Brian P Wiegand | Pratt Institute (original) (raw)

Papers by Brian P Wiegand

SAE technical paper series, Apr 5, 2016

Evaluation of the performance potential of an automotive conceptual design requires some initial ... more Evaluation of the performance potential of an automotive conceptual design requires some initial quantitative estimate of numerous relevant parameters. Such parameters include the vehicle mass properties, frontal and plan areas, aero drag and lift coefficients, available horsepower and torque, and various tire characteristics such as the rolling resistance... A number of rolling resistance models have been advanced since Robert William Thomson first patented the pneumatic rubber tire in 1845, most of them developed in the twentieth century. Most early models only crudely approximate tire rolling resistance behavior over a limited range of operation, while the latest models overcome those limitations but often at the expense of extreme complexity requiring significant computer resources. No model extant seems well suited to the task of providing a methodology for the estimation of a tire’s rolling resistance that is simple to use yet accurate enough for modern conceptual design evaluation. It is the intent of this paper to suggest a methodology by which this seeming deficiency may be rectified.

SAWE Journal "Weight Engineering", Winter 2011-12, 2012

It seems to be an inherent conceit of the modern era that ancient people weren’t as intelligent a... more It seems to be an inherent conceit of the modern era that ancient people weren’t as intelligent as people of modern times; ironically this is a conceit born of ignorance and lack of imagination. For instance, the wheel is a simple concept, but to convert that concept to a useful reality, given the resources available in prehistory, would prove daunting to even the most capable people alive today. The wheel, and many other things, was doubtless conceived of by prehistoric man, but to arduously fashion some wheels, an axle, and a chassis from trees with stone tools would have been a grave misallocation of labor; the constant struggle for food, shelter, and the other necessities of survival meant that such advances would have to wait until the prevailing conditions of life became conducive to such development and use. Such conditions would first be attained in what is termed the “Neolithic” period of human development.

SAWE Journal "Weight Engineering", 2011

Previously this author wrote an article about the "Dynosphere" (a.k.a. "Dynasphere") vehicle whic... more Previously this author wrote an article about the "Dynosphere" (a.k.a. "Dynasphere") vehicle which was designed and built by Professor Dr. John Archibald Purves of Taunton, England, circa 1932; that article was published in the Spring 2011 Issue of Weight Engineering. This is a follow-up article about Ernest Fraquelli and his equally outrageous vehicle called the "Gyrauto". The Gyrauto differed from the Dynosphere in that the Dynospere consisted of just one big wheel, while the Gyrauto consisted of two big wheels side-by-side on a common axle-line. The idea behind both of these vehicles seems to have been to achieve unprecedented efficiency by reducing an automobile to its essentials, i.e., just one big wheel. This is not quite as foolish as it seems; much later Jack Northrop was to pursue an aeronautical analogy in that he was to conceive of an aircraft as just one big flying wing, and that dream was eventually realized in the success of the B-2 bomber.

81st SAWE International Conference on Mass Properties Engineering, 2022

In 1984, for the 43rd Annual International Conference of the SAWE, this author presented Paper Nu... more In 1984, for the 43rd Annual International Conference of the SAWE, this author presented Paper Number 1634, “Mass Properties and Automotive Longitudinal Acceleration”. In that paper the effects upon automotive acceleration of varying the relevant mass property parameters were explored by use of a computer simulation. The computer simulation of automotive longitudinal acceleration allowed for the study of each individual parameter because a simulation allows for the decoupling of the parameters in a way that is not possible physically. The principal mass property parameters involved were the vehicle weight and rotating component inertias, collectively known as the “effective mass”, plus the longitudinal and vertical coordinates of the vehicle center of gravity.

However, just as it is important for a vehicle to be able to accelerate, it is perhaps even more important for a vehicle to be able to decelerate. The same mass properties that were relevant to the matter of automotive acceleration are also relevant to the matter of automotive deceleration, a.k.a. braking, although for the braking case that collective of vehicle translational inertia and rotational component inertias known as the “effective mass” requires somewhat different handling. As was the case with automotive acceleration, automotive braking will be explored by use of a computer simulation whereby the effect of variation of each of the mass property parameters can be studied independently. However, this task is considerably easier as the creation of a braking simulation is a minor effort compared to the creation of an acceleration simulation.

70th Annual International Conference of the Society of Allied Weight Engineers, Inc., Houston, TX, 14-19 May 2011, 2011

The basic intent of this paper is to counter the commonly held simplistic concept of the role mas... more The basic intent of this paper is to counter the commonly held simplistic concept of the role mass properties play in determining ride and road-contact. For those that have never undertaken any study of the matter, the general presumption seems to be that all that is required to achieve optimum performance is to minimize the weight and to obtain a balanced mass distribution. The reality is that there are many aspects to automotive performance, and what constitutes an optimum mass properties condition is generally a very complex matter which often necessitates difficult compromises. Tailoring some mass property parameters so as to achieve a desirable level of behavior with regard to one performance criterion will often adversely affect other performance criteria.

Although this paper is restricted to mass properties issues related to performance resulting from motion in the vertical direction, occasional reference will be made to those mass properties requirements necessitated by performance considerations associated with the longitudinal (acceleration, braking) and lateral (maneuver, roll-over, and directional stability) directions, as revealed in the previous investigations noted earlier. To do otherwise would be to work in a vacuum; the nature of reality tends to be such that all things are ultimately interrelated. To the fullest extent possible, the greater intent herein is to approach reality through the totality of the papers and articles written by this author on the subject of mass properties and automotive performance.

70th Annual International Conference of the Society of Allied Weight Engineers, Inc., 2011

There are a number of automotive performance aspects which are associated with accelerations in t... more There are a number of automotive performance aspects which are associated with accelerations in the lateral direction: maneuver (transient and steady state), roll-over, and directional stability. For each of these automotive performance aspects certain mass property parameters play significant roles; it is the intent of this paper to make explicit exactly how those mass property parameters affect each of those automotive performance aspects.
With regard to maneuver, the maximum lateral acceleration which can be attained in steady-state turning is an important index of performance and safety. The obtaining of high maximum lateral acceleration levels has inherent vehicle weight and center of gravity (longitudinal, lateral, and vertical) implications. However, before attaining a steady-state condition, a turning maneuver must first go through a transient phase. When the transient phase is included in the full maneuver picture, the previous list of significant vehicle mass properties parameters acquires two more members: the mass moments of inertia about the roll and yaw axes.
For modern passenger vehicles, the lateral acceleration point at which roll-over can occur is generally at a level significantly greater than the maximum lateral acceleration. That is, a modern car will tend to slide out of control long before there is a possibility of overturn. Accidents involving rollover generally occur because the vehicle was “flipped” by obstacles in the roadway, not because the vehicle traction was great enough to reach the critical lateral acceleration level. However, the level at which rollover could occur is still an important index of safety, and the most significant mass property for the determination of that level is the vertical center of gravity.
Lastly, there is the matter of directional stability, which has to do with the lateral tire traction force balance front-to-rear, and the front-to-rear “drift angle” relationship of the vehicle tires due to those forces. The lateral force/drift angle relationship is dependent upon normal load, so the most significant mass properties with regard to directional stability are the vehicle weight and static longitudinal and lateral weight distribution.
However, the static normal loads are dynamically modified in response to lateral directional “disturbance” forces. Such disturbances generate initial lateral inertial reactions at the vehicle c.g.; the consequent roll moment not only causes lateral changes in the normal load distribution, but also longitudinal changes due to the front-to-rear suspension roll resistance balance. Such changes readjust the initial lateral force/drift angle relationship front-to-rear, and thereby affect the lateral inertial reaction. If this reaction augments the effect of the original disturbance, then the vehicle is termed unstable or “oversteering”; if the reaction is such as to diminish the effect of the original disturbance, then the vehicle is termed stable or “understeering”. Therefore, for directional stability, the primary mass property parameters are the vehicle weight, and total weight distribution (longitudinal, lateral, and vertical).

