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# 2008 Formula SAE Detailed Design Document

Formula SAE West, June 17-21, 2008, California Speedway, Fontana, CA. [1]

2008 Formula SAE Rules [2]

By Evan Gorski

## Suspension

### Wheel Anatomy

By Evan Gorski

Source: [3]

#### Bolt pattern

The bolt pattern or bolt circle is the diameter of an imaginary circle formed by the centers of the wheel lugs. Bolt patterns can be 4, 5, 6, or 8 lug holes, however tuner applications are typically 4 or 5 lug. Bolt circles are measured in both inches and millimeters, therefore you may hear a bolt pattern referred to as both (i.e. 5x114.3 mm is also referred to as 5x4.5). A bolt circle of 5x114.3 mm would indicate a 5 lug pattern on a circle with a diameter of 114.3mm.

The diagram is an example of the proper method for measuring bolt patterns.

Source: [4]

#### Center Bore: Hub Centric vs. Lug Centric

The centerbore of a wheel is the size of the machined hole on the back of the wheel that centers the wheel properly on the hub of the car. Centerbores on wheels are typically a standard size by brand or size (measured in inches or mm). Hub sizes vary by vehicle brand and style.

When this hole is machined to exactly match the hub so the wheels are precisely positioned, minimizing the chance of a vibration, it is said that the wheel is “hub centric”.

Some wheels require centering rings that lock into place in the back of the wheel in order to become hub centric and reduce the risk of vibration while driving. This is an acceptable alternative.

If you do not have hub centric wheels (lug centric), they should be torqued correctly while the vehicle is still off of the ground so they center properly. The weight of the vehicle can push the wheel off-center slightly while you're tightening them down if left on the ground.

Source: [5]

#### Offset

The offset of a wheel is the distance from its hub mounting surface to the centerline of the wheel. The offset can be one of three types:

Zero Offset
The hub mounting surface is even with the centerline of the wheel.
Positive
The hub mounting surface is toward the front or wheel side of the wheel. Positive offset wheels are generally found on front wheel drive cars and newer rear drive cars.
Negative
The hub mounting surface is toward the back or brake side of the wheels centerline.

Calculating the Offset of a Wheel

Calculating the offset of a wheel is a fairly easy mathematical equation. First, measure the overall width of the wheel (remember, just because a wheel is 18x7.5, does not mean that the OVERALL width is 7.5”. It means that the measurement from outboard flange to the inboard flange is 7.5” See Fig. 2). Next, divide that width of the wheel by two; this will give you the centerline of the wheel.

Overall width/2 = Centerline

After determining the centerline, measure from the mounting pad to the edge of the inboard flange (if the wheel were laying flat on the ground – face up – your measurement would be from the ground to the mounting pad). This is your back spacing.

:Centerline – Back Spacing = Offset in Inches

Inches x 25.4 = Offset in mm

### Tire Anatomy

By Evan Gorski

Source: [6]

#### Tire Dimensions

When you are considering changing the wheel and tire size on your vehicle, the important thing to remember is that the overall diameter of the tire/wheel combination should be close to the original sizing. To find out the overall diameter of your original tire/wheel combination the first thing you must be able to do is read the tire:

Example:

205/40R13

205 – Section Width in mm (Section Width or Tire Width is the measurement of the tire from sidewall to sidewall)

40 – Section Height/Aspect Ratio (Aspect Ratio is the ratio of the height of the tire’s cross-section to its width. In this example, 40 means that the height is equal to 65% of the tire’s width. This is also sometimes referred to as “Series”.)
R – Construction (The "R" stands for radial, which means that the body ply cords, which are layers of fabric that make up the body of the tire, run radially across the tire from bead to bead. A "B" indicates the tire is of bias construction, meaning that the body ply cords run diagonally across the tire from bead to bead, with the ply layers alternating in direction to reinforce one another. Newer tires also have new sport constructions, such as Z. See your preferred tire manufacturer’s website for details.)
13 – Wheel Diameter (13” diameter)

Sometimes your tire will have a letter in front of this information indicating “P” for passenger car or “LT” for light truck.

Formula for Calculating Tire Dimensions Using the above example once again - 225/40R18

1. 205 mm divided by 25.4 = 8.07” (section width)
2. Multiply 8.07 (section width) by .40 (aspect ratio) = 3.228” (section height)
3. Multiply 3.228 (section height) x 2 then add the rim diameter (13) = 19.4567” which rounds up to 19.5”.
19.5” would be the tire dimension for this particular example.

Source: [7]

#### Contact patch

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

is the term applied to the portion of a vehicle's tire that is in actual contact with the road surface. The shape of a tire's contact patch can have a great effect on the handling of the vehicle to which it is fitted. Specifically, for the type of wide tire fitted to many modern performance cars, a contact patch that is wider than it is long will increase the tendency for the vehicle to 'tramline' or follow uneven road contours. Furthermore in front wheel drive cars, the offset between the centroid of the contact patch and the point about which the wheel steers can lead to a condition known as torque steer.

#### Slip Angle

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

This deflection gives rise to the slip angle, and to the cornering force.

Because the forces exerted on the wheels by the weight of the vehicle are not distributed equally, the slip angles of each tire will be different. (See Load Transfer) The ratios between the slip angles will determine the vehicle's behavior in a given turn. If the ratio of front to rear slip angles is greater than 1:1, the vehicle will tend to understeer, while a ratio of less than 1:1 will produce oversteer. Actual instantaneous slip angles depend on many factors, including the condition of the road surface, but a vehicle's suspension can be designed to promote specific dynamic characteristics. A principal means of adjusting developed slip angles is to alter the relative roll couple (the rate at which weight transfers from the inside to the outside wheel in a turn) front to rear by varying the relative amount of front and rear lateral load transfer. This can be achieved by modifying the height of the Roll centers, or by adjusting roll stiffness, either through suspension changes or the addition of an anti-roll bar.

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

describes the behaviour of tires under load. Conventional pneumatic tires do not behave as classical friction theory would suggest. Friction theory says that the maximum horizontal force developed should be proportional to the vertical load on the tire. In practice, the maximum horizontal force Fy that can be generated is proportional, roughly, to the vertical load Fz raised to the power of somewhere between 0.7 and 0.9, typically.

Production car tires typically develop this maximum lateral force at a slip angle of 6-10 degrees, although this angle increases as the vertical load on the tire increases. Formula 1 car tires may reach a peak sideforce at 3 degrees

Example

As an example, here is data extracted from Milliken and Milliken's "Race Car Vehicle Dynamics",

The same sensitivity is typically seen in the longitudinal forces, and combined lateral and longitudinal slip.

Cornering force is the sideways force produced by a vehicle tyre during cornering. Tyre force is generated by tyre slip. In the case of cornering, tyre force is proportional to slip angle. Slip angle describes the deformation of the tyre contact patch, this deflection of the contact patch deforms tyre in a fashion akin to a spring.

As with deformation of a spring, deformation of the tyre contact patch generates a reaction force in the tyre; the tyre lateral force. Integrating the force generated by every tread element along the contact patch length gives the total tyre force. Although the term, "tread element" is used, the compliance in the tyre then leads to this effect is actually a combination of sidewall deflection and deflection of the rubber within the contact patch. The exact ratio of sidewall compliance to tread compliance is a factor in tyre construction and inflation pressure. The diagram is misleading because the tyre force would appear to be acting in the wrong direction. It is simply a matter of convention to quote positive tyre force as acting in the opposite direction to positive tyre slip so that calculations are simplified, since a vehicle cornering under the influence of a tyre force to the left will generate a tyre slip to the right.

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

#### Weight Transfer

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

In automobiles, weight transfer (often confused with load transfer) refers to the redistribution of weight supported by each tire during acceleration (both longitudinal and lateral). This includes braking, or deceleration (which can be viewed as acceleration at a negative rate). Weight transfer is a crucial concept in understanding vehicle dynamics. Weight transfer occurs as the vehicle's center of gravity (CG) shifts during automotive maneuvers. Acceleration causes the sprung mass to rotate about a geometric axis resulting in relocation of the CG. Front-back weight transfer is proportional to the ratio of the center of gravity height to the vehicle's wheelbase, and side-to-side weight transfer (summed over front and rear) is proportional to the ratio of the center of gravity height to the vehicle's track. Liquids, such as fuel, readily flow within their containers, causing changes in the vehicle's CG. As fuel is consumed, not only does the position of the CG change, but the total weight of the vehicle is also reduced.

By way of example, when a car accelerates, a weight transfer toward the rear wheels is said to occur. An outside observer can witness this as the car visibly leans to the back, or "squats". Conversely, under braking, weight transfer toward the front of the car will occur. Under hard braking it is clearly visible even from inside the car as the nose "dives" toward the ground. Similarly, during changes in direction (lateral acceleration), weight transfer to the outside of the direction of the turn occurs.

Weight transfer causes the available traction at all four wheels to vary as the car brakes, accelerates, or turns. For example, because of the forward weight transfer under braking, the front wheels do most of the braking. This bias to one pair of tires doing more `work' than the other pair results in a net loss of total available traction. The net loss can be attributed to the phenomenon known as tire load sensitivity.

An exception is during positive acceleration when the engine power is driving two or fewer wheels. In this situation where all the tires are not being utilized weight transfer can be advantageous. As such, the most powerful cars are almost never front wheel drive, as the acceleration itself causes the front wheels' traction to decrease. This is why sports cars always have either rear wheel drive or all wheel drive (and in the all wheel drive case, the power tends to be biased toward the rear wheels under normal conditions). If (lateral) weight transfer reaches the tire loading on one end of a vehicle, the inside wheel on that end will lift, causing a change in handling characteristic. If it reaches half the weight of the vehicle it will start to roll over. Some large trucks will roll over before skidding, while passenger vehicles and small trucks usually roll over only when they leave the road. Fitting racing tires to a tall or narrow vehicle and then driving it hard may lead to rollover.

