AUTOMOTIVE DYNAMICS and DESIGN: LONGITUDINAL DYNAMICS

CRASH!

BRAKE!

ACCELERATE! Brian Paul Wiegand, B.M.E., P.E. AUTOMOTIVE DYNAMICS and DESIGN

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LONGITUDINAL “WEIGHT TRANSFER”

LATERAL “WEIGHT TRANSFER”

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The difficulty of obtaining a solution to the automotive longitudinal acceleration problem is belied by the apparent simplicity of the underlying relationship: "F = m a". Consider the matter of the accelerative force "F". Values for the automotive accelerative force must ultimately be derived from torque-speed relationship of the particular engine involved, such as that depicted here: AUTOMOTIVE DYNAMICS and DESIGN

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The curve depicted is fairly representative of internal combustion reciprocating engines, with a low torque output at low engine speed. This is exactly the opposite of the ideal for an automotive propulsion unit: high torque at stall. To be made suitable for automotive use, the torque-speed relationship inherent in the piston engine must be modified in transmission to the drive wheels. Depending on engine speed, the appropriate torque values from the WOT curve are translated and transmitted through the drivetrain resulting in accelerative forces at the drive wheels, which becomes the net accelerative force "F" when the rolling resistance force "FR" and the aerodrag force "D" are subtracted:

Where: F = The accelerative force (lb, kg). T = Engine torque (lb-ft, kg-m). TR = Transmission torque ratio (dimensionless). TE = Transmission energy efficiency (dimensionless). AR = Axle torque ratio (dimensionless). AE = Axle energy efficiency (dimensionless). RD = Dynamic rolling radius at drive wheels (ft, m). FR = Tire rolling resistance force (lb, kg). D = Aerodynamic resistance force (lb, kg).

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While the rolling resistance force “FR”…

…and the aerodynamic drag force “D”…

…are explicit and obvious functions of vehicle velocity, the engine torque also relates directly to velocity, at least after the initial transient "start-up" of an acceleration run. The relation between engine speed and vehicle speed is:

Symbols unique to these equations: rpm = Rotational speed of the engine (“revolutions” per minute). V = Velocity of the vehicle (mph, kph). K = Translational to rotational motion units constant (14.005635 for “V” units of mph and “RD” units of ft). CR = Dynamic coefficient of rolling resistance of a tire (lb/lbmph2.5). KR = The static coefficient of rolling resistance of a tire (lb/lb). N = The “normal” (weight) load on a tire (lb).

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Following a somewhat circular chain of reasoning, it can be shown that automotive acceleration is to some extent a function of itself: a = f(F) F = f(T) >>>> a = f(T) T = f(rpm) >>>> a = f(rpm) rpm = f(V) >>>> a = f(V) V = f(a, t) >>>> a = f(a, t) This indicates that it will not be possible to put the dependent and independent variables in correspondent form; that the ultimate relation will be transcendental. Transcendental equations can’t be solved by algebraic means; transcendental relations are amenable only to numeric approaches. AUTOMOTIVE DYNAMICS and DESIGN

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Moreover, the accelerative force generated by the engine is limited in application by the available traction at the drive wheels. This traction is dependent on the normal loads at the tires. These normal loads are heavily influenced by the accelerative “weight transfer” and “torque reaction”. In other words, there is yet more reason to suspect a futility inherent in analytic attempts at solution.

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Further analytic difficulty derives from the "m" variable of the basic relation "F = m a". This "m" is not just a matter of vehicle weight divided by the gravitational constant as would be the case with a simple homogeneous body. An automobile is not a homogeneous body; some components are not just accelerated translationally, but rotationally as well. To account for the overall effects of this variegated behavior the concept of "effective mass" or “me” must be substituted for the fundamental mass "m”:

The symbols unique to this equation are as follows: W = The weight of the vehicle (lb, kg). g = The gravitational constant, required only for English units (32.174 ft/s2). I1 = Rotational inertia about front axle line (lb-ft2, kg-m2). I2 = Rotational inertia about the crankshaft axis (lb-ft2, kg-m2). I3 = Rotational inertia about transmission 3rd motion axis, plus 1st and 2nd transmission motion axis inertias translated to the 3rd motion axis (lb-ft2, kg-m2). I4 = Rotational inertia about rear axle line (lb-ft2, kg-m2). AUTOMOTIVE DYNAMICS and DESIGN

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A concrete appreciation of how the individual terms in the effective mass equation contribute to the total effective mass can be obtained through study of an example set of parameter values representative of an actual passenger car. For this purpose a 1958 Jaguar XK150S was taken to be representative of conventional configuration passenger cars:

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Considering just those basic aspects of the acceleration problem as have been discussed so far, it should be apparent that the automotive longitudinal acceleration relation is: • Extremely complex, non-linear, encompassing many variables. • Consisting of numerous interconnected subrelations such that the total problem is perhaps best expressed as a series of partial differential equations. • Discontinuous by virtue of the gear changes and the transient condition at the start of the acceleration run.

In view of the theoretical and practical complications inherent in the automotive longitudinal acceleration problem, it should not be surprising that an analytic solution is not possible. Yet, despite the lack of an analytic solution, over eighty years ago engineers were able to predict accelerative performance with fair accuracy using a method of “hand” calculation and graphical integration. AUTOMOTIVE DYNAMICS and DESIGN

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The traditional “hand” method of automotive acceleration performance has been called the "Koffman Method", after the English engineer J. L. Koffman who in the 1950's published a series of articles the "Automobile Engineer". However, the essence of the method was a part of common practice long before the appearance of Koffman's articles. Certain authorities have credited the origin of the method to the English professor W.E. Dalby, F.R.S., in the 1930's. Whatever the origin of the method, what is important is that it circumvented the lack of an analytic solution by utilizing desk calculators and drafting equipment. Besides being tedious and slow, the limitations of such an approach necessitated that certain aspects of the acceleration problem be simplified: •Neglect of “weight transfer” and its effects (vertical c.g. not input). •Neglect of “torque reaction” and its effects (track not input). •Neglect of rolling radius variation (rolling radius held constant). •Neglect of any initial or transient conditions (problems of initial engine rpm, wheel spin, clutch slip, etc, were not addressed; longitudinal c.g. was not input). AUTOMOTIVE DYNAMICS and DESIGN

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The traditional “hand” method established that the maximum acceleration was obtained at WOT with “upward” gear shifts at every intersection point of the acceleration-in-gear curves (except if redline occurs first):

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In contrast to "hand" calculation approaches to acceleration performance problems, a computer simulation has the following inherent advantages:

• Less time-intensive. • Consistent results from analysis to analysis due to a constant methodology and application. • More significant digits, less round-off error. • Constitutes a more readily transferable form of knowledge (if properly documented) which results in less demanding personnel requirements. • Greater accuracy through smaller incrementation size. • More realistic model possible with fewer simplifications. • Facilitates a systems engineering approach to design, resulting in an optimized system as opposed to a collection of optimized parts. AUTOMOTIVE DYNAMICS and DESIGN

