**Chapter 10 | Reading Collision Data**

**Introduction**

Virtual CRASH 3 is a unique motor vehicle simulation package that allows its users to quickly and efficiently converge upon solutions to accident cases. As a physics simulation tool, Virtual CRASH uses rigid body dynamics calculation methods based on the Kudlich-Slibar model to simulate collisions between objects within the simulation environment. Users have the ability to access the dynamical variables and collision parameters associated with their collision, using the Virtual CRASH user interface. Here, we will walk you through an example collision, and demonstrate how to access collision data.

**Stage a Collision**

First, set up two vehicles in your Virtual CRASH 3 environment. The figure below illustrates an inline collision between a Pontiac Grand Prix (orange) and a Saturn L300 (blue). The vehicles are positioned such that they have identical yaw orientations of 0 degrees and identical \(y\) coordinates of 0 feet. The Pontiac is placed at \(x\) = -10 feet and the Saturn is placed at \(x\) = 10 feet. The Saturn’s initial speed is set to 5 mph, and the Pontiac’s initial speed is set to 21 mph.

As you set your vehicles’ initial speeds, you’ll notice the Virtual CRASH 3 system immediately updates the simulation to show you the final result. Using the time slider in the lower right hand corner, you can scroll back and forward in time to isolate the moment of impact. Keep in mind that Virtual CRASH is an impulse-momentum based simulator, which approximates impulses as being instantaneously delivered to objects undergoing collisions.

**The Auto-EES Data Container**

Now that you’ve set up a collision, let’s have a look at the associated collision data. Left click on “auto-ees” in the left side control panel (see below).

Next, left click on “defaults,” “misc,” and “selection” to reveal all of the auto-ees features.

**Depth of Penetration**

Virtual CRASH is a rigid body dynamics simulator, as opposed to a SMAC-based simulator, and therefore it does not rely on any force models as functions of deflection; however, the user has the option to set the maximum penetration depth into the vehicle shells. The “depth of penetration” feature (see previous figure, left control panel under “defaults”) allows the user to set the approximate location of the impulse (force) centroid within the volume of the vehicle. This is particularly useful in collisions with large amounts of crush damage, where the amount of rotational energy delivered to a vehicle can strongly depend on lever-arm length. The depth of penetration, \(\Delta t_{p}\), is set in the time domain, meaning that, starting from first engagement of the two vehicles at \(t_i\), the time in which the equal and opposite impulses are delivered to the vehicles is at \( t_i + \Delta t_p \). The actual position of the impulse (force) centroid within each vehicle will be further discussed below.

*Friction*

Frictional effects are simulated in Virtual CRASH. The “friction” setting allows the user to specify the maximum coefficient of friction used by the collision model (see previous figure). Generally, the vehicles are brought to common velocity along the normal and tangent collision axes at the points of contact; however, the relative separation velocity vector may not tend to zero magnitude if the maximum coefficient of friction is set below a given threshold. This threshold will be dependent upon the closing-velocity vector, the impact orientation of the two vehicles, inertial properties of the vehicles, and the coefficient of restitution. For a sideswipe-type collision, the user may wish to limit the maximum allowed coefficient of friction to ensure the simulated result yields a scenario in which common velocity is not reached along the tangent axis.

*Restitution*

This setting allows the user to specify the coefficient of friction used by the collision model. The coefficient of restitution is defined as the negative ratio of the normal-axis projected closing to initial velocity vector components, or:

$$ \varepsilon = -{\bar{v}^P_{Rel,f} \cdot \hat{n} \over \bar{v}^P_{Rel,i} \cdot \hat{n}} $$

This can take on a value between -1 to 1. A value of 0 represents the scenario in which all available collision energy is lost to inelastic effects. A coefficient of 1 represents the scenario where no available collision energy is lost to inelastic effects. A coefficient less than 0 represents scenarios in which the surfaces of contact did not reach a common velocity along the normal axis, such as in cases where components break off at the area of contact of one vehicle during collision.

*Pitch*

Under “pitch” you will see the pitch angle of the normal axis of the collision model. This can be useful in cases of extreme front-end underride.

**Select a Collision Event**

In Virtual CRASH each collision event has its own associated set of collision data which is accessible through the left side control panel. To access this data, simply press “next contact” in the left side control panel beneath “selection” (see below). For simulations with multiple collision events, you can continue pressing “next contact” to cycle them all.

Once you have pressed “next contact,” you will see an impressive display in the user environment, where the impulse vectors are visible, as well as the “friction cones” (in blue) and the plane that runs orthogonal to the normal collision axis (red). You will also see a wealth of data displayed in the left side control panel which summarizes the collision event (see below). The tangent axis will be contained within this plane. The friction cone depicts the upper limit of the volume in which the impulse vector must occupy for the collision. As one decreases the allowed maximum coefficient of friction for the simulation, the size of the cone will decrease, indicating that this volume of space has also decreased. In the extreme case, where the maximum allowed coefficient of friction is set to 0, the cone will effectively enclose no volume and is represented by a line pointing along the normal axis projection, indicating that only normal impulse components will act on the vehicles.

Under “contact” you will see the magnitude of the impulse delivered to each vehicle during this event as well as the total energy lost.

Under the “defaults” section, you will find the user adjustable parameters used by the collision model. These were discussed previously above.

Left click on “object 1” and “object 2” in the left control panel to reveal the resulting values associated with this collision event.

Next, expand “position-local” and “rotation-local” to see the position of the impulse centroid and the impulse normal axis orientation.

**User Defined Contacts**

Scroll to the bottom of the auto-ees menu in the left side control panel. Now, left click on “create user contact.” By creating a user contact, you can modify the inputs to the collision model for this event.

**Simulated Vehicle Deformation**

Next, make sure your new “ees” object is selected, and scroll to the top of the new user created ees menu in the left side control panel (see below). There you will see the “deform” option disabled. Left click the box to the left of “deform” to enable simulated deformation.

**Adjust Impulse Centroid Position**

Now we are going to customize our impulse centroid position. This is the position in three-dimensional space at which the equal and opposite impulse vectors act on each vehicle. Click on the box to the left of “auto-position” to disable automatic positioning of the impulse vectors (see below). When Virtual CRASH automatically sets the centroid positions, it uses the overlap of the vehicle bounding boxes at the instant of momentum exchange.

Scroll down to the bottom of the ees menu in the left control panel, and you should now see the position and orientation input controls.

Let’s now adjust the \(z\)-position of the impulse centroid. We are going to align this \(z\)-position with the vehicle centers-of-gravity in order to eliminate rotational effects from our simulation (by causing the lever-arms to have 0 length). Under “position-local”, set \(z\) = 1.772 feet:

Let’s shift the \(x\) position of the impulse centroid at \(x\) = 4 feet to simulate a case where the bullet vehicle’s front-end stiffness is much larger than the target rear-end vehicle’s stiffness. Now scroll up and set the “Depth of penetration” value to 0.06 seconds in order to exaggerate the crush damage. Note, by scrolling down the left side control panel, and left clicking on “timing,” you will see the time at which the vehicles begin to first come into contact.

As you advance your time slider forward, you’ll notice at time greater than 0.16 seconds (initial contact time) + 0.06 seconds (from depth of penetration setting), the impulses and crush damage will have been imparted to both vehicle shells.

Finally, scroll up and left click to expand “object 1” and “object 2” in the left side control panel to reveal the vehicle data for your collision event (see below). We will now analyze this data.

Thus, the Virtual CRASH simulated energy loss value is within less than 0.5% and therefore in excellent agreement with our expectations from basic physics and standard accident reconstruction methods.

**Energy Lost**

From rigid body dynamics, for inline collisions, where torque can be neglected, the total energy lost in a collision can be estimated by:

$$ E_{Loss} = {1 \over 2}\cdot(1-\varepsilon^2)\cdot \bar{m}\cdot(\bar{v}^P_{Rel,i}\cdot \hat{n})^2 $$

where \(\bar{v}^P_{Rel,i}\) is the initial relative velocity vector at the point of contact,\(\bar{m}\) is the system \(\varepsilon\) reduced mass, and is the coefficient of restitution. Let’s now compare our expectations for this quantity versus what is reported by Virtual CRASH in the left hand control panel. Note the parameter “deformation energy” is equal to 19,141.047 J = 14,117.71 ft-lbs in our simulation. The Saturn has a total weight of 3,183.475 lbs. The Pontiac has a total weight of 3,496.531 lbs. This implies the reduced mass is equal to 51.79 slugs. The coefficient of restitution is set equal to 10%. The relative velocity vector has a magnitude of 16 mph. The closing velocity vector is completely aligned with the x-axis, as are the impulse vectors. With this information, we can calculate the expected energy loss for our simulation.

$$ E_{Loss} = {1 \over 2}\cdot(1-0.1^2)\cdot (51.79~slugs)\cdot(23.467~ft/s)^2 = 14,117.73~ft-lbs$$

*The Impulse*

The magnitude of the normal component of the impulse vector delivered to each vehicle can be estimated by:

$$ |\bar{J}\cdot\hat{n}| = (1+\varepsilon)\cdot\bar{m}\cdot |\bar{v}^P_{Rel,i}\cdot \hat{n}| $$

Plugging in our values, this is:

$$ \bar{J}\cdot\hat{n} = (1+0.1)\cdot (51.79~slugs) \cdot (23.467~ft/s) = 1336.89~lbs-s $$

Reading off the reported impulse from your left control panel, you will see a value of 5946.847 N-s = 1336.904 lbs-s, which is in excellent agreement with our hand calculation above.