#### Slip ratio

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

When a vehicle is being driven along a road in a straight line its wheels rotate at virtually identical speeds. The vehicle’s body also travels along the road at this same speed. When the driver applies the brakes in order to slow the vehicle, the speed of the wheels becomes slightly slower than the speed of the body, which is travelling along under its own inertia. This difference in speed is expressed as a percentage, and is called ‘slip ratio’. The ideal slip ratio for maximum deceleration is 10 to 30%. Slip ratio is calculated as follows: - Slip Ratio % = [(Vehicle Speed – Wheel Speed)/Vehicle Speed] x 100

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

Scrub radius is the lateral distance measured in front or rear view between the center of the tire contact patch and the intersection of the steering axis with the ground. Scrub radius and kingpin inclination determine the moment arm about the steering axis for longitudinal (braking and acceleration) forces acting at the tire contact patch. When both tires are equally loaded the steering moments due to longitudinal forces on the left and right wheels cancel each other within the steering system and are not transmitted to the steering wheel (driver). If the tires are not equally loaded (e.g., bumps) there is a net torque transmitted to the steering wheel (the car “pulls” to one side). If the scrub radius (moment arm) is zero there is no moment from longitudinal forces and the driver does not feel any “kick back” over bumps.

#### Tire uniformity parameters

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

Axes of measurement

Tire forces are divided into three axes: radial, lateral, and tangential. The radial axis runs from the tire center toward the tread, and is the vertical axis running from the roadway through the tire center toward the vehicle. This axis supports the vehicle’s weight. The lateral axis runs sideways across the tread. This axis is parallel to the tire mounting axle on the vehicle. The tangential axis is the one in the direction of the tire travel.

Insofar as the radial force is the one acting upward to support the vehicle, radial force variation describes the change in this force as the tire rotates under load. As the tire rotates and spring elements with different spring constants enter and exit the contact area, the force will change. Consider a tire supporting a 1,000 load running on a perfectly smooth roadway. It would be typical for the force to vary up and down from this value. A variation between 995 pounds and 1003 pounds would be characterized as an 8 pound radial force variation, or RFV. RFV can be expressed as a peak-to-peak value, which is the maximum minus minimum value, or any harmonic value as described below.

Harmonic analysis

RFV, as well as all other force variation measurements, can be shown as a complex waveform. This waveform can be expressed according to its harmonics by applying Fourier Transform (FT). FT permits one to parameterize various aspects of the tire dynamic behavior. The first harmonic, expressed as RF1H (radial force first harmonic) describes the force variation magnitude that exerts a pulse into the vehicle one time for each rotation. RF2H expresses the magnitude of the radial force that exerts a pulse twice per revolution, and so on. Oftentimes, these harmonics have known causes, and can be used to diagnose production problems. For example, a tire mold installed with 8 bolts may thermally deform as to induce an eighth harmonic, so the presence of a high RF8H would point to a mold bolting problem. RF1H is the primary source of ride disturbances, followed by RF2H. High harmonics are less problematic because the rotating speed of the tire at highway speeds times the harmonic value makes disturbances at such high frequencies that they are damped or overcome by other vehicle dynamic conditions.

Lateral force variation

Insofar as the lateral force is the one acting side-to-side along the tire axle, lateral force variation describes the change in this force as the tire rotates under load. As the tire rotates and spring elements with different spring constants enter and exit the contact area, the lateral force will change. As the tire rotates it may exert a lateral force on the order of 25 pounds, causing steering pull in one direction. It would be typical for the force to vary up and down from this value. A variation between 22 pounds and 26 pounds would be characterized as a 4 pound lateral force variation, or LFV. LFV can be expressed as a peak-to-peak value, which is the maximum minus minimum value, or any harmonic value as described below. Lateral force is signed, such that when mounted on the vehicle, the lateral force may be positive, making the vehicle pull to the left, or negative, pulling to the right.

Tangential force variation

Insofar as the tangential force is the one acting in the direction of travel, tangential force variation describes the change in this force as the tire rotates under load. As the tire rotates and spring elements with different spring constants enter and exit the contact area, the tangential force will change. As the tire rotates it exerts a high traction force to accelerate the vehicle and maintain its speed under constant velocity. Under steady-state conditions it would be typical for the force to vary up and down from this value. This variation would be characterized as TFV. In a constant velocity test condition, TFV would be manifested as a small speed fluctuation occurring every rotation due to the change in rolling radius of the tire. TFV is not measured in production testing.

Conicity

Conicity is a parameter based on lateral force behavior. It is the characteristic that describes the tire’s tendency to roll like a cone. This tendency affects the steering performance of the vehicle. In order to determine Conicity, lateral force must be measured in both clockwise (LFCW) and counterclockwise direction (LFCCW). Conicity is calculated as one-half the difference of the values, keeping in mind that CW and CCW values have opposite signs. Conicity is an important parameter is production testing. In many high-performance cars, tires with equal conicity are mounted on left and right sides of the car in order that their conicity effects will cancel each other and generate a smoother ride performance, with little steering effect. This necessitates the tire maker measuring conicity and sorting tires into groups of like-values.

Plysteer

Plysteer is a parameter based on lateral force behavior. It is the characteristic that is usually described as the tire’s tendency to “crab walk”, or move sideways while maintaining a straight-line orientation. This tendency affects the steering performance of the vehicle. In order to determine Plysteer, lateral force must be measured in both clockwise (LFCW) and counterclockwise direction (LFCCW). Plysteer is calculated as one-half the sum of the values, keeping in mind that CW and CCW values have opposite signs. Plysteer is not measured in production testing.

Radial runout Radial Runout (RRO) describes the deviation of the tire’s roundness from a perfect circle. RRO can be expressed as the peak-to-peak value as well as harmonic values. RRO imparts an excitation into the vehicle in a manner similar to radial force variation. RRO is most often measured near the tire’s centerline, although some tire makers have adopted measurement of RRO at three positions: left shoulder, center, and right shoulder.

Lateral runout Lateral Runout (LRO) describes the deviation of the tire’s sidewall from a perfect plane. LRO can be expressed as the peak-to-peak value as well as harmonic values. LRO imparts an excitation into the vehicle in a manner similar to lateral force variation. LRO is most often measured in the upper sidewall, near the tread shoulder.

Sidewall Shear Displacement the amount the sidewalls are displaced from their at rest center line. In a hard turn, you can notice the sidewall flexing giving some cars the appearance that actual wheel is almost touching the ground. Or you can look at the picture above and notice the rear tire as the front of the vehicle lifts.

Tread Shear Displacement the amount the tread particles are displaced from their at rest center. By examining the picture under “slip,” one can notice that the tread shear displacement is represented by the contact pitch, which is offset.

Total Shear Displacement the combined amount the tread, sidewall/carcass and belt are displaced from their at rest center line.

Tread Shear Angle the angle of tread particle displacement within the contact patch.

Sidewall Shear Angle the angle of sidewall, carcass and belt (radial tire) displacement from their at rest center line.

Total Shear Angle the combined tread and sidewall/carcass angle of shear.

Trailing Edge Slip Percentage the percentage of tread particles that have exceeded their coefficient of friction at the trailing edge of the contact patch in relation to the contact patch’s length.

Tread Shear Angle the angle in which, during tire deformation, the tread particles are moved in the different of the lateral forces.

Tread Particles tread particles do not act independently of each other but rather push and pull one against the next much like the fibers of a cleaning brush. In the case of tire tread depth, a shorter fiber of equal strength will product a higher force for an equal amount of shear.

#### Racing Slicks

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

Since there is no tread pattern, slick tire tread does not deform too much under load. The reduced deformation allows the tire to be constructed of softer compounds without excessive overheating and blistering. The softer rubber gives greater adhesion to the road surface, but it also has a lower treadwear rating; i.e. it wears out much more quickly than the harder rubber tires used for driving on the streets. It is not uncommon for drivers in some autosports to wear out multiple sets of tires during a single day's driving.

Drag racing slicks are typically very large, to deal with the enormous power delivery. For "closed wheel" cars, often the car must be modified merely to account for the size of the slick, raising the body on the rear springs for the height of narrower slicks, and/or replacing the rear wheel housings with very wide "tubs" and narrowing the rear axle to allow room for the wider varieties of tires. Open wheel dragsters are freed from any such constraint, and can go to enormous tire sizes. Some utilize very low pressures to maximize the tread contact area, producing the typical sidewall appearance which leads to their being termed "wrinklewall" slicks. Inner tubes are typically used, to ensure that the air does not suddenly leak catastrophically as the tire deforms under the stress of launching.

"Wrinklewall" slicks are now specifically designed for the special requirements of drag racing, being constructed in such a way as to allow the sidewall to be twisted by the torque applied at launch, softening the initial start and thus reducing the chances of breaking traction. As speed builds, the centrifugal force generated by the tire's rotation "unwraps" the sidewall, returning the stored energy to the car's acceleration. Additionally, it causes the tires to expand radially, increasing their diameter and effectively creating a taller gear ratio, allowing a higher top speed with the same transmission gearing.

### Vehicle Axis System

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

### Race Car Suspension Anatomy

By Evan Gorski

Source:[8]

#### Pushrod and pullrods

These are the diagonal bars between the car's body and the upright (where the suspension arms are attached to the wheels, near the brakes). There is always one for each wheel, but a car does not have pull and push rods at the same time. That would be completely useless, as these arms just do the same, it's only another way to get the same effect. The difference can be found in its name, as the pull rod pulls the rocker, while the push rod pushed it. On the picture we have push rods (when the wheel is pushed up, due to a burb or something, the push rod pushed the rocker up) connecting a rocker in the upper part of the chassis with the lower upright. A pull rod goes the other way, connecting a rocker located low in the chassis, with the upper site of the wheel, almost where the upper suspension arms meet the upright. The advantages of a pull rod lie in the possibility to make the nose lower, assemble most suspension parts lower to the ground and thus lowering the height of the center of gravity.