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A simulation program termed "MAXGLONG.BAS“ was written in 1984. The automotive acceleration problem may be divided into two distinct stages, which is reflected in the simulation having two parts: the “starting method” and the “continuing method”. The driving or independent variable was taken to be the velocity, which relates directly to engine rpm. The starting method addresses the fact that at the commencement of the acceleration run (t = 0, V = 0) not all the boundary values are known, principally the initial engine rpm. This initial rpm (“rpm1”) is determined on the basis of finding the maximum rpm on the WOT torque-rpm curve for which the corresponding torque value does not cause wheelspin (with its attendant decrease in traction). This is not as simple a problem as it might seem, for the attainment of this maximum initial acceleration is not instantaneous. Clutch slip, "wind-up" in the drivetrain, tire deformation slip, etc., all ensure a transition period of some milliseconds between “a = 0” and “a = maximum”; enough time for a “weight transfer” to take effect modifying the acceleration potential. The problem is therefore circular and requires some iteration for solution. How this solution is obtained may be best understood by considering the flowchart of the initial-engine-rpm subroutine… AUTOMOTIVE DYNAMICS and DESIGN

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After the clutch is engaged at the initial engine rpm, there ensues the transient period of simultaneously decreasing engine rpm and increasing vehicle velocity. What is happening during this period is that the kinetic energy of the rotational mass "I2" is in the process of being "shared" with the mass of the entire vehicle. The engine rpm ceases to drop when an energy balance is achieved at some lower rpm (“rpm2”):

The energy output by the engine “E” during this period of rpm drop is generally not much of a factor, at least not for conventional passenger vehicles. What is important is that “rpm1” and the inertial quantity “I2” are large enough so that “rpm2” is not equal to, or less than, the engine stall rpm. The flowchart of the subroutine to determine “rpm2” is… AUTOMOTIVE DYNAMICS and DESIGN

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The determination of “rpm2” marks the transition between the starting method and the continuing method. The continuing method is actually the average of two different approaches to the same end. The “interpolation” approach is predicated on an assumed short-term linear relation between vehicle velocity and the accelerative force, and is derived directly from the basic relation "F = m a". For this approach the elapsed time and traversed distance increments are determined by:

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The “integration” approach is predicated on a curvilinear relation between vehicle velocity and accelerative force. In this connection the assumed parabolic torque-rpm model is utilized to allow the necessary integration to derive the elapsed time and traversed distance increment expressions:

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The reason for the use of the average of these two sets of “Δt” and “Δs” figures is graphically illustrated below; it is only the averaged time and distance increments that allow the MAXGLONG.BAS program to closely mimic the empirical velocitytime curve:

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This average value algorithm step is labeled “CALC TIME, DISTANCE INCREMENTS & SUM” in the continuing method flowchart :

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It should be noted that in the case of the MAXGLONG.BAS program a very complex reality had to be reduced to a handful of simple algorithms. A certain amount of arbitrariness was introduced in the choice of “adjustment” factors to account for clutch slip, and in the choice of a “three-point parabolic spline” as the torque-rpm curve function. For instance, the parabolic torque-rpm curve is very well suited to the actual torque-rpm nature of the Jaguar XKl50S engine, but would not be so well suited to the Porsche 944 engine (the torquerpm curve is almost flat in the 2500-5500 rpm range). For a simulation of a vehicle with such a flat torque-rpm relation, the “integration” portion of the continuing method algorithm would have to be disabled, and a “table look-up” with linear interpolation substituted for the parabolic torque-rpm subroutine. This is not to denigrate the utility of the program, it’s just that for each basic configuration to be analyzed the procedure is not just a matter of “type in the parameters and run”. Some adjustment or “bedding-in” of the program may first be necessary by means of a known “benchmark” or “baseline” run. Otherwise, the results may have a relative validity with respect to each other but not necessarily much of a relation to reality. AUTOMOTIVE DYNAMICS and DESIGN

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THE MAXGLONG.BAS INPUT FILE:

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THE MAXGLONG.BAS OUTPUT FILE (SHORT FORM):

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FOR THE MAXGLONG.BAS VALIDATION THREE VARIENTS OF THE 1958 JAGUAR XK150S WERE USED:

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FOR THE MAXGLONG.BAS VALIDATION THREE VARIENTS OF THE 1958 JAGUAR XK150S WERE USED:

TWO

ONE

THREE

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* MAXGLONG.BAS NOTES: AN INPUT FILE TEMPLATE, A COPY OF “MASS PROPERTIES AND AUTOMOTIVE LONGITUDINAL ACCELERATION”, AND PROGRAM FILE OF MAXGLONG.BAS / SAMPLE INPUT & OUTPUT FILES / “KEDIT” / “GWBASIC” WILL BE PROVIDED EVERY INTERESTED STUDENT WHO HAS SURVIVED SO FAR. * OTHER ACCELERATION PROGRAMS: “STRAIGHTLINE ACCELERATION SIMULATOR” BY J. TODD WASSON OF PERFORMANCE SIMULATIONS. THERE ARE MANY OTHERS AVAILABLE WITH VARYING DEGREES OF ACCURACY. AUTOMOTIVE DYNAMICS and DESIGN

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Braking is just the reverse of acceleration; just as effective mass was very significant with regard to acceleration, it also is important with regard to braking. The simplest (2-dimensional) depiction of a braking vehicle of weight “Wt” initially moving with a velocity “V”, but sliding to a stop in a distance “d”, is:

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The only force in line with the vehicle displacement is the dynamic friction force “f”, so this is the only force doing any work. The total work done by “f” between Point 1 and Point 2 is “f × d”, and since “f” is directionally opposite the displacement this represents negative work. If the vehicle comes to a complete stop (“V = 0”) at Point 2, then the friction work done at that point has completely dissipated (equaled) the vehicle’s kinetic energy as it existed at Point 1, where the braking effort was initialized:

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However, braking to a stop requires dissipating all the kinetic energy of the vehicle, which means not just the energy associated with the translationally moving mass, but all the rotationally moving mass as well. Substituting for “m” the “me” of previous discussion, but dropping the “I2” term for a “clutch disengaged” condition, brings the model a little closer to reality:

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Another step toward reality involves “f”; there is no such single force acting on the vehicle to slow it down. There are traction forces at the tire/ground contact points, which result from forces at the brake friction surfaces generating rotation resisting torques “Tf” and “Tr”, and then there are rolling resistance forces (not shown), plus an aerodynamic drag force:

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Even this model is not completely realistic. However, it does show the aero forces “D” (drag) and “L” (lift) acting at the “CP” (center of pressure). More importantly, it now shows the individual traction forces at the front and rear (2-dimensional model) tire/road contact areas, and indicates how those forces are influenced by longitudinal “weight transfer” (which is modified due to the aero moments) resulting from the “ma × h” moment:

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The previous equation revised in accord with this greater realism is:

The aero drag “D” and lift “L” forces may be calculated (with “V” now in feet-per-second) per:

The areas “Af” and “Ap” are in square-feet and the resulting “D” and “L” forces are in pounds. AUTOMOTIVE DYNAMICS and DESIGN

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The rolling resistance at the front axle “FRf” and the rolling resistance at the rear axle “FRr” are expressed by the equations: FRf = CSf Nf + 3.24 CDf (V/100)2.5 Nf

FRr = CSr Nr + 3.24 CDr (V/100)2.5 Nr

Here the velocity “V” is in units of mph, while the axle normal forces “Nf” and “Nr” and the resulting axle rolling resistance forces ““FRf” and “FRr” are all in terms of pounds. The axle traction forces associated with braking “ff” and “fr” are also dependent on the axle normal loads “Nf” and “Nr” : However, complication results from the fact the traction coefficients “μf” and “μr” are themselves a function of normal load… AUTOMOTIVE DYNAMICS and DESIGN

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…or, more precisely, functions of contact area pressure “Pc” (since “Pc = N/Ac”):

Some typical tire specific values for “a” and “n” might be “15.7369” and “-0.67791”, respectively. The “15.7369” is the value of “a” for pressure units in psi; for pressure units in kPa use “58.2587” for “a”. Of course, the contact areas will also vary in accord with the normal loads… AUTOMOTIVE DYNAMICS and DESIGN

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The front and rear tire contact areas (multiply by ”2” for axle area) vary in accord with normal loads per:

Where: Ac = Tire to ground plane gross contact area (in2) Lc = Tire to ground contact area length (in). tw = Tire tread width, assumed constant with load (in). Ri= Tire no-load inflated radius (in). d = Tire vertical deflection under load (in). AUTOMOTIVE DYNAMICS and DESIGN

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To use those area equations requires calculation of the tire deflection “d” under normal load “N” (lb)…

…and also requires the width of the tire tread “tw” which, when lacking a measured value, can be approximated per the formula: Where for these last two equations: KZ = Tire vertical stiffness (lb/in). tw = Tire tread width, assumed constant with load (in). = Tire section aspect ratio (dimensionless). SN = Tire nominal section width (mm). N = The normal load on the tire (lb). d0 = Tire deflection function “y-intercept” value (in). AUTOMOTIVE DYNAMICS and DESIGN

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Note the deflection equation further requires calculation of the tire vertical spring rate “Kz”:

Where: KZ = Tire vertical stiffness (kg/mm). Pi = Tire inflation pressure (kPa). = Tire section aspect ratio (dimensionless). SN = Tire nominal section width (mm). DR = Wheel rim nominal diameter (mm). AUTOMOTIVE DYNAMICS and DESIGN

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An initial concentration on the normal loads would seem to be key; the normal loads, which result from the static longitudinal weight distribution as modified by dynamic “weight transfer” and by aerodynamic drag and lift are:

Where: Wt = Total vehicle weight (lb). Wb = Vehicle wheelbase (in). LCG = Longitudinal distance of CG from front axle (in). me = Vehicle “effective mass” (lb). a = Vehicle deceleration (in/sec2). VCG = Vertical distance of CG from ground plane (in). D = Aerodynamic drag force (lb). VCP = Vertical distance of CP from ground plane (in). L = Aerodynamic lift force (lb). LCP = Longitudinal distance of CP from front axle (in). AUTOMOTIVE DYNAMICS and DESIGN

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The brakes on any modern car can easily “lock” the wheels, but that is not maximum longitudinal deceleration. For maximum longitudinal deceleration the braking force “f” must be exactly equal, not greater than the maximum static traction force “N μ” that the tires are capable of. This means that the torque “T” produced by the brakes can not be more than “f R”:

Traditionally this means that a lot of time and effort was spent on developing brake proportioning systems, and later Anti-skid Braking Systems (ABS). Skilled drivers and modern ABS can be so good that the above equations of perfect brake balance may be assumed to hold. It is this assumption of perfect brake proportioning which makes the functioning of the braking computer simulation program “MAXDLONG.BAS” possible. AUTOMOTIVE DYNAMICS and DESIGN

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THE MAXDLONG.BAS FLOW CHART:

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THE MAXDLONG.BAS INPUT FILE:

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THE MAXDLONG.BAS OUTPUT FILE (SHORT FORM):

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THE MAXDLONG.BAS VALIDATION:

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* AN INPUT FILE TEMPLATE, AN EXCERPT FROM “MASS PROPERTIES AND ADVANCED AUTOMOTIVE DESIGN”, AND PROGRAM FILE OF MAXDLONG.BAS / SAMPLE INPUT & OUTPUT FILES WILL BE PROVIDED EVERY INTERESTED STUDENT WHO HAS SURVIVED SO FAR. * OTHER BRAKING SIMULATION PROGRAMS: ADAMS (Automatic Dynamic Analysis of Mechanical Systems) computer programs as used to model and simulate the performance of an anti-lock braking system (as written about by B. Ozdalyan and M.V. Blundell, Sch. of Eng., Coventry Univ., UK) . CarSim is a commercial software package that predicts the performance of vehicles in response to driver controls (steering, throttle, brakes, clutch, and shifting) in a given environment (road geometry, coefficients of friction, wind). CarSim is produced and distributed by an American company, Mechanical Simulation Corporation, using technology that originated at The U. of Michigan Transportation Research Institute (UMTRI). AUTOMOTIVE DYNAMICS and DESIGN

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Automotive safety has two main aspects: the “active” and the “passive”. The “active” aspect of automotive safety is the subject of accident avoidance, which involves such things as acceleration, braking, cornering, maneuverability, and directional stability; each of which is a complex subject in its own right. Also there are safety aspects not inherently part of automotive design; such as roadway construction, speed limits, and traffic regulation. What is the sole concern of this crash segment is the “passive” aspect of automotive design: the minimization of automotive crash consequences: fatality, injury, and property loss. Of those three consequences fatality is the most grave, making crash survival the greatest imperative of automotive design!!! AUTOMOTIVE DYNAMICS and DESIGN

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Crash survival is a matter of reducing the magnitude of injury and thus the likelihood of death. To reduce the magnitude of injury one must begin by considering the

human physique

which, like any other structure, is prone to failure when subjected to excessive stress levels; stress “S” is expressed as force “F” per area “A”:

S = F/A The forces associated with the deceleration of the masses act in accord with Newton’s Second Law of Motion:

F=ma AUTOMOTIVE DYNAMICS and DESIGN

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By combining those two equations it becomes obvious that injurious or fatal stresses inflicted upon the human physique by sudden decelerations may be reduced in two ways:

