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Two steps were done in order to complete the design optimization model. The first thing that needed to be done is to find what the optimal stopping distance must be before we can determine what the shortest spring length should be. This device is only using the rear brake to slow the bike to a stop. As the bike beginsto slow, the weight is transferred to the front tire, therefore the normal forceon the rear tire is reduced, producing less stopping force than. The excel model in figure 2 shows the maximum stopping force and therefore the minimal stopping distance. This force is then extracted from the model and inputted into the optimization model for the minimal spring length. Now knowing the maximum stoppingforce, we can calculate the stopping torque and use the solver to find the minimal spring length as shown in figure 3.Figure2: Optimize to find the Minimal Stopping DistanceFinds the Minimal Allowable Stopping Distance (in Meters) Variables and Constants Constraint Equations vi 5 m/s Rf + Rr - W = 0 0Rf 420.428571 N -Rf(L1) + Rr(L- L1) + f(h) = 0 1E-06Rr 462.471429 N W 882.9 N L 1.5 m Note: Only uses back brake to stop L1 1.1 m f 231.2357145 N u 0.5 h 1.2 m D 4.865165411 m Output Parameteres rw 0.33 m T 76.30778579 Nm ? 14.74292549 rad Energy 1126.147959 J INFO m 90kg a 2.569285717 m/s2 t 1.946066164 s g force 0.261904762 gFigure 3: Minimize to find the Shortest Feasible Spring LengthMin feasible spring lengthInput ParametersConstraint Equationsrw0.33mT-k*xi*ri =0(equation in matlab)T86.75221471NmE - .5 * k * (xf-xi)^2 = 0(equation in xf)?12.96796864radTheta - ((xf-xi) / rave) = 0#NAME?Energy1126.147959JPercent E return100%Variablesc (gear ratio)1.136872389k25000N/mri#NAME?mrf#NAME?mrave#NAME?mxi0.046908859mxf0.347061881m

2.4 Interpretation of ResultsThe solver found that the minimum spring compression length is 0.35 meters, andby using a common rule of total spring length is 1.5 times the compression length the total spring length is 0.52 meters or almost 21 inches. The spring constant was chosen to be in a reasonable range of 25000 N/M, but the spring length seems to converge around the same optimal length as k goes higher. The only activeconstraint that is present is the final radius of the cone. This active constraint is expected because the smaller the final radius is the less the spring willbe compressed and with the number of times the wheels rotate.3 Our Product in the marketplace.3.1 BenchmarkingThere are no other products exactly like the RBS currently in the marketplace. However, there are several products available to consumers which make bicycle tra

nsportation easier. One product is an electric bike which uses pedaling to storeenergy in the batteries of the bicycle, and then to re-use this energy from thebatteries (via an electric motor) to assist when riding a bicycle uphill.1 Another vehicle which uses regenerative braking is a two-wheeled electric scooter which uses the braking system to recharge the batteries. However, this stores energy as electrical rather than mechanical1 http://www.electricvehiclesnw.com/main/regen.htmenergy.2 However, we have come across no product currently on the market for a purely mechanical regenerative braking system (RBS)3.2 Patent SearchOne patent of note was found during our patent search was Patent #4,744,577. This is a patent for a mechanical RBS for a bicycle, using an elastic band as the energy storage device. This appears to be a device that is integrated with the bi

cycle, and not able to be added to any bicycle bought separate from the device.However, it does not appear to be currently marketed, as the patent was established in 1988 and no device of this sort has been seen since.3.3 Maximizing ProfitIn order to determine how well our product will perform in the market, we must reformulate our objective. Our new objective function will be the maximization ofthe profit returned from the sales of the RBS. Our costs will be determined bythe materials and parts we use in the device. We can keep this low by minimizing/maximizing the following variables:MAX(profit) = MAX(revenue cost)

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MIN(spring strength: k)MIN(spring length: x)MIN(cost per spring: Ck)MIN(cone length: L)MAX(difference of cone radii: rf-ri)MAX(angle of cone rotation: ?)MIN(# of parts purchased: N)MIN(cost of parts purchased: Co)MAX(selling price: P)MIN(start-up costs: Cs)MIN(tooling costs: Ct)MAX(# units sold per year: n)Enter these cheats while playing, don't press pause. It is not advised to save your game with cheats enabled. From the following list, pick the type of cheat you are looking for, or just browse through the list and see what catches your eye. Weapons, Health, Armor & Money Police, Stats & Gangs Spawning Objects Vehicles Gameplay Weather & TimeKeep an eye on this GTAForums thread for all the latest cheats.