#### Rockers

These are also known as bell cranks or linkages. This is the lever that translates the push\pull rods motion into the rotary force on the torsion bar and the up\down motion of the damper. the rocker also has mounts for antiroll bars and sensors for wheel travel. The rocker translates the wheel movement onto the dampers with a multiplier. The movements of the damper are thus larger than those of the wheel itself. That means if a wheel moves 1cm, the damper will undergo a movement of about 2 to 3 cm (these are only estimated numbers). It's partially this principle of multiplying the movement onto the damper that causes the enormous stiffness of the suspension.

On this particular drawing you can also notice the torsion bar passing trough the middle of the rockers. The torsion bar is thereby fixed onto the chassis, allowing the rocker to rotate around it. When a wheel pushed the rocker up, it twists and pushed the damper down. As you can also see on the picture, both rockers on each side are connected with each other with an anti-roll bar (roll : see types of weight transfer). Anti-roll bars resist roll by twisting themselves, acting as torsion springs. The anti-roll bar should be handling approximately 50% of the front roll resistance, with the other 50% split between the front springs. To avoid some misunderstandings, a roll bar has nothing whatsoever to do with spring rate. Changing bars can only make the front end stiffer or softer in terms of roll rate and not spring rate.

#### Springs or torsion bars

These are the parts of the suspension that actually absorb the bumps. In simple terms, the softer the suspension on the car, the quicker it will travel through a corner. This has the adverse effect of making the car less sensitive to the drivers input, causing sloppy handling. A harder sprung car will have less mechanical grip through the corner, but the handling will be more sensitive and more direct. Torsion bars operation similarly to springs however their purpose in a race cars suspension are to transfer the spring load from one side of the vehicle to the other. This will sacrifice the bite of the outside tire in a turn by transferring the load back to the the inside tire. This effectively increases the roll stiffness of the vehicle in addition to higher spring rates.

#### Shock absorbers

They do not absorb impacts, but damp the motion of the vehicle. As the name itself says, it particularly acts on the first impact, while the springs work during all the event. If you would have a car with springs, but no or bad shock absorbers, you will keep bumping up and down for a while, and in corners, a wheel might get off the ground a lot easier, because the opposite wheel bends down too much. Shock absorbers are thus tie-down devices for springs which control the springs' oscillation. Oscillation is the up and down movement of a spring, and unless it has a damping device on it, the spring will oscillate infinitely until internal friction in the spring stops its movement. Shock absorbers can be adjusted for "rebound' and "bump".

#### Packers

Also known as bump rubbers can be used to prevent the springs or torsion bars compressing too far. This allows the suspension to be soft, and preserves the car to hit the ground due to the high downforce. These packers should although not come into play in corners, because if the suspension is that soft that it leans on the packers in a corner, no more energy is dissipated into the suspension, which results in decreased grip. They are useful on modern cars to preserve the wooden plank under the car, the rules stating that no more than 1 mm can be worn during the race. (Hence Schumacher's exclusion from Spa 1994) In the typical torsion bar pushrod set up described below the torsion bars pass through the center of the rockers and fix to the front of the chassis. The Rocker pivots on the torsion bar. The push rod pushed the rocker and twists the torsion bar to provide the spring in the suspension, the rocker then compresses the damper and operates the antiroll bar if the car is in roll.

Black - Pushrod
Yellow - Rocker
Dark Yellow - Rocker splined to Torsion bar
Light blue - torsion bar
Red - Spring & Damper

By Evan Gorski

### The Bicycle Model vs. Steady State Pair Analysis

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

The Bicycle model simplifies the vehicle system by analyzing the front and rear tire of one side of the vehicle. While this elementary method allows easy calculation of a single tire force, this negates the effects two tires. Pair analysis models the wheels on a single track or axle. The vehicle performance is determined relative performance of the front and rear vehicle tracks. For example, the yawing moment on the vehicle is simply the difference between the total lateral forces at the front and rear, multiplied by their respective distances from CG. The total tire force is the sum of the lateral track forces. The steering moment is determined by the front track. Yaw response time is controlled by the rear track.

Parameters that change track performance over assumed in the theoretical model:

Static Wheel Loads- These are the results of the gravitational acceleration acting on the mass on the mass of the vehicle. Any change is mass distribution longitudinally or laterally will affect the individual static wheel loads.

#### Longitudinal Weight Transfer

The loads on the front and rear tracks change when steady braking or acceleration forces are applied at the tire/ground contact. These load changes occur because the D’Alembert inertia force acts at the CG which is above ground level; the couple thus induced must be reacted by vertical forces at the tires. Suspension anti-forces tending to lift, dive, or squat the vehicle under acceleration may change the CG height; thus must be considered in an accurate calculation.

#### Lateral Weight Transfer

In a steady turn the lateral tire forces acting at the ground and lateral inertia force produce a rolling moment which is reacting by changes in vertical wheel loads. The total rolling moment is distributed between the front and rear pairs of wheels The distribution is performed in two parts. The first part involves the rolling of the body on the suspension springs about the roll axis of the suspensions. This part (the lateral inertia force times the vertical distance between the CG and the roll axis) is distributed to the front and rear tracks in proportion to the suspension roll stiffness. This is referred to as roll couple distribution. The second part (the lateral inertial force times the distance between the roll axis and the ground) is distributed in inverse proportion to the distance between the CG and the tracks and in direct proportion to the roll center heights at the tracks. Here the details of the suspensions must be taken into account for accurate results. The roll centers may move laterally and vertically in a nonlinear fashion and affect the distribution of the load changes between the wheel pair.

#### Anti-Roll Bars

These are usually in the form of a torsion bar spring which connects the vertical motions of thee left and right wheels. No twist of the torsion bar takes place if the wheels move up and down together (ride,) but in roll the bar is twisted as one wheel moves down and other moves up from the initial position. Twisting of the bar adds load to one wheel and removes it equally from the other. Anti-roll bars change the distribution of the lateral load transfer between the front and rear tracks, and also reduce the body roll angle and add to the one-wheel bump rate of the suspension.

#### Wedge or Diagonal Weight Jacking

This results in a change in the static load on the wheels of an axle (one wheel carries more load the other carries less.) The total load on the axle remains the same unless the CG is moved. A change in left-right load on one track results opposite change in load distribution on the other track. In short, increasing the spring preload (jacking) on the RH front wheel tends to rotate the body about a diagonal axis through the LH front and RH rear wheels.

#### Stagger

This is the difference in diameter between the tires on a track (axle.) It is usually measured as the difference in tire circumference and controlled by tire selection. Depending on the tire design there may or may not be a range of diameters available due to manufacturing tolerances and changes during use. As far as tire loads are concerned, stagger has the same type of effect as diagonal weight jacking Stagger on a drive axle results in direct vehicle yawing moment; this varies with the type of differential used in the axle.

#### Engine Torque Reaction

Unless the final drive unit is mounted on the chassis (independent of deDion type suspension), the engine torque reaction passes into the suspension springs and produces “diagonal” load changes on the wheels.

#### Geometric Steers and Cambers

Because of the suspension and steering system geometry, steer and camber changes can occur as the wheels travel in ride. The various effects are defined separately in terms of body motions:

Ride Toe
Roll Steer
Brake Steer
Acceleration Steer
Ride Camber
Roll Camber
Brake Camber
Acceleration Camber

In addition, steer and camber due to deflections in the suspension and steering system under the application of lateral forces and aligning torques at the wheels:

Lateral Force Compliance Steer
Lateral Force Compliance Camber
Aligning Torque Compliance Steer
Aligning Torque Compliance Camber
Race cars minimized compliances by eliminating rubber bushings in their design.
Structural compliances in the presence of large cornering loads can make a significant change in wheel operating conditions.

#### Longitudinal Slip Ratio

The lateral force capability of a tire is reduced by the application of a driving or braking force. Friction circle effects on driven or braked tires can be taken into account in calculating the lateral track force performance.

#### “g-g” Diagram

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

Source: [9]

A method for characterizing the performance of a driver-vehicle system, including the influence of roadway surface conditions. It quantifies the capability envelope of the vehicle and demonstrates how much of this capability is utilized by the driver. The horizontal axis represents cornering (left and right) and the vertical axis represents acceleration and braking.

### Steady State vs. Transient Analysis

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

Steady State Analysis can determine the vehicle’s constant speed in a constant radius turn, constant deflection environment, assuming the driver is not changing steering inputs mid-turn. Transient analysis takes these factors into account further analyzing the turn entry and recovery. Variables such as yawing and lateral velocity and path curvature are changing with time. To simplify the calculations most transient analyses use the fixed control assumption. This is where the force control from driver’s steering input, steering torque inputs from the car are assumed to be constant to avoid a very complex and irregular problem.

### The Spring Mass Damper System (SMD)

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

The Statics are Fairly straightforward. A mass is applied on the system and it will deflect an amount that determines the spring constants of the components. Since acceleration and velocity are zero in steady steady, the inertial reaction and damping forces are also zero. The Dynamics of the SMD system are far more interesting that its statics. The two important parameters that completely define the dynamics of the system are the undamped natural frequency and damping ratio. The undamped natural frequency is the frequency that a mass will oscillate about the zero reference if it pushed or pulled a distance and released. The damping ratio shows the influence of the damping constant on transient response. A quarter car SMD can be modeled for a quarter car. The car’s sprung mass will be divided into 4 depending on the weight distribution of the vehicle. A 50/50 WD is preferred for neutral handling and ease of calculation. The sprung mass will be all chassis weight independent of the suspension and wheel/hub assembly (unsprung weight). The unsprung weight will be modeled in series with the car’s weight. A spring damper system will connect the two masses and another spring will be used to model the tire’s spring rate before the system is constrained to the ground surface. These springs are in series.