S=ma/A One way is to increase the areas (“A”) over which the forces are distributed, and the other way is to decrease the decelerations (“a”) involved. Hence the modern emphasis on padded dashboards and recessed hard points for automotive interiors, and the ancient emphasis upon helmets and armor in combat; it was all an attempt to dilute the forces involved. AUTOMOTIVE DYNAMICS and DESIGN

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The survivable limits of human deceleration are not clear-cut. A great deal depends on the particular individual involved and on the particular circumstances of the accident. A burly longshoreman is physically quite different from a petite secretary, but which one would be the most likely to survive dangerous impact loadings? This depends on physiological factors which are not necessarily visible or even readily identifiable; microscopic matters such as cell structure and capillary formation may be involved. Macroscopically, a sturdy skeleton and robust configuration must be weighed against the disadvantage of greater mass. Genetics, sex, age, size, nutrition, physical condition and many other factors may play a part in determining individual deceleration limits. AUTOMOTIVE DYNAMICS and DESIGN 51

What is known is that there are six general survival criteria factors which are amenable to manipulation; these factors are: 1. Magnitude of the Deceleration (usually measured in gravity units or “g’s”). 2. Rate of Onset of the Deceleration (also known as “jerk”, which is the rate of variation in the deceleration level, usually measured in “g’s/sec”). 3. Duration of the Deceleration (the time elapsed at some deceleration level, usually measured in “seconds”). 4. Position/Packaging (orientation of the subject with respect to the deceleration vector, and then

maintaining that orientation. 5. Vibration (impact vibration is a highly intense random oscillation over a very short time span, so a statistical approach is required that quantifies the power of each vibration input over the frequency range). 6. Angular Acceleration (measured in degrees or radians per second squared; angular acceleration rates at onset, at peak, and throughout the duration are all significant).

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(Koelle, H.H. (Editor-in-Chief); Handbook of Astronautical Engineering, NY, NY; McGraw-Hill, 1961, pg. 26-42) AUTOMOTIVE DYNAMICS and DESIGN

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The “Lovelace Chart” presents the approximate deceleration level limits for human survival. However, severe deceleration events leading to near human fatality generally do not have accelerometers present, so for events like near fatal automobile accidents the “g” levels can only be estimated from such data as can be recorded at the scene. The survived incident of the “55 ft (16.76 m) fall with 4 in (10.16 cm) deceleration” provides enough such information that the estimation technique used to produce the chart may be determined. AUTOMOTIVE DYNAMICS and DESIGN

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Since the deceleration distance is 4 in or 0.33333 ft, the following distance-average deceleration “ā” equation can be written:

Into this equation the known values may be “plugged”:

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There are two unknowns, the average deceleration “ā” and the duration time “t”, so one more equation is necessary for solution. The velocity change with time provides this:

Again, the known values may be inserted:

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“Solving” this for “t” results in:

Substituting this for “t” in the distance equation results in:

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This may now be solved for the average deceleration “ā” resulting in:

Since 141.0 g’s is close (97%) to the chart-indicated deceleration rate of 145 g’s, it is reasonable to assume that average deceleration calculations such as this just carried out were used to estimate the deceleration levels for the “severe auto accidents”. This is notable as it means that deceleration levels significantly greater than the indicated average deceleration levels of the chart were endured and survived (though for shorter duration!). AUTOMOTIVE DYNAMICS and DESIGN

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“David Charles Purley…(26 January 1945 – 2 July 1985) was a British racing driver… best known for his actions at the 1973 Dutch Grand Prix, where he abandoned…(his race car)…and attempted to save…fellow driver Roger Williamson, whose car was…on fire...Purley was awarded the George Medal for his courage in trying to save Williamson, who suffocated...During pre-qualifying for the 1977 British Grand Prix Purley sustained multiple bone fractures (when)…he crashed into a wall. His deceleration from 173 kph (108 mph) to 0 in a distance of 66 cm (26 in) is thought to be one of the highest G-loads in human history…He died in a plane crash in…1985.” AUTOMOTIVE DYNAMICS and DESIGN

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“…(Purley) survived an estimated 179.8 g’s when he decelerated from 173 km/h (108 mph) to 0 in a distance of 66 cm (26 inches)… This was the highest measured (sic) g-force ever survived by a human being…(until in 2003, Kenny Bräck’s crash violence recording system measured 214 g’s)…” Using the same methodology as previous we may make our own estimate of the average Purley Gload:

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(Koelle, H.H. (Editor-in-Chief); Handbook of Astronautical Engineering, NY, NY; McGraw-Hill, 1961, pg. 26-43) AUTOMOTIVE DYNAMICS and DESIGN

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(Harris, Cyril, and Charles E. Crede; Shock and Vibration Handbook, NY, NY; McGraw-Hill, 1961, pg. 44-43) AUTOMOTIVE DYNAMICS and DESIGN

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(Koelle, H.H. (Editor-in-Chief); Handbook of Astronautical Engineering, NY, NY; McGraw-Hill, 1961, pg. 26-36.) AUTOMOTIVE DYNAMICS and DESIGN

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“The study of the automobile …shows that complete body support and restraint of the extremities provide maximum protection against accelerating forces and give the best chance for survival. If the subject is restrained in the seat, he makes full use of the force moderation provided by the collapse of the vehicle structure, and is protected against…bringing him in contact with interior surfaces…” ( Harris, Cyril, and Charles E. Crede; Shock and Vibration Handbook, NY, NY; McGrawHill, 1961, pg. 44-34.) (A concept of the course instructor’s regarding “good “ packaging of the automotive occupants ) AUTOMOTIVE DYNAMICS and DESIGN

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Harsh fluctuating deceleration input compounds any detrimental effects on the human physique, and even more so if it should excite “resonance” of any of the internal organs (for example, the natural frequency of the Thorax-abdomen system of a human subject is between 3 and 4 cps…). In such a case large organ displacement effects are possible, even when the exciting deceleration inputs may be relatively small. The aerospace technique used to combat the effects of such vibration, which has similarity to the vibration characteristic of aerodynamic buffeting, rocket liftoff, re-entry splashdown, etc., is to prevent internal organ displacement by use of a tight fitting garment of flexible but inelastic material: a “g-suit”. Obviously the expedient of dressing up like an astronaut just to drive to the local market is impractical for everyday automotive application (and we won’t even talk about the “immersion” technique lest someone design a combination car and swimming pool!). AUTOMOTIVE DYNAMICS and DESIGN

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Angular acceleration warrants being listed as a major factor in crash survival due to the human brain’s particular sensitivity to sudden rotational movements. Boxers have long been aware that a cross or a hook can be more effective than a jab of equal magnitude; any blow that tends to twist the head about the neck is generally rated high in effectiveness. This is especially interesting in light of the fact that about 70% of all automotive fatalities are caused by head/neck injuries. Many of these fatal injuries involve tearing of the tissue at the back of the brain stem area, and much of that is due to rotational shearing effects. AUTOMOTIVE DYNAMICS and DESIGN

