Rocket engine nozzles typically feature a shape that first converges then diverges. This is because the flow of the air fuel combustion reaction enters the nozzle at a subsonic velocity, below the speed of sound. As the nozzle converges, the flow's velocity increases to a sonic velocity that forms a shockwave in front of it as pressure decreases. It has now reached a speed of sound with a Mach number of exactly 1. Then the nozzle begins diverging, because the flow is supersonic. The conditions for supersonic flow are inverted, so the nozzle diverges, rather than converges, to increase velocity. Pressure continues to decrease at this point and beyond. In the design of the NASA space shuttle, the cooling system of the divergent supersonic flow rocket engines borrowed cooling techniques used in 1880s internal combustion engines.

Cars- what amazing marvels of technology. Perhaps one of the most taken for-granted products in people's lives today. The modern automobile is likely the most technologically complex possession in the average American person's life. Modern cars are the result of exhaustive computational analysis in fluid mechanics to design an aerodynamically optimized body shell shape (Such as the C7 generation of Chevrolet Corvette requiring approximately 700 hours of CFD numerical computerized analysis), involving super computers calculating multivariable calculus and partial differential equations at incredible speed including double and triple flux integration techniques. The 1989 Lexus LS400, a pinnacle of automotive engineering standards, was the result of some 1400 engineers working tirelessly. Designing a modern day Internal Combustion Engine from scratch is absurdly complex, involving fluid mechanics, thermodynamics, chemistry, and engine dynamics. Transmissions are even more mind boggling, containing approximately 700-800 parts in a modern day automatic drive train.

Following in the foot steps of the theoretically impossible engineering standards set by the Lexus Launch, the 1992 Generation-3 SXV10 Toyota Camry's Non-synchronized automatic transmission revolutionized the automotive industry in technological sophistication and refinement. While non-synchronization was nothing new to the industry, and the Japanese actually refined the technique after being taught it by American experts, who traveled to Japan from American universities and car companies. Non-synchronous transmissions are typically reserved for use on heavy commercial vehicles or agricultural vehicles. In essence, modern automatic transmissions rely hugely on mechatronic systems, much more than a manual with a traditional clutch. Specifically, there are chambers in which hydraulic transmission fluid, of which the viscosity is optimized for use, flows through hydraulic chambers. In place of a flywheel on a manual transmission's clutch, an automatic transmission features a fluid-powered turbine known as a torque converter. When you press the accelerator, fluid spins the turbine, which builds up inertia in the converter. This is why automatic transmissions lag, because the torque converter needs to build up inertia using hydraulic actuation.This way, when your car is stopped, the engine will not stall out, since the transmission hooks up to the crankshaft of the engine. In the year 1989, Toyota developed an automatic transmission that can essentially double-clutch itself, in a fraction of a second. This means the transmission has an advanced computing system known as a "TCU" or Transmission Control Unit. This computer communicates with the car's "ECU" or engine computing system. Every second, millions of calculations derived in the Laplace Transformation as well as Fourier series transform of Ordinary and Partial Differential Equations are computed by the automobile. This is essentially an artificial human nervous system for a car. The TCU and ECU are all parts to a greater complete Powertrain Control System/Module. Analogous biologically to the human central nervous system, hundreds of sensors in the car, such as the Oxygen Sensor, or damping systems, act in the same fashion as nerve endings in the human body. They essentially can sense parameters, send vast amounts of information back to the A.I. Automotive brain circuitry, in which linearly interpolated massive data tables can quickly respond a feedback output to the engine and transmission in order to make constant adjustments for optimal performance, efficiency, and emission regulations regardless of operating conditions such as humidity, Tinf, Another automotive sensor is referred to as an “Anti-knock sensor”. This small, simple-appearing apparatus can, essentially, determine the chemical makeup and specific octane of fuel inputed. If the car has too low of an octane inputed, the sensor is capable of telling the ECU that the ignition timing and fuel injection must be immediately optimized in the best possible way to mitigate engine wear and knocking effects, which would send combustion chamber pulsations which causes significant wear. The transmission computing system is hooked to solenoid actuators. The computer tells the solenoids how to distribute hydraulic fluid. This fluid is what drives the torque converter, which is mechanically related to a series of planetary gear sets. The 1992 Camry's transmission was one of the smoothest shifting automatic transmissions on the automotive market at the

time of debut, and is still fairly advanced. In a traditional automatic transmission, the shifts are synchronized. This means that one planetary gear rotating with great angular velocity omega meshes with another gear at rest. This results in a harsher shift. It also results in loss of energy efficiency to the wheels, and more wear from stress and impact shock. In a non-synchronized transmission, before shifting, one gear builds up angular velocity until it matches in speed with the already rotating gear. Then, the two gears mesh while both rotating. The result is a much faster, smoother, shift. This is similar to releasing the clutch slowly in a manual, and shifting quickly. But it accomplishes it in a fraction of a second. Additionally, the Gen 3 Camry transmission featured Over-Drive, which is an extra flywheel and set of electronically controlled cyclic gearsthat prevents transmission hunting at 35-45 MPH, and gives a boost of performance. It also featured "Shift Lock Override", which was a button to force the transmission out of locking. Additionally, the transmission features Economy and Power mode, in which the transmission computer changes the shift points for either better fuel economy or higher performance. In Data Acquisition, all electrical parts have mechanical analogies. This is how automotive sensors work, since they can translate mechanical motion into electrical equivalencies.

To understand just how remarkable and what an engineering feat the automatic transmissions were in SXV10 Toyota Camry’s, one must understand how absurdly difficult programing the TCU was to accomplish this, especially 25 years in the past. The programming of a non-synchronizing automatic transmission in itself is very precise and demanding, simply because the transmission must be intelligent enough not only to match gear sets in velocity, but also offset the gear teeth and mesh them with zero grinding. Additionally, the automatic transmission in this car was so complex that the driver could literally optimize the transmission with 4 combos: (Overdrive Off, Econ Mode; Overdrive On, Econ mode; Overdrive off, Power mode; Overdrive On, Power mode). When these buttons were pushed, the TCU immediately changes the shift logic and points of RPM change, while simultaneously driving and ensuring that no gears grind. Non-synchronous and self-double clutching automatic transmissions are not always attempted because of their difficulty to successfully execute.

Dimpling the sheet metal of an automobile will NOT improve its aerodynamics. It only works on a golf ball. This is because the golf ball operates coincidentally in a very specific pressure gradient. The ball moves at a high velocity relative to its size, where as a car moves slower relative to its much larger size. Because of this, the boundary layer, which seperates at the "adverse pressure gradient", will not be inhibited to seperate further back using dimples, like a golf ball achieves. Therefore, there is no rear turbulence reduction using dimples. In order to achieve a low drag coefficient on an automobile, designers and engineers must make a car which is curved and streamlined all the way to the tail end. At the tail end, the trunk lid may protrude outwards, and, the rear bumpers will be creased. This inhibits the seperation of the boundary layer of air flowing over the car, further back, reducing rear turbulence. This is appropriate for low-performance environmental cars, like the Toyota Prius, or Chevy Volt

However, high performance cars usually have a relatively high coefficient of drag. This is because they require extreme downforce. This means they need essentially inverted wings, which pushes cars towards the ground, to the point where at 90 mph and higher, most formula 1 cars can theoretically drive upside down. Additionally, high performance cars utilize diffusers, which, at subsonic flow, acts as a series of diverging nozzles. With aid of a flat under tray, the rear diffuser increases air pressure, while lowering velocity To account for the pressure differential created as a result, the air traveling under the car prior to the rear diffuser has to speed up substantially to equilibrate the pressure difference. This makes the entire car act like an inverted wing, essentially.

In designing automotive camshafts, when choosing calculus/differential equation based piecewise functions for your displacement model, one must choose a function which will not "run out" of derivatives from displacement in which ds/dt is velocity, in which dv/dt is acceleration, and da/dt becomes jerk. It is then often necessary to select a sinusoidal or cosine type function which derives and integrates between cosine and sine, and therefore does not encounter a mathematical "Dirac delta function", which results in infinity spikes starting at acceleration and passing on to jerk, which theoretically states that the cam lobe is experiencing zero stress and force. This is the opposite of the truth, as this would result in a sharply pointed cam lobe, which would experience massive stress concentration at its tip, which would rub off into a

blunter normal shaped cam from the incredible stress, there by proving how nature always seeks equilibrium automatically. In calculus, these "Infinity spikes" are the results of vertical lines in the velocity diagram which creates discontinuities. A dwell is a location where a cam lobe has zero velocity and acceleration. Non-dwell piecewise functions at non-zero velocity and acceleration must be linked continuously to dwells with zero velocity and acceleration according to the fundamentals of cam design.  

A multivariable Riemann sum in calculus can be used to approximate any 3 dimensional volume by approximating the shape with rectangular subsections. Increasing the amount of ever smaller rectangles gives an infinitely more accurate approximation of the volume of the solid. It can be seen that a higher iteration of smaller rectangles gives a much more accurate approximation of the volume.

 I have interests in fluid mechanics although my knowledge is for the most part fairly limited. Fluid Mechanics has many applications, one of which is basically aerodynamics for land vehicle design, and a lot of multivariable differential calculus is used to determine fluid flow over surfaces by approximating surfaces and shapes as the sum of various functions in three dimensional space, like a 3-dimensional, multivariable riemman sum. Double and triple integrals can be performed by computer algorithms to determine ideal aerodynamic shape to optimize downforce in race cars, and fluid flow can be approximated by Partial differential equations, since fluid dynamics involves multivariable equations with partial derivatives. Multivariable calculus is very helpful in fluid dynamics since it involves vectors, and vector flow is used by Computational Fluid Dynamics software.

 A venturi style ground effect in high performance cars can also optimize down force. The Venturi was also applied to Carburetors, which used this partial vacuum concept to blend air and fuel for use in the combustion chambers, before EFI (Electronic Fuel Injection) and Direct Fuel Injection (direct injection into chamber) were fully implemented. Unfortunately, venturis have a tendency to "ice up" on freezing cold days. Modern cars have become amazingly efficient with the implementation of electronic fuel injection, which allows a car to burn what a vintage carbureted engine would fail to burn. This means that modern cars have surperior fuel economy and very clean emissions. A venturi style ground effect creates inverted lift in high performance cars can also optimize down force. Fluid Dynamics algorithms can be achieved through Stoke's Theorem, Divergence, and Greens Theorem as a basis among many more theorems. The venturi is integrated into the monocoque/unibody structure with air intakes which allows air to flow in, creating inverted lift in a partial vacuum of greater pressure over the venturi, pushing the car into the ground, allowing a higher speed when cornering, resulting in a higher G-turn force.

Automotive technology has, in the latest years, been advancing so fast that the FIA has had to put strict restrictions LMP and Formula 1 cars just so the car's performance isn't so extreme that drivers can still operate the car. These days, formula 1 engines run at exceptionally high Revs, typically maximizing near 20,000 rpm. This means that every second, the pistons in a Formula 1 car's engine makes about 334 revolutions immediately before shifting up. This kind of RPM is pushing the engine's components to the limit, and the springs to control the movement of the intake and exhaust valves over the combustion chamber gets to a point where the up-down motion is so incredibly fast that severe valve float is a problem to be dealt with in Hyper performance vehicle design. The valves are vibrating with a resonant frequency that causes the valve float.

Beyond constant-acceleration Kinematic equations in physics, Ordinary Differential Equations can be used to derive velocity and position equations for real world movement including non-linear air resistance. This is why the Bugatti Veyron Super Sport needs a whole 200 hp more than the standard Veyron to achieve only a few mph faster top speed, because at those relative speeds the air resistance has grown exponentially relative to increase in velocity so much more power needs to be added to the car.

Thermodynamics and ideal gas laws are used in the design of internal combustion engines. Internal combustion engines in cars are considered open systems in thermodynamics, the engine has dependencies in changes from the surroundings outside the engine boundaries, including the intake of air and fuel through the intake valve, and after ignition from the spark plugs, exhaust exits, contrast to a isolated piston

in an isolated cylinder, which would be considered a control mass closed system. Density is mathematically defined as the limit as volume approaches a volume differential, and as this volume differential approaches zero, density's inverse relationship (since Density= Lim (v to (dv/dt)) m/v), Density goes into infinity. As infinity is an irrational mathematical concept, to get around this you choose your volume differential to be the smallest possible value while retaining a definite rational density value. Pressure is the Limit as Area approaches Area differential of the expression Force Normal/ Area, so the same concept applies, but with area instead (Pressure= Lim (A to (dA/dt)) Fnormal/Area).

The first law of Thermodynamics is essentially a formal restatement of the law of the conservation of energy. In an automotive internal combustion engine, the energy derived from the air and fuel mixture used to power the vehicle is the energy inputted subtracted from the energy rejected into the exhaust system, which is necessary for the heat cycle to regenerate.

The average ideal stoichiometric ratio of air to gasoline in the combustion chamber of an architypical car is 14.7:1. Deviation from this typical standard in most cars results in a "lean burn" (excess air) or "rich burn" (excess fuel). Often, in mathematical thermodynamic analysis of automotive engines, Air-standard assumptions are made to simplify analysis since so much more air burns than relative fuel.

  A hemi engine is developed as a hemi-spherical head of the combustion chamber is shaped by advanced 3-dimensional calculus.

 In an internal combustion engine, one may lay out the camshafts in various ways in the design of the engine. A SOHC is a "single overhead cam system", and a DOHC is a "Dual-Overhead Cam system". When not an overhead system, pushrods are used to transmit the offset from the cam lobe to the rocker arm to open and close valves, referred to as an OVH engine, or "Overhead Valves". The push rod is used since the camshaft is below the level of the valves atop the cylinder head.

 Ordinary or Partial Differential Equations are used to shape camshafts and camshaft lobes. Timing belts are mathematically timed to relate the movement of the exhaust and intake valves with the crankshaft to move the pistons up and down. Many people question why timing belts are used in cars when engineers could use timing chains which don't risk blowing the engine since chains don't typically snap. The answer is that cars meant for very smooth and quiet operation such as luxury sedans should use a timing belt which is more appropriate for cars such as a Lexus or Mercedes Benz where as a Chain might be better suited for something like a Jeep Cherokee Classic or Toyota FJ Cruiser.

 Differential Equations is critical for engineers in order to shape gear teeth and also ideal gear ratios. A rear differential's gear curvature is highly dependent on Differential equations for effective use. A cylinder or combustion chamber may have varying amounts of valves, both intake or exhaust. One can have 2 valves, one intake and one exhaust, or you can have 4, 2 exhaust and 2 intake for improved performance, and even 5 valves per cylinder. For optimal performance, most of the time you will find larger intake valves and smaller exhaust valves.

  A major issue with Inline four cylinder engines are secondary force imbalances. Looking at a force summation, Sigma F in x and y components, the orientation of 4 pistons in a line creates a non-equilibrium in forces as the crankshaft rotates. Engineers solve this issue with engine balance shafts, and two are required to bring to engine to equilibrium for smooth operation. They feature counterweights on a shaft to balance engine forces.

     One may increase the amount of air in the combustion chamber with a turbocharger, but this will involve a phenomenon known as "turbolag". Turbochargers use exhaust driven turbines for forced induction, cramming more air into the combustion chambers. There are also superchargers, which is also a forced induction system, compared to naturally aspirated engines. A turbo charger "whines" at a high pitch because it is running at about 200,000 to 300,000 RPM typically, on a car.

     A catalytic converter consists of a honeycomb structure which uses chemical reactions to greatly reduce harmful pollutants and makes a car much less harmful to the environment. The catalyst consists of a ceramic monolith substrate which uses chemical reactions to convert highly harmful pollutants such as methane into water, oxygen, and carbon dioxide. Modern cars impact the environment about 1/100th that of a vintage car from the 1950s. In fact, a two-stroke lawnmower contributes about 50 times the affect of a modern car, and rickshaws in India contribute about 50 times as much, but The Colorado State University Engines and Energy Conversion Lab took care of that. Little performance may be lost but for most street cars, even performance and enthusiast oriented machines, the pros far outweigh the cons. Exhaust systems actually affect performance alot more than many people intuitively think.

    Modern cars are filled with computer sensors for data aquisition of moving components and can quickly make adjustments many times every second to optimize performance. Modern cars feature an ECU or PCM, which is a small computer usually located near your glove compartment. If you drive any fairly modern car, your car is making millions of calculations every second to control your engine, and has Data Aquisition Systoms in which the oxygen sensor adjusts stoichiometric air:fuel ratio depending on the environment your car is driving in. This is all related to how the engine operates, all being meticulously controlled by a computer checking tables of data millions of times a second. Ignition and injection timing is optimized. Older modern cars have a distributor controlled by a computer, but very new cars have distributorless engines in which coils sit directly above the spark plugs, also controlled by the ECU.

     Conservation of energy, conservation of momentum, force, and inertia is considered in crumple zone and crash safety design.

      I own a 3rd generation Toyota Camry LE Sedan- Aluminum Alloy-head/iron block 2.2 Liter 16-valve 135 hp DOHC EFI In-line 4, 4 valves per cylinder, flat-faced cam follower with no rocker arms,soundproof body shell, steel monocoque unibody construction with asphalt composite sound insulation and adhesive bonding. Side Impact Door Beams, triple sealed doors, fluid filled engine mounts, dual engine balance shafts in the oil sump, Dolby Surround Sound, Direct Panel-to-Panel Bonding and one piece doors, Electronic Controlled Transmission, Overdrive, High Tensile Strength Steel unibody and shell, and shift lock override. The 3rd gen Camry or Camry Vienta/Scepter was one of the 1990s super touring series race cars. It competed in Austrailian Super Touring and South African Super Touring through FIA racing. Rod Millen took 2nd place in the Super Touring Camry in the 1997 North American Touring Car Championship. The car ran on a very highly tuned 2.0 Liter In line four making 300 horsepower... I believe it was naturally aspirated. This car is arguably one of the most highly engineered cars ever made, especially in just a standard midsize sedan. Its engineering and design is generally very highly regarded in the automotive industry, along with the 1989 Lexus LS400 and 1992 Lexus ES300, which the Camry was built from. Ford made a strong effort to keep Mary Walton's exposure of her book Car: A Drama of the American Workplace from becoming largely known outside of industry. Even the body styling is a marvel- To achieve the wide stance required, the engine bay and cradle had to be widened from the Japanese variant which was very difficult, and the stamping process was beyond what luxury marques were doing.

    The tolerances and craftsmanship of the components in the car is another amazing story within itself. The engineering excellence of the 1992 Camry can be proven from calculus, in the definition of the Limit. 1992 Camry engineers designed every component so meticulously to have some of the tightest component tolerances in automotive history. The definition of a limit proves this by showing that if the ideal part dimensions are the Limit L, and the tolerance allowance is plus/minus Delta/Epsilon, then the 1992 Camry has among the smallest tolerance rectangles surrounding the Limit L, to symbolize each component individually. the precise definition of a limit gives the ideal limit itself, and the plus/minus epsilon/delta margin of error the L+/- delta on the x axis and L+/- Epsilon on the y axis forms a margin of error around the limit known as an "Error Tolerance Rectangle"... a 3 dimensional part is just the multivariable calculus version... The 1992 Camry's component tolerances have among the smallest of these tolerance rectangles in automotive history, which is quite expensive for mass production, but due to the yen dollar relationship when this car came out, Toyota could over-engineer every aspect, including the aerodynamically contoured

body which was an incredibly rigid steel unibody monocoque with a thick, high tensile strength steel skin with extremely rigorous rust proofing. It is, in fact, one of the most well engineered cars ever created. The Lexus LS400 based styling of the body shell required an ultra-advanced state of the art stamping process at the time to form the compound curve of the Shoulder at the base of the C-pillars. Mercedes Benz and Audi weren't even capable of this in 1992. Additionally, it is one of the few cars featuring a one-piece roof lacking a rain gutter. BMW even reverse engineered the 1992 Toyota Camry sedan to understand, simply, how Toyota built such an incredible car and sell it in the midsize segment. Customers didn't know, but it was Toyota's secret way of "scaring" the competition of their technological capabilities. Toyota has cut down on this kind of engineering quality on each generation following the 3rd camry.

     NVH in the automotive industry is Noise, Vibration, and Harshness Dampening, which involves computer data acquisition programs and computerized feedback loops.This was accomplished from advanced mathematics and physics including a topic in Ordinary Differential Equations, Laplace Transforms, which transforms variables in both ordinary and partial differential equations into a parameter through an exponential single integration, then the limit of said integration from zero to infinity transforming a differential equation into pure parameters, after a partial fraction decomposition, like a constant in a given state. Toyota assigned several hundred mechanical and electrical engineers on developing NVH, or Noise, Vibration Harshness, reduction. Computerized feedback control systems in the 1992 Camry including sophisticated engine management systems used the Laplace Transforms and performed it in a fraction of a second to reduce NVH and improve stability. Differential equations is also used for developing the state-of-the art non-synchronous automatic transmission of its day, specifically the gear teeth curvatures and I would assume fluid flow for the hydraulic fluid through the chambers. Toyota had developed an incredibly transmission in which gears feel like they simply glide seamlessly into place.

    Laplace Transforms are also critical for making possible cruise control, and self driving technologies. Cruise Control is actually quite advanced. Your car needs tremendous DAQ (Data Aquisition) systems with feedback control loops that regulate engine rpm, and even senses a tend of gravitational acceleration or deceleration when driving downhill or uphill, respectively, in idle. This is because velocity is a directional vector in x-y coordinates, so if the car is traveling ideally perfectly straight, so it can be viewed from the side as a simple 2-D x-y dynamic coordinate, there is a gravitational weight MG pushing down, balanced by an equivalent force pushed up by the earth, known as your normal force. when the car ascends or descends, the car now has more of its velocity in the y direction, so the gravitational force acts in this direction, slowing the car as it drives uphill and speeding it up while going downhill. A cruise control system can logic through dynamics and physics and signal for braking pressure or a boost in engines rpm as appropriate.

    Modern internal combustion engines require extensive use of Mathematics and physics for the design of the engine. The connecting rods have to be optimized as to when the piston will "Bottom out" upon its cycle. This is similar to a piston being heated until it hits stops in a closed system. The system is isobarric as the piston is free to move- if you neglect the frictional forces (which are cut down with engine lubricants as much as possible). Isobarric is a constant pressure state that is the result of a free moving piston that offsets the added heat to the system, coming from the ignition of the air fuel mix in the combustion chamber, in which a spark plug ignites the system. This heat forces the piston down to offset the pressure increase, and optimization is performed to see when and where to bottom out the con rods on the crankshaft. When a piston is forced to stop but heat is added, the system becomes isometric and non-isobaric. A fixed volume forces the piston to build up in pressure since the piston can't achieve boundary work (the single integral of the area under the PV curve at the vapor dome for working fluids), causing a vertical line up in the PV curve. The Camshafts, as stated before, are designed using differential equations. The connecting rods have to be designed using Engine Dynamics. The next question comes to be, how do you get this piston to return to its original location? Answer: you reject heat out of the system, so you open the exhaust valves and release the exhaust into the exhaust manifold. Thus, the piston is free to continue in its cycle. Your car probably accomplished all that in about 1/50th of a second of time. And it does it again. F1 cars can do this at over 300 times a second when almost red-lining the RPMs.

    BDC and TDC refer to Bottom Dead Center and Top Dead Center, and compression ratio is a volume-dependent ratio, not a pressure ratio. The combustion chamber is at maximum volume at Bottom dead center and least volume at top dead center. Hot Rodders will sometimes play with the compression ratio by "shaving the heads" which makes TDC volume smaller. The piston bottoms out at bottom dead center. The Carnot efficiency of an engine is a maximum theoretical ideal efficiency of any given engine. The idea is to approach this efficiency as well as possible in reality, but it is physically impossible to achieve it no matter how advanced engine technology becomes because there will always be a hardware limitation of the engine that can NEVER reach the theoretical Carnot maximum efficiency. A perpetual motion machine isn't theoretically possible since it would be 100% efficient, and the carnot efficiency which is always under 100% can't even be achieved only approached. So, as engines advance, you could say that engines will approach carnot efficiency in the style of a Limit. Engineers can approach it, but the laws of physics prevent it from ever being achieved. Every heat engine and cycle is limited by a maximum Carnot efficiency.

    EGR is knwon as Exhaust Gas Recirculation, which recirculates exhaust gases to lower combustion temperature and therefore reduces NOx emmisions (Nitrogen Oxide).

    The ideal spark-ignition cycle is the Otto cycle, and the diesel cycle is seperate, with a lack of a spark plug, but with a glo plug to start off the engine

    Engine knock can result from premature ignition in at least one cylinder in engines. This can cause pre-mature wear of the engine when it knocks.

    Solid Mechanics is used to design automotive structures such as chassis and unibody monocoques. There is a requirement for a car's body structure to hold up during loads, and certain parts, known as crumple zones, must deform in a controlled manner in order to absorb energy and slow down the rate of deceleration. Strain gauges can measure this, and a 3-gage strain rossette is the only current method for measuring shear strain, since no other method is capable of experimentally measuring shear strain. Strain on a structure is a dimensionless measure of deformation per unit length of a deformable body, but expressed as a unit over the same unit, often denoted in epsilon or micro-epsilon. Thermal strain is a type of normal strain and therefore thermal strain can be set equal to normal strain to solve for a  variable ((delta/Initial length)=(alpha*change in temperature)). In many cases, loaded systems can be solved using statics, and force and moment summations. However, in certain systems of standard and torsional loads, too many unknowns exist, and it becomes indeterminate. This now involves using Hooke's law, sigma=E(epsilon), which forms delta=FL/AE. For a temperature induced variation as well, it becomes delta=(FL/AE+(change in temp(coefficient of thermal expansion)(initial Length)). Now, the system is solvable. In torsional loading, angle of twist rho=TL/JG. J is the polar moment of inertia. When steel reaches what is known as the "yield point" in solid mechanics, it reaches a point where permenant deformation has occured.

The Lockheed Martin "Skunkworks" SR-71 Blackbird, debut in 1964, was a highly advanced jet capable of over Mach 3. To keep the fuselage from failing due to air friction, the jet was built out of a Carbon-Titanium composite body, and was currogated to allow massive expansion and contraction.

In materials science and engineering, atomic structure is critical in correctly selecting optimal materials for your engineering applications. Metallic bonding is a type of bonding in which the valence electrons form a "Sea of electrons", and this makes intuitive sense as to why metal alloys such as aluminum alloys or carbon steel is ductile. The electron sea allows large amounts of plastic deformation to occur. As an example, one reason aluminum is optimal for automotive shell structures is because not only is it light weight, making it ideal, but its ductility due to its metallically bonded atomic structure makes it ideal for energy absorbtion in car impacts. The valence electrons are not in fixed locations, and are non-directional in nature. Essentially, metallically bonded materials have de-localized bonds. Many polymers deform quite easily since the atomic makeup does a poor job resisting shear forces applied to the atomic structure, along the axis. Polymers are made up of primary covalent bonds which are linked by secondary bonds, known as Van Der

Waals Bonds. Secondary bonding is vastly weaker than primary bonds. As a result, one can see that polymers require a low heat to dislocate the van der waals bonds. Modern Toyotas have had issues with melting dashboards since the polymer was engineered poorly as the secondary bonds were too weak for the environment the car will be subjected to.  Bonding energy is directly proportional to melting temperature. This is intuitive and reasonable, since heat, or high temperature, is a measure of high energy. Then, it makes sense that a material with very strong bonds will require immense heats in order to melt the material, which requires the bonding in the solid state to break apart, or dislocate. Looking at an energy well, a steep curve with a large trough represents high bond energy, which will require a large energy to bring to the X axis, allowing for the dislocation of valence electrons, essentially melting the material. Elastic Modulus is dependent on interatomic bonding properties, not microstructure. Resultantly, treatment of metals and cold working will not change elastic modulus, which is the slope of the linear initial stress strain line. In fact, quantum mechanics even plays a role in materials engineering. The "Wave Particle Duality", which was discovered via the double-slit experiment, is a very strange phenomenon in which electrons may behave as particles or waves, and oddly, the act of observation may play a role in the outcome. According to a friend, the nuclear forces from the observational system influences the behavior of the electrons.

The venturi ground effect in a Formula 1 car

Volume of a Dodge "Hemi" cylinder head using multivariable calculus

Computational Fluid Dynamics software utylizes vector calculus and partial differential equations.

SOHC Overhead Valve engine

Laplace Transforms in Differential Equations-used for Engine Management, NVH engineering, and cruise control, and aircraft autopilot

The “Fourier Series” Transformation accompanies the Ordinary Differential Equation “Laplace Transforms” as the foundation of the theorizing operators of modern Automotive and Aircraft Control Systems Logic and NVH reduction.

Theoretically Impossible based on the current limits of engineering physics in the 1980s, Toyota’s 1989 UCF10 Generation-1 Lexus LS400 is a benchmark of Industry, even today. It revolutionized the entire automotive industry. One of the only cars in history with an engine certified for aircraft use due to its tolerances and aerospace level build standards. The reason the car was “Theoretically physically impossible” is that it had to be more structurally sound, more isolated, stronger, yet more fuel efficient, and somehow still faster accelerating to a faster top speed than literally any other luxury car in the world. The only way Lexus accomplished it was through

a Data Acquisition and NVH dampening system second-to-none. It is still more advanced than most modern cars. In fact, the 2015 Jeep Grand Cherokee’s “Quadralift Air-Ride Suspension” is actually taken from the 1989 Lexus LS400’s optional computer-adjusted air ride pneumatic suspension developed in the 1980s. It even self-lowered, the same way a modern Bugatti Veyron does. It’s NVH is regarded as one of the best in the world, and a champagne glass can be placed on the engine valve cover at 4500 rpm and barely be disrupted. The “Anti-aging covenant” utilized a factor of 8X chromium rust protectant coating than the industry average, as well as an interior made to far outlast all competitors. Additionally, the windows are specially doped to reflect UV in a very advanced way from standard tinting. Lastly, the car was specified to last 50,000 miles with literally no precievable wear under normal use to the human perception.

Toyota used all techniques and standards to develop the 1992 “Generation-3” Toyota Camry SXV10, using the same standard double Wishbone, independent MacPherson strut suspension. The Sports Edition shown above has an entirely custom tuned Engine and Transmission Computing system for higher performance and better driving dynamics from standard models. It is regarded as the Benchmark of the midsize segment. It is infact, the only model year of Camry ever built to Lexus Standards and Tolerances. People often refer to this car as the “Nokia of Cars”.

Both cars have high-tensile sheet steel which is alloyed or “atomically doped” with Nickel-Carbide which fights rust from starting and growing.

A U.S. law came within literally mere hours of going into effect that would cause all Lexus-grade models to have a sales tax in the United States set at 100%, making the LS400 a 100,000 dollar car in 1990, which would likely have destroyed Lexus’ chances in America. Fortunately, Toyota reached an agreement and the US Government called it off.

The 1992 Toyota Camry was detrimental mainly to Ford Motor Company, and caused the Taurus to temporarily be discontinued until Ford moved it out of the midsize segment. It even led to the 2008 Bailout of Ford after the Taurus was killed off in a “500” body shell. The entire metropolis of Detroit was largely ruined economically by Lexus and Toyota from the early 1990s. At one time, Ford possessed a whopping 30 1992 Camry sedans and about 12 Lexuses. I am not sure what happened to them all.

The “Nissan R33 Skyline GTR” is one of the world’s most advanced automobiles. It’s illegal until 25 years of age to import to the United States in order to protect the American economy. The Car’s ECU system can literally display it’s physics using a series of real-time scatter plots and graphs on a display screen to the driver. It is often coined “The Sega Dreamcast Car”

The Next-Generation “Nissan R34 Skyline GTR” is also illegal to import into the United States until it reaches 25 years of age.

5 Valves per cylinder. (Honda Vtec)

Dual Overhead Cams

The automatic transmission torque converter. An Automatic Transmission has about 700-800 individual components. A dedicated computer system can interpolate massive data tables about 8 million times a second, and can use mechatronic hydraulic actuators known as “Solenoids”. When these solenoids activate, they channel hydraulic transmission fluid through an incredibly complex

system of chambers, which spins up a turbine inside the torque converter. This allows the crankshaft not to stall when the car stops.

The exhaust catalytic converter makes modern cars incredibly clean burning

Direct fuel injection into combustion chamber, allows fuel to burn much more completley than old carb engines. This is a Dual overhead cam setup with 4 valves per cylinder.

The modern Automatic Transmission Cutaway, which operates on its own computer control system

A carburetor. Almost all modern cars are fuel injected. Carbs feature a venturi in order to move the air/fuel mixture via a pressure difference based on Bernoulli's theorem.

Vintage automobiles relied on the concept of a partial vacuum creating a pressure differential known as the “Venturi Effect”. Relying upon Burnoulli’s theorems, Carburetors used this technique to blend air and fuel, which caused problems including icing up on cold days and efficiency loss as well as poor emissions. The advent of fuel injection revolutionized the modern automotive industry as we are familiar with today.

Borrowing from Avian Birds and Bats, the Bernoulli concept simply states that, when the two airstreams split at the front wing tip, the same “Air sample differential” must meet up again and match on the trailing edge. Resultantly, the top surface, being more curved, forces air to move faster to compensate a larger distance, and therefore, a partial vacuum is created. Given that the higher velocity decreases pressure, the high pressure vacuum below forces a Net effect of Lifting Force.

In an automobile, the concept is simply inverted. This Front Engine, Front Wheel Drive Configured Scion TC Drift competition Car uses “Inverted Lift” As a result, the car actually is forced to “Suck into the ground”, which gives the tire better Gripping capability. This means the car is more stable not to lift up or flip, and also can corner at much higher speeds.