Formula:

$\omega_n \operatorname{=} \sqrt{\frac{g}{\delta}}$

### Ride Frequency Design Constraints

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

To qualify in the design final the vehicle must weigh no more than 450lbs. SAE requires that there is at least 2inch of suspension deflection, 1in jounce / 1in rebound.

### Ideal Vehicle Geometry Summary

By Josh Wang

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

#### King Pin Inclination

The king pin inclination is the angular difference between true vertical and a line drawn through the center of the upper and lower ball joints as viewed from the front of the wheel (as seen in the diagram). The king pin axis is referred to as a line drawn from the upper and lower ball joints similarly to the king pin inclination, however, viewed from the outer face of the wheel and compared to a center line drawn down the wheel face. The king pin inclination contributes to the length of the scrub radius and ultimately the dynamic camber gain/loss due to the offset of the upper control arm when compared to the lower control arm.

The effects of kingpin inclination on handling are as follows. Positive kingpin inclination steers in positive camber on the outside wheel during cornering. This decreases the cornering force generated by the outside tire. Positive kingpin inclination steers in positive camber on the inside wheel during steering. This increases the cornering force generated by the inside tire. However, since the highly loaded outside tire produces most of the cornering force the negative effect on the outside tire is much greater than the positive effect on the inside tire.

#### King Pin Axis

The king pin axis is the angle measured from the upper and lower ball joints as viewed from the side of the vehicle. The king pin axis has much say in the anti-dive characteristics of the vehicle dispersing forward braking motion throughout all the suspension components (control arms, push rods, springs, etc.).

#### Mechanical Trail

Mechanical trail is the longitudinal distance measured in side view between the center of the tire contact patch and the intersection of the steering axis with the ground. Mechanical trail and caster determine the moment arm about the steering axis for lateral (cornering) forces acting at the tire contact patch.

#### Steering axis

The steering axis is the axis that the steering knuckle, wheel, and tire rotate about as the front wheels are steered. The steering axis is defined geometrically as the line connecting the two points at the center of the upper and lower ball joints. Caster and kingpin inclination are the two angles that define the orientation of the steering axis. The angular orientation of the steering axis and the location of the spindle with respect to the steering axis determine the scrub radius and the mechanical trail.

#### Camber

The angle made by the wheel of an automobile; specifically, it is the angle between the vertical axis of the wheel and the vertical axis of the vehicle when viewed from the front or rear. By adding the right amount of negative camber, the vehicle can have better lateral grip as the contact patch is further used under high lateral loads.

#### Caster

Caster angle – the angular displacement from the vertical axis of the suspension of a steered wheel in a car, bicycle or other vehicle, measured in the longitudinal direction (along side the vehicle). Adding caster will send more vibration to the chassis but will add more dynamic camber.

During cornering positive caster produces forces that tend to return the steering to center. Negative caster produces forces that tend to move the steering away from center (unstable). During cornering (steering) positive caster raises the outside wheel and lowers the inside wheel which transfers vertical load from the outside wheel to the inside wheel (dynamic wedge). When the wheels are steered caster also causes increased negative camber on the outside wheel (which increases cornering force) and increased positive camber on the inside wheel (which also increases cornering force).

#### Toe

The symmetric angle that each wheel makes with the longitudinal axis of the vehicle, as a function of static geometry, and kinematic and compliant effects. In most instances, toeing out the front wheels gives the vehicle better turn in. Toeing in does the opposite but makes the vehicle more stable at high speeds in a straight line.

#### Roll Center

The location of the geometric roll center is solely dictated by the suspension geometry. The SAE definition of the force based roll center is "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll." The roll center can be found by initially solving for the left and right instant centers. The instant centers (IC) are found by drawing lines from the upper and lower control arms and locating the intersections. From there, a line must be drawn from the exact center of the contact patch to the opposing side instant center (e.g. left roll center, right tire contact patch). The intersection of these lines is the vehicle’s roll center. Key placement of the roll center in double control arm systems is ground level and directly under the longitudinal centerline. This roll center position is key in reducing the effects of scrubbing and jacking allowing the vehicle to be more stable under lateral loads as well as decreasing the height change of the inner tire during turns.

#### Bump Steer

 It is defined as the tendency of a wheel to steer as it moves upwards into jounce. It is typically measured in degrees per meter or degrees per foot. Bump steer in many stock vehicles is usually noticed by lowering the ride height, changing the suspension geometry. This is mainly due to the tie rod not moving in the same arc motion as the control arm (upper or lower depending on suspension type). The examples below will further explain bump steer.
##### Example #1: Bump Steer Scenario
 The picture displays the FRONT RIGHT section of a typical Formula SAE chassis. As can be seen, there are two A-arms and a stationary steering rack (silver bar) with a tie rod. This will represent the situation of a driver with no steering input (zero degrees of steering angle). The tie rod as well as the A-arms are connected to the upright which hold the wheel hub, brake rotor, caliper, wheel, and tire.

 Initially the vehicle has no toe in or out and is traveling in a straight line. All seems well as the driver holds the wheel steady with no input over the smooth pavement road.

 Suddenly the driver hits a pothole compressing the front suspension. As can be seen, the front tire immediately toes in making the vehicle less predictable and unstable. The steering can also feel a bit light and loose under bump steer. The same issue can occur with hard braking which would compress the front suspension due to forward weight transfer. As seen below, due to the high difference in angle and length of the tie rod, the arc motion is completely off when compared to the upper A-arm. As the upper A-arm loses its lateral (left to right) displacement under jounce, the tie rod gains lateral distance pushing the upright out toeing in the front suspension.

##### Example #2: Scenario without Bump Steer

 As can be seen, the silver stationary steering rack seen in the previous example has been removed with a tie rod placed right on the upper bar of the chassis where the steering rack should be (assuming the designer wanted the tie rod on the upper portion of the upright). A picture of the vehicle prior to a bump or heavy braking can be seen below.

 The tie rod now hides behind the upper A-arm at the front view. It can already been seen that this situation is more advantageous as the arc of tie rod will be more similar to the arc motion of the upper control arm.

 And with load or heavy braking, the wheel still has no toe in or toe out. The driver no longer has the light feeling through the steering wheel over bumps and dips. The vehicle is in turn far more stable and predictable than the bump steer scenario.

#### Ackermann Steering Geometry

Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii. In ideal no slip situations, Ackermann steering would make perfect sense, but with issues such as slip angle and varying tire coefficients (due to temperature, vehicle speed, steering angle, etc), several variations of the Ackermann steering geometry have been used instead. True Ackermann geometry would be a situation as seen by Figure 19.2 (a) where both wheels turn on arcs parallel to one another. As can been seen, the slip angle of the inside wheel is greater than the outside wheel. Parallel Ackermann steering is defined by having the same slip angle on both the inside and outside wheel (Figure 19.2 (b)). Reverse Ackermann is the exact opposite of true Ackermann geometry as the outside wheel is at a higher slip angle than the inside wheel.

Low Lateral Acceleration

At low speeds when the tires have minimal tire shear losses on dry, clean pavement, the true Ackermann steering geometry is beneficial as the tires are in almost a perfect situation of minute slip angle. Parallel or reverse Ackermann in this scenario would push (or under steer) the front of the car away from the desired path. In both situations, the inside tire contributes to this push similarly to a centrifugal force.

High Lateral Acceleration

At high lateral accelerations, true Ackermann becomes disadvantageous as loads on the outside wheel increase and the greater slip angle of the inside tire creates higher tire temperatures and slows down the car due to tire drag. The inside tire has also surpassed the maximum slip angle of grip assuming the outer tire is already at the optimum slip angle. Parallel or reverse setups are more advantageous in this situation as both the inside and outside tires still have lateral grip. Reverse Ackermann steering can even be more beneficial than the parallel Ackermann geometry since the outside tire (which currently has more load due to weight transfer) is at the optimum slip angle and the inside is at a lower slip angle with less grip. This in turn allows the inside tire to have grip but less than the outside tire, decreasing the effects of under steer.

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

##### Ideal Vehicle Dimensions

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

See MAE189 for equations.

The Ackermann steering model assumes an un-banked, constant radius & speed turn simulating FSAE’s 50ft regulation skid pad test. For simplicity, it also includes the following ideal conditions: Front Wheels Turning Only, Negligible Weight Transfer Difference between the Tires, & No Compliance in Chassis or Suspension systems. Therefore, with the following factors involved the Ackermann approximation holds true for ONLY low speed / low lateral acceleration turns for our vehicle. Furthermore the radius of the skid pad turn is 25ft, but it is preferable for the driver to have a vehicle capable of a cornering radius of less than 25ft for small radius turns in other dynamic events in the competition such as the autox and endurance.

Design Constraints

SAE requires that the wheelbase be no less 60”. SAE also requires that the rear track is no less than 75% of the front track. Finally, the track width must be no more than 58” to fit within the transport trailer.

Calculator:

Each parameter was evaluated within its allowable range isolating the other variables with the same values.

Graphed below are the Steering angles of the Inner and Outer wheels and the Minimum Radius Turn for each varying parameter.

EXAMPLE CALCULATION:

### Maximum Lateral Speed on a Skidpad

By Evan Gorski

Source: Milliken, William F. & Douglas L. Race Car Vehicle Dynamics. Warrendale: SAE, 1995.