74th SAWE International Conference on Mass Properties Engineering, 2015

The intent of this paper, again revised (Rev. G), is to show that a vehicle designed in true acco... more The intent of this paper, again revised (Rev. G), is to show that a vehicle designed in true accordance with the balanced viewpoint of a professional mass properties engineer may not only demonstrate superior acceleration, braking, and handling, but superior ride, stability, fuel economy, and safety as well. If a design begins with the first principles of how mass properties affect automotive performance in all its aspects , and is optimized accordingly in an integrated manner, then the resulting advanced automotive design may truly “go where none have gone before”.

74th SAWE International Conference On Mass Properties Engineering, 2015

As a small start-up company competing against long established automotive concerns such as Ferrar... more As a small start-up company competing against long established automotive concerns such as Ferrari, Colin Chapman’s Lotus Engineering Company did not have the capability to gain advantage through advanced engine design, or even via the design of most of the other major mechanical systems. Most such components were commercially sourced, and so the only way a decisive advantage could be obtained was through an uncompromising emphasis on gaining performance “edges” from the remaining design elements of structure, body, and suspension. Because the automotive performance aspects of acceleration, braking, and handling are so dependent on various vehicle mass properties the optimization of those mass properties became the “Holy Grail” of Lotus design as directed by Colin Chapman.

80th SAWE International Conference, 2021

The quantification of automotive directional stability may be expressed through various stabil... more The quantification of automotive directional stability may be expressed through various stability metrics, but perhaps the most basic of these automotive stability metrics is the “Understeer Gradient” (Kus). The Understeer Gradient (in degrees or radians per unit gravity) appears extremely uncomplicated when viewed in its most common formulation:

Kus = [Wf / (g Csf)] - [Wr / (g Csr)]

This metric appears to depend only on the front and rear axle weight loads (Wf, Wr), and on the front and rear axle cornering stiffnesses (Csf, Csr). However, those last quantities vary with lateral acceleration, and the nature of that variation is dependent upon many other parameters of which some of the most basic are: Total Weight, Sprung Weight, Unsprung Weight, Forward Unsprung Weight, Rear Unsprung Weight, Total Weight LCG, Sprung Weight LCG, Total Weight VCG, Sprung Weight VCG, Track, Front Track, Rear Track, Roll Stiffness, Front Roll Stiffness, Rear Roll Stiffness, Roll Axis Height, Front Roll Center Height, and Rear Roll Center Height. Note that exactly half of these automotive directional stability parameters as listed herein are mass properties.

The purpose of this paper is to explore, through a skidpad simulation, the relative sensitivity of automotive directional stability (as quantified through the Understeer Gradient) to variation in each of the noted vehicle parameters, with special emphasis on the mass property parameters.

The simulation is constructed in a spreadsheet format from the relevant basic automotive dynamics equations; the normal and lateral loads on the tires are determined as the lateral acceleration is increased incrementally by a small amount (thereby maintaining a “quasi-static” or “steady-state” condition). The normal loads are used for the calculation of the lateral traction force potentials at each tire, with the required (centripetal) lateral traction forces apportioned accordingly. From those required (actual) lateral tire forces the corresponding tire cornering stiffnesses are determined; this determination is based upon a tire model developed through a regression analysis of tire test data.

This construction of a fairly comprehensive lateral acceleration simulation from basic automotive dynamic relationships, instead of depending upon commercial automotive software such as “CarSim” (vehicle model) and Pacjeka “Magic Formula” (tire model), constitutes a unique aspect of this paper; this return to basics hopefully provides a clearer view and understanding of the results than would be the case otherwise. Even more unique is this paper’s emphasis on, and exploration of, the role specific mass property parameters play in determining automotive directional stability.

SAWE Journal "Weight Engineering", 1982

This article was originally published in the Winter 1982/83 Issue of the Society of Allied Weight... more This article was originally published in the Winter 1982/83 Issue of the Society of Allied Weight Engineers (SAWE) Journal, pp. 10 to 15, copyright Brian Paul Wiegand/SAWE. It was the precursor to the SAWE Paper #3528, “Mass Properties and Automotive Lateral Acceleration”, presented in 2011 for the 70th Annual International Conference of the SAWE at Houston Tx. It was also the seed for what ultimately sprouted into the SAWE seminar “Automotive Lateral Dynamics and Mass Properties” given initially at the 2017 SAWE Regional Conference (Irving, Tx), and then again at the 2019 SAWE International Conference (Norfolk, Va).
The maximum lateral acceleration level which an automobile can attain in turning is an important index of performance and safety. The obtaining of high maximum acceleration levels has certain inherent weight and center of gravity implications of great significance for the automotive design engineer. The purpose of this article is to examine the physics of automotive turning maneuvers so as to make those weight and c.g. implications explicit.

The primary forces which determine the dynamic behavior of aircraft are aerodynamic forces genera... more The primary forces which determine the dynamic behavior of aircraft are aerodynamic forces generated by pressure differentials acting over the aerosurface areas. In contrast, the primary forces which determine the dynamic behavior of automobiles are friction forces generated by contact pressure acting over the tire-to-road contact areas.
It is the tires that transmit the forces that accelerate, decelerate, and maneuver the automotive road vehicle. It is the tires that play a major role in isolating the vehicle, its cargo and passengers, from the shock and vibration effects of road surface irregularities. Last, but not least, the tires play an absolutely critical role in providing vehicle directional stability. What tires do is necessary and very complex, so much so that in nearly 125 years of development no adequate substitute has been found for the pneumatic-elastic rubber and cord structure known as the tire. The tire has prevailed over all those years, undergoing innumerable improvements and refinements, despite still not being fully understood in its mechanisms and behavior.
This document attempts to fully explain and understand tire mechanisms and behavior, and is an excerpt from a larger work entitled "Mass Properties and Advanced Automotive Design" presented at the 74th Annual International Conference of the Society of Allied Weight Engineers Inc. in May 2015. That paper, and this excerpt, have undergone considerable revision since then in an ongoing attempt to eliminate all spelling, grammatical, typographical, and other errors.

Evaluation of the performance potential of an automotive conceptual design requires some initial ... more Evaluation of the performance potential of an automotive conceptual design requires some initial quantitative estimate of numerous relevant parameters. Such parameters include the vehicle mass properties, frontal and plan areas, aero drag and lift coefficients, available horsepower and torque, and various tire characteristics such as the rolling resistance...
A number of rolling resistance models have been advanced since Robert William Thomson first patented the pneumatic rubber tire in 1845, most of them developed in the twentieth century. Most early models only crudely approximate tire rolling resistance behavior over a limited range of operation, while the latest models overcome those limitations but often at the expense of extreme complexity requiring significant computer resources. No model extant seems well suited to the task of providing a methodology for the estimation of a tire’s rolling resistance that is simple to use yet accurate enough for modern conceptual design evaluation.
It is the intent of this paper to suggest a methodology by which this seeming deficiency may be rectified.