**Delta-V**

This impulse can be related to the normal component change-in-velocity for each vehicle by:

$$ m_1 |\Delta \bar{v}_1 \cdot \hat{n} | = m_2 |\Delta \bar{v}_2 \cdot \hat{n} | = |\bar{J} \cdot \hat{n} | = (1 + \varepsilon)\cdot \bar{m}\cdot |\bar{v}^P_{Rel,i}\cdot\hat{n}| $$

In our current simulation, we can assume that \(\Delta \bar{v}_1\) and \(\Delta \bar{v}_2\) are perfectly aligned with the x-axis, therefore, for the Saturn we have:

$$ | \Delta \bar{v}_1 | = {|\bar{J}\cdot\hat{n}| \over m_1} = {1336.89~lbs-s \over 98.95~slugs}=9.21~mph $$

and for the Pontiac:

$$ | \Delta \bar{v}_2 | = {|\bar{J}\cdot\hat{n}| \over m_2} = {1336.89~lbs-s \over 108.68~slugs}=8.39~mph $$

Both of these estimates are in excellent agreement with the values displayed in the left side control panel.

**Deformation**

The deformation value for a given vehicle is determined by estimating the distance between the bounding box of the vehicle and the impulse centroid position, as measured along the normal collision axis. Initially, the damage centroid is automatically placed on the tangent plane, whose orientation will depend upon how the vehicle bounding boxes overlap. The overlap will directly depend on the depth of penetration time as well as the pre-impact orientations and positions of the vehicles. In our example, the auto-position feature of our ees object was disabled, so that we could move the centroid further into the Saturn’s rear. Thus, we should see a larger value for deformation for the Saturn compared to the Pontiac.

This is indeed what we see in our simulation, as the Pontiac has a deformation value of 0.059 feet and the Saturn has a deformation value of 1.396 feet.

**Equivalent Energy Speed**

Virtual CRASH 3 defines the equivalent energy speed (EES) as given by Burg. Below we will give a short review. First, let’s suppose the total energy lost to deformation for each vehicle can be expressed by:

$$ E_{Loss,1} = {1 \over 2}\cdot | \langle \bar{F}_1 \cdot \hat{n} \rangle \cdot C_1 | = {1 \over 2}\cdot m_1 \cdot EES_1^2 $$

$$ E_{Loss,2} = {1 \over 2}\cdot | \langle \bar{F}_2 \cdot \hat{n} \rangle \cdot C_2 | = {1 \over 2}\cdot m_2 \cdot EES_2^2 $$

where \(\langle F_1 \cdot \hat{n} \rangle\) and \(\langle F_2 \cdot \hat{n} \rangle\) are the average normal projected forces on each vehicle, and \(C_1\) and \(C_2\) are the total deformation values for each vehicle. Let’s now assume Newton’s 3rd law implies:

$$ | \langle \bar{F}_1 \cdot \hat{n} \rangle | = | \langle \bar{F}_2 \cdot \hat{n} \rangle | $$

Using the above, this implies we can write the ratio:

$$ {EES_1 \over EES_2} = \sqrt{{m_2 \over m_1} \cdot {C_1 \over C_2}} $$

Let’s now express the total energy lost in the collision by the sum:

$$ E_{Loss} = E_{Loss,1}+E_{Loss,2} $$

which we can rewrite as:

$$ E_{Loss} = {1 \over 2} \cdot m_1 \cdot EES_1^2 + {1 \over 2} \cdot m_2 \cdot EES^2_2 $$

$$ E_{Loss} = {1 \over 2} \cdot m_1 \cdot \left(EES_2 \cdot \sqrt{{m_2 \over m_1} \cdot {C_1 \over C_2}} \right)^2 + {1 \over 2} \cdot m_2 \cdot EES^2_2 $$

$$ E_{Loss} = {1 \over 2}\cdot m_2 \cdot EES_2^2 \cdot \left(1+{C_1 \over C_2} \right) $$

Finally, we can solve for \(EES_2\):

$$ EES_2 = \sqrt{ {2E_{Loss} \over m_2 \cdot \left( 1 + {C_1 \over C_2} \right) } } $$

Once \(EES_2\) is obtained, \(EES_1\) can be obtained from the above relations.

Let us now see how our hand calculations compare with the values from Virtual CRASH. We solved for the total energy lost in the collision above. This gave us \(E_{Loss}\) = 14,117.73 ft-lbs. From our estimates of deformation above, we have \(C_1 =\) 1.396 ft and \(C_2 =\) 0.059 ft. Plugging in these values, we have:

$$ EES_2 = \sqrt{ {2\cdot\left(14,117.73~ft-lbs\right) \over \left(108.68~slugs\right) \cdot \left( 1 + {1.396~ft \over 0.059~ft} \right) } } = 2.213~mph $$

With this, we can solve for \(EES_1\):

$$ EES_1 = EES_2 \cdot \sqrt{{m_2 \over m_1 }\cdot {C_1 \over C_2}} $$

$$ EES_1 = \left(2.213~mph\right) \cdot \sqrt{{108.68~slugs \over 98.95~slugs}\cdot{1.396~ft \over 0.059~ft}} = 11.281~mph $$

Both of these are in excellent agreement with the values shown in the left control panel.

Tags: DeltaV, Delta-V, DV, dV, restitution, epsilon, coefficient of restitution, impulse centroid, EES, equivalent energy speed, auto-ees, contact.

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