The car can be analyzed as a point mass for skidpad accelerations. Vehicle parameters affecting ride height and center of gravity can be neglected in order to determine the theoretical maximum acceleration in a constant radius turn. The skidpad will be modeled after the competition regulations (50ft diameter.) Therefore if all lateral forces are transferred from a point mass to the center of the turn the forces will be F=mv^2/r. Theoretically the only element providing this reaction force is tire friction. Since the tire is modeled as a rigid point mass as well the friction coefficient is constant. The frictional forces are therefore equal to the product of the normal force of the point mass and this friction coefficient (F= µN). When these two equations are set equal the mass of the car cancels assuming it “feels” its own weight (no aero), leaving the lateral acceleration v^2/r to equal µg. The speed of the skidpad event is thereby calculated: v=sqrt(rµg).

Contrary to common belief, the lateral forces of a competitive vehicle can exceed 1g. The two factors that can increase this characteristic are tire properties and aerodynamics. Race tires when achieving optimal operational temperature can achieve friction coefficients higher than 1.0 on tarmac. The softness of the tire as this temperature compound allows it to melt easily and seep into the irregularities of the surface creating an adhesion to the surface. Furthermore, if the friction is between previously imbedded rubber in the track’s tarmac (common on a popular driving lines best example is on a skidpad event) then the effective coefficient of friction will rise to the product of the two frictional coefficients. For example, a vehicle with no aero advantage with racing slicks that achieve a frictional coefficient of 1.1 is racing on a turn with its rubber now acting as its ground surface will develop a 1.1*1.1=1.21 frictional coefficient. Theoretically this vehicle can achieve 1.21g’s on the skidpad. The second advantage is aerodynamics. By using advantages in the vehicles aerodynamics, the normal force of the vehicle can exceed the weight of the vehicle. Using Bernoulli’s equation, the vehicle can exhibit more effective down force using the incoming air velocity reflecting off of the exterior vehicle shape as a result increasing the drag coefficient of the vehicle. For example, a Formula car can exhibit exceedingly more than its weight in down force (1.8g) to be able to drive upside down in a tunnel at around 180mph.

## Engine

### Power Cycle 600cc engine

by Evan Gorski

Otto cycle for one cylinder of the Yamaha FZ6 600cc motorcycle engine to estimate the indicated thermal efficiency, indicated mean effect pressure (IMEP), indicated specific fuel consumption (ISFC), and maximum power output.

The specification of the mentioned engine:
total volume: 599cc
total cylinder volume for one cylinder: V=150cc
rpm: 12000
bore: 65.5mm
stroke: 44.5mm
connecting rod: 150mm
swept volume for one cylinder: Vsv=137.5cc
compression ratio: CR=12.2:1
fuel: octane
calorific value: Cfl=43.5 MJ/kg
air to fuel ratio: AFR=14.95
Air is the reference atmospheric conditions:
$P_{at}=1.01325$
$T_{at}=20C$
$p_{at}=P_{at}/RT_{at}=1.205$

For point 1:

$P_1 = P_{at} = 101325 Pa$
$T_1=T_{at}= 20C$
$V_1=150cc$
$m_1=P_1 V_1/RT_1=101325*150*10^{-6}/287*293=1.807*10^{-4}$
$m_{ta}=P_1 V_{sv}/RT_1=101325*137.5*10^{-6}/287*293=1.657*10^{-4}$
$m_{as}=the mass of air supplied to the cylinder$
$m_{derf}= the mass of air must be supplied to the cylinder at standard reference conditions$
Delivery Ratio: $DR=m_{as}/m_{derf}=1$

(because of the air supplied is the standard condition)

$AFR=m_{ta}/m_{tf}$
$m_{tf}= the mass of fuel trapped to the cylinder$
$m_{tf}=m_{ta}/AFR=1.657*10^{-4}/14.95=1.1*10^{-5}$
$Q_23=ncm_tf*cf_l=1*1.1*10^{-5}*44.5*10^6=489.5J$
$Q_{23}= total heat transfer equal to heat energy in fuel$

Process 1-2, Adiabatic and Isentropic Compression:

$P_2=P_1*(V_2/V_1)^{-r}=P_1CR^{r}=101325*12.2^{1.4}=33.401*10^{5} Pa$
$T_2=T_1*(V_2/V_1)^{1-r}=T_1CR^{1-r}=293*12.2^{.4}=796.914 K$
$W_{12}=-m_1C_v*(T_2-T_1)=-1.807*10^{-4}*718*(796.9-293)=-65.377 J$

Process 2-3, Constant Volume Combustion:

$Q_{23}=m_1Cv(T_3-T_2)$
$T_3=T_2+Q_{23}/m_1*C_v=796.9+489.5/(1.807*10^{-4}*718)=4570 K$
$P_3=P_2*V_2/V_3*T_3/T_2=33.401*10^{5}*1*4570/796.9=191.55*10^5 Pa$

Process 3-4, Adiabatic and Isentropic Expansion:

$T_4=T_3(V_4/V_3)^{1-r}= T_3(CR)^{1-r}=1680.24 K$
$P_4=P_3(V_4/V_3)^{-r}= P_3(CR)^{-r}=5.77*10^5 Pa$
$W_{34}=-m_1C_v(T_4-T_3)=-374.925 J$

Process 4-1, To complete the Cycle

$Q_{41}=m_1Cv(T_1-T_4)=1.807*10^{-4}*718*(293-1680)=-180 J$

Net Values:

$W_{net}=W_{12}+W_{34}=-65.4+374.925=309.525 J$
$n_t=W_{net}/Q_{23}=309.5/489.5=0.632$
$IMEP=W_{net}/V_{sv}=309.5/137.5*10^{-6}=22.59*10^5 Pa$
$Power: P=W_{net}*rpm/120=309.5*12000/120=30.95*10^3 W = 41.5hp$
$m_f=m_{tf}*rpm/120=1.1*10^{-5}*12000/120=1.1*10^{-3} kg$
$ISFC=m_f/P=3.55*10^{-8} kg/Ws=.128 kg/kWh$

### Engine Selection

By Evan Gorski

Source:[10] Source:[11] Source:[12] Source:[13] Source:[14] Source:[15]

SAE requires that the power plant is a 4-stroke motor that with no more than a 610cc displacement. With that being said, a popular choice is a 600cc 4 cylinder sport bike motor. The lightweight aluminum blocks, built-in sequential transmissions, and overall high-end horsepower output make these power plants excellent motors for racing applications. An alternative is the 2 or 1 cylinder dirtbike/atv motors that weigh approximately half as much dry than the 4 cylinder sportbike motors, however their light weight sacrifices their high end horsepower capabilities.

### Engine Control Unit (ECU) Selection

By Evan Gorski

Source:[16] Source:[17] Source:[18] Source:[19] Source:[20] Source:[21] Source:[22]

The ECU plays a vital role in the operation of any vehicle. Thorough engine management provides the driver with optimal control over the motor’s performance. While considering weights of the ECU, these factored in very little to overall weight of the vehicle (less than .5%.) However, packaging is a bigger issue. The ECU must be as small as possible to maintain space efficiency within the chassis. Final considerations were to lean out the costs of the overall vehicle, so overall price was compared. The processor speed, the variety of output functions, the ease of installation and variety of tuning parameters were all bases of comparison. Finally, the ECU’s were evaluated by their tuneability of the motor functions. This system requires complete fuel and spark control and extensive mapping control.

By Evan Gorski

Source:

Changua Lin, Jeffrey Saunders, Simon Watkins. The Effect of Changes in Ambient and Coolant Radiator Inlet Temperatures and Coolant Flowrate of Specific Dissipation. Pennsylvania, SAE 2000.
Frank Incropera, David Dewitt, Theordore Bergman, Adrienne Lavine. Fundamentals of Heat and Mass Transfer. New Jersey, John Wiley & Sons 2007.

Typical Automotive Radiators are forced air-cooled cross-flow heat exchangers. At the hot side, the hot coolant is forced to flow downwards through the vertical tubes or from one side of the radiator core to another through the horizontal tubes. At the cold fluid side, atmospheric air is forced to flow across the fined tubes to remove the heat from the coolant. Since the coolant flow is divided into a number of separated tube flows with no cross mixing, the coolant flow is assumed as unmixed flow. Like the coolant flow, the air flow, because of the structure of the louvred fins, is also divided into a larger number of separate flows with no large-scale mixing so that the air flow is also considered as unmixed flow. Consequently, the radiator can be modeled by a cross-flow heat exchanger with both fluids unmixed.

The heat produced by either the engine or a heat bench is transported to the radiator by the coolant. The heat is then transferred to the cooling air from the coolant to the radiator. The coolant and cooling air in the radiator move orthogonally to one another with no mixing.

#### Assumptions:

a. Velocity and temperature at the entrance of the radiator core on both air and coolant sides are uniform.
b. There are no phase changes (condensation or boiling) in all fluid streams.
c. Fluid flow rate is uniformly distributed through the core in each pass on each fluid side. No stratification, flow bypassing, or flow leakages occur in any stream. The flow condition is characterized by the bulk speed at any cross section.
d. The temperature of each fluid is uniform over every flow cross section, so that a single bulk temperature applies to each stream at a given cross section.
e. The heat transfer coefficient between the fluid and tube material is uniform over the inner and outside tube surface for a constant fluid mass flow rate.
f. For the extended fin of the radiator, the surface effectiveness is considered uniform and constant.
g. Heat transfer area is distributed uniformly on each side
h. Both the inner dimension and the outer dimension of the tube are assumed constant.
i. The thermal conductivity of the tube material is constant in the axial direction.
j. No internal source exists for thermal-energy generation.
k. There is no heat loss or gain external to the radiator and no axial heat conduction in the radiator.
l. Thermal conduction parallel to the flow direction of both the wall and the fluids are equal to zero.
m. Properties of the fluids and the wall, such as specific heat, thermal conductivity, density are only dependent on temperature.

#### Solution using the Effectiveness-NTU method:

Maximum Heat Transfer Rate is modeled in the worst case scenario, forced air from the fan only (no vehicle motion.)

