1. C 7.3: Drag Force of a Sign Mounted on a Moving Vehicle Rebecca Currier February 15, 2007 BIEN 301- Individual Project

2. The problem  Pizza delivery sign mounted on car going 40 mph  If the sign is mounted facing bluntly into the wind, how much will that effect the drag force as opposed to putting the sign parallel to the wind?

3. Given  Sign is 1.5 ft by 5 ft (7.5 feet 2 )  Kinematic viscosity of air: 1.61e-4 ft 2 /s  Density of air: 2.34 e-3 slug/ft 3  C D of car is 0.4  A of car is 40 ft 2  Rolling resistance is 40 lbf  Car provides 10 hp / gal gas / hr

4. Required  (a) Drag on sign alone in both orientations  (b) Total drag on car and sign in both orientations  (c) Horsepower required by engine to drive car in both orientations  (d) Fuel efficiency in mi/gal for both orientations

5. Assumptions  Standard temperature and pressure  Airflow around car is turbulent and viscous  Car has no acceleration  One dimensional airflow  When sign faces parallel to wind, identical boundary layers form; when sign faces bluntly into the wind, boundary layer forms on each side of sign

6. Setting it up  A // = 7.5 ft 2, A f = 15 ft 2 (two boundary layers) (7.45 for flat plate in turbulent flow) C D// = 0.004, C Df = 1.19 (Table 7.3 for rectangular flat plate flow, b/h = 5/1.5)

7. Drag forces  F Dfsign = 71.96 lbf  F D//sign = 0.12 lbf (7.62), therefore For drag on sign + car, simply add C D s and Areas together in equation  F Df = 346.52 lbf  F D// = 76.04 lbf

8. Power  P f = 378 hp  P // = 114 hp

9. Fuel efficiency  FE f = 1.1 mi/gal  FE // = 3.5 mi/gal

10. Conclusion  Mounting sign parallel to wind reduces large drag force to almost nothing  Drag force with sign into wind adds a huge force to the car, almost twice as large as the rolling resistance  Even with minimized drag, 10 hp is not enough to power this car efficiently

11. Biomedical Application  This problem illustrates the important effects of orientation on drag.  When placing a catheter into blood flow, an engineer must carefully design both the catheter and the insertion device so that the implanted object is properly orientated to minimize drag.

12. Questions?