Vehicle Crash Dynamics P2 potx

1.47 Radar Braking Velocity Diagram1.29 NOTES: 1 Lead vehicle starts to brake at To 2 T includes the radar warning time and reaction time of following vehicle driver before applying brak

Fig 1.44 Slipping on an Incline due to Down Push

(1.26)

(1.27)

Fig 1.45 Normalized Push to Slide on an Incline

From the solutions for Ps and Pd above, the relationship between them can be obtained and is shown as follows:

Given a coefficient of friction, :, and an inclination angle, 2, it can be concluded that

(1) Pd < Ps for 0 < 2 < 2r where 2r( angle of repose )= tan-1 :

(2) Pd = Ps for 2 = 0 and 2 = 2r

The relationship Pd # Ps can also be verified by the curves shown for the side and down pushes shown in Fig 1.45

Special Cases: (1) for no inclination, 2 = 0, the normalized push P/W (where W=mg) is equal to the

coefficient of friction, : (i.e., P/W = 9 for both side push and down push when : = 0.9 shown in the plot); (2) for no normalized push, P/W = 0, then the inclination angle, 2, is equal to the angle of repose, tan!1: (i.e., for : = 0.9, 2 = tan!1: = 42 deg shown in the plot)

Fig 1.46 Safe Distance

(1.28)

1.4.4 Calculation of Safe Distance for Following Vehicle

Use the kinematic relationships and derive the formula below for the safe distance as a function

of initial velocities and decelerations of both leading and following vehicles [10,11]

The first term in the equation for ls, based on the kinematic relationship (3) in Eq (1.12), is the total braking distance required for the following vehicle, (2), to stop; the second term for the leading vehicle #1 The difference of the first two terms is then the minimum safe distance needed for no collision The third term is the extra distance needed due to the reaction time of the driver in the following vehicle to apply his brakes

Special Cases: If v1 = 0, the minimum safe distance needed is the braking distance to stop for the following vehicle (the first term) If v1 = v2 , and b1 = b2, the minimum safety distance is zero (This excludes the reaction times of the drivers shown in Table 1.4.)

Table 1.4 Typical Braking Performances on Various Road Surfaces

Road

Surface

Leading Vehicle Deceleration, b 1 m/s 2 (g)

Trailing Vehicle Deceleration, b 2 m/s 2 (g)

Reaction Time, T R s

Case Study (Exercise): Radar Braking Kinematics

For a given set of initial traffic conditions:

1 Following Distance ()X), ft

2 Lead Vehicle Speed (VL), mph

3 Following Vehicle Speed (VF), mph

4 Lead Vehicle Deceleration (AL), g

5 Following Vehicle Deceleration (AF), g

Determine T, the time at which the following vehicle must brake to just avoid a crash, i.e., the two vehicles reach the same velocity at the same position If a collision is inevitable, determine the speeds

of the two vehicles and the time at collision

Fig 1.47 Radar Braking Velocity Diagram

(1.29)

NOTES:

(1) Lead vehicle starts to brake at To

(2) T includes the radar warning time and reaction time of following vehicle driver before applying brakes

(3) Use the velocity diagram and derive a set of closed-form kinematic relationships to solve the problem

(4) There are four possible kinematic combinations:

Case 1: VL ˜ VF, AL — AF, Case 2: VL ˜ VF, AL š AF

Case 3: VL ™ VF, AL — AF, Case 4: VL ™ VF, AL š AF

1.5 IMPACT AND EXCITATION: VEHICLE AND SLED TEST KINEMATICS

In a rigid barrier test, the vehicle is subjected to a direct impact and the occupant is then excited

by the crash pulse of the passenger compartment It is often more cost effective to test certain components (such as an air bag, belt and steering column restraint system, or instrument panel ) on

a Hyge sled than in a rigid barrier test In a Hyge sled test, the sled is impacted on by an accelerator which produces a sled test pulse similar to the barrier crash pulse The occupant is subsequently excited by the sled pulse Since deceleration forward in the barrier test is equal to acceleration backward in the sled test, the effect of component design changes on the occupant responses can then

be quickly evaluated using the sled test setup

In this section, the basic kinematic relationships applicable to vehicle and occupant impact analysis are presented The unbelted occupant kinematics in the vehicle compartment are analyzed for an air bag deployment decision in a crash How the kinematic variables, such as energy density and its derivative, can be utilized in detecting an occupant crash severity for activating an air bag sensor is also covered