$Q_{max}=m_{a}c_{p,a}(T_{c,i}-T_{a,i})=(.278m^{3}/s)( 1.1614kg/m^{3})(1007J/kgK)( 373K-303K)= 22740.86W$

Using a 225mm fan with 588cfm=.278m^3/s
Air Density at 300K ambient using Table A.4=1.1614kg/m^3
Air Specific Heat at 300K ambient using Table A.4=1007J/kgK
Using a average coolant inlet temperature for this motor=100C=373K
Using the ambient air temperature=30C=303K

Heat Transfer Rate in the coolant transport:

$Q=m_{c}c_{p,c}(T_{c,i}-T_{c,o})=(.158kg/s)(4208J/kgK)(373K-343K)=19945.92W$

Using a coolant flow rate of .158kg/s from figure below to find the lowest possible heat :rejection during motor operation.
Coolant flow rates for a typical 600cc sport bike motor:
Coolant Specific Heat at an average operating temperature of 350K for water (SAE regulation) using Table A.4=4208J/kgK
Using a average coolant inlet temperature for this motor=100C=373K
Using a average coolant outlet temperature for this motor=70C=343K

$\epsilon=Q/Q_{max}=.877$

Minimum and Maximum Capacity Rates:

$C_{min}=C_{a}=m_{a}c_{p,a}=324.87W/K$ $C_{max}=C_{c}= m_{c}c_{p,c}=664.83W/K$

Heat Capacity Ratio:

$C_{r}=C_{min}/C_{max}=.4886$

Using the heat capacity ratio and the Radiator Effectiveness above in Fig. 11.14 to find NTU (number of transfer units) for a single-pass, cross flow heat exchanger with both fluids unmixed.

NTU=1

Therefore the Required Cooling Area can be determined: $A=(NTU C_{min})/U=(1)(324.87W/K)/(100Wm^{2}/K)=3.25m^{2}$

Using an overall heat transfer coefficient for water and air: 100Wm^2/K

To determine the core size dimensions we use typical louvred fin dimensions and model them as rectangular fins:

Fin width= 2.5fins/in
Fin Length=25fins/in
Fin Density=62.5fins/in^2
Fin Depth=? (Core Depth)

Fin Width=.4in

$3.25m^{2}=5014.17in^{2}=(.4in)(1.5in)(62.5fins/in^{2})(X in^{2}/fins)$

Using a typical 1.5in thick radiator
Core Area= X=134.53in^2

Therefore an appropriate geometry for this configuration could be 14”x10”x1.5”

#### Solution using a simple convection analysis:

A general rule is that the cooling system must be able to reject one third of the heat produced by the motor.

$Q_{motor}=75hp/3=18642W$

Using a 75hp engine

Therefore the convection equation is:

$Q=18642W=hA(T_{c,i}-T_{a,i})=(100Wm^{2}/K)(A)(373K-303K)$

Using an overall heat transfer coefficient for water and air: 100Wm^2/K
Using a average coolant inlet temperature for this motor=100C=373K
Using the ambient air temperature=30C=303K

$A=2.66m^{2}$

To determine the core size dimensions we use typical louvred fin dimensions and model them as rectangular fins:

Fin width= 2.5fins/in
Fin Length=25fins/in
Fin Density=62.5fins/in^{2}
Fin Depth=? (Core Depth)

Fin Width=.4in

$2.66m^{2}=4129.277in^{2}=(.4in)(1.5in)(62.5fins/in^{2})(X in^{2}/fins)$
Using a typical 1.5in thick radiator

$Core Area= X=110.113in^{2}$

Therefore an appropriate geometry for this configuration could be 14”x8”x1.5”

### Intake Design

By Evan Gorski

Source: 2006-01-3653, A Theoretical and Experimental Study of Resonance in a High Performance Engine Intake System: Part 1. SAE, 2006.

Source:[www.vtmotorsports.com/team.asp]

#### Introduction

Restricting the airflow on an engine is a convenient and therefore common form of regulating engine performance in many forms of motorsport. Formula SAE enforces a 610cc engine displacement coupled with a 20mm diameter intake restrictor for Gasoline fueled engines and 19mm for E-85. This reduces the amount of air that the engine can induce and hence restricts the maximum power capability of these engines to a much safer level. The intake manifold is one of the most important tuning mechanisms for increasing the performance of a fuel-injected engine. A well-designed manifold will improve the volumetric efficiency by up to twenty percent over an un-tuned induction system. The idea of ‘tuning’ the intake manifold means that torque output of an engine is designed to increase at a certain engine speed. The manifold and engine is, thus, ‘tuned’ for a particular engine speed. However, an engine is rarely operated at only one engine speed, especially in racing applications. The intake manifold shall be designed for the best torque response over a range of operating engine speeds.

#### Runners

The distance that the air must travel from the bell mouths inside the plenum to intake valves is known as the “runner length.” This length significantly affects the performance of the engine and determines the engine speed that maximum torque is produced. According to the Helmholtz Resonance Theory, Longer intake runners produce greater pressure pulses that enter the combustion chamber which equates to greater torque. However at higher engine speeds the pressure pulses are lost and the long runners act as restrictors and therefore lose the high-end power relative to short length runners.

#### Plenum:

The volume of the plenum chamber downstream of the intake restrictor is also known to influence the performance of restricted engines. Blair recommends that the plenum is a large as possible, however gains are less apparent beyond a certain volume.

#### Diffuser

The existence of a diffuser after the restrictor is essential as it allows a higher flow rate to be achieved which in turn develops more power from the engine. The longer the diffuser length the less the restrictor obstructs the airflow, reducing the velocity of the air entering the plenum. Therefore the slowly and evenly charging plenum producing more high-end torque from the engine. A shorter diffuser causes the air to ‘jet’ as it enters the plenum through the restrictor. This reduces the power in two ways. First it limits the amount of air able to pass through the restrictor and second the air is not evenly distributed throughout the four cylinders (rather only 2&3.)

#### Mathematical Model

A number of design techniques, such as the organ pipe and Helmholtz resonator theories, do exist to obtain a close approximation model. The designer decided that the Engelman method (1973) of intake design would be implemented. This method utilizes an accurate mathematical model of a multi-cylinder intake manifold to predict the resonant frequencies of the manifold. These frequencies enable the manifold to increase the air flow and air density over a range of engine speeds. Properly tuning the manifold by designing its geometry to certain resonant frequencies results in a supercharging effect. Engelman’s mathematical model is a powerful design tool because it can accurately predict the engine speed at which the most benefit will occur. The model, however, is limited in that it cannot define engine performance or the performance gained by tuning. Engelman establishes his mathematical model of the intake manifold by developing an electrical circuit analogy of the intake system. In the analogy, the inductors and capacitors correspond to runner inductances (defined as the length-to-area ratio) and intake system secondary volumes. Resonant frequencies of the circuit are related to those of the intake system, therefore allowing numerical analysis of the intake system to be conducted by analyzing the electrical circuit. The basic acoustical model of a four-cylinder is shown in Figure 2. This model is analyzed by a mathematical method used for electrical resonant circuits. The electrical analog is shown in Figure 3. Comparisons of the components in the electrical and acoustical models are presented in Table 2. For the variables in acoustical model, VD is the cylinder volumetric displacement, r is the compression ratio, l represents the length of the component, A as the cross-sectional area of the component, and V is the volume of the named component.

Acoustical model of intake manifold:

Electrical analog of intake manifold:

Variables for electrical and acoustical models:

The characteristic equation for the analog circuit is described by

where the variables a, b, L1, and C1 are defined in Table 2. The two solutions for equation (1) are the two resonant frequencies, given by

where f1 is the lower and f2 the higher resonant frequency. Frequency ratios X1 and X2 are defined as the ratios of f1 and f2 to the factor fp, which is determined from a single intake pipe and is given by

The resonant frequencies of the intake system are then functions of these frequency ratios so that

where N1 and N2 are the resonant frequencies and Np is tuning peak of a single cylinder Helmholtz resonator model and defined as

where Np is the rpm at which the tuning peak occurs, Cs is the speed of sound in the pipe in m/sec, and A, L and VD are in centimeters. The constant 642 provides for conversion of units and sets the Helmholtz resonance at 2.1 times piston frequency.

#### Orifice Flow Calculation

By Praveen DeSilva

To determine the flow through an orifice, the following equations can be used:

Where:

V - Velocity in feet per minute (fpm)
C - Orifice Coefficient
K - Constant = 14,786 when P is expressed in In. Hg

21,094 when P is expressed in PSIG
4,005 when P is expressed in In. of Water
(Above constants are based on an air density of 0.075 lbs/ft )

P - Pressure differential across the orifice
Q - Flow rate in cubic feet per minute (CFM)
A - Total orifice area expressed in square feet
VP - Velocity pressure (units are those of pressure)

The Orifice Coefficient (C) depends on the shape of the orifice opening. The following diagram shows several values of common orifice profiles:

### Exhaust Design

By Du Dinh

Source Burns Stainless

#### Exhaust Theory

As the piston approaches top dead center, the spark plug fires igniting a fireball just as the piston rocks over into the power stroke. The piston transfers the energy of the expanding gases to the crankshaft as the exhaust valve starts to open in the last part of the power stroke. The gas pressure is still high (70 to 90 p.s.i.) causing a rapid escape of the gases (blowdown). A pressure wave is generated as the valve continues to open. Gases can flow at an average speed of over 350 ft/sec, but the pressure wave travels at the speed of sound (and is dependent on gas temperature). Expanding exhaust gases rush into the port and down the primary header pipe. At the end of the pipe, the gases and waves converge at the collector. In the collector, the gases expand quickly as the waves propagate into all of the available orifices including the other primary tubes. The gases and some of the wave energy flow into the collector outlet and out the tail pipe.