Above is a Generation 3 Toyota Camry 4-door Sedan Super Touring race car. The aerodynamic kit, designed by Pikes Peak Hill Climb champion Rhys Millen’s father Rod Millen, but sold as aftermarket by Rhys Millen Racing, is optimized for the car. Like the Scion exhibited prior, being a Front Engine, Front Wheel Drive vehicle, note

the front “Ground effect lip”. Note the diverging side groove. As the car is flowing subsonically, at compressible flow of non-transient, steady state fluid mechanical analysis, the ground effect captures air and forces it to diverge. In effect, it causes a frontal localized air pressure increase and lower velocity. Like a rear diffuser on a Rear Wheel drive race car, the air of the entire front bumper must speed up substantially to equilibriate this pressure, and bring the surroundings into equilibrium. This in effect causes substantial frontal downforce. A small wing in the rear scoops air with a slight inverting wing which balances downforce in the rear to prevent a loose tail.

A rear diffuser and “Underbody Tray” on this Lamborghini Gallardo makes the entire automobile shell essentially an inverted wing.

A “Front Splitter” creates downforce by trapping air which forces the car into the ground.

This competitor vehicle, a BMW 328i sedan, is Front Engine Rear Wheel drive, and therefore it’s frontal aerodynamics require completely different optimization.

The generalized Energy Equation governing fluid mechanics

The official Bernoulli Equation of governing fluid mechanics.

The basic scientific principle of a Rocket Engine

A modern Aircraft “Turbofan”. Behind the frontal fan is what is known as the “Compressor”. Like an automobile engine which “Compresses air from Bottom Dead Center to Top Dead Center”, the axial compressor condenses and densifies air molecules which makes the air more volatile and gives it more energy potential, which now is ready for combustion. Two fuel injectors squirt jet fuel directly into the air stream behind the axial turbine compressor, in which the ignition of air-fuel mixture causes a massive energy release, which provides thrust.

An automobile Internal Combustion Engine Turbocharger is a type of Forced Induction method using a turbine which uses exhaust gas to spin about 200,000 to 300,000 RPM. This crams in more air to the combustion chamber. A small delay is noted at the turbine “Spools” to about 300,000 RPM. Once released, a very distinctive sound is made by the car like a “Hissing air dissipating” sound.

A secondary option of Forced Induction in Automobiles with Internal Combustion engines is “SuperCharging”, inside one can note two helical sweep stile cork screw turbines which cram air into the combustion chambers of the engine.

This is a “TRD” V-6 Supercharger, or “Toyota Racing Development” Supercharger for the Toyota Aurion, a high-performance sister car of the American generation 6 Toyota Camry.

Aluminum-Silicon Eutectic Phase Diagram:

Why Gen 3 Toyota Camry engines last so long

An example of “ECU Mapping”, a type of modern “Open Source Tuning” in which the Automotive Engine Control Computing System, essentially a modern car’s artificial intelligence, is re-programmed and modified. Care must be taken not to blow the

engine or destroy the transmission, such as causing planetary gear sets to literally grind into one another.

These cars have modified ECU Maps and are re-programed. Additionally, the Turbochargers inside are literally so large in diameter, that the only way to work the laws of physics into getting the system to produce enough rotational inertial in order to “spool” the huge turbine up to 200,000-300,000 RPM is for the ECU computer to “Dump fuel” or “sacrifice fuel” into the exhaust stream and ignite it, giving the exhaust stream a surge of chemical energy, allowing the turbine to spool up. That is why the exhaust spit out flames.https://www.youtube.com/watch?v=XNWbZ53_CZo

The Sound of a “Turbo Spool”https://www.youtube.com/watch?v=lCdkFyUE8bA

Custom ECU Mapping Demonstration:https://www.youtube.com/watch?v=nYPt-dLTRd4

The potential of “ECU Mapping/Open Source Tuning” and “Turbocharging” using turbines so large that the car must ignite it’s own exhaust to build up adequate driving inertia to “spool” the turbine literally to about 300,000 RPM.https://www.youtube.com/watch?v=rUggWF40JiMExample #2:https://www.youtube.com/watch?v=GaqgAZuQwE8

The All-New 2015 Ford F-150

The all-new 2015 Ford F-150 Truck and the CCT Diagram of Materials Physics:

The 2015 Ford F-150’s Aluminum chassis and Body panels rely heavily on quenching and hardening treatments to maximize strength and integrity with minimal weight possible.

The “Anti-Knock Sensor” is an ECU connected sensor which helps the car’s “Artificial Mind” figure out if an improper octane of fuel was placed. The engine computer can constantly custom tune the engine on the go and optimize it for different octanes to prevent engine knock.

The above picture exhibits how an automobile delays the “Seperation of the Adverse Pressure Gradient” in the Same manner a Golf Ball achieves with Dimples. However, A dimpled car would be aerodynamically worse because the gradient is not favorable in any car in the world.