Transportation: Vehicle Power andPerformanceTheaerodynamicdragforce（气动阻力)actingonavehicleisgiven as the pCp AV/2, where p is the mass density of air(kg/m3),Ais the frontal area (迎风面积)(m2)of the vehicle, Vis the vehicle speed (m/s), and C,is the drag coefficient· The drag coefficientis determined by testing vehicle modelsin a wind tunnel (风洞), and its value (in the range of 0.25-0.5)dependsverymuchon the vehicleshapeand externalsmoothnessThe correspondingpower needed to overcomethe airresistanceis the product of the force times the vehiclevelocityPV3Pair =(C,A2
Transportation: Vehicle Power and Performance • The aerodynamic drag force (气动阻力) acting on a vehicle is given as the ρCD AV2 /2, where ρ is the mass density of air (kg/m3 ), A is the frontal area (迎风面积) (m2 ) of the vehicle, V is the vehicle speed (m/s), and CD is the drag coefficient • The drag coefficient is determined by testing vehicle models in a wind tunnel (风洞), and its value (in the range of 0.25– 0.5) depends very much on the vehicle shape and external smoothness • The corresponding power needed to overcome the air resistance is the product of the force times the vehicle velocity 2 ( ) 3 V Pair CD A =
Transportation: Vehicle Power andPerformanceThe source of rolling resistance lies in the deflection (偏转)of the tirewhereitcomesintocontactwiththeground-Thisdeflectionisnecessarytosupporttheweightofthevehicleandtoprovidea contactareabetween the tireand the road topreventthetireslipping(打滑）alongtheroadsurfaceThedeflectionissuchthat,whenthewheelrotates,theroadsurfaceexertsaretardingtorque（减速力矩)onthewheel,whichmustbeovercomebytheenginedrivesystem,anda correspondingretardingforceonthewheelaxle(轮轴) This force is usually specified as Crmg, and the corresponding power PrllbecomesPrll = CrmgVwheremisthevehicularmass,gistheaccelerationofgravity,VisthevehiclespeedandCisasmall dimensionlessconstantwhosevaluedependsuponthetireconstructionandpressure
Transportation: Vehicle Power and Performance • The source of rolling resistance lies in the deflection (偏转) of the tire where it comes into contact with the ground – This deflection is necessary to support the weight of the vehicle and to provide a contact area between the tire and the road to prevent the tire slipping (打滑) along the road surface – The deflection is such that, when the wheel rotates, the road surface exerts a retarding torque (减速力矩) on the wheel, which must be overcome by the engine drive system, and a corresponding retarding force on the wheel axle ( 轮轴) • This force is usually specified as CRmg, and the corresponding power Proll becomes where m is the vehicular mass, g is the acceleration of gravity, V is the vehicle speed and CR is a small dimensionless constant whose value depends upon the tire construction and pressure Proll = CR mgV
Transportation: Vehicle Power andPerformanceWhen climbing a hill of rise angle , the force of gravity actingon the vehicle, mg, has a component mg sin opposing theforwardmotion(向前运动)ThepowerrequiredtomaintainasteadyclimbrateisPil = mgV sin
Transportation: Vehicle Power and Performance • When climbing a hill of rise angle θ, the force of gravity acting on the vehicle, mg, has a component mg sin θ opposing the forward motion (向前运动) • The power required to maintain a steady climb rate is Phill = mgV sin
Transportation: Vehicle Power andPerformanceTheinstantaneouspower（瞬时功率）requiredtoacceleratethevehicle,Pacc,is simplythetime rate(时间变化率)ofincreaseofvehicularkineticenergy,m(1+e)V/2,ord (m(1+:)V2)= m(1 + )vdV0C2dt (dtwhere e is a small dimensionless constantthat accountsforthe rotationalinertia(转动惯量)of thewheels and drive train(传动系统),and dv/dt is theaccelerationof thevehicleWhen the vehicle decelerates (dv/dT < O) by using the brakesorclosingthethrottle,thenegativepowerofequationdoesnot put power back into the engine, so that Pacc is effectivelyzero during deceleration
Transportation: Vehicle Power and Performance • The instantaneous power (瞬时功率) required to accelerate the vehicle, Pacc, is simply the time rate (时间变化率) of increase of vehicular kinetic energy, m(1 +ε)V 2 /2, or where ε is a small dimensionless constant that accounts for the rotational inertia (转动惯量) of the wheels and drive train (传动系统), and dV/dt is the acceleration of the vehicle • When the vehicle decelerates (dV/dT < 0) by using the brakes or closing the throttle, the negative power of equation does not put power back into the engine, so that Pacc is effectively zero during deceleration dt dV m V m V dt d Pacc (1 ) 2 (1 ) 2 = + + =
Transportation: Vehicle Power andPerformanceThetotalpowerthusbecomesu+pP = Pace + Prol + PwilhilladvA(1+ 8Crg+gsin0=mV12dt? For a given driving cycle, heavy cars will require morepowerful engines and will consume more fuel, more or less inproportion to vehicle mass, than will light vehicles- A very fuel efficient vehicle is necessarily a light oneFor driving at a steady speed, only rolling and aerodynamicresistance must be overcome, the power required being1)PV3Psteady=CrmgV +(C,A)D2
Transportation: Vehicle Power and Performance • The total power thus becomes • For a given driving cycle, heavy cars will require more powerful engines and will consume more fuel, more or less in proportion to vehicle mass, than will light vehicles – A very fuel efficient vehicle is necessarily a light one • For driving at a steady speed, only rolling and aerodynamic resistance must be overcome, the power required being 2 (1 ) sin 3 V C g g C A dt dV mV P P P P P R D acc roll hill air + = + + + = + + + 2 ( ) 3 V Psteady CR mgV CD A = +