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THE CHARACTER OF AUTOMOTIVE CRASHES MUST BE STUDIED IN HOW IT RELATES TO THE SURVIVAL FACTORS…

THE AREA UNDER THE “CURVE” REPRESENTS THE ENERGY USED IN CRUSHING THE VEHICLE STRUCTURE, WHICH IN TURN IS RELATED TO…

Edeform = Etranslation + Erotation + Eengine - Elosses AUTOMOTIVE DYNAMICS and DESIGN

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THE “Etranslation + Erotation “ REPRESENTS THE TOTAL KINETIC ENERGY POSSESSED BY THE VEHICLE AT THE TIME OF IMPACT, WHICH BRINGS US BACK TO OUR OLD FRIEND “EFFECTIVE MASS”:

THE REASON WHY THAT IS NOT MORE EMPHASIZED IS BECAUSE IN A CRASH IT IS NOT POSSIBLE TO BE VERY CERTAIN HOW MUCH OF THE KINETIC ENERGY WILL BE UTILIZED FOR DEFORMATION. SOMETIMES THE ROTATIONAL ENERGY ISN’T EVEN CONSIDERED:

Edeform = Etranslation - Elosses AUTOMOTIVE DYNAMICS and DESIGN

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ENERGY PRODUCED DURING A FRONTAL CRASH BY THE ENGINE “Eengine” IS MINISCULE, AND THE ROTATIONAL KINETIC ENERGY OF THE ENGINE AND MUCH OF THE DRIVETRAIN TENDS TO GET “LOST”:

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ENERGY IS ALSO “LOST” TO THE DEFORMATION OF PRIMARY STRUCTURE DUE TO THE SHEDDING OF MASS DURING A COLLISION:

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Energy can also be dissipated in a number of other ways: light, sound, vibration, heat, and friction. An automotive crash usually involves all of these forms of energy dissipation, but primarily it is by work, the deformation of the vehicle structure, that most of the available vehicle kinetic energy is dissipated. However, exactly how much energy that is constitutes a problem. As a rough “rule of thumb”, for full frontal collisions take the effective weight to be the crash weight plus an extra 3.7 percent to account for any rotational energy input. AUTOMOTIVE DYNAMICS and DESIGN

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1954 TWO CAR HEAD ON CRASH TEST:

(Harris, Cyril, and Charles E. Crede; Shock and Vibration Handbook, NY, NY; McGraw-Hill, 1961,pg. 44-48) AUTOMOTIVE DYNAMICS and DESIGN

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1963 HEAD ON BARRIER CRASH TEST:

(Patrick, Laurence M. (Editor); 8th Stapp Car Crash and Field Demonstration Conference, Detroit, MI; Wayne State University Press, 1966, pg. 296-297) AUTOMOTIVE DYNAMICS and DESIGN

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THE FACT THAT THE DECELERATION TRACE CAN VARY ALL OVER THE HUMAN BODY AND BE SIGNIFICANTLY AT VARIANCE WITH THE MAIN VEHICLE TRACE USUALLY BODES ILL FOR THE VEHICLE OCCUPANTS, BUT CAREFUL ENGINEERING CAN MAKE BENEFICIAL USE OF SUCH A SEPERATION OF OCCUPANT DECELERATION BEHAVIOR FROM THAT OF THE CAR:

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“The available space for seat or passenger travel using the principle of energy absorption…must be considered carefully…seat belts and other crash restraint(s)… (using) extensible fabrics have been found to be extremely hazardous since their load characteristics cannot be sufficiently controlled…increase in exposure time must be considered as well as the reduction in peak acceleration. For very short exposure times where the body’s tolerance…is…not (limited by) the peak acceleration, the benefits derived from reducing the peak loads would disappear.” “Many attempts have been made to incorporate energy-absorptive devices…in a harness or in a seat with the intent to change the acceleration-time pattern by limiting peak accelerations…The benefits derived from such devices are usually small since little space for body or seat motion is available in…automobiles…” (Harris, Cyril, and Charles E. Crede; Shock and Vibration Handbook, NY, NY; McGraw-Hill, 1961, pg. 44-35 and pp. 44-34 to 44-35.) AUTOMOTIVE DYNAMICS and DESIGN . 75

1976 HEAD ON BARRIER CRASH TEST:

(Ishisaka, Takashi; Masanori Tani, Osamu Fujii, and Kyosuke Hamada; “Analysis of Crashworthiness of Automobile Body in Collision (Simulation of Frontal Collision)”, Mitsubishi Heavy Industries Technical Review, June 1976, pg. 130). AUTOMOTIVE DYNAMICS and DESIGN

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For impact velocities of around 30-35 mph (48-56 kph), the automotive barrier crash traces have been undergoing radical change for about forty years. This effect started with FMVSS compliance testing, and has accelerated with NCAP rating testing. NCAP frontal crash testing for rating is very similar to the FMVSS 208 frontal crash testing for compliance. Both involve full frontal crash into an immovable barrier, but the NCAP requires impact at “35 mph” (56.3 kph) while FMVSS 208 requires impact at only “30 mph” (48.3 kph), which represents a 36% difference in kinetic energy dissipation. Instrumented dummies are used for both FMVSS and NCAP. Various acceleration, deflection, and strain readings are taken from the instrumented dummies during the crash duration from which four criteria are derived to rate the vehicle’s frontal crash performance. Compliance tests require that only “passive” restraints be used, which usually means seatbelts are unfastened (unless they fasten automatically) and the dummies generally have to rely on only the airbags for their salvation. NCAP, however, allows the dummies the advantage of both belts and bags. AUTOMOTIVE DYNAMICS and DESIGN

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1) Head Injury Criterion (HIC), which for FMVSS compliance “traditionally” had to be < 1000 for the 50th percentile “adult male” dummies serving as “driver” and “passenger”, but “recent” changes involve a HIC limit of 700 and use of 5th percentile “small adult female” dummy as “passenger”. As of MY 2011 NCAP testing requires the 50th percentile “male” dummy as “driver” and the 5th percentile “female” dummy as “passenger”. 2) Neck Injury Criterion is a relatively new requirement for FMVSS compliance; for the 50th percentile dummy limiting neck tension/compression loads are 937/899 lb (4170/4000 N), and for the 5th percentile dummy are 589/566 lb (2620/2520 N). Interestingly, NCAP neck injury measurements of 12 vehicles MY2011-MY2014 registered a max tension reading of 360 lb (1600 N). 3) Chest Acceleration/Compression Criterion, which for FMVSS compliance “traditionally” had to be < 60 g’s (except where duration at this peak is < 3 ms) or < 3 in (7.62 cm) (this became 2.5 in or 63 mm after year 2000). Again, for NCAP there are no pass/fail levels, but scoring under the compliance pass/fail levels would seem to be commendable. 4) Femur Axial Load Criterion, which for FMVSS compliance “traditionally” must be < 2250 lb (10 kN) for a 50th percentile “adult male”. NCAP only “recently” included a < 1530 lb (6.8 kN) 5th percentile “small adult female” in its front crash rating evaluation. AUTOMOTIVE DYNAMICS and DESIGN 78

THE PRESENT HEAD INJURY CRITERIA FORMULATION:

Where: HIC = Head Injury Criterion (dimensionless). t1 = Time at start of interval of interest (seconds). t2 = Time at end of interval of interest (seconds). a = Resultant (total) deceleration (g’s) as per:

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HEAD INJURY CRITERIA USAGE CIRCA 1980:

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1999, THE EFFECT OF FMVSS AND NCAP: “Over the past fourteen years of NCAP testing, on average, the total crush…has increased, the peak deceleration…has decreased, and the time duration…has increased. The trend…is consistent with a reduction in the total stiffness of frontal structures…the less stiff have higher NCAP rating.”

(Park, Brian T., James R. Hackney, Richard M. Morgan, and Hansun Chan; “The New Car Assessment Program: Has It Led to Stiffer Light Trucks and Vans Over the Years?”, SAE International Congress & Exposition, Detroit, MI, March 1999, pp. 7-8, 14) AUTOMOTIVE DYNAMICS and DESIGN

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THE EFFECT OF FMVSS AND NCAP HAS BEEN TO MAKE POSSIBLE THE CALCULATION OF THE FRONTAL CRASH PERFORMANCE OF VEHICLES SOLD IN THE U.S.,

AS WILL

BE DEMONSTRATED. (Note that problems in dynamics generally are solved by use of any one or more of three basic methods: force and acceleration, work and kinetic energy, and impulse and momentum; these are just different ways of looking at a common underlying reality. The method(s) used to investigate a particular dynamics problem depends upon the specific nature of the problem. Problems involving that most severe form of automotive longitudinal deceleration, crashing, often requires the application of all three methods.) AUTOMOTIVE DYNAMICS and DESIGN

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WE START WITH SOME OF THE BASIC FORCEDEFLECTION FUNCTIONS: SPRING (no permanent deformation , increased duration)

CONSTANT (most stroke efficient, high rate of onset)

RAMP or “PROGRESSIVE” (intermediate between Spring and Constant) AUTOMOTIVE DYNAMICS and DESIGN

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MODERN SECONDARY AND PRIMARY STRUCTURE FORCE-DEFLECTION FUNCTIONS:

INDEPENDENT BUMPER BODY DESIGN INTEGRATED BUMPER BODY DESIGN GOOD DAMAGE PROTECTION, HIGH RATE OF ONSET, NOT A SMOOTH DECELERATION TRACE.

POOR DAMAGE PROTECTION, LOW RATE OF ONSET, A SMOOTH DECELERATION TRACE.

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MODERN SECONDARY AND PRIMARY STRUCTURE FORCE-DEFLECTION FUNCTIONS: “…automobile companies are increasingly requiring that bumpers contribute to the deceleration of the automobile in high-speed crashes…” (Krishnaswamy, Prakash; and Ayyakannu Mani, “Crash Codes Pave the Way to Safer Vehicles”, Mechanical Engineering, April 1991, pg.61)

“…bumper system…designed to collapse at a predetermined load level, which limits the load…transmitted to the…frame structure.” (Ibid, referring to a historical bumper illustration)

“The bumper and the support structure…(are designed)…so that the bumper makes the necessary contribution to the overall deceleration pulse.” (Ibid, pg. 62)

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THANKS TO NCAP WE CAN ASSUME THAT THE ENTIRE FRONTAL CRUSH DISTANCE IS USED TO ABSORB ALL THE VEHICLE KINETIC ENERGY IN A 35 MPH BARRIER CRASH:

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The 1996 Dodge Neon and the 2006 Honda Ridgeline will serve as representatives of the generic “small light” and “large heavy” vehicles. To determine the kinetic energy of each at 35 mph we will assume the following about their “effective mass”:

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The value for “F0” will be assumed sufficient to generate an instantaneous deceleration value of 3 g’s (probably overly generous), and the maximum force “Ft” will be such that:

Which also tells us the max g’s of each vehicle in the NCAP barrier crash: =

73,279 lb, or 24.34 g’s

= 110,686 lb, or 21.61 g’s AUTOMOTIVE DYNAMICS and DESIGN

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The values for “F0” and “Ft”, along with the crush distances “Xt”, allow us to draw the vehicle forcedeformation “curves” (note we have assumed zero “spring-back”):

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All of the assumptions and calculations made so far allow us to determine what would happen if these two generic representatives were to crash head on:

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The “small light” car utilizes all its available crush energy capacity, just as it did in the barrier crash: = 123,303 ft-lb

While all the “small light” car’s crush distance (2.996 ft, 913.2 mm) is used, a considerably smaller crush distance “x” is inflicted on the “large heavy” car. This distance “x” is easily determined by using the stiffness “KF” for the “large heavy” and the ultimate force “F” generated between the two vehicles in the equation:

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Now the work energy expended on deforming the “large heavy” car can be determined:

So the “large heavy” vehicle fares better than the “small light” vehicle with less deformation at 2.022 ft (616.3 mm) vs. 2.996 ft (913.2 mm), and less deformation energy absorbed at 89,620 ft-lb (121.5 kJ) vs. 123,303 ft-lb (167.2 kJ). Also, the “large heavy” maximum deceleration is only 14.31 g’s while the “small light” maximum deceleration is 24.34 g’s (same as in the barrier crash). This indicates that a head-on crash would be rough on the occupants of the “small light” vehicle, but very easy on those in the “large heavy” vehicle, which is in accord with reality. AUTOMOTIVE DYNAMICS and DESIGN

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This sort of result has been corroborated by actual empirical observations:

“…the crush distances of the heavy and light cars in rigid barrier impact are…850 mm and 550 mm. Yet in a head-on collision, by virtue of equal forces at the interface, the heavier car crush decreases to 620 mm while the lighter car crush increases to 870 mm.” (Prasad, Priya (Ed.); and Jamel E. Belwafa (Ed.), Vehicle Crashworthiness and Occupant Protection; Southfield, MI; American Iron and Steel Institute, 2004, pg. 92) AUTOMOTIVE DYNAMICS and DESIGN

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Anyway, the performance of the “large heavy” and “small light” vehicles together in the “head-on” crash was quite different from the individual barrier crash tests. This illustrates why the NHTSA says that the (up to) “5-star” (front crash) safety ratings can only be used to compare vehicles within the same (weight) class. Of course, these are only the results with a head-on crash that did not violate the “small light” vehicle’s passenger space; anything more severe (but totally possible) would have been very bad indeed for the “small light” vehicle’s occupants)… AUTOMOTIVE DYNAMICS and DESIGN

