At the tire, the forces are definded according to the main plane, which is defined as the plane perpendicular to the rotational axle of the wheel. The force perpendicular to this plane and in parallel to the rotational axle is called lateral force (Fy). The characteristic value for the lateral force ist the lateral slip angle (alpha) (also called side slip angle) which is defined as the angle between the wheel main plane and the direction of the wheel center velocity.

The longitudinal force (Fx) is the force in direction of the main plane, the characteristic vaule is the longitudinal slip, calculated as the relative velocity in the contact patch (velocity difference of  wheel center speed and wheel circumferential speed) divided by the wheel center speed or the wheel circumferential speed accordingly (depending on the definiton for acceleration or braking).

In addition to the statements above: The diagram attached shows the connection of longitudinal (Längskraft Fx) and lateral (Seitenkraft Fy) forces at the contact surface of tyre and road for an exemplary tyre and a load of 3000 N. As you can see, the maximum total force is always a sum of Fx and Fy. This type of diagram is called the "Kammscher Kreis", or in English spoken areas: circle of forces, traction circle, friction circle, or friction ellipse.

Kind regards,

Mario