Drag Forces on Cars. Figure 1: Cars of different shapes

Transcription

1 Drag Forces on Cars Figure 1: Cars of different shapes Purpose: To measure the drag force and the drag coefficient on different car models using a wind tunnel and assess the effects of speed and shape of the car. Introduction In this experiment, we will use a wind tunnel to measure the drag force on car models with different shapes and see how the drag force changes with the wind speed. We will then scale our results to estimate the drag force on real cars. The drag force on a car depends on the speed of the car v, the cross sectional area A, and the density of the air ρ: 1 Av 2 Dρ FD = C LLLLLLLLLLLLLLLLL (1) 2 C D is a dimensionless quantity known as the drag coefficient. At low speeds, it is approximately constant, which means the drag force is proportional to v 2. The drag coefficient is affected by the object s features, like the shape, the material, the surface finish etc. The drag coefficient can only be measured experimentally. However, once it is measured, we can use Equation (1) to calculate the drag force at different speeds, or scale the force to find the drag on real cars from a model car. For our wind tunnel, the wind speed is related to the Dwyer manometer height by 1 2 ρ airv = P0 P = ρ 2 where ρ air = 1.20 kg/m 3 and ρ water = kg/m 3 at room temperature. water ghlllllllllllllll (2) 1124 Drag Forces on Cars - 1 Saved: 6/11/12, printed: 6/11/12

2 Name: Partner(s): Desk #: 1124 section: Date: Drag Force on Cars Materials Computer with Logger Pro, force sensor, model cars, wind tunnel. Procedure Part 1: Scaling of the car model Make a sketch of the kind of car shape that you would expect to produce a low drag force. Make a sketch of the kind of car shape that you would expect to produce a high drag force. Make a sketch of the shape of the car model that you are going to measure today Drag Forces on Cars - 2 Saved: 6/11/12, printed: 6/11/12

3 Find on the internet a real world car that is closest to your car model. Give the url of the website that has the dimensions and the picture of the car. What year and make is it? Find the dimensions of the real world car from the internet and measure the dimensions of your model car. Calculate the scaling factors. Length l Width w Height h Cross sectional area (l w) Real-world car Model car Scaling factor (real car/model car) 1124 Drag Forces on Cars - 3 Saved: 6/11/12, printed: 6/11/12

4 Part 2: Measuring the drag force of the model car Put your model car in the wind tunnel by screwing the attachment bolt into the force sensor. Place the force sensor firmly onto the bottom Lego sheet, adding more Lego pieces as necessary to make sure the bottom of the car does not hit the bottom sheet. Double-check that the force sensor is set on the 10N range. With the fan not running, zero the Dwyer manometer. In Logger Pro, zero the force sensor. Then, record the drag force at different air speeds (different h). Collect data at each speed for 5 seconds and take a mean of the drag force reading. The air speed can be calculated from the Dwyer height h using Eq. (2). The drag force of a model car in a wind tunnel Dwyer height h (inches) Air speed v (m/s) Drag force F D (N) Drag Forces on Cars - 4 Saved: 6/11/12, printed: 6/11/12

5 Part 3: Determining the drag coefficient If the drag coefficient C D is constant for different car speeds, a plot of F D vs. v 2 should be a straight line. Create such a plot using Excel to confirm this. Find the slope of the trendline (you may have to convert the unit of F D to mn to show enough digits) and calculate the C D of your model car. Does the plot of F D vs. v 2 appear to be a straight line? Yes No Slope: (Don t forget the units!) R-squared value: Calculate the drag coefficient C D below: The drag force at 100 km/h on the model car should be in the previous table. Calculate the drag force in the real car that your model car represents using the scale factor you got earlier. Show the calculations below and put the result in the table. Record other desk s results too. Calculate the drag force at 100 km/h for the real car: The Drag Coefficient and the Drag Force of Different Cars Make, Model and Year of the Car Drag Force at 100 km/h Drag Coefficient C ( N ) D Model car Real car 1124 Drag Forces on Cars - 5 Saved: 6/11/12, printed: 6/11/12

6 Part 4: Real-world meaning of results Given the C D, we can compare the forces and energy cost of different cars at different speeds. To relate the drag force to energy cost, recall that: The work done by the drag force: W = FDd The work done against the drag force: W = FDd where d is the distance traveled. The latter is the energy cost due to the drag force. To keep things simple, we will assume that the car is moving along a straight, flat highway going at constant speed for 100 km. We can further translate this to fuel cost by assuming the following: The energy density of gasoline = 34.8 MJ/L (Wikipedia Gasoline ) Typical car efficiency in extracting that energy into moving the car = 15% Today s gas price = $1.43/L. First, let s look at the effect of speed. Fill the table below for the real car corresponding to your model. You may want to start with 100 km/h, for which you already calculated the drag force. For other speeds, assuming Eq. (1) is valid and C D is constant (and is the same as your model car). When calculating the fuel needed, remember that the efficiency is only 15%. Effect of speed on fuel cost for traveling 100 km, for car Speed (km/h) Distance (m) Drag Force (N) Work Done against Drag (J) Fuel used due to Drag (L) Cost of Fuel used due to Drag ($) Find on the internet fuel economies for this type of car. What is the average cost of fuel per 100 km? How much of it was spent on the drag force? What is the effect of the speed? 1124 Drag Forces on Cars - 6 Saved: 6/11/12, printed: 6/11/12

7 Next, we will explore the effect of car shapes. Use v = 100 km/h for all the cars. Effect of car shape on fuel cost at 100 km/h speed Type of the Car Drag Coefficient Drag Force (N) Work Done to Overcome Drag (J) Fuel used to Overcome Drag (L) Cost of Fuel to Overcome Drag ($) Consider the drag alone, what shape of the car is most economic? Why are not all cars made in this shape? 1124 Drag Forces on Cars - 7 Saved: 6/11/12, printed: 6/11/12