1.5.1 Vehicle Kinematics in a Fixed Barrier Impact

The first and second integrals of the vehicle deceleration, a, are shown below The initial velocity and initial displacements of the vehicle are vo and xo, respectively

Fig 1.48 Rocker B-Post Kinematics of a Mid-Size

Car in a 14 mph Rigid Barrier Test

Fig 1.49 Sled Test Set Up

The longitudinal deceleration, a, measured at the Left/Rocker on the B-pillar of an aluminum intensive vehicle, in a 14 mph perpendicular barrier test, is shown in Fig 1.48

Plotted along with the deceleration curve are the integrated velocity and displacement The line segment tangent to the vehicle displacement curve at time zero is the free-flying displacement where the slope is the vehicle initial impact velocity, vo The maximum displacement of the vehicle (dynamic crush) is about 10 inches and occurs at 76 ms, as shown in Fig 1.48 The vehicle stops against the barrier at the time of dynamic crush, then rebounds until it separates from the barrier at 115 ms At the time of vehicle-barrier separation, the vehicle rebound velocity becomes constant over a small window of time and would remain constant if there were no external impulses acting on the vehicle The vehicle rebound velocity (or separation velocity) in this test is !3 mph and the vehicle displacement at the separation time (static crush) is about 9 inches Since the dynamic crush is 10 inches, the elastic rebound displacement (springback) of the vehicle structure (dynamic crush!static crush) is 10!9 = 1 inch The coefficient of restitution (relative separation velocity / relative approach velocity) is 3/14 = 0.21

In the fixed barrier test, vehicle speed is reduced (velocity decreases) by the structural collapse, therefore, the vehicle experiences a deceleration in the forward direction To study the effect of vehicle deceleration on occupant-restraint performance in the laboratory, the crash pulse is duplicated

on the sled A schematic showing an accelerator which imparts the acceleration to the sled is shown

in Fig 1.49 Consequently, it can be stated that “deceleration forward in a barrier test is equal to an acceleration backward in a sled test.” The sled test is more economical than the barrier test for studying the dynamic performance of occupant and restraint systems in an impact

1.5.2 Unbelted Occupant Kinematics

In a fixed barrier impact, the initial velocity of a free-flying occupant is constant, vo Therefore, the acceleration is zero (ao = 0), and the free-flying displacement is equal to vot The relative

Fig 1.51 Mid-Size Sedan 14 mph Rigid Barrier and

Sled Test Kinematics

Fig 1.50 Unbelted Occupant Kinematics in a

Mid-Size Sedan 14 mph Barrier Test

kinematics of an unbelted occupant with respect to the vehicle are defined as follows

a', v', x': Relative acceleration, velocity, and displacement of an unbelted occupant w.r.t vehicle,

a, v : Vehicle acceleration and velocity, measured with respect to inertial frame (e.g., ground)

1.5.2.1 Kinematics Based on Accelerometer Data

The kinematic relationship between the unbelted occupant and the vehicle during a crash is expressed in the equations above It should be noted that the magnitude of the unbelted occupant acceleration relative to the vehicle is equal to that of the vehicle deceleration The kinematics of the unbelted occupant with respect to a vehicle in a 14 mph rigid barrier test is shown in Fig 1.50

The differences between the barrier and sled test kinematic analysis are the sign of the acceleration and initial velocity The vehicle velocity profile in the barrier test is then parallel to that

in the sled test as shown in Fig 1.51

Fig 1.52 Vehicle-Barrier 14 mph Crash and Sled

(Occupant free-flight) Displacement

Fig 1.53 Dummy Seating Position

The kinematic relationships (deceleration, velocity, displacement) between the fixed barrier and sled tests are summarized as follows (for the in-depth analysis, see Section 4.2 of Chapter 4) A: The sled pulse is the negative of the vehicle barrier crash pulse,