Based on the above visualization, two basic phenomenon are at work in the exhaust system: gas particle movement and pressure wave activity. The absolute pressure differential between the cylinder and the atmosphere determines gas particle speed. As the gases travel down the pipe and expand, the speed decreases. The pressure waves, on the other hand, base their speed on the speed of sound. While the wave speed also decreases as they travel down the pipe due to gas cooling, the speed will increase again as the wave is reflected back up the pipe towards the cylinder. At all times, the speed of the wave action is much greater than the speed of the gas particles. Waves behave much differently than gas particles when a junction is encountered in the pipe. When two or more pipes come together, as in a collector for example, the waves travel into all of the available pipes - backwards as well as forwards. Waves are also reflected back up the original pipe, but with a negative pressure. The strength of the wave reflection is based on the area change compared to the area of the originating pipe.

This reflecting, negative pulse energy is the basis of wave action tuning. The basic idea is to time the negative wave pulse reflection to coincide with the period of overlap - this low pressure helps to pull in a fresh intake charge as the intake valve is opening and helps to remove the residual exhaust gases before the exhaust valve closes. Typically this phenomenon is controlled by the length of the primary header pipe. Due to the 'critical timing' aspect of this tuning technique, there may be parts of the power curve where more harm than good is done. Gas speed is a double edged sword as well, too much gas speed indicates that that the system may be too restrictive hurting top end power, while too little gas speed tends to make the power curve excessively 'peaky' hurting low end torque. Larger diameter tubes allow the gases to expand; this cools the gases, slowing down both the gases and the waves.

Exhaust system design is a balancing act between all of these complex events and their timing. Even with the best compromise of exhaust pipe diameter and length, the collector outlet sizing can make or break the best design. The bottom line on any exhaust system design is to create the best, most useful power curve. All theory aside, the final judgement is how the engine likes the exhaust tuning on the dyno and on the track.

Various exhaust designs have evolved over the years from theory, but the majority are still being built from 'cut & try' experimenting. Only lately have computer programs like X-design or high end engine simulation programs been able to help in this process. Practical tools like adjustable length primary pipes and our B-TEC and DynoSYS adjustable collectors allow quicker design changes on the dyno or in the car. When considering a header design, the following points need to be considered:

• 1) Header primary pipe diameter (also whether constant size or stepped pipes).
• 2) Primary pipe overall length.
• 3) Collector package including the number of pipes per collector and the outlet sizing.
• 4) Megaphone/tailpipe package.

There are many ideas about header pipe sizing. Usually the primary pipe sizing is related to exhaust valve and port size. Header pipe length is dependent on wave tuning (or lack of it). Typically, longer pipes tune for lower r.p.m. power and the shorter pipes favor high r.p.m. power. The collector package is dependent on the number of cylinders, the engine configuration (V-8, inline 6, etc.), firing order and the basic design objectives (interference or independence). The collector outlet size is determined by primary pipe size and exhaust cam timing.

#### Mean piston speed

The mean piston speed is the average speed of the piston in a reciprocating engine. It is obtained by multiplying the stroke length times two for each revolution of the crankshaft by the rotational speed of the engine, since the piston moves up and down the stroke per revolution.

For example, a piston in Yamaha FZ6 engine which has a stroke of 44.5 mm will have a mean speed at 10500 rpm of

(44.5 / 1000) * 2 * (10500 / 60) = 15.575 m/s = 934.5 m/min.

## Drive Train

By Du Dinh & Alex Yang

### Brake System

#### Friction, Leverage Force, and Hydraulics

Brake systems work on the principle of energy transfer. For an automobile, kinetic energy is taken away through friction, in which the car’s kinetic energy is converted into heat. Now how much friction can be created depends on the material of whatever’s being rubbed together and how much force they are being pushed upon each other. This great force is accomplished through the use of leverage and hydraulic force multiplication.

As you probably have learned from physics, forces can be increased with the use of hydraulic pistons. Note that the relationship between the two forces are F2 = F1xA2/A1 so the bigger the ratios of the cross-sectional area of the two cylinders (i.e. the bigger the difference) the greater the force multiplication.

Another familiar physical phenomenon is the way that a fulcrum gives what’s called leverage. Similarly to the hydraulic example, the two forces on both sides of the fulcrum (or pivot) need to be equal. To find this, statics will tell you that the force on the left, F needs to be balanced by a force J on the right. If you do it right, you should find that J = FxR1/R2 in which R1 is the moment arm on the left and R2 is the moment arm on the right. Friction, as stated above is the force required to slide an object across another object. This force is proportional to the force between the two surfaces and a coefficient that the surfaces exhibit. This friction force is usually labeled µ and it is a material property, broadly describing how rough a surface is. Friction is used in a car’s brake system to transfer the car’s kinetic energy into the car’s brake discs or drums in the form of heat. Keep these three things (friction, leverage, and hydraulic force transfer) in mind as you read further; they are the basis of all brake systems!

### Pedal

Brake pedals are so simple and understandable that they are often forgotten as having any science in them. Besides having to be comfortable, strong, and efficiently designed, a brake pedal serves as the first point in force transfer in the brake system. To be specific, the brake pedal serves as a lever that increases the force that the driver applies with his foot. To calculate the force multiplication, measure the distance between the pivot point of the pedals to the foot pad. Now, find the distance from the pivot to the master cylinder actuator. This will give you the force ratios!

### Master Cylinder

The master cylinder transfers the force from your foot on the pedal to hydraulic motion that travels to the individual pistons of the car’s brakes. “To increase safety, most modern car brake systems are broken into two circuits, with two wheels on each circuit. If a fluid leak occurs in one circuit, only two of the wheels will lose their brakes and your car will still be able to stop when you press the brake pedal. The master cylinder supplies pressure to both circuits of the car. It is a remarkable device that uses two pistons in the same cylinder in a way that makes the cylinder relatively failsafe. The combination valve warns the driver if there is a problem with the brake system, and also does a few more things to make your car safer to drive.”[1]

### Proportioning Valve

“The proportioning valve reduces the pressure to the rear brakes. Regardless of what type of brakes a car has, the rear brakes require less force than the front brakes. The amount of brake force that can be applied to a wheel without locking it depends on the amount of weight on the wheel. More weight means more brake force can be applied. If you have ever slammed on your brakes, you know that an abrupt stop makes your car lean forward. The front gets lower and the back gets higher. This is because a lot of weight is transferred to the front of the car when you stop. Also, most cars have more weight over the front wheels to start with because that is where the engine is located. If equal braking force were applied at all four wheels during a stop, the rear wheels would lock up before the front wheels. The proportioning valve only lets a certain portion of the pressure through to the rear wheels so that the front wheels apply more braking force. If the proportioning valve were set to 70 percent and the brake pressure were 1,000 pounds per square inch (psi) for the front brakes, the rear brakes would get 700 psi.” [1]

### Uprights

Uprights serve a very important purpose on the formula car. In both the front and rear of the car, the uprights contain wheel bearings. They also contain the mounts for the brake calipers, as well as points to connect to the upper and lower control arms. In the front of the car, the uprights connect to the steering rack in order to control the directions in which the wheels spin. In the rear of the car, the control arms connect to a rigid point to control the toe of the rear tires. Below is an image of a rear upright with its assembly components. These uprights are almost always made out of some sort of metal. Magnesium, Chromoly, Aluminum, or Steel are common materials which these uprights are made out of. There are many different processes that are also used to fabricate these uprights. Some uprights are machined with a billet of material, while others contain simply fabricated parts and are welded together. image source

#### Wheel Bearings

Wheel bearings allow an inner radius to spin while maintaing the outer raidus in a static position. In the front of the car, the wheel bearings simply ensure that the wheels spin about a specific axis, while in the rear they are attached to driveshafts with constant velocity joints in order to transfer the power of the motor. There are many different types of bearings, but the most commonly used type is a tapered roller bearing because of its ability to withstand forces that aren't on the rotation axis. Attached below is a picture of the different types of bearings which are used. image source

### Drive Shafts

Drive shafts are cylindrical shafts which are used to transfer rotation about an axis. Usually, these shafts are hollow(but they can be solid!) and are composed of hardened tool steel. Chromoly and other metals can also be used, depending on the loading conditions. On the formula car, the cylindrical shafts contain constant velocity joints in order to allow the rotation to transfer about different axes.

#### Differential

Differentials are a set of mechanical gears that equalize the power transmitted to the left and right wheels. This is essential during cornering, when the outside wheel travels further than the inside wheel. There are many different types of differentials, but the ones which are constantly used on the formula cars is the Torsen-type differential, because it is easily adapted to a sprocket. See the figure below to look at how a torsen diff looks like. image source

#### Constant Velocity (CV) Joint

Constant Velocity joints serve the purpose of transmitting axial loads from one axis to another. Constant Velocity Joints allow a rotating shaft to transmit loads through different angles at constant rotational speed, without a tremendous increase in friction or drivetrain slop. They are commonly found in front wheel drive cars and cars with independent rear suspensions (the formula car).

Parts which form the CV Joint: 1. driveshaft from transmission, 2.steel balls (in this case 6) in a 'cage'. The balls run in grooves in the dome. 3. cage, splined to the driveshaft 4. spherical 'dome' and outer driveshaft, part of the hub of the wheel. source for images and list of parts

### Sprocket

A sprocket is a wheel with teeth that meshes with a chain. It is used on the formula car by setting the proper final drive for the rear differential. These sprockets are typically lightened to reduce the weight as well as the inertia. Sprockets for the formula car can be found on both the output shaft of the transmission as well as on the input of the differential.

By Evan Gorski

Source:[23]

Source:[24]

Source:[25]

## Body

By Praveen Desilva

Source: Landa, Henry Clyde and Douglas Cox Clyde. The Automotive Aerodynamic Handbook. Wichita: F.I.C.O.A, 1991.

Source: Katz, Joseph. Race Car Aerodynamics Designign for Speed. Bentley Publishers, 2005.