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The difference is because a head-on crash between two cars is fundamentally different from individual barrier crashes! At the end of the barrier crash event the velocity “V2” is zero (ignoring any velocity reversal due to “spring-back”); the delta velocity is essentially just “-V0” (DV = V2 -V1 = 0 – V0 = -V0). But in a head-on crash between two cars the post-event velocity may not be zero; the two cars may continue moving as a unit at some reduced post-crash velocity. This means that not all of the pre-crash kinetic energy (proportional to the closing velocity “Vc” squared) gets utilized for deformation of structure, just the energy associated with twice the average delta velocity “ ” squared. For such situations equations derived using the methodology of impulse and momentum must be employed. AUTOMOTIVE DYNAMICS and DESIGN 95

The average delta velocity of this two vehicle crash can be determined from the delta kinetic energy involved and the work energy spent in deformation: So, input the parameter values:

From this average it is easy to find the individual “ vehicle “∆V’s” if the momentum relation “∆V2/∆V1 = me1/me2” holds true, which means: and AUTOMOTIVE DYNAMICS and DESIGN

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So “plug in” the vehicle parameter values:

The average delta velocity would indeed seem to have been about 28.0 mph. Of far more interest is what would the closing velocity “Vc” have been, as that is an important indicator of what constitutes an upper limit on the severity of a crash before fatality occurs. AUTOMOTIVE DYNAMICS and DESIGN

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The closing velocity “Vc” is determined per the formula:

“Plugging in” the appropriate “small light” and “large heavy” vehicle values results in:

(Prasad, Priya (Ed.); and Jamel E. Belwafa (Ed.), Vehicle Crashworthiness and Occupant Protection; Southfield, MI; American Iron and Steel Institute, 2004, pg. 91) AUTOMOTIVE DYNAMICS and DESIGN

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So for the two vehicles considered here a closing velocity of 57.9 mph constitutes the limit for a head on crash without fatality. Note that the closing velocity less the two individual delta velocities leaves almost 2 mph (3.2 kph); the two wrecks continued moving in unison post-crash at this speed:

Vc - ∆V1 - ∆V2 = 57.9 – 35.21 – 20.70 = 1.99

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Obviously this calculated maximum closing velocity without fatality merely provides a “figure of merit” by which the crash safety of automotive designs may be judged; there is no guarantee that a head on crash between the two vehicles in question would not result in a fatality. The closing velocity calculation provides us with a “tool” to evaluate certain crash situations, to one of which we already have an answer as it was provided by the NHTSA itself. Let us see if our “tool” provides us with the same answer… AUTOMOTIVE DYNAMICS and DESIGN

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NHTSA says that two cars of the same class (explicitly a matter of weight but implicitly a matter of size as well) performing well in the NCAP 35 mph (56 kph) barrier crash will also perform equally well together in a 70 mph (113 kph) head-on crash. We can use the already calculated information on the “small light” (or the “large heavy”) vehicle and conduct a thought experiment wherein two identical vehicles (thereby definitely of the same “class”) experience a head on crash. Utilizing the “small light” (1996 Dodge Neon) results in the following… AUTOMOTIVE DYNAMICS and DESIGN

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The individual delta V’s in such a crash would be identical:

The maximum closing velocity without fatality (NHTSA : “performing well”) would be:

It would seem the NHTSA statement is verified, and that our automotive crash analysis methodology is fairly sound. AUTOMOTIVE DYNAMICS and DESIGN

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This methodology provides us with a rational way to answer a number of questions involving automotive crash (head on) safety: •Can a “large heavy” weight vehicle and a “small light” weight vehicle do equally well in the barrier crash test? •If so, then how will the same vehicles fare in a head-on crash against each other? That is, does the “large heavy” vehicle necessarily fare better than the “small light” vehicle? •Heavy vehicles tend to also be larger than light vehicles, but what role does size play independent of weight? That is, if the weight is equal, does the larger vehicle necessarily fare better? •If, as commonly suspected, a “small light” car is at an inherent safety disadvantage to a “large heavy” car, then what can be done to “level the playing field”? AUTOMOTIVE DYNAMICS and DESIGN

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The answers may be divined from the following summary of a number of calculated crash possibilities:

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From the investigations conducted, it would seem that the “small light” car will always be at a great disadvantage in a crash to a “large heavy” car given the way the current “safety system” works. Designing a vehicle so as to minimize deceleration levels in a 35 mph (56.3 kph) barrier crash test only gives some assurance of safety in a crash wherein a vehicle moving at 35 mph (56.3 kph) impacts flush with, and orthogonal to, an immobile and unyielding barrier. In real world crashes circumstances that exactly replicate such conditions are rare; the structural softness required of small light cars to score well in the NCAP barrier crash test ensures that in many real world crashes the vehicle passenger space is crushed and mangled. Since human tolerance to acceleration is very high if properly “packaged”, it makes sense to stiffen the structure of small light vehicles and to correspondingly enhance the occupant “packaging”. Even if the stiffer structure were to incur higher deceleration levels in an accident, the possibility of surviving such levels beats the impossibility of surviving being crushed or torn to pieces. AUTOMOTIVE DYNAMICS and DESIGN

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“When cars of the same wheelbase but different mass collided, the driver of the lighter car was more likely to be killed than the driver of the heavier car. When cars of similar mass but different wheelbase collided…the differences…were too small to be detected by the same method…they concluded that mass is the dominant causative factor in the large dependence of driver fatality risk on “size” in two-car crashes...” (Fildes, B.N.; S.J. Lee, and J.C. Lane; “Vehicle Mass, Size, and Safety”, Report No. CR133, Federal Office of Road Safety; Canberra, Australia, 1993., pg. 8) AUTOMOTIVE DYNAMICS and DESIGN

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The desire to score well in the 35 mph (56.3 kph) NCAP test seemingly drives current automotive design. This situation has certain consequences, not all of them beneficial:

“To absorb all the kinetic energy, which is proportional to the square of the velocity, the deformable structure length must have a specific stiffness.” (Witteman, Willem; “Adaptive Frontal Structure Design to Achieve Optimal Deceleration Pulses”, Paper #05-0243, Proceedings of the 19th International Conference on Enhanced Safety of Vehicles; Washington D.C., USA, 2005, pg. 1)

“…designing vehicles for the NCAP testing promotes the stiffness of the structure to be proportional to the mass of the vehicle. The heavier the vehicle the stiffer its front structure will be.” (Prasad, Priya (Ed.); and Jamel E. Belwafa (Ed.), Vehicle Crashworthiness and Occupant Protection; Southfield, MI; American Iron and Steel Institute, 2004, pg.86) AUTOMOTIVE DYNAMICS and DESIGN