74th SAWE International Conference, Alexandria VA, 18 May 2015

Problems in dynamics may be solved by any one or more of three basic methods: force and accelerat... more Problems in dynamics may be solved by any one or more of three basic methods: force and acceleration (F=m a), work and kinetic energy (Fd=½ mV^2), impulse and momentum (〖Imp〗_(1→2)=mV_2-mV_1); 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, are no exception.
Even at the most elementary level, as represented by the previous equations, the unifying role of mass properties is evident. Notable in the basic formulae of all three methods for the solution of problems in dynamics is the common parameter “m” (mass). However, this represents just the “tip of the iceberg”; at the detailed level representative of actual engineering problems the full role played by mass properties is often revealed to be far more complicated than that indicated by such simple basic equations.
For instance, an automobile traveling at a particular velocity will possess a certain amount of kinetic energy which must be dissipated for the vehicle to come to a stop. The dissipation can be controlled and orderly as in the case of braking a car to a stop at an intersection, or it can be somewhat more violent as in the case of a collision with a concrete abutment. In both cases the outcome is directly dependent upon the magnitude of the kinetic energy involved. Initially the mass properties involvement seems to be very simple: the kinetic energy of any body of mass “m” moving at a velocity “V” is expressible as “½ mV^2”; to come to a stop that energy must be dissipated through the work done by a deceleration force “F” times the distance “d” traveled during the deceleration.
However, the kinetic energy possessed by an automobile is much more than would be indicated by a simple determination of its mass “m” from its weight (“m= W/g”). Many components of an automobile possess not only translational kinetic energy, but rotational as well. Thus the simple mass “m” is not the appropriate value needed for kinetic energy determination; there is a greater value “me”, termed the “effective mass”. The calculation of “me” involves the rotational inertia of such components as the wheels, tires, brakes, shafts, bearings, etc.
Thus not only the mass of the automobile as a whole, but that of various components, come into play when calculating the amount of kinetic energy which, in turn, determines the magnitude of the deceleration forces required to affect a complete stop in a certain distance. When the deceleration is a matter of braking, certain other vehicle mass properties come into play: the vehicle longitudinal, lateral, and vertical CG. When the deceleration is a matter of crashing, then the vehicle mass density and mass density distribution also have significance.
The purpose of this paper is to make explicit the exact role that all the mass properties play in determining the automotive deceleration performance during a crash. This has a direct bearing on the survivability of a crash, which can be enhanced through thoughtful mass properties engineering.

The crash of an automobile into an immovable object is an event of only a little more t... more The crash of an automobile into an immovable object is an event of only a little more than a tenth of a second in duration. During that time the structure of the vehicle is deformed in a random series of resistance force spurts and lapses until the work energy (force × deformation) expended during deformation roughly equals the vehicle kinetic energy at the moment of contact. Since the deceleration “a” is equal to the deformation resistance force “F” divided by the vehicle mass “m”, the deceleration history also constitutes a random series of spurts and lapses.
The deceleration magnitude and duration has a direct bearing on the survivability of a crash, as does the magnitude and duration of the rate of change in deceleration “j” known as “jerk” (“j = Δa/Δt”). In the interest of human survivability, modern automotive structures are designed so as to smoothly decelerate the vehicle as much as possible, i.e., with a minimum of “jerk”, while keeping deceleration magnitude and duration within reasonable limits. The two most common force-deformation models utilized to achieve such deceleration are the constant force deformation model and the progressive force deformation model; the former is used mostly for energy absorbing bumper design and the latter for the automotive structure proper, hence the significance of this mathematical study of the properties of these models.

Perhaps the most curious aspect of the modern piston engine is that utilizes a reciprocal motion ... more Perhaps the most curious aspect of the modern piston engine is that utilizes a reciprocal motion more reminiscent of the inefficient reciprocating motion of nature (people, monkeys, birds, fish) than some of mankind’s more efficient creations (wheeled). The reciprocating motion characteristic of the piston engine has been dismissively referred to as “monkey motion”, and with good reason. This fact has long been recognized, and much effort has expended to find a rotary substitute for the reciprocating, such as the Wankle engine or the gas turbine, but as of this writing the reciprocating engine still reigns supreme for automotive propulsion.

Although Sir Isaac Newton (1642-1726) formulated “F = m a” as his Second Law of Motion, he inexpl... more Although Sir Isaac Newton (1642-1726) formulated “F = m a” as his Second Law of Motion, he inexplicably thought that the formulation for determining the kinetic energy of a moving body was “KE = m V”. For many contemporaries interested in physics this seemed questionable. The Dutch experimenter W.J. Gravesande (1688-1742) conducted a series of experiments which consisted of dropping lead weights into a bed of soft clay; the greater the weight, or height of the drop, then the greater the measured depth of the resulting indentation. This corroborated that the kinetic energy was proportional to the mass and velocity at the time of impact. However, Gravesande left the determination of exactly how the kinetic energy varied with mass and velocity to his friend Émilie du Châtelet (1706-1749) , whose analysis of the experimental data resulted in “KE = m V^2”. Why this expression lacks the “½” factor has been given various explanations. However, when subject to a modern approach the derivation of the correct “KE = ½ m V^2” formulation is readily made.

The conventional automotive configuration of two axle lines and four wheels, with each wheel loca... more The conventional automotive configuration of two axle lines and four wheels, with each wheel located in the corner of the automotive plan view, is one of only a large number of possible wheel/axle configurations, but has prevailed for so long that this fact is often forgotten. The choice of which wheels steer and which wheels are driven compounds the number of configuration variations possible. When other configuration variations are also considered, such as varying the vehicle tire/wheel size/type fore to aft or even side to side (as on some circle track racers), or whether the engine is to be front, mid, or rear located, then the number of all possible configurations becomes infinite.

SAWE Journal "Weight Engineering", Spring 2011

43rd Annual International Conference of the Society of Allied Weight Engineers, May 21, 1984

Automotive longitudinal acceleration is dependent upon a large number of interconnected parameter... more Automotive longitudinal acceleration is dependent upon a large number of interconnected parameters, some of the most important of which are mass properties. The purpose of this paper is to explore the individual mass property effects.

The approach taken to achieve this purpose was to decouple the parameters by means of a computer simulation of an automotive acceleration "run". Each individual mass property parameter was then varied over a wide range while all other parameters were held constant. The acceleration results so obtained were plotted, and the conclusions were drawn from the behavior thus exhibited.

Several conclusions have been drawn from this effort. First, the effects of a mass property parameter variation are not necessarily constant over the entire speed range. For instance, increasing weight tends to cause an almost linear increase in the elapsed times for the lower speed ranges, but the higher speed ranges exhibit ever greater time increases in an almost parabolic relationship. This is a matter of the increased rolling resistance associated with greater weight making itself felt at the higher speeds.

The longitudinal center of gravity (LCG) and the vertical center of gravity (VCG) both affect acceleration through traction. If the situation is not traction critical, then c.g. relocation can be of no help in obtaining better acceleration. When a situation is traction critical then acceleration is much more sensitive to change in LCG then in VCG.

Increasing the vertical center of gravity tends to benefit the acceleration of rear wheel drive vehicles. For rear wheel drive vehicles the VCG generates increased traction through weight transfer. In the case of front wheel drive, the VCG can have no beneficial effect as the weight transfer is in the direction away from the drive axle; minimizing the VCG becomes the priority. Due to the effect of weight transfer, a front wheel drive vehicle will always be inferior in acceleration to a rear wheel drive vehicle if everything else is equal and the propulsive capability is great enough.

