C 7.3: Drag Force of a Sign C 7.3: Drag Force of a Sign Mounted on a Moving VehicleMounted on a Moving Vehicle

Rebecca CurrierRebecca Currier

February 15, 2007February 15, 2007

BIEN 301- Individual ProjectBIEN 301- Individual Project

The problemThe problem

Pizza delivery sign mounted on car going 40 mphPizza delivery sign mounted on car going 40 mph If the sign is mounted facing bluntly into the wind, If the sign is mounted facing bluntly into the wind,

how much will that effect the drag force as how much will that effect the drag force as opposed to putting the sign parallel to the wind?opposed to putting the sign parallel to the wind?

GivenGiven Sign is 1.5 ft by 5 ft (7.5 feetSign is 1.5 ft by 5 ft (7.5 feet22)) Kinematic viscosity of air: 1.61e-4 ftKinematic viscosity of air: 1.61e-4 ft22/s/s Density of air: 2.34 e-3 slug/ftDensity of air: 2.34 e-3 slug/ft33

CCDD of car is 0.4 of car is 0.4 A of car is 40 ftA of car is 40 ft22

Rolling resistance is 40 lbfRolling resistance is 40 lbf Car provides 10 hp / gal gas / hrCar provides 10 hp / gal gas / hr

RequiredRequired

(a) Drag on sign alone in both orientations(a) Drag on sign alone in both orientations (b) Total drag on car and sign in both (b) Total drag on car and sign in both

orientationsorientations (c) Horsepower required by engine to drive (c) Horsepower required by engine to drive

car in both orientationscar in both orientations (d) Fuel efficiency in mi/gal for both (d) Fuel efficiency in mi/gal for both

orientationsorientations

AssumptionsAssumptions

Standard temperature and pressureStandard temperature and pressure Airflow around car is turbulent and viscousAirflow around car is turbulent and viscous Car has no accelerationCar has no acceleration One dimensional airflowOne dimensional airflow When sign faces parallel to wind, identical When sign faces parallel to wind, identical

boundary layers form; when sign faces boundary layers form; when sign faces bluntly into the wind, boundary layer forms bluntly into the wind, boundary layer forms on each side of signon each side of sign

Setting it upSetting it up

AA//// = 7.5 ft = 7.5 ft22, A, Aff = 15 ft = 15 ft22 (two boundary layers) (two boundary layers)

7/17/1

7/1

//

031.0

LVC airDsign

(7.45 for flat plate in turbulent flow)(7.45 for flat plate in turbulent flow)

CCD//D// = 0.004, C = 0.004, CDfDf = 1.19 (Table 7.3 for rectangular flat plate flow, b/h = 5/1.5) = 1.19 (Table 7.3 for rectangular flat plate flow, b/h = 5/1.5)

Drag forcesDrag forces

FFDfsignDfsign = 71.96 lbf = 71.96 lbf

FFD//signD//sign = 0.12 lbf = 0.12 lbf

AV

FC DD 2

2

(7.62), therefore(7.62), therefore

2

2D

D

ACVF

For drag on sign + car, simply add CFor drag on sign + car, simply add CDDs and Areas together in equations and Areas together in equation

FFDfDf = 346.52 lbf = 346.52 lbf

FFD//D// = 76.04 lbf = 76.04 lbf

PowerPower

PPff = 378 hp = 378 hp

PP//// = 114 hp = 114 hp

)(* DfRollRf FFVP

Fuel efficiencyFuel efficiency

FEFEff = 1.1 mi/gal = 1.1 mi/gal

FEFE//// = 3.5 mi/gal = 3.5 mi/gal

f

carf P

VEFE

*

ConclusionConclusion

Mounting sign parallel to wind reduces large Mounting sign parallel to wind reduces large drag force to almost nothingdrag force to almost nothing

Drag force with sign into wind adds a huge Drag force with sign into wind adds a huge force to the car, almost twice as large as the force to the car, almost twice as large as the rolling resistancerolling resistance

Even with minimized drag, 10 hp is not Even with minimized drag, 10 hp is not enough to power this car efficientlyenough to power this car efficiently

Biomedical ApplicationBiomedical Application

This problem illustrates the important effects This problem illustrates the important effects of orientation on drag.of orientation on drag.

When placing a catheter into blood flow, an When placing a catheter into blood flow, an engineer must carefully design both the engineer must carefully design both the catheter and the insertion device so that the catheter and the insertion device so that the implanted object is properly orientated to implanted object is properly orientated to minimize drag.minimize drag.

Questions?Questions?