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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 tunneland 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 differentshapes 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 carv, the cross sectional areaA, and the density of theair:

)1(2

1 2LLLLLLLLLLLLLLLLLAvCF DD =

CD is a dimensionless quantity known as the drag coefficient. At low speeds, it is approximatelyconstant, which means the drag force is proportional to v

2. The drag coefficient is affected by theobjects features, like the shape, the material, the surface finish etc. The drag coefficient can only bemeasured experimentally. However, once it is measured, we can use Equation (1) to calculate the dragforce 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

)2(2

10

2LLLLLLLLLLLLLLLghPPv waterair ==

where air= 1.20 kg/m3 andwater= 1000. kg/m

3 at room temperature.

1124 Drag Forces on Cars - 1 Saved: 6/11/12, printed: 6/11/12

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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.

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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 theforce sensor firmly onto the bottom Lego sheet, adding more Lego pieces as necessary to make surethe bottom of the car does not hit the bottom sheet. Double-check that the force sensor is set on the 10Nrange.

With the fan not running, zero the Dwyer manometer. In Logger Pro, zero the force sensor. Then, recordthe drag force at different air speeds (different h). Collect data at each speed for 5 seconds and take amean 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 speedv(m/s)

Drag forceFD(N)

0.05

0.1

0.2

0.4

0.7

1.0

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Part 3: Determining the drag coefficient

If the drag coefficient CDis constant for different car speeds, a plot ofFD vs. v2 should be a straight line.

Create such a plot using Excel to confirm this. Find the slope of the trendline (you may have to convertthe unit ofFD to mN to show enough digits) and calculate the CD of your model car.

Does the plot ofFD vs. v

2

appear to be a straight line?

Yes

No

Slope: __________________________ (Dont forget the units!)

R-squared value: __________________

Calculate the drag coefficient CