Mousetrap Racer Assignment

8/3/2019 Mousetrap Racer Assignment

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Mousetrap Racer AssignmentEngineering Technology 2011

Isobel Arbiter


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Table of Contents

1.0 INTRODUCTION

2.0 INVESTIGATION

WHEEL-AXLE EFFICIENCY 2.1METAL FATIGUE IN SPRINGS2.2MATERIALS TESTING2.3

3.0 IDEATION

MODEL ANALYSIS OPTIMUMSELECTION

4.0 OPTIMUM SELECTION

ORTHOGRAPHIC PROJECTION 4.1

MODEL4.25.0 INVESTIGATION

DEVELOPING THE SPRING CONSTANT ACTUAL VELOCITY 5.1THEORETICAL MAXIMUM VELOCITY5.2PERFORMANCE5.3OTHER MODELS PERFORMANCE5.4FUTURE IMPROVEMENTS5.5


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IntroductionThe primary focus of this paper is to explore the efficiency and limitations of thespring mechanism found in a household mousetrap, and its subsequent effectiveness at powering a model vehicle. In analysing the vehicles efficiency, allfactors must be taken in to consideration, and this paper will individuallyaddress all components of the spring and vehicle functions to provide a completeevaluation of the mechanics of the entire system. Through assessing wheel-axleefficiency, methods to achieve highest velocity, metal fatigue in springs andinnumerable other facets of the operation of a Mouse-Trap Racer, the efficiencyand capability of creating an effective model vehicle powered by a spring, and itsrepresentativeness of common vehicle inefficiencies, will be gaged.


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Investigation

2.1 Wheel-Axle Efficiency of the Mousetrap RacerTable 1: Factors Compromising Wheel-Axle Efficiency

Cause Visual Depiction Effect Castor Angle The Castor controls the

steering of a vehicle, andmust remain in a positiveregion for efficient steeringand straight line driving.When the rear or front of avehicle is elevated over theother the castor angle iscompromised, it results in theaxle becoming angled to one

side of the car, increasingfriction upon the axlebearings and ultimatelydetracting from the efficiencyand safety of the vehicle.

Camber Angle For the highest level of wheelefficiency the Camber anglemust remain at 0 . Whenthere is tilt in either thenegative or positive direction,premature wear upon thetires is caused as theincreased weight upon thepart of the tyre increasesroad friction. Unalignedwheels also diminish thevehicles straight line drivingability, as the wheel with themost positive camber willlead the vehicle, againincreasing axle-bearing

friction.Toe Toe is the angle at which thewheels are positionedinwards or outwards fromthe car. Too great an angle ineither direction willcompromise safety of steering and premature tirewear. For the greatest level of efficiency, toe angle must remain at a 0 angle.

All images from autorepar.about.com


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AnalysisIn modern vehicle design wheel-axle efficiency is one of the key factors inreducing the effects of friction and allowing the car to function at the highest possible standard. The basis of wheel-axle efficiency lies in wheel alignment.Ideally the car axle is to sit at a 90 angle, with both wheels perfectly parallel toeach other. However a number of mechanical factors may influence the integrityof the wheel-axle alignment , as shown in Table 1. The process of wheelalignment is employed by mechanics, to analyse the cause of the vehiclesproblems and repair them. In this process the angles of the camber, toe andcastors are measured, and if found to be extending overly in to positive ornegative regions, are adjusted. This practice is crucial to maintaining theeffective operation of a vehicle.In recent years engineers have developed new ways to overcome the detrimentalforce of friction upon axle bearings, in order to allow vehicles to lose minimalamounts of energy. One of the most innovative

engineering designs is the differential, anapplication of 3 rd century Chinese mechanicaldesign. In a paper by Michigan Institute of Technology alumni Pearlman, the differential isexplained as having two functionalrequirements, these being Distribute powerfrom car transmission shaft to a pair of Left-Right wheels while allowing wheels to rotate at different speeds, (Pearlman , 2011). The needfor the differential is highlighted in Figure 1,displaying the arcs of the wheels when turning,

and thus the need for a mechanical device toallow them to turn at different speeds to achievethe correct arc. Without the utilisation of differentials, the wheels would turn at the same speed resulting in both poor steering ability unsafe driving- andincreased friction on the axle bearings, which in turn decreases from theefficiency of the vehicle.In conclusion there are a number of methods and mechanical applications that engineers employ to increase wheel-axle efficiency. In short wheel-axleefficiency is the result of reducing all causes of friction. Through wheel alignment the uneven pressure, resulting in friction, upon axle casings is reduced, as shownin Table 1, highlighting the varying methods used in wheel alignments.Applications of mechanical systems, such as the differential, allow for the wheelsto move independently of each other and thus decreases wheel-road friction through the skidding that may be caused on a turn where the tyres cannot change speed, wearing down the tract on the tyres and thus having a detrimentaleffect on the cars safety and axle-bearing friction by reducing uneven pressurecaused when the wheels are moving at the same speed. Overall engineers havebeen very successful in reducing wheel- axle friction that reduces the vehiclesefficiency and many of these techniques, in particular wheel alignment, may beapplied to the mousetrap racer, to allow for the most efficiency.


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2.2 Metal Fatigue in springsEncyclopaedia Britannica defines spring steel as a low alloy, medium carbonsteel or high carbon steel with a very high yield strength. The main alloycomponent of the spring steel alloy is silicon, however other materials such asvanadium and chromium may be included to the alloy to achieve certain othermechanical properties. However despite the alloying of steel with certain metalsto produce steel suitable for springs, the spring is still susceptible to forms of fatigue. The Metallurgical Consultancy association defines metal fatigue as, aprogressive localized damage due to fluctuating stresses and strains on thematerial , (http://www.materialsengineer.com/CA-fatigue.htm ). Europeanspring and steel specialisation company, Lesjfors, expands upon this idea,noting A spring fatigue problem starts with the development of a micro fatiguecrack which grows for every pulsation. When the stress in the remainingmaterial reaches the ultimate tensile strength the spring will break ,(http://www.lesjoforsab.com ). To prevent stress raisers and such fatigue avariety of methods are employed to protect the spring against potential failure;these range from alloying steel to achieve different mechanical properties to anarray of external treatments that provide the spring with desired mechanicalproperties.

Initially, as previously noted, steel may be alloyed with a number of otherelements to achieve a certain grade of spring steel, suitable to its chosenapplication. For example, according to St Hildas Technology Resources textbook,Chromium imparts strength and corrosion resistance, to steel alloys which areimportant in maintaining the integrity of the spring so that it may continue toeffectively function and imparts properties that a mild steel alone cannot provide

(St Hildas, Engineering Technology Resources, 2010 , p76). Another commonlyused metal to alloy in a spring is Molybdenum, which is important in preventingcreep, a tendency of metals to deform when withstanding high levels of stressthat occur under the yield strength, which may cause deform in springs,compromising their ability to regain work and resist plastic deformation.

In his work, Failure Prevention of Plant and Machinery, engineer and authorHattengadi writes that, Springs do not require any maintenance as there is nowear or deterioration if they are designed correctly. It is only necessary to seethat there is no corrosion of springs during service, (Hattengadi, 2007, p.141).Therefore to prevent spring fatigue, corrosion preventative methods must beemployed. These range from surface treatments to employment of a sacrificialanode, to protect from environmental factors such as wind or rain- or chemicalcorrosion in certain systems- such as acid wear. In systems where the spring is of high importance, and difficult to perform enduring maintenance on, metalplating may be employed, to provide long term protection from corrosion. Amore inexpensive option to be employed for short-term use is surface painting,which also prevents surface corrosion caused by external elements. In largersystems sacrificial anodes may be employed, which prevent rust on the springitself by being consumed in preference of the spring steel.

There are also a number of surface treatments to impart certain mechanicalproperties unto the spring steel. Heat treatments, such as the processes of
http://www.materialsengineer.com/CA-fatigue.htmhttp://www.materialsengineer.com/CA-fatigue.htmhttp://www.materialsengineer.com/CA-fatigue.htmhttp://www.lesjoforsab.com/http://www.lesjoforsab.com/http://www.lesjoforsab.com/http://www.lesjoforsab.com/http://www.materialsengineer.com/CA-fatigue.htm


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quenching, may improve steels hardness forming martensite. However,generally, these processes are not desirable when working with spring steel, asthe increase in hardness decreases the steels toughness, a property integral to itsfunction, which if decreased would surely lead to premature fatigue. The St Hildas Engineering Technology resource book suggests that tempering mayserve to increase spring steels toughness through, removing internal stressesfrom martensitic structures, (St Hildas Engineering Technology Resources,2010, p236). In the case of steel, an extremely high temperature, of 300 o to adark blue heat is required to produce an effective spring.

However, perhaps the most beneficial treatment to spring still, that will impart the mechanical property of hardness, whilst maintaining the toughness of the material, are surfacetreatments. Carburising is defined as the impregnationof the surface of the material, being ferrous, withsufficient carbon to raise its composition to theeutectoid level. This is achieved through a process of dissociation of carbon monoxide in to carbon dioxideand carbon. As a result of this the surface of thematerial is hence protected from surface imperfectionsthat may lead to stress raisers and cause failure. Shot Peening is another highly effective method to employ

when decreasing steels life cycle, through the process of cold working metal by assaulting the surface through use of an air blast or centrifugal blast wheel system. In a joint paper from the Beijing Aeronautical Company and the Nanjing AeronauticsFactory on the effects of shot peening in decreasing spring fatigue, it is stated,shot -peening can not ably improve the fatigue property of compressive coilsprings of stainless steel, (Baoo, Zhenhuan, Chunlin, Rehnzi, 1990, p.6). Thisclaim is substantiated in Figure 2, which illustrates the increase of compressivestrength in a spring, post shot peening (Naito, Ochi, Takahashi, Suzuki , 1990,

p.522). In light of this it can be seen that there are a variety of methods that may beemployed to reduce metal fatigue in springs, which will impart the appropriate metal

properties unto them, ranging from alloying metals to heat and surface treatments.

Figure 2: Relation between springfatigue limit and residual stress


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2.3 Materials TestingThere are a variety of grades of steel or steel alloys that may be employed forcommercial use, and here the grade of metal most appropriate for application inthis scenario will be found, on the basis of the appropriateness of its mechanicalproperties.

Graph 2: Grades of Steel Stress Strain Diagram

(http://pages.uoregon.edu/ )

Graph 1 displays the respective yield and ultimate tensile strengths of HighCarbon and Mild Carbon Steel. From this graph it can be seen that the yieldstrength of High carbon steel far exceeds that of mild carbon steel, meaning that the material is not subject to plastic deformation at higher stress levels,therefore maintaining its shape. By comparison mild steel has a far greaterplastic deformation limit, however this makes it unsuitable for springapplication. Thus, from graph 1, it can be seen that high carbon steel is the most appropriate grade of steel for spring application, due to its high yield strengthand lack of plastic deformation.

Table 2: Grades of Spring Steels/Metals and Mechanical PropertiesMetal Mechanical Properties

High Carbon Spring Steel Cost Efficient Easily worked High yield strength

Alloy Spring Steel Heat resistance Toughness
http://pages.uoregon.edu/http://pages.uoregon.edu/http://pages.uoregon.edu/http://pages.uoregon.edu/


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Stainless Spring Steel Heat resistance(288 o>Temperature)

Corrosion resistant Copper Base Spring Alloy Poor cost efficiency

Corrosion resistance Conductive Heat resistance

Nickel Base Spring Alloy Heat resistance Corrosion resistant Poor conductivity

In light of this analysis of the grades of spring metals it appears that high carbonsteel will provide the most effective spring for implementation in the mousetrapmechanism. This is due primarily to its cost efficiency, which is appropriate forthe mousetrap whose price generally sits around less than $1. The material alsoimparts high yield strength, ensuring that the spring will not snap under the loadbeing employed in the mousetrap racer system. It is important to note, however,that high carbon spring steel is not corrosion resistant, and therefore if thespring were to be employed long term in such a system where the spring isexposed some form of corrosion resistant coating, (plating, painting) would needto be employed.

Testing of Chosen Steel GradeIn the engineering industry the primary means of materials testing is throughTensile and Compression Testing. Through this process the chosen material issubjected to tensile loading, and the subsequent reactions of the material arerecorded and plotted on a stress -strain diagram such as displayed in Graph 1. It is from such a graph that the mechanical properties of a material can beanalysed. Here analysis will be performed upon the stress-strain diagram of highcarbon steel.

AnalysisFrom Graph 1 it can be deduced that high carbon steel possesses a number of extremely important mechanical properties that make it a suitable material.Primarily the elastic limit of the material is extremely high, as modelled byHookes law, which dictates that the m aterial will withstand loading without

plastic deformation, making it an appropriate spring material. The material alsodisplays high hardness properties, preventing the formation of stress raisersupon the surface, which may cause premature fracture. Conversely, due to theincreased hardness of the material, its toughness is extremely low, meaning that it may fail under cyclic loading or shock loading. Therefore to increase thetoughness of the material an annealing process may be employed to decrease theinternal stresses of the material, making it more appropriate for application. It isin light of this suggestion that it can be asserted that, in conjunction with someform of process to increase the materials toughness, the material, High CarbonSteel, is appropriate for application in the aforementioned scenario.


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3.0 Ideation

Model 1

Strengths Weaknesses Lightweight structure Simple construction Good wheel sizing ratios

Lack of extension arm

Model 2

Strengths Weaknesses Minimal air

resistance/friction Good wheel sizing ratios

Difficult construction Frame may not be able to

support mousetrap force Lack of extension arm


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Model 3

Strengths Weaknesses Extension Arm Simple construction

Heavy frame/Increasedfriction

Poor wheel sizing ratios

AnalysisIn light of the strengths and weaknesses identified in each model, it is apparent that Model 1 is the most appropriate choice of model for the mousetrap racervehicle. However its weakness, lack of extension arm, will need to be rectified inorder for the vehicle to achieve its maximum velocity. The combination of thechosen model and the addition of the extension arm will provide a potentially,highly effective vehicle whose design features will minimise the effects of frictionthrough methods as explored in unit 2.0.


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4.1 Computer Generated Orthographic Projection

S i d e V i e w

I s o

m e t r i c V i e w

T o p V i e

w

B

a s e V i e w


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4.2 Model VisualsTable 3: Images and Corresponding Descriptions of Vehicle

Model DescriptionImage of finished model: differingfrom model chosen in ideationthrough utilisation of extension armand length of body. Additionalstructural supports have been addedto ensure that the body staystogether.

Focus on mousetrap: Mousetrap

mechanism is clearly displayed andthe means of connecting theextension arm to the mousetrap arm,through utilisation of grip-ties.

Focus on rear axle: The rear

mechanism through which the stringpasses on the vehicle is displayed.This provides no mechanicaladvantage, simply secures the stringto the axle.

Pro Desktop generated projection of model: displayed in side view, thefront to rear wheel ratio is displayed,along with an accurate measure of the size of the car body and design of the front wheel.


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Evaluation

Developing the Spring Constant There are two primary methods utilised to acquire the spring constant, bothcentring on the same equation. In this paper the average found through thegraphical method has been used, however the algebraic method proves equallyas efficient.

Method 1 GraphicallyTable 4: Graphical Method of finding Spring Constant

Force (N) Angle ( ) Radian Dcos Fr k 3.92 10 0.1745 0.041 0.161 0.9234.41 12 0.209 0.041 0.181 0.8664.9 20 0.349 0.039 0.191 0.575

5.39 28 0.489 0.037 0.199 0.407

5.88 37 0.646 0.034 0.2 0.316.37 42 0.733 0.031 0.197 0.269Average Spring Constant 0.554

Method 2 AlgebraicallyUsing the force 4.41N

(This method would then be applied to all forces and averaged)

k = 0.554


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5.1 Actual Velocity Table 5: Time vs. Distance trials

Trial Time (seconds) Distance (m)1 1.17 12 1.09 13 1.00 1

Average Time =

m/s

Actual Kinetic Energy Calculation

5.2 Theoretical Maximum Velocity

Theoretical Kinetic Energy

Table 6: Kinetic energy and Velocity ValuesVelocity (m/s) Kinetic

Energy (J)Energy Lost

(%)Efficiency (%)

Actual 0.92 0.04 98.1 13.7

Theoretical 6.71 2.115 0 100

Values for Calculationm= 94g

=0.094kgv = 0.92 m/s

Values forCalculationm = 0.094kgx = k = 0.554M = 18.33g

= 0.01833kgn = 3


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5.3 Analysis of difference between Theoretical Maximum Velocity and Actual Velocity

Speed (actual) 0.92 m/s ; Speed (theoretical) 6.71 m/s ; Energy Lost 98.1%

There are a number of factors that may decrease the mousetrap racers potentialto reach its theoretical maximum velocity. These include design faults in themousetrap, the effects of friction and design faults with the mousetrap body. Theprimary design fault of the traditional mousetrap, here used to provide springenergy to power the mousetrap racer, is the increased friction in the mousetrapspring. Wheel-axle efficiency may also be the cause of some of the vehiclesinefficiency coupled with minimal surface area on the wheels, which caused lack of friction/grip, preventing the vehicle from moving whilst harnessing all of itspotential force.

Mousetrap Design Fault (Friction)In the mousetrap spring system, the primary hindrance to its ability to achieveits maximum efficiency is the high amount of friction caused by metal on metalcontact. Spring steel, used in the traditional snap mouse -trap, has an extremelyhigh coefficient of friction when in contact with another steel, being 0.8. Thisfault, however, may be easily remedied by utilising a form of lubricant in areas of direct metal on metal contact, which will result in a reduced coefficient of friction, to 0.16.

Wheel-Axle inefficiency Due to the nature of the vehicle, proper wheel alignment techniques could not becompletely utilised. Thus it can be asserted that the toe and camber angles mayhave impacted upon the vehicles efficiency. Increased Camber angle in thepositive region increased axle-bearing friction, which prevented the axle fromfreely moving, as well as causing friction between the large rear wheels and carbody. In regards to toe angle, while the increased angle in the negative anglewould have a negligible impact, as there is no steering involved in the movement of the vehicle, it is important to note that this had some effect upon the integrityof the vehicles directional movement.

Lack of Wheel Surface AreaDue to the nature of the wheels selected, which had a depth of 1.1mm, theminimal amount of friction created between the wheel and surface prevented thevehicle from moving forward with surface grip. This caused unnecessary spin onthe wheels, as traction could not be created.


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5.4 Other Model Analysis

Heather Wolbers

Speed 0.87 m/s; Energy lost 88% (approx.)

Wolbers vehicle was the most inefficient of those studied in this paper. This maybe due to design fault, such as poor wheel ratios and increased axle-bearingfriction caused by poor wheel alignment during construction. The poor design of the string dispenser, which could not hold nor dispense string correctly,prevented the vehicle from moving the entire 1m distance. It was anamalgamation of these issues that prevented Wolbers vehicle from achieving itscomplete potential velocity, or even a significant fraction of it. Futureimprovements that may be suggested are lubrication on the bearings, to reducefrictional energy loss and increasing the size of rear wheels, to improve thewheel-sizing ratio of the car, which will, in turn, allow for a mechanicaladvantage in the vehicle. Traction on the rear wheels would also be suggested to

increase, for a better transfer of energy between the vehicle and the road.