Weapons, Health, Armor & Money

LXGIWYL = Weapon Set 1, Thug's ToolsPROFESSIONALSKIT = Weapon Set 2, Professional ToolsUZUMYMW = Weapon Set 3, Nutter ToolsHESOYAM = Health, Armor, $250kBAGUVIX = Semi-Infinite HealthCVWKXAM = Infinite OxygenANOSEONGLASS = Adrenaline ModeFULLCLIP = Infinite Ammo, No Reload

Police, Stats & Gangs

TURNUPTHEHEAT = Increase Wanted Level Two StarsTURNDOWNTHEHEAT = Clear Wanted LevelBTCDBCB = FatBUFFMEUP = Max MuscleKVGYZQK = SkinnyAEZAKMI = Never WantedBRINGITON = Six Star Wanted LevelWORSHIPME = Max RespectHELLOLADIES = Max Sex AppealVKYPQCF = Max StaminaPROFESSIONALKILLER = Hitman In All Weapon StatsNATURALTALENT = Max All Vehicle Skill Stats

Spawning Objects

AIWPRTON = Spawn RhinoOLDSPEEDDEMON = Spawn Bloodring BangerJQNTDMH = Spawn RancherVROCKPOKEY = Spawn RacecarVPJTQWV = Spawn RacecarWHERESTHEFUNERAL = Spawn RomeroCELEBRITYSTATUS = Spawn StretchTRUEGRIME = Spawn Trashmaster

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RZHSUEW = Spawn CaddyJUMPJET = Spawn HydraKGGGDKP = Spawn Vortex HovercraftAIYPWZQP = Have ParachuteROCKETMAN = Have JetpackOHDUDE = Spawn HunterFOURWHEELFUN = Spawn QuadAMOMHRER = Spawn Tanker TruckITSALLBULL = Spawn DozerFLYINGTOSTUNT = Spawn Stunt PlaneMONSTERMASH = Spawn Monster

Vehicles

CPKTNWT = Blow Up All CarsWHEELSONLYPLEASE = Invisible carSTICKLIKEGLUE = Perfect HandlingZEIIVG = All green lightsYLTEICZ = Aggressive DriversLLQPFBN = Pink trafficIOWDLAC = Black trafficFLYINGFISH = Boats flyEVERYONEISPOOR = Traffic is Cheap CarsEVERYONEISRICH = Traffic is Fast Cars

CHITTYCHITTYBANGBANG = Cars FlyJCNRUAD = Smash n' BoomSPEEDFREAK = All Cars Have NitroBUBBLECARS = Cars Float Away When HitOUIQDMW = Free Aim While DrivingGHOSTTOWN = Reduced TrafficFVTMNBZ = Traffic is Country VehiclesBMTPWHR = Country Vehicles and Peds, Get Born 2 Truck Outfit

Gameplay

SPEEDITUP = Faster GameplaySLOWITDOWN = Slower Gameplay

AJLOJYQY = Peds Attack Each Other, Get Golf ClubBAGOWPG = Have a bounty on your headFOOOXFT = Everyone is armedGOODBYECRUELWORLD = SuicideBLUESUEDESHOES = Elvis is EverywhereBGLUAWML = Peds Attack You With Weapons, Rocket LauncherLIFESABEACH= Beach PartyONLYHOMIESALLOWED = Gang Members EverywhereBIFBUZZ = Gangs Control the StreetsNINJATOWN = Ninja ThemeBEKKNQV = Slut MagnetCJPHONEHOME = Huge Bunny HopKANGAROO = Mega Jump

STATEOFEMERGENCY = Riot ModeCRAZYTOWN = Funhouse ThemeSJMAHPE = Recruit Anyone (9mm)ROCKETMAYHEM = Recruit Anyone (Rockets)

Weather & Time

PLEASANTLYWARM = Sunny WeatherTOODAMNHOT = Very Sunny WeatherALNSFMZO = Overcast Weather

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AUIFRVQS = Rainy WeatherCFVFGMJ = Foggy WeatherYSOHNUL = Faster ClockNIGHTPROWLER = Always MidnightOFVIAC = Orange Sky 21:00SCOTTISHSUMMER = ThunderstormCWJXUOC = Sandstorm

The following cheats were not implemented: Drive On Water Do Nothing Hookers Pay You

MIN(# workers: w)MIN(salaries: S(wi))MAX(# years in service: Y)