In general, a rotational mass is disproportionately detrimental to acceleration because it has to be accelerated both rotationally and translationally. The greatest return for the effort involved in mass reduction can be obtained from a reduction in rotational masses.

The engine rotational masses, other than the flywheel, represent a special case outside the scope of this paper. Vehicle characteristics and use demand a certain minimal rotational inertia for the flywheel to counteract engine stall-out tendencies at the onset of acceleration and to ensure smooth engine operation. In fact, higher flywheel inertia can produce an initially quicker vehicle. This initial response has to be considered against the detrimental longer-term effects of accelerating a greater flywheel inertia throughout the speed range; flywheel design involves a high degree of compromise.

SAE technical paper series, Apr 5, 2016

Evaluation of the performance potential of an automotive conceptual design requires some initial ... more Evaluation of the performance potential of an automotive conceptual design requires some initial quantitative estimate of numerous relevant parameters. Such parameters include the vehicle mass properties, frontal and plan areas, aero drag and lift coefficients, available horsepower and torque, and various tire characteristics such as the rolling resistance... A number of rolling resistance models have been advanced since Robert William Thomson first patented the pneumatic rubber tire in 1845, most of them developed in the twentieth century. Most early models only crudely approximate tire rolling resistance behavior over a limited range of operation, while the latest models overcome those limitations but often at the expense of extreme complexity requiring significant computer resources. No model extant seems well suited to the task of providing a methodology for the estimation of a tire’s rolling resistance that is simple to use yet accurate enough for modern conceptual design evaluation. It is the intent of this paper to suggest a methodology by which this seeming deficiency may be rectified.

SAWE Journal "Weight Engineering", Winter 2011-12, 2012

It seems to be an inherent conceit of the modern era that ancient people weren’t as intelligent a... more It seems to be an inherent conceit of the modern era that ancient people weren’t as intelligent as people of modern times; ironically this is a conceit born of ignorance and lack of imagination. For instance, the wheel is a simple concept, but to convert that concept to a useful reality, given the resources available in prehistory, would prove daunting to even the most capable people alive today. The wheel, and many other things, was doubtless conceived of by prehistoric man, but to arduously fashion some wheels, an axle, and a chassis from trees with stone tools would have been a grave misallocation of labor; the constant struggle for food, shelter, and the other necessities of survival meant that such advances would have to wait until the prevailing conditions of life became conducive to such development and use. Such conditions would first be attained in what is termed the “Neolithic” period of human development.

SAWE Journal "Weight Engineering", 2011

Previously this author wrote an article about the "Dynosphere" (a.k.a. "Dynasphere") vehicle whic... more Previously this author wrote an article about the "Dynosphere" (a.k.a. "Dynasphere") vehicle which was designed and built by Professor Dr. John Archibald Purves of Taunton, England, circa 1932; that article was published in the Spring 2011 Issue of Weight Engineering. This is a follow-up article about Ernest Fraquelli and his equally outrageous vehicle called the "Gyrauto". The Gyrauto differed from the Dynosphere in that the Dynospere consisted of just one big wheel, while the Gyrauto consisted of two big wheels side-by-side on a common axle-line. The idea behind both of these vehicles seems to have been to achieve unprecedented efficiency by reducing an automobile to its essentials, i.e., just one big wheel. This is not quite as foolish as it seems; much later Jack Northrop was to pursue an aeronautical analogy in that he was to conceive of an aircraft as just one big flying wing, and that dream was eventually realized in the success of the B-2 bomber.

81st SAWE International Conference on Mass Properties Engineering, 2022

In 1984, for the 43rd Annual International Conference of the SAWE, this author presented Paper Nu... more In 1984, for the 43rd Annual International Conference of the SAWE, this author presented Paper Number 1634, “Mass Properties and Automotive Longitudinal Acceleration”. In that paper the effects upon automotive acceleration of varying the relevant mass property parameters were explored by use of a computer simulation. The computer simulation of automotive longitudinal acceleration allowed for the study of each individual parameter because a simulation allows for the decoupling of the parameters in a way that is not possible physically. The principal mass property parameters involved were the vehicle weight and rotating component inertias, collectively known as the “effective mass”, plus the longitudinal and vertical coordinates of the vehicle center of gravity.

However, just as it is important for a vehicle to be able to accelerate, it is perhaps even more important for a vehicle to be able to decelerate. The same mass properties that were relevant to the matter of automotive acceleration are also relevant to the matter of automotive deceleration, a.k.a. braking, although for the braking case that collective of vehicle translational inertia and rotational component inertias known as the “effective mass” requires somewhat different handling. As was the case with automotive acceleration, automotive braking will be explored by use of a computer simulation whereby the effect of variation of each of the mass property parameters can be studied independently. However, this task is considerably easier as the creation of a braking simulation is a minor effort compared to the creation of an acceleration simulation.

70th Annual International Conference of the Society of Allied Weight Engineers, Inc., Houston, TX, 14-19 May 2011, 2011

The basic intent of this paper is to counter the commonly held simplistic concept of the role mas... more The basic intent of this paper is to counter the commonly held simplistic concept of the role mass properties play in determining ride and road-contact. For those that have never undertaken any study of the matter, the general presumption seems to be that all that is required to achieve optimum performance is to minimize the weight and to obtain a balanced mass distribution. The reality is that there are many aspects to automotive performance, and what constitutes an optimum mass properties condition is generally a very complex matter which often necessitates difficult compromises. Tailoring some mass property parameters so as to achieve a desirable level of behavior with regard to one performance criterion will often adversely affect other performance criteria.

Although this paper is restricted to mass properties issues related to performance resulting from motion in the vertical direction, occasional reference will be made to those mass properties requirements necessitated by performance considerations associated with the longitudinal (acceleration, braking) and lateral (maneuver, roll-over, and directional stability) directions, as revealed in the previous investigations noted earlier. To do otherwise would be to work in a vacuum; the nature of reality tends to be such that all things are ultimately interrelated. To the fullest extent possible, the greater intent herein is to approach reality through the totality of the papers and articles written by this author on the subject of mass properties and automotive performance.

70th Annual International Conference of the Society of Allied Weight Engineers, Inc., 2011

There are a number of automotive performance aspects which are associated with accelerations in t... more There are a number of automotive performance aspects which are associated with accelerations in the lateral direction: maneuver (transient and steady state), roll-over, and directional stability. For each of these automotive performance aspects certain mass property parameters play significant roles; it is the intent of this paper to make explicit exactly how those mass property parameters affect each of those automotive performance aspects.
With regard to maneuver, the maximum lateral acceleration which can be attained in steady-state turning is an important index of performance and safety. The obtaining of high maximum lateral acceleration levels has inherent vehicle weight and center of gravity (longitudinal, lateral, and vertical) implications. However, before attaining a steady-state condition, a turning maneuver must first go through a transient phase. When the transient phase is included in the full maneuver picture, the previous list of significant vehicle mass properties parameters acquires two more members: the mass moments of inertia about the roll and yaw axes.
For modern passenger vehicles, the lateral acceleration point at which roll-over can occur is generally at a level significantly greater than the maximum lateral acceleration. That is, a modern car will tend to slide out of control long before there is a possibility of overturn. Accidents involving rollover generally occur because the vehicle was “flipped” by obstacles in the roadway, not because the vehicle traction was great enough to reach the critical lateral acceleration level. However, the level at which rollover could occur is still an important index of safety, and the most significant mass property for the determination of that level is the vertical center of gravity.
Lastly, there is the matter of directional stability, which has to do with the lateral tire traction force balance front-to-rear, and the front-to-rear “drift angle” relationship of the vehicle tires due to those forces. The lateral force/drift angle relationship is dependent upon normal load, so the most significant mass properties with regard to directional stability are the vehicle weight and static longitudinal and lateral weight distribution.
However, the static normal loads are dynamically modified in response to lateral directional “disturbance” forces. Such disturbances generate initial lateral inertial reactions at the vehicle c.g.; the consequent roll moment not only causes lateral changes in the normal load distribution, but also longitudinal changes due to the front-to-rear suspension roll resistance balance. Such changes readjust the initial lateral force/drift angle relationship front-to-rear, and thereby affect the lateral inertial reaction. If this reaction augments the effect of the original disturbance, then the vehicle is termed unstable or “oversteering”; if the reaction is such as to diminish the effect of the original disturbance, then the vehicle is termed stable or “understeering”. Therefore, for directional stability, the primary mass property parameters are the vehicle weight, and total weight distribution (longitudinal, lateral, and vertical).