Source: Fall 2006 Design Team. 2007 UCI Formula SAE Detail Design. California, UC Irvine 2007.

Source: Harney, Paul. “Race Tech 104: Gurney Flap.” Inside Race Technology. 2000. 08 June 2007 [26]

### Formula SAE

#### Aerodynamics

• Purpose

The aerodynamics of a racing car is an essential part of the cars performance. A racing car body that has a bad aerodynamic profile would greatly reduce the cars top speed and thereby affects the cars acceleration and cornering characteristics. In addition any road going vehicle with a bad aerodynamic profile would consume a lot of fuel since poor aerodynamics lead to greater drag through skin friction and would there by lose its overall efficiency. One of the themes for the 2008 UCI Formula SAE team requires the racing car to be as efficient as possible and thereby consume the least amount of fuel for higher performance. Therefore it is necessary to research into the aerodynamic drag properties associated with automotive designing when designing the body for the 2008 F-SAE racing car.

• Research:

The design of the race car body is governed by its overall features and composition. When designing the body, many F-SAE teams use programs such as SolidWorks or SurfaceWorks to create the contours of the body. Next they used these contours to build the full scale body out of different types of materials. The materials used would depict the ease of designing and redesigning the shape of the body. Materials such as fiberglass can be overlaid and shaped to any contour desired, while materials like steel sheeting are harder to modify once built. The 2006 F-SAE car body was designed by shaping a single high-density foam block into the desired body shape and then using its contours to build a mold which was then used to overlay the fiberglass structure. This method of manufacturing required great skill and many man hours as the foam mold must be hand carved to a great degree of precision. This method of manufacturing the body would greatly reduce the ability to conduct any aerodynamic testing since the contours of the body have not developed through any design software. In comparison, the 2007 F-SAE team designed their body using much more refined method of manufacturing. As shown in Figure 1 the body was designed by first deriving major clearance points from the chassi design using SolidWorks and using these points to develop splines in SurfaceWorks. A surface was then created using these splines and the final design was uploads to AutoCAD, which split the contours into sections and these sections were then printed and traced onto 2 inch thick foam blocks. As seen in Figure 2 the foam blocks were then joined together to create the fiberglass mold used to create the final body design. This method manufacturing allows the designer to upload the SurfaceWorks model into CFD analysis software such as STAR-Works by CD-adapco which allows the user to see flow patterns around the body design and also perform stress analysis on the model. Therefore, it is important to generate a computer model when designing the body in order to ensure proper aerodynamic efficiency of the design.

Figure 1

Figure 2

To have a successful body design, one must start with simple sketches and building up different design concept that encompass the teams goals of creating a lightweight, efficient and high accelerating vehicle. Figures 3 and 5 below show some of the initial design concepts evoked on paper. In order to have good aerodynamic characteristics, the design of the body must have a small frontal area. The smaller the cross sectional profile of the body, the less drag is induced on the body. The following aerodynamic equation shows how the frontal area of a vehicle affects the power required to overcome aerodynamic drag PDa:

Where Da is the drag force, CD is the coefficient of drag, A is the frontal area and V is the velocity of the vehicle. Therefore as the frontal area increases, the power required to overcome aerodynamic forces such as drag also increases. In addition to the frontal area of the design, the body must also play a crucial role in increasing the down force of the car. As seen through professional racing such as Formula 1 and NASCAR racing, greater down force increases the overall stability of the car and also allows the car to take sharper corners by forcing the wheels to stay on the ground. Therefore the use of a rear spoiler or special winglets helps increase the overall performance of the car. The conventional spoiler design requires a high wetted area of airflow in order to affectively increase the down force of a car. In comparison the race inspired Gurney Flap is a more useful method of creating down force as it uses a small wetted area to create significant down force as shown in Figure 4 below. Since many F-SAE cars use a mid engine layout, the Gurney Flap can be used at the rear of the vehicle to increase the down force of the race car.

The composition of the body is also a vital part of creating a successful aerodynamic design. Therefore several materials have been taken into consideration to manufacture the car body. These include both carbon fiber and fiber glass and also steel sheeting. The bulk pricing and material characteristics are shown both Tables 1 below.

Figure 3:

Figure 4:

Figure 5:

Table 1:

#### Materials

Using Composites: A fiber glass body can have a low weight by reducing the number of layers of fiber glass used for the body construction and also by including carbon fiber or fiber glass ribs on the inner body cavity. As seen here on a F1 application, thinning the composite layer greatly reduces the overall weight of the body while holding its overall structural rigidity.

The Formula SAE competition requires students to design a weekend racer; therefore the car must be both efficient and fun to drive. In order to accomplish this, the racing car must produce the most amounts of horsepower and lateral G’s while keeping the fuel consumption to a minimum. Therefore the car must be lightweight and agile, and keeping this weight down is the key in accomplishing all these goals that will make a great weekend racer. Fiber glass is formidable material when it comes to light weight material. It is both strong and lightweight and also allows the construction of complex designs. Several reasons for using fiber glass for body construction include:

• Fibrous composites are more versatile than metals and can be tailored to meet performance needs and complex design requirements.
• Higher specific strength (material strength/density material). Aramide and Carbon Fiber reinforced epoxies have approx. 4 to 6 times higher spec. tensile strength than steel or aluminum.
• Great fatigue endurance especially for aramide and carbon reinforced epoxies, compared with metals.
• Excellent weather/water resistance. Material has almost no corrosion, takes on little water which leads to low maintenance cost especially on the long run.
• Great thermal isolation habits, fire retardancy habits, and high temperature performance.
• Great freedom of shape. Double curved and complex parts can be simple produced.

These are several reasons why high performance racing teams such as F1 and Lemans series cars use composite as the construction material for their complex, aerodynamic bodies.

Composites do have their downside when it comes to overall cost and construction time. Building a body out of fiberglass requires the construction of a mold, which takes weeks of prepping and priming in order to be used. In addition, the amount of material needed leads to a high cost of construction, which leads to an overall expensive car. Therefore, the use of composites is both effective and costly. Thus the best method of using composites is by minimize the overall materials used and by using new methods of creating molds such as using Liquid Urethane Mold Rubber or Silicone Mold Rubber along with clay moldings.

#### Using Sheet Metal:

Sheet metals body construction is widely used in NASCAR Racing, and has proven to be a quick an easy method of making car bodies. This method of construction requires very little preparation and can be easily put together using rivets. Nevertheless, a sheet metal body construction leaves very little room for aerodynamic designing as one faces difficulty creating complex shapes on sheet metal. Such limitations are partly why high performance racers such as F1 cars do not use sheet metal for their body construction.

Sheet metals come in a variety of materials, including aluminum alloys, nickel alloys, carbon alloys and stainless steel alloys. Each has a distinctive density and specific hardness that makes them applicable for various uses. The following chart shows the density of several common alloys:

The use of sheet metals will reduce the overall cost of construction since they are much cheaper both in raw material and manufacturing costs. In addition sheet metals have lower or comparable densities to composites; therefore they would reduce the overall weight of the body. Using sheet metals would hinder the overall aerodynamic design of the car, but would help reduce both the weight and cost of construction.

#### General Aerodynamic Calculations:

Lift Coefficient CL

Drag Coefficient CD

Pressure Coefficient CP

#### Conclusion:

Having seen and compared the two different methods implemented to create both the 06 and 07 body designs, it is clear that using design software to create the body greatly enhances the aerodynamic characteristics of the body. In addition the usage of added aerodynamic features such as the Gurney Flap and also possible spoiler shapes, greatly increase the down force of the car. Using a combination of both carbon fiber and fiber glass would greatly ease the sculpturing of the body and would also increase the durability of the body while keeping the overall weight at a minimal. Thus the body design would abide by the main goals set forth by the 08’ F-SAE team to manufacture a environmentally friendly, fast and efficient racing car.

Many racing enthusiasts know how important engine performance, suspension setup and tire selection is to winning a car race, but many do not realize how important body design and aerodynamics are for winning races. Tires play a significant role in cornering speed, but tires can only provide so much grip on high speed corners. The front and rear wings used in Formula 1 race cars greatly increase the car’s cornering speed. As the lateral forces (force felt when cornering) overcome the frictional forces applied between the road and tire, the car will lose its grip and spin out. Therefore additional downward forces are needed to increase the effectiveness of the tire contact patch and keep the car planted to the track. These downward forces are provided by using the very things that make airplanes take off; wings. By using the same physics that make airplanes take off, racing cars can generate the needed down force by inverting the airplane wing which then instead of moving a body upward, it pushes it down. Therefore, the car body design and its related aerodynamics is an important aspect of producing a high performance racing car.

A high performance race car must be lightweight in order to have exceptional handling qualities. A part of keeping this weight down is by reducing the overall weight of the body and is sub structures. Therefore the designer must choose a material that is both light weight and structurally stable. This leads to two choices of material: either using composite material such as carbon fiber and fiber glass, or using sheet metals made of either aluminum alloy or low carbon steel. The manufacturing processes used for the two types of material are very much different from one another. In order to use composites, one must build a plug and subsequently a mold from it. In comparison, when using sheet metal, one must be experienced at using an English Wheel, which is used to curve the sheet metal into desired shapes. The two manufacturing processes require different skills and have different designing aspects. One can create complicated shapes and body structures using carbon fiber while it is much more difficult to create similar shapes using sheet metal. On the other hand, when used wisely, sheet metal can be much lighter than fiber glass, thereby reducing both the overall weight and build time since sheet metal take less work to construct. The final choice of materials lies in its application, the more complex the body design the better it is to use fiberglass, while the simpler and inexpensive the project is the better it is to use sheet metal. If the project requires both high performance and lightweight construction, then a hybrid of the two materials could be used; fiberglass for complex shaped areas and sheet metal for curved surfaces.