B: The sled velocity profile is a shifted barrier velocity curve, by the magnitude of the initial barrier impact velocity, vo At tm , the time of dynamic crush, the sled velocity is equal to vo The magnitude of velocity change between time zero and tm for both barrier and sled tests is vo., C: The sled displacement at any time t is equal to vot - d (free-flying occupant absolute displacement minus vehicle-barrier displacement in a fixed barrier test, see Fig 1.52) The sled displacement

at tm is equal to votm - c, where c is the vehicle dynamic crush in the barrier test

The sled displacement curve is useful in obtaining the timing, t, when the sled or unbelted dummy moves a displacement of d; or obtaining the displacement when the time, t, is given For example, it would take an unbelted dummy 60 ms to move 5 inches in a 14 mph mid-size sedan to barrier test Therefore, according to the 5"!30 ms criterion, an air bag sensor system would need to activate at 60!30 = 30 ms after impact

Assuming that the distance between the hub of steering wheel to the torso of the occupant is 15 inches, as shown in Fig 1.53, the torso-hub contact time is about 100 ms and the relative contact velocity is about 16.5 mph At the time of hub contact, the unbelted occupant is still accelerating w.r.t the vehicle (a') at !3 g as shown in Fig 1.51 Since the vehicle rebounds (v = 0) at 76 ms where the torso relative velocity, v', is 14 mph, the torso contacts the hub during the rebound phase of the vehicle Therefore, the torso-hub contact velocity in this test is greater than the initial vehicle impact velocity of 14 mph due to vehicle rebound The 14 mph rigid barrier test is a threshold test condition where an air bag deployment is warranted since there is an injury potential to an unbelted occupant

in a frontal crash at this speed or higher speeds [6]

Fig 1.54 Unbelted Driver Motion from Crash Test Film

Fig 1.55 Vehicle Crush, Sled Displacement, and Centroid

1.5.2.2 Kinematics Based on Crash Film Records

The kinematic analysis of an unbelted crash dummy in a mid-size car in a 14 mph rigid barrier test is compared to that based on accelerometer data The relative displacements of the head and shoulder targets w.r.t the target on the rocker at B-pillar are shown in Fig 1.54 The two curves are fairly close to each other due to the free-flight motion of the unbelted dummy However, due to seat friction and minor resistance acting on the lower extremities, the upper body has a small amount of pitching motion and moves a little bit ahead of the shoulder after 60 ms This timing from crash film analysis agrees fairly well with that obtained from the double integral of the accelerometer signal shown in Fig 1.50

1.5.2.3 Vehicle Crush, Sled Displacement, and Crash Pulse Centroid

It will be shown that at any given time, the sum of the vehicle displacement and the corresponding sled displacement (or unbelted occupant relative displacement to vehicle) equals the occupant free-flight distance This is evident from Eq (1.30) in that x + xN = vot, where x is the vehicle displacement (crush), xN is the sled displacement, and vot is simply the occupant free-flight displacement Fig 1.55 shows the relationship between the vehicle crush, sled displacement, and crash pulse centroid

The dynamic crush of the vehicle at tm is C = 10.1 inches and the sled displacement is 8.5 inches; these add up to 18.6 inches, the occupant free-flight displacement as shown by point F Since the vehicle stops momentarily at tm (= 76 ms, at point E), the corresponding occupant relative velocity at

tm is then the same as the initial impact velocity Since line segment ONB is a tangent to the sled curve OGON at ON, and line segment OHF is a tangent to the curve OAE at O, the two line segments ONB and OHF are parallel

The horizontal intercept, H, of line segment CE (dynamic crush) and the slope (initial velocity),

OF, tangent to the vehicle displacement at time zero, is the area centroid of the crash pulse It is shown in Chapter 2 that the intercept, B, of the tangent ONB and the zero displacement reference axis

is also the centroid time The shape of a crash pulse is mainly controlled by the relative centroid location which is the ratio of centroid time, tc, to the time of dynamic crush, tm

The point E on the vehicle displacement curve is where the vehicle dynamic crush occurs and the corresponding point on the sled displacement curve is ON at tm It will be shown in Chapter 2 that in general, points E and ON do not coincide In other words, vehicle dynamic crush does not equal the sled displacement at tm Points E and ON will coincide only when the crash pulse is symmetrical at its centroid location Crash pulses such as square, halfsine, haversine, and symmetrical triangular pulses are examples of pulses where points E and ON coincide Recognition of such a special condition makes the impact analysis easier The severity of headform impact in terms of head injury criteria (HIC) will be covered at the end of Chapter 2 The analysis is made easier because only the displacement change of a symmetrical crash pulse, such as a halfsine pulse, is needed