74th SAWE International Conference on Mass Properties Engineering, 2015

The intent of this paper, again revised (Rev. G), is to show that a vehicle designed in true acco... more The intent of this paper, again revised (Rev. G), is to show that a vehicle designed in true accordance with the balanced viewpoint of a professional mass properties engineer may not only demonstrate superior acceleration, braking, and handling, but superior ride, stability, fuel economy, and safety as well. If a design begins with the first principles of how mass properties affect automotive performance in all its aspects , and is optimized accordingly in an integrated manner, then the resulting advanced automotive design may truly “go where none have gone before”.

74th SAWE International Conference On Mass Properties Engineering, 2015

As a small start-up company competing against long established automotive concerns such as Ferrar... more As a small start-up company competing against long established automotive concerns such as Ferrari, Colin Chapman’s Lotus Engineering Company did not have the capability to gain advantage through advanced engine design, or even via the design of most of the other major mechanical systems. Most such components were commercially sourced, and so the only way a decisive advantage could be obtained was through an uncompromising emphasis on gaining performance “edges” from the remaining design elements of structure, body, and suspension. Because the automotive performance aspects of acceleration, braking, and handling are so dependent on various vehicle mass properties the optimization of those mass properties became the “Holy Grail” of Lotus design as directed by Colin Chapman.

80th SAWE International Conference, 2021

The quantification of automotive directional stability may be expressed through various stabil... more The quantification of automotive directional stability may be expressed through various stability metrics, but perhaps the most basic of these automotive stability metrics is the “Understeer Gradient” (Kus). The Understeer Gradient (in degrees or radians per unit gravity) appears extremely uncomplicated when viewed in its most common formulation:

Kus = [Wf / (g Csf)] - [Wr / (g Csr)]

This metric appears to depend only on the front and rear axle weight loads (Wf, Wr), and on the front and rear axle cornering stiffnesses (Csf, Csr). However, those last quantities vary with lateral acceleration, and the nature of that variation is dependent upon many other parameters of which some of the most basic are: Total Weight, Sprung Weight, Unsprung Weight, Forward Unsprung Weight, Rear Unsprung Weight, Total Weight LCG, Sprung Weight LCG, Total Weight VCG, Sprung Weight VCG, Track, Front Track, Rear Track, Roll Stiffness, Front Roll Stiffness, Rear Roll Stiffness, Roll Axis Height, Front Roll Center Height, and Rear Roll Center Height. Note that exactly half of these automotive directional stability parameters as listed herein are mass properties.

The purpose of this paper is to explore, through a skidpad simulation, the relative sensitivity of automotive directional stability (as quantified through the Understeer Gradient) to variation in each of the noted vehicle parameters, with special emphasis on the mass property parameters.

The simulation is constructed in a spreadsheet format from the relevant basic automotive dynamics equations; the normal and lateral loads on the tires are determined as the lateral acceleration is increased incrementally by a small amount (thereby maintaining a “quasi-static” or “steady-state” condition). The normal loads are used for the calculation of the lateral traction force potentials at each tire, with the required (centripetal) lateral traction forces apportioned accordingly. From those required (actual) lateral tire forces the corresponding tire cornering stiffnesses are determined; this determination is based upon a tire model developed through a regression analysis of tire test data.

This construction of a fairly comprehensive lateral acceleration simulation from basic automotive dynamic relationships, instead of depending upon commercial automotive software such as “CarSim” (vehicle model) and Pacjeka “Magic Formula” (tire model), constitutes a unique aspect of this paper; this return to basics hopefully provides a clearer view and understanding of the results than would be the case otherwise. Even more unique is this paper’s emphasis on, and exploration of, the role specific mass property parameters play in determining automotive directional stability.

SAWE Journal "Weight Engineering", 1982

This article was originally published in the Winter 1982/83 Issue of the Society of Allied Weight... more This article was originally published in the Winter 1982/83 Issue of the Society of Allied Weight Engineers (SAWE) Journal, pp. 10 to 15, copyright Brian Paul Wiegand/SAWE. It was the precursor to the SAWE Paper #3528, “Mass Properties and Automotive Lateral Acceleration”, presented in 2011 for the 70th Annual International Conference of the SAWE at Houston Tx. It was also the seed for what ultimately sprouted into the SAWE seminar “Automotive Lateral Dynamics and Mass Properties” given initially at the 2017 SAWE Regional Conference (Irving, Tx), and then again at the 2019 SAWE International Conference (Norfolk, Va).
The maximum lateral acceleration level which an automobile can attain in turning is an important index of performance and safety. The obtaining of high maximum acceleration levels has certain inherent weight and center of gravity implications of great significance for the automotive design engineer. The purpose of this article is to examine the physics of automotive turning maneuvers so as to make those weight and c.g. implications explicit.

The primary forces which determine the dynamic behavior of aircraft are aerodynamic forces genera... more The primary forces which determine the dynamic behavior of aircraft are aerodynamic forces generated by pressure differentials acting over the aerosurface areas. In contrast, the primary forces which determine the dynamic behavior of automobiles are friction forces generated by contact pressure acting over the tire-to-road contact areas.
It is the tires that transmit the forces that accelerate, decelerate, and maneuver the automotive road vehicle. It is the tires that play a major role in isolating the vehicle, its cargo and passengers, from the shock and vibration effects of road surface irregularities. Last, but not least, the tires play an absolutely critical role in providing vehicle directional stability. What tires do is necessary and very complex, so much so that in nearly 125 years of development no adequate substitute has been found for the pneumatic-elastic rubber and cord structure known as the tire. The tire has prevailed over all those years, undergoing innumerable improvements and refinements, despite still not being fully understood in its mechanisms and behavior.
This document attempts to fully explain and understand tire mechanisms and behavior, and is an excerpt from a larger work entitled "Mass Properties and Advanced Automotive Design" presented at the 74th Annual International Conference of the Society of Allied Weight Engineers Inc. in May 2015. That paper, and this excerpt, have undergone considerable revision since then in an ongoing attempt to eliminate all spelling, grammatical, typographical, and other errors.

