong
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Nov 19, 2008 #2
    Without getting into this too deeply, the amount that a car will roll is also dependent on the suspension design, which sets the roll centers for the front and rear suspension. The springs and the anti-roll bars resist the roll. The roll couple refers to the distribution of the front and rear roll resisting forces.

    Where to find more info? I've been reading books about this for the last twenty years and I've come across some good ones. Carroll Smith's books are fairly straight forward. There is some cheap software out there that'll show you the results of entered variables. Here are some links.


    The last one gives you a graph of the tire's actual C of friction for various loads and explains why that is important.
  4. Nov 19, 2008 #3
    Interesting, I'll definitely look into those.

    Would you say that the sway bar is the only thing (other than the vertical springs) that resists the roll?

    Right now my simulation is giving me incredibly unrealistic results, which results in massive normal forces at the tires (the springs in the suspension are probably being compressed beyond what's possible), and incredible cornering.

    The pacejka formula generally gives larger force for greater normal forces peaks from 4 deg to 10 deg depending on the normal force, so obviously its impossible.

    I guess the normal force at all 4 wheels should add up to the car's total normal force, but the simulator gets huge G's in corners because the force applied to the wheel gets larger, so the lateral force in pacejka gets larger, and it keeps on going until the springs hit a limit I've set.

    Currently I'm doing net force at the wheel to determine how fast the car moves up/down, but I have no torques applied along the X axis. Maybe a better solution would be to calculate the net torque on the car as applied by the four springs and find the angular velocity? I'm afraid this might be too small for floating point math, but I'll see what happens.

    Thanks for responding, those websites are giving me some ideas!

    (edit: I know roll is disliked; why is this? It seems that more force on the outside tires provides greater lateral force?)
  5. Nov 19, 2008 #4
    Roll is both good and bad. Good because it gives the driver feedback about how hard the car is cornering and bad because it usually changes how flat the tire tread is on the road as well as introducing steering effects because of the unequal lengths in the steering and suspension parts.

    Yes, the sway bars and the springs are the parts that resist roll.

    Use the second tire load chart on the last link to check your before and after forces at the tires. With no weight transfer, the resultant cornering should be higher than after you figure that in. More force on the outside tires gives a lower C of friction because although the grip increases, the load for that grip goes up even more. It sounds like you're getting a positive feedback when you should be getting a negative.

    I'm sorry if this explanation isn't using the correct phrases for this forum. I are a race car mechanic and am presently under the weather, so the brain box isn't quite up to snuff at the moment. I hope the meaning comes through though.
  6. Nov 19, 2008 #5
    No, you're explaining yourself fine! I'm new here myself, and I appreciate your help.

    I'm using the pacejka magic formula to calculate lateral force, it is explained in detail here: http://www.racer.nl/reference/pacejka.htm

    Basically, it models the relation between slip angle (difference in car velocity direction and wheel direction) and lateral force of the tire on the vehicle. It is given the inputs for vertical load, camber angle, and slip angle, and generate a force in newtons.

    According the pacejka, the more normal force, the greater the force generated will be.
  7. Nov 20, 2008 #6


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    Note that one issue when cornering is that maximum lateral force doesn't increase linearly with normal force, but slightly less, due to tire load sensitivity.


    I don't know if pacejka takes this into account. Pacejka also has issues at very slow speeds. For example, it can't deal with a situation like a car at rest on a sloped surface.
  8. Nov 20, 2008 #7
    Yeah, I'm pretty sure pacejka increases with more Fz.

    At a certain point I assume, the wheel can no longer generate that kind of force though.

    I wish there was a better reference for pacejka online, though.
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