Caitlyn Withers

Speed 0.98m/s; Energy lost 85.4% (approx.)Withers vehicle may be considere d inefficient for a number of reasons.Primarily, as the spring snapped back in to position, the front wheel was stoppedby the arm, halting movement. Inefficiency was also caused by the arms inabilityto rotate 180 o, therefore not allowing it to achieve maximum springenergy/kinetic energy from a complete rotation. Improvements may be made bydecreasing traction on the front wheel to reduce frictional resistance and

redesign the rotation arm to prevent interaction between arm and front wheelthat prevents movement.


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Vanina Varnier

Speed 1.16m/s; Energy Lost- 83.4% (approx.)Varniers vehicle was the most efficient of those analysed. This may be attributedto the streamlined shape, reducing air resistance in movement, traction on therear wheels, efficiently distributing energy between surface and vehicle, andextended extension arm with complete rotational ability, increasing springenergy and resulting kinetic energy. Improvements may be made throughdecreasing the weight of the vehicle, through exclusion of cardboard body bracesand plastic axle, which has increased mass as compared to traditional woodenaxles. It must here be noted, however, that due to the laminated surface of theaxle, bearing-axle friction is reduced, and thus it must be considered which asset is most valuable; reduced friction verses reduced mass.

5.5 Future ImprovementsFrom the information gathered in units 2.0 and 5.0 it is clear that the vehicle

constructed is inefficient for a number of reasons. These inefficiencies beingwheel-axle inefficiency, lack of wheel surface area and mousetrap design fault-may be easily remedied to create a vehicle with greater efficiency in the future.As noted in 5.3 the coefficient of friction created by the metal-on-metal contact inthe mousetrap may be decreased through lubrication, which would allow forsmoother movement of the arm and string, resulting in an even force beingapplied to the axle. In regards to the lack of wheel surface area, while the size of the wheel created a mechanical advantage for the vehicle, the lack of tractioncaused spin that prevented movement. Thus, to remedy this inefficiency, wheelsof the same size with rubber traction (as seen on Withers and Varniers vehicles )may prove to reduce spin whilst maintaining the mechanical advantage. Finallythrough a rigorous process of wheel alignment and lubrication of the bearings,the friction caused through the wheel-axle inefficiency would be decreasedsubstantially, allowing the axles greater movement.


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Bibliography

Baoo, Zhenhuan, Chunlin & Rehnzi, (1990) Effect of Shot-Peening on fatiguebehaviour of Compressive coil springs , The Shot Peener library, Beijing

Naito, Ochi, Takahashi & Suzuki (1990 ), Effect Of Shot Peening On The FatigueStrength Of Carburized Steels , The Shot Peener Library, Nippon

Pearlman, A, (2011) Differentials, http://web.mit.edu/2.972/www/reports/differential/differential.html

St Hildas Engineering Technology Resource book (2010)

Spring Fatigue , http://www.lesjoforsab.com, (12/08/11)

Metal Fatigue , http://www.materialsengineer.com/CA-fatigue.htm, (11/08/11)

Wheel-Axle Efficiency , www.autorepair.com , (11/08/11)

Stress/Strain Diagrams , http://pages.uoregon.edu , (21/08/11)
http://web.mit.edu/2.972/www/reports/differential/differential.htmlhttp://web.mit.edu/2.972/www/reports/differential/differential.htmlhttp://www.lesjoforsab.com/http://www.lesjoforsab.com/http://www.materialsengineer.com/CA-fatigue.htmhttp://www.materialsengineer.com/CA-fatigue.htmhttp://www.autorepair.com/http://www.autorepair.com/http://www.autorepair.com/http://pages.uoregon.edu/http://pages.uoregon.edu/http://pages.uoregon.edu/http://pages.uoregon.edu/http://www.autorepair.com/http://www.materialsengineer.com/CA-fatigue.htmhttp://www.lesjoforsab.com/http://web.mit.edu/2.972/www/reports/differential/differential.html

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Mousetrap Racer Assignment