Evaluation of the performance potential of an automotive conceptual design requires some initial ... more Evaluation of the performance potential of an automotive conceptual design requires some initial quantitative estimate of numerous relevant parameters. Such parameters include the vehicle mass properties, frontal and plan areas, aero drag and lift coefficients, available horsepower and torque, and various tire characteristics such as the rolling resistance...
A number of rolling resistance models have been advanced since Robert William Thomson first patented the pneumatic rubber tire in 1845, most of them developed in the twentieth century. Most early models only crudely approximate tire rolling resistance behavior over a limited range of operation, while the latest models overcome those limitations but often at the expense of extreme complexity requiring significant computer resources. No model extant seems well suited to the task of providing a methodology for the estimation of a tire’s rolling resistance that is simple to use yet accurate enough for modern conceptual design evaluation.
It is the intent of this paper to suggest a methodology by which this seeming deficiency may be rectified.

74th SAWE International Conference, Alexandria VA, 18 May 2015

Problems in dynamics may be solved by any one or more of three basic methods: force and accelerat... more Problems in dynamics may be solved by any one or more of three basic methods: force and acceleration (F=m a), work and kinetic energy (Fd=½ mV^2), impulse and momentum (〖Imp〗_(1→2)=mV_2-mV_1); 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, are no exception.
Even at the most elementary level, as represented by the previous equations, the unifying role of mass properties is evident. Notable in the basic formulae of all three methods for the solution of problems in dynamics is the common parameter “m” (mass). However, this represents just the “tip of the iceberg”; at the detailed level representative of actual engineering problems the full role played by mass properties is often revealed to be far more complicated than that indicated by such simple basic equations.
For instance, an automobile traveling at a particular velocity will possess a certain amount of kinetic energy which must be dissipated for the vehicle to come to a stop. The dissipation can be controlled and orderly as in the case of braking a car to a stop at an intersection, or it can be somewhat more violent as in the case of a collision with a concrete abutment. In both cases the outcome is directly dependent upon the magnitude of the kinetic energy involved. Initially the mass properties involvement seems to be very simple: the kinetic energy of any body of mass “m” moving at a velocity “V” is expressible as “½ mV^2”; to come to a stop that energy must be dissipated through the work done by a deceleration force “F” times the distance “d” traveled during the deceleration.
However, the kinetic energy possessed by an automobile is much more than would be indicated by a simple determination of its mass “m” from its weight (“m= W/g”). Many components of an automobile possess not only translational kinetic energy, but rotational as well. Thus the simple mass “m” is not the appropriate value needed for kinetic energy determination; there is a greater value “me”, termed the “effective mass”. The calculation of “me” involves the rotational inertia of such components as the wheels, tires, brakes, shafts, bearings, etc.
Thus not only the mass of the automobile as a whole, but that of various components, come into play when calculating the amount of kinetic energy which, in turn, determines the magnitude of the deceleration forces required to affect a complete stop in a certain distance. When the deceleration is a matter of braking, certain other vehicle mass properties come into play: the vehicle longitudinal, lateral, and vertical CG. When the deceleration is a matter of crashing, then the vehicle mass density and mass density distribution also have significance.
The purpose of this paper is to make explicit the exact role that all the mass properties play in determining the automotive deceleration performance during a crash. This has a direct bearing on the survivability of a crash, which can be enhanced through thoughtful mass properties engineering.

The crash of an automobile into an immovable object is an event of only a little more t... more The crash of an automobile into an immovable object is an event of only a little more than a tenth of a second in duration. During that time the structure of the vehicle is deformed in a random series of resistance force spurts and lapses until the work energy (force × deformation) expended during deformation roughly equals the vehicle kinetic energy at the moment of contact. Since the deceleration “a” is equal to the deformation resistance force “F” divided by the vehicle mass “m”, the deceleration history also constitutes a random series of spurts and lapses.
The deceleration magnitude and duration has a direct bearing on the survivability of a crash, as does the magnitude and duration of the rate of change in deceleration “j” known as “jerk” (“j = Δa/Δt”). In the interest of human survivability, modern automotive structures are designed so as to smoothly decelerate the vehicle as much as possible, i.e., with a minimum of “jerk”, while keeping deceleration magnitude and duration within reasonable limits. The two most common force-deformation models utilized to achieve such deceleration are the constant force deformation model and the progressive force deformation model; the former is used mostly for energy absorbing bumper design and the latter for the automotive structure proper, hence the significance of this mathematical study of the properties of these models.

Perhaps the most curious aspect of the modern piston engine is that utilizes a reciprocal motion ... more Perhaps the most curious aspect of the modern piston engine is that utilizes a reciprocal motion more reminiscent of the inefficient reciprocating motion of nature (people, monkeys, birds, fish) than some of mankind’s more efficient creations (wheeled). The reciprocating motion characteristic of the piston engine has been dismissively referred to as “monkey motion”, and with good reason. This fact has long been recognized, and much effort has expended to find a rotary substitute for the reciprocating, such as the Wankle engine or the gas turbine, but as of this writing the reciprocating engine still reigns supreme for automotive propulsion.

Although Sir Isaac Newton (1642-1726) formulated “F = m a” as his Second Law of Motion, he inexpl... more Although Sir Isaac Newton (1642-1726) formulated “F = m a” as his Second Law of Motion, he inexplicably thought that the formulation for determining the kinetic energy of a moving body was “KE = m V”. For many contemporaries interested in physics this seemed questionable. The Dutch experimenter W.J. Gravesande (1688-1742) conducted a series of experiments which consisted of dropping lead weights into a bed of soft clay; the greater the weight, or height of the drop, then the greater the measured depth of the resulting indentation. This corroborated that the kinetic energy was proportional to the mass and velocity at the time of impact. However, Gravesande left the determination of exactly how the kinetic energy varied with mass and velocity to his friend Émilie du Châtelet (1706-1749) , whose analysis of the experimental data resulted in “KE = m V^2”. Why this expression lacks the “½” factor has been given various explanations. However, when subject to a modern approach the derivation of the correct “KE = ½ m V^2” formulation is readily made.

The conventional automotive configuration of two axle lines and four wheels, with each wheel loca... more The conventional automotive configuration of two axle lines and four wheels, with each wheel located in the corner of the automotive plan view, is one of only a large number of possible wheel/axle configurations, but has prevailed for so long that this fact is often forgotten. The choice of which wheels steer and which wheels are driven compounds the number of configuration variations possible. When other configuration variations are also considered, such as varying the vehicle tire/wheel size/type fore to aft or even side to side (as on some circle track racers), or whether the engine is to be front, mid, or rear located, then the number of all possible configurations becomes infinite.

SAWE Journal "Weight Engineering", Spring 2011

43rd Annual International Conference of the Society of Allied Weight Engineers, May 21, 1984

Automotive longitudinal acceleration is dependent upon a large number of interconnected parameter... more Automotive longitudinal acceleration is dependent upon a large number of interconnected parameters, some of the most important of which are mass properties. The purpose of this paper is to explore the individual mass property effects.

The approach taken to achieve this purpose was to decouple the parameters by means of a computer simulation of an automotive acceleration "run". Each individual mass property parameter was then varied over a wide range while all other parameters were held constant. The acceleration results so obtained were plotted, and the conclusions were drawn from the behavior thus exhibited.

Several conclusions have been drawn from this effort. First, the effects of a mass property parameter variation are not necessarily constant over the entire speed range. For instance, increasing weight tends to cause an almost linear increase in the elapsed times for the lower speed ranges, but the higher speed ranges exhibit ever greater time increases in an almost parabolic relationship. This is a matter of the increased rolling resistance associated with greater weight making itself felt at the higher speeds.