In summary, use of crash film digitized data of the unbelted occupant displacement relative to the vehicle (or the sled displacement with zero initial velocity) provides more than just the occupant/sled displacement information It also provides the vehicle transient kinematics such as the displacement, velocity, relative centroid location, and crash pulse shape

1.6 VEHICLE AND OCCUPANT KINEMATICS IN FIXED OBJECT IMPACT

The vehicle and occupant kinematics using various threshold speeds and impact modes are compared Two of the modes are rigid barrier tests, one at 8 mph and one at 14 mph, and one mode

is a rigid pole test at 21 mph for a full-size passenger car The objective is to evaluate the occupant-vehicle impact severity in a crash where an air bag deployment decision is to be made Shown in Table 1.5, the 14 mph rigid barrier and 21 mph pole tests are for an air bag “must deploy” test condition, while the 8 mph test is a “must not deploy” condition

Table 1.5 Air Bag Deployment Threshold Tests

C1 14 mph perpendicular barrier C2 8 mph perpendicular barrier

1.6.1 Vehicle Kinematics in Different Test Modes

Three crash tests (C1, C2, C3) involving a full-size passenger car in an 8 and 14 mph perpendicular rigid barrier test and in one 21 mph center pole test were made in order to compare the vehicle kinematics for a fixed object impact The compartment crash pulses obtained from the three tests are shown in Fig 1.56 The crash pulse duration for the 8 and 14 mph rigid barrier tests are about the same, 125 ms, while that for the 21 mph pole test is about 170 ms This duration is longer due to the softer localized impact The times of dynamic crush (the maximum crush during collision) for the three tests can be found from the velocity and displacement curves shown in Figs 1.57 and 1.58 These are about 80 ms for the barrier tests and 140 ms for the pole test For a given vehicle structure, the crash pulse duration, and time of dynamic crush depend greatly on the crash mode For a given impact mode, these timings do not vary significantly with the initial impact velocity

Fig 1.57 Vehicle Velocity vs Time in Three Crash Tests

Fig 1.58 Vehicle Displacement vs Time in Three Crash Tests Fig 1.56 Vehicle Deceleration in Two Barrier and One Pole

(21mph) Crash Tests

Fig 1.59 Vehicle Energy Densities in Three Crash Tests

1.6.2 Vehicle Energy Density

The energy density (e = energy/mass) of a vehicle during a crash can be computed by integrating the accelerometer data, given an initial velocity The energy density at the time of dynamic crush can then be expressed as e = 4 v2, where the unit of e is g-in, and v, mph The formula is derived as follows

Shown in Fig 1.59, the energy density curve for the 8 mph test has only one slope, which is the average deceleration of the vehicle in that period However, there exist two line segments for the 14 mph barrier and 21 mph pole tests The slope of the second segment is higher than the slope of the first Therefore, the vehicle experiences a low deceleration first and then a high deceleration later due

to encountering higher structure and/or component resistance Using the formula e = 4 v2, the total energy density for the 8, 14 mph rigid barrier, and 21 mph rigid pole tests are 25.6, 78.4, and 176.4 g-in, respectively The computed values based on the formula agree fairly well with those maximum energy densities at the test dynamic crush shown in Fig 1.59

In a localized impact test where a passenger car was crashed at a speed of 21 mph into a rigid pole, the pre- and post-test kinematics of the engine compartment are shown in Figs 1.60 and 1.61 The engine bottoms out on the pole and the total vehicle crush is 34 inches with a total energy density,

e = 0.4 v2 = 0.4×(21 mph)2 = 176.4 g-in The pole starts interacting with the engine block at about 27 inches of penetration, where the vehicle deceleration magnitude (slope of a point on e vs x), a, increases from 4 to 14 g The vehicle energy density in the pole test shown in Fig 1.59 increases from zero at 4 inches and reaches 90 g-in at about 27 inches Therefore, the slope of the first segment of the e vs x curve is 90/(27!4) Ñ 4 g