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“The use of the same fixed deformable barrier in crash tests for light and heavy cars could lead to less compatibility in crashes between small and large cars.” (Witteman, Willem; “Adaptive Frontal Structure Design to Achieve Optimal Deceleration Pulses”, Paper #05-0243, Proceedings of the 19th International Conference on Enhanced Safety of Vehicles; Washington D.C., USA, 2005, pg. 2)

“For compatibility it is necessary to have a stiffer structure in case of a heavy opponent and a softer structure in case of a lighter opponent.” (Witteman, Willem; “Adaptive Frontal Structure Design to Achieve Optimal Deceleration Pulses”, Paper #05-0243, Proceedings of the 19th International Conference on Enhanced Safety of Vehicles; Washington D.C., USA, 2005, pg. 1) AUTOMOTIVE DYNAMICS and DESIGN

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“…the majority of collisions occur with partial frontal overlap and under off-axis load directions against other cars with much greater or smaller masses and structural stiffnesses. Realistic crash tests with partial overlap have shown that conventional longitudinal structures are not capable of absorbing all the energy in the car front without deforming the passenger compartment…To protect the occupants the passenger compartment should not be deformed and intrusion must be avoided…” (Witteman, Willem; “Adaptive Frontal Structure Design to Achieve Optimal Deceleration Pulses”, Paper #05-0243, Proceedings of the 19th International Conference on Enhanced Safety of Vehicles; Washington D.C., USA, 2005, pg. 1) AUTOMOTIVE DYNAMICS and DESIGN

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“…LTVs are a growing component of…US…vehicles …incompatibility…in an accident causes the…LTV to impose greater intrusion and higher deceleration to the…passenger car…” “…mismatch between two colliding vehicles in terms of their mass, geometry, and structural stiffness can greatly increase the aggressivity (sic) of the larger vehicle.” (Tay, Y.Y.; A. Papa, L.S. Koneru, R. Moradi, and H.M. Lankarani; “A Finite Element Approach in Estimating Driver Fatality Ratio of a Fleet of LTV’s Striking a Passenger Car Based on Vehicle’s Intrusion, Acceleration, and Stiffness Ratios in Side-Impact Accidents”, Journal of Mechanical Science and Technology, pp. 1231-1242, 2015, pg. 1231.) AUTOMOTIVE DYNAMICS and DESIGN

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“When two vehicles designed for NCAP testing are involved in a frontal collision, the deformation in the heavier vehicle is expected to be more than that in the lighter vehicle…But, that doesn’t happen in real crashes…the small car likely sustains more crush with potential for intrusion into the passenger compartment.” (Prasad, Priya (Ed.); and Jamel E. Belwafa (Ed.), Vehicle Crashworthiness and Occupant Protection; Southfield, MI; American Iron and Steel Institute, 2004, pg. 87.)

“In Europe…two-thirds of accidents were between vehicles of equal masses…mass ratios of vehicles…in the US are not well established. Additionally, in the US, when SUV’s and LTV’s crash into cars, the issue of having front structures of different heights comes into play. This issue is referred to as geometric mismatch.” (Ibid, pg. 95)

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“Another interesting test for the compatibility problem is a test with a moving deformable barrier. Such a test simulates much better collisions between cars and could improve fleet compatibility. In this case the smaller vehicle is subjected to a harsher crash environment due to the higher energy absorption and a higher velocity change yielding a stiffer structure. On the other hand the large car would be subjected to a less severe crash environment in terms of velocity change, so a softer structure gives a temperate crash pulse.” (Witteman, Willem; “Adaptive Frontal Structure Design to Achieve Optimal Deceleration Pulses”, Paper #05-0243, Proceedings of the 19th International Conference on Enhanced Safety of Vehicles; Washington D.C., USA, 2005, pg. 3.) AUTOMOTIVE DYNAMICS and DESIGN

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“Ernst et al (1991) maintained that it is possible to optimize vehicle design for car-to-car collisions by stiffening the structure of smaller vehicles while at the same time ensuring that the stiffness of large vehicles underwent a linear increase in stiffness (starting soft and getting stiffer). “There are costs associated with increasing vehicle-vehicle compatibility, namely the rigid barrier (single vehicle) collision performance of both cars is compromised. The stiffer small vehicle will undergo less deformation, resulting in higher decelerations. Concurrently, the larger vehicle with linearly increasing stiffness has surrendered energy absorbing potential through softening the structure.”

(Fildes, B.N.; S.J. Lee, and J.C. Lane; “Vehicle Mass, Size, and Safety”, Report No. CR133, Federal Office of Road Safety; Canberra, Australia, 1993. pg. 4.) AUTOMOTIVE DYNAMICS and DESIGN

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“As delta-V is one of those factors which determine the forces the occupant has to withstand in a collision, those in heavier cars will always (be) better off than those of lighter ones (all other factors being equal).” (Fildes, B.N.; S.J. Lee, and J.C. Lane; “Vehicle Mass, Size, and Safety”, Report No. CR133, Federal Office of Road Safety; Canberra, Australia, 1993. pg. 4.)

“One study reported that an unbelted driver in a 2000 kg car had the same amount of protection as a belted driver in a 1140 kg car. It was further claimed that drivers of small cars gained more from being restrained than those of larger ones.” (Prasad, Priya (Ed.); and Jamel E. Belwafa (Ed.), Vehicle Crashworthiness and Occupant Protection; Southfield, MI; American Iron and Steel Institute, 2004, pg. 86) AUTOMOTIVE DYNAMICS and DESIGN

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With the proper crush stiffness, structural integrity, occupant restraint, and geometric compatibility not only can any “small light” car be made as safe, if not safer, than any “large heavy” car, but all automotive crash survival could be enhanced. Of course, the NHTSA could always have gotten the necessary information from NASCAR (significant information regarding automotive crash safety could also have been obtained from the SCCA, FIA, NHRA, etc.), but that wouldn’t have allowed for the spending of billions of taxpayer dollars over the course of decades to achieve modest results.

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• NO COMPUTER PROGRAM FOR AUTOMOTIVE CRASH ANALYSIS HAS BEEN WRITTEN BY THE INSTRUCTOR (TBD). HOWEVER, A COPY OF “MASS PROPERTIES AND AUTOMOTIVE CRASH SURVIVAL” WILL BE PROVIDED EVERY INTERESTED STUDENT. • AUTOMOTIVE CRASH SIMULATION PROGRAMS: PC-Crash 10.1 is a full vehicle FEA program which has an innovative collision model for simulating vehicle collisions. MEA Forensic sells and supports PC-Crash™ in North America. Dr. Steffan Datentechnik GmbH (DSD) of Linz, Austria, is the originating corporation. Virtual CRASH version 1.0 is a new generation program for the simulation of vehicle accidents. Its complex real time calculations can be performed on a personal computer; by VCRASH of Nové Zámky, Slovakia. AUTOMOTIVE DYNAMICS and DESIGN

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