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.
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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.
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.
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).
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.
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.
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.
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.
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 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.
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.
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.
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.
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).
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
“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.
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.
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.
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.
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.
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.
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.
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 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.