Intervehicle friction, as simulated by original SMAC and EDSMAC, is in the form of simple Coulomb friction. It requires the existence of a force perpendicular to the contact region and it is proportional to that force.
In actual collisions, tensile forces which are independent of a normal force, frequently act along the vehicle-to-vehicle interface. Also, significant resistance to rotations relative to the collision partner is sometimes generated by interlocking of the damaged structures.
The inputs on cards 16 and 18 are in the form of impulsive linear and angular constraints that resist relative motions of the two vehicles. They are modeled as reaction constraints that act only to resist relative motions. The m-smac program conserves both the linear and the angular momentum of the two-body system in the absence of external (i.e., tire/pavement) or fixed object collision forces. Thus, any interacting forces and/or moments that are applied to resist relative motions and, thereby, to improve the predicted position and heading at rest of Vehicle #1 will also affect the corresponding position and heading at rest of Vehicle #2. The analytical approach to input selection consists of iterative adjustments to achieve acceptable matches of the positions and headings at rest of both vehicles. The rationale is the concept that inappropriate inputs can not achieve acceptable responses of both vehicles.
It should be noted that fields 3 and 4 of card 18 permit the input of viscous damping of the linear constraint for the case of long duration linear constraints where oscillations may occur.
The linear constraint aspect of Snag is input as the maximum impulse (Fdt) that can resist relative motion:
The average snag force (F) acts for a finite duration (dt), and the impulse therefore is equal to Fdt
The maximum speed-change that can be associated with the Impulse can be approximated from the equation:
m∆V = Fdt
1000 lb-sec impulse acting on a 3000 lb. vehicle imparts a speed-change (∆V) of approximately 7.3 MPH.
∆V = Fdt/m = (1000 lb-sec)/((3000 lb.)/386.4 in/sec2 )= 128.8 inches/sec
500 lb-sec impulse acting on a 3000 lb. Vehicle imparts a Speed change (∆V) of approximately 3.7 MPH.
∆V = Fdt/m = (1000 lb-sec)/((3000 lb.)/386.4 in/sec2 )=64.4 inches/sec
Specification of the duration of the snag impulse should include consideration of the type of vehicle interaction which is being simulated.
1) If the additional vehicle interaction occurs only during the normal period of a typical collision interaction, then its duration should be less than approximately 0.05 seconds. A finite time is required for the vehicles to interact to the point where an impulsive constraint/snag occurs, so the total duration of the collision and snag should be typically less than approximately 0.15 seconds.
2) If the actual impulsive/snag interaction acts to completely prevent the vehicles from separating then the duration may exceed that of a typical collision duration.
Generally, a starting point for snag impulses which are supplemental to collision crush forces ranges from 100–1500 lb-sec. The starting range for snag impulses which are used to supplement narrow overlap impacts may be larger (e.g., see Example: Snag Option inputs). The ultimate test of the duration and force associated with a snag is that it results in acceptable responses in both vehicle trajectories.
The moment constraint aspect of Snag (Card 18, Field 1 & 2) is input as the maximum angular impulse (Fhdt) that can resist relative rotations:
A 2000 lb-ft-sec angular impulse acting on a vehicle with a moment of inertia of 20,000 lb-sec2-in imparts an angular velocity change of 1.20 rad/sec (68.8 deg/sec)
The impulse of the linear constraint may be approximated by the product of the entries in Fields 6, 7 and 2 of Card 16:
(AKSP) (DELPSM) (TSWIND) ≅ LB-SEC
The impulse of the moment constraint may be calculated from the product of the entries in Card 18, Field 1 and Card 16, Field 2:
The moment constraint is applied in the form of equal and opposite couples that resist relative rotations of the two vehicles (i.e., it is independent of the locations of application on the vehicles). Note that the linear constraint (the SNAG as specified on card 16) resists relative motion and produces moments on the two vehicles that are dependent upon the locations of the points of application of the linear constraints. It follows that the simulation of a specific resultant resistance to relative motion requires a different value of the moment constraint for each location of the linear constraint.
The program outputs of m-smac now include an auxiliary output of the effective linear and angular impulses that act during an application of cards 16 and 18. The output can be found on the m-edit View menu in 1-Input Echo, 2-Run Messages or B-Complete Output Dataset. The output includes a breakdown of the various contributions of the snag impulses and a calculation of the resulting DeltaV produced by the snag.
Resultant Impulse Linear = 952. 950. Lb-sec
Angular = -322. -3239. Lb-Ft-Sec
Impulse due to Linear Components:
Impulse due to Angular Components:
Snag Force = 2457. -6018. Lb-Ft-sec
Moment Constraint = -2779. 2779. Lb-Ft-Sec
Refinement in the Simulation of Structural Interactions During Collisions