The longitudinal center of gravity (LCG) and the vertical center of gravity (VCG) both affect acceleration through traction. If the situation is not traction critical, then c.g. relocation can be of no help in obtaining better acceleration. When a situation is traction critical then acceleration is much more sensitive to change in LCG then in VCG.

Increasing the vertical center of gravity tends to benefit the acceleration of rear wheel drive vehicles. For rear wheel drive vehicles the VCG generates increased traction through weight transfer. In the case of front wheel drive, the VCG can have no beneficial effect as the weight transfer is in the direction away from the drive axle; minimizing the VCG becomes the priority. Due to the effect of weight transfer, a front wheel drive vehicle will always be inferior in acceleration to a rear wheel drive vehicle if everything else is equal and the propulsive capability is great enough.

In general, a rotational mass is disproportionately detrimental to acceleration because it has to be accelerated both rotationally and translationally. The greatest return for the effort involved in mass reduction can be obtained from a reduction in rotational masses.

The engine rotational masses, other than the flywheel, represent a special case outside the scope of this paper. Vehicle characteristics and use demand a certain minimal rotational inertia for the flywheel to counteract engine stall-out tendencies at the onset of acceleration and to ensure smooth engine operation. In fact, higher flywheel inertia can produce an initially quicker vehicle. This initial response has to be considered against the detrimental longer-term effects of accelerating a greater flywheel inertia throughout the speed range; flywheel design involves a high degree of compromise.

The presence of gears in a mechanical system can have important implications with respect to the ... more The presence of gears in a mechanical system can have important implications with respect to the effective mass properties. This is especially true for the automotive case in the acceleration and deceleration (braking) modes.

Even though rollover is unlikely as an automotive accident modality, it still merits serious conc... more Even though rollover is unlikely as an automotive accident modality, it still merits serious concern. As part of the “New Car Assessment Program” (NCAP), the NHTSA rates vehicles for rollover resistance based on a mathematically derived figure of merit called the “Static Stability Factor” (SSF), plus the empirical results of a test procedure known as the “Fishhook Test”. The reliance on an expensive empirical procedure is mandated by the gross optimism of the use of the rigid model based SSF by itself. This author promised the development of an equation for estimation of the rollover acceleration that would be far superior to the SSF over 7 years ago during a discussion of SSF limitations in his paper “Mass Properties and Automotive Lateral Acceleration” (SAWE #3528, 2011, pp. 66-67). This rollover equation paper, now in its “Rev B” edition, represents the fulfillment of that promise.

“Advanced Topics” is Part 8 of a ten part presentation series "Automotive Dynamics and Design". T... more “Advanced Topics” is Part 8 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia. Part 6 constitutes a study of friction vs. traction, normal load vs. deflection, normal load vs. contact area, load capacity, vertical stiffness, lateral traction, longitudinal traction, %Slip, Slip Angle, Traction Ellipse, rolling resistance, temperature effects, speed effects. Part 7 constitutes a study of Navier-Stokes Equations, dimensionless indicators (Reynolds Number, Mach Number), streamlines, Bernoulli’s Equation, drag, lift, boundary layer, separation, wake, vortices, center of pressure, aerodynamic stability, wings, fences, spoilers. Part 8 constitutes a study of camber, caster, toe in/out, scrub, kingpin angle, scrub radius, effective spring rate, roll stiffness, suspension geometry, roll axis, steering geometry, turn centers, geared and equivalent gearless systems, products of inertia, gyroscopic reactions, fuel economy, standing wave, hydroplaning. Part 9 introduces the concept of Design (a.k.a. Styling), Design Schools, Design Practitioners, Design Process, Exterior Design, Interior Design. Part 10 deals with the business and manufacturing aspects of automotive endeavors: business plan (product, market, cash flow, P&L, capitalization, ROI, etc.), profit and loss statements, break-even analysis, in-house or subcontract decisions, plant location and layout, jigs and fixtures, equipment, supply and inventory, customer service & relations strategy.

“Lateral Dynamics” is Part 3 of a ten part presentation series "Automotive Dynamics and Design". ... more “Lateral Dynamics” is Part 3 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia. Part 6 constitutes a study of friction vs. traction, normal load vs. deflection, normal load vs. contact area, load capacity, vertical stiffness, lateral traction, longitudinal traction, %Slip, Slip Angle, Traction Ellipse, rolling resistance, temperature effects, speed effects. Part 7 constitutes a study of Navier-Stokes Equations, dimensionless indicators (Reynolds Number, Mach Number), streamlines, Bernoulli’s Equation, drag, lift, boundary layer, separation, wake, vortices, center of pressure, aerodynamic stability, wings, fences, spoilers. Part 8 constitutes a study of camber, caster, toe in/out, scrub, kingpin angle, scrub radius, effective spring rate, roll stiffness, suspension geometry, roll axis, steering geometry, turn centers, geared and equivalent gearless systems, products of inertia, gyroscopic reactions, fuel economy, standing wave, hydroplaning. Part 9 introduces the concept of Design (a.k.a. Styling), Design Schools, Design Practitioners, Design Process, Exterior Design, Interior Design. Part 10 deals with the business and manufacturing aspects of automotive endeavors: business plan (product, market, cash flow, P&L, capitalization, ROI, etc.), profit and loss statements, break-even analysis, in-house or subcontract decisions, plant location and layout, jigs and fixtures, equipment, supply and inventory, customer service & relations strategy.

Steering is required to control the direction of the vehicle, and for this to occur efficiently i... more Steering is required to control the direction of the vehicle, and for this to occur efficiently it is necessary that tire scrub, which produces disturbance forces, be minimized. Minimization of tire scrub from other causes other than steering, i.e. suspension scrub resulting from lateral linkage movement/toe in-out/camber changes/castor and-or kignpin angle, are also investigated. However, the handling, i.e. steering and stability, character of an automobile depends mainly upon its responses to steering and disturbance inputs. To investigate the nature of automotive steering and stability a simplified (linear relationships, no suspension, low speeds, steady-state) mathematical model is initially presented and then developed further. Therefore this paper begins with the steering geometry…

“Conclusion, Business and Manufacturing” is Part 10 of a ten part presentation series "Automotive... more “Conclusion, Business and Manufacturing” is Part 10 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Conclusion, Business and Manufacturing"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia. Part 6 constitutes a study of friction vs. traction, normal load vs. deflection, normal load vs. contact area, load capacity, vertical stiffness, lateral traction, longitudinal traction, %Slip, Slip Angle, Traction Ellipse, rolling resistance, temperature effects, speed effects. Part 7 constitutes a study of Navier-Stokes Equations, dimensionless indicators (Reynolds Number, Mach Number), streamlines, Bernoulli’s Equation, drag, lift, boundary layer, separation, wake, vortices, center of pressure, aerodynamic stability, wings, fences, spoilers. Part 8 constitutes a study of camber, caster, toe in/out, scrub, kingpin angle, scrub radius, effective spring rate, roll stiffness, suspension geometry, roll axis, steering geometry, turn centers, geared and equivalent gearless systems, products of inertia, gyroscopic reactions, fuel economy, standing wave, hydroplaning. Part 9 introduces the concept of Design (a.k.a. Styling), Design Schools, Design Practitioners, Design Process, Exterior Design, Interior Design. Part 10 deals with the business and manufacturing aspects of automotive endeavors: business plan (product, market, cash flow, P&L, capitalization, ROI, etc.), profit and loss statements, break-even analysis, in-house or subcontract decisions, plant location and layout, jigs and fixtures, equipment, supply and inventory, customer service & relations strategy.

Abstract: “Design (Styling)” is Part 9 of a ten part presentation series "Automotive Dynamics and... more Abstract:
“Design (Styling)” is Part 9 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia. Part 6 constitutes a study of friction vs. traction, normal load vs. deflection, normal load vs. contact area, load capacity, vertical stiffness, lateral traction, longitudinal traction, %Slip, Slip Angle, Traction Ellipse, rolling resistance, temperature effects, speed effects. Part 7 constitutes a study of Navier-Stokes Equations, dimensionless indicators (Reynolds Number, Mach Number), streamlines, Bernoulli’s Equation, drag, lift, boundary layer, separation, wake, vortices, center of pressure, aerodynamic stability, wings, fences, spoilers. Part 8 constitutes a study of camber, caster, toe in/out, scrub, kingpin angle, scrub radius, effective spring rate, roll stiffness, suspension geometry, roll axis, steering geometry, turn centers, geared and equivalent gearless systems, products of inertia, gyroscopic reactions, fuel economy, standing wave, hydroplaning. Part 9 introduces the concept of Design (a.k.a. Styling), Design Schools, Design Practitioners, Design Process, Exterior Design, Interior Design. Part 10 deals with the business aspects of automotive endeavors: business plan, profit and loss statements, break-even analysis, in-house or subcontract, plant location and layout, jigs and fixtures, equipment, supply and inventory, customer service & relations.

“Areodynamics” is Part 7 of a ten part presentation series "Automotive Dynamics and Design". The ... more “Areodynamics” is Part 7 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia. Part 6 constitutes a study of friction vs. traction, normal load vs. deflection, normal load vs. contact area, load capacity, vertical stiffness, lateral traction, longitudinal traction, %Slip, Slip Angle, Traction Ellipse, rolling resistance, temperature effects, speed effects. Part 7 constitutes a study of Navier-Stokes Equations, dimensionless indicators (Reynolds Number, Mach Number), streamlines, Bernoulli’s Equation, drag, lift, boundary layer, separation, wake, vortices, center of pressure, aerodynamic stability, wings, fences, spoilers. Part 8 constitutes a study of camber, caster, toe in/out, scrub, kingpin angle, scrub radius, effective spring rate, roll stiffness, suspension geometry, roll axis, steering geometry, turn centers, geared and equivalent gearless systems, products of inertia, gyroscopic reactions, fuel economy, standing wave, hydroplaning.

“Tire Behavior” is Part 6 of a ten part presentation series "Automotive Dynamics and Design". The... more “Tire Behavior” is Part 6 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia. Part 6 constitutes a study of friction vs. traction, normal load vs. deflection, normal load vs. contact area, load capacity, vertical stiffness, lateral traction, longitudinal traction, %Slip, Slip Angle, Traction Ellipse, rolling resistance, temperature effects, speed effects.

“Mass Properties Analysis and Control” is Part 5 of a ten part presentation series "Automotive Dy... more “Mass Properties Analysis and Control” is Part 5 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions. Part 5 constitutes a study of the ten mass properties equations, the ten mass properties uncertainty equations, standard deviation, normal distribution, regression analysis, coefficient of determination, correlation, degrees of freedom, total weight estimation, unsprung weight estimation, sprung weight estimation, estimation of the total weight c.g., estimation of the unsprung weight c.g., estimation of the sprung weight c.g., estimation of the total mass moments of inertia, estimation of the unsprung mass moments of inertia, estimation of the sprung mass moments of inertia, estimation of the total products of inertia, estimation of the sprung roll moment of inertia.

“Vertical Dynamics” is Part 4 of a ten part presentation series "Automotive Dynamics and Design".... more “Vertical Dynamics” is Part 4 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration. Part 3 constitutes a study of oversteer, understeer, directional stability, rollover, lateral acceleration: transient and steady state. Part 4 constitutes a study of springing, damping, shock attenuation, road contact, road vibration transmissibility, ride motions.

“Longitudinal Dynamics” is Part 2 of a ten part presentation series "Automotive Dynamics and Desi... more “Longitudinal Dynamics” is Part 2 of a ten part presentation series "Automotive Dynamics and Design". The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study. Part 2 constitutes a study of automotive acceleration, braking, and crash deceleration.

"Automotive Dynamics and Design" is Part 1 of a ten part presentation series of the same name. Th... more "Automotive Dynamics and Design" is Part 1 of a ten part presentation series of the same name. The intent is to form a comprehensive series of lectures providing instruction in the design of automobiles from both a practical and a stylistic viewpoint. The ten segments constitute the core (reading assignments, homework, and test material not included) of a class to be given over a period of about twelve weeks. The ten course segments are:

1. "Automotive Dynamics and Design"
2. "Longitudinal Dynamics"
3. "Lateral Dynamics"
4. "Vertical Dynamics"
5. "Mass Properties Analysis and Control"
6. "Tire Behavior"
7. "Aerodynamics"
8. "Advanced Topics"
9. "Design (Styling)"
10. "Summary"
    Part 1 is essentially an introduction to, and a syllabus for, the course of study.

"Estimation of the Rolling Resistance of Tires", 2016

Evaluation of the performance potential of an automotive conceptual design requires some initial ... more Evaluation of the performance potential of an automotive conceptual design requires some initial quantitative estimate of numerous relevant parameters. Such parameters include the vehicle mass properties, frontal and plan areas, aero drag and lift coefficients, available horsepower and torque, and various tire characteristics such as the rolling resistance coefficient(s)...
A number of rolling resistance models have been advanced since Robert William Thomson first patented the pneumatic rubber tire in 1845, most of them developed in the twentieth century. Most early models only crudely approximate tire rolling resistance behavior over a limited range of operation, while the latest models overcome those limitations but often at the expense of extreme complexity requiring significant computer resources. No model extant seems well suited to the task of providing a methodology for the estimation of a tire’s rolling resistance “coefficient” that is simple to use yet accurate enough for modern conceptual design evaluation.
It was the intent of the paper "Estimation of the Rolling Resistance of Tires" (SAE 2016-01-0445) to suggest a methodology by which this seeming deficiency may be rectified. This is the presentation which accompanied the paper at the 2016 SAE World Congress in Detroit.

This is a PDF/Scribd version of the PowerPoint material for a SAWE seminar given initially at the... more This is a PDF/Scribd version of the PowerPoint material for a SAWE seminar given initially at the 2017 SAWE Regional Conference (Irving, Tx), and then again at the 2019 SAWE International Conference (Norfolk, Va). The course objective was to enable the student to make reasonably accurate maximum lateral acceleration, rollover lateral acceleration, directional stability, and steering responsiveness determinations in the course of vehicle design. The student was also to become acquainted with such things as the calculation of roll resistance, suspension roll center location, sprung mass roll axis inclination, sprung mass roll inertia, sprung mass roll moment arm, sprung mass roll angle under lateral acceleration, vehicle roll gain, vehicle dynamic index in yaw, transient center of rotation location, and transient yaw inertia. There was also considerable time spent on the behavior of tires under lateral load and “Ackermann Steering Geometry” relationships.
This seminar is very important for anyone engaged in vehicle design, in particular those designing with an emphasis on performance, and special effort has been expended to make it particularly relevant for those involved in the SAE Student Formula Design Competition. However, no one completing this course will walk away without having acquired some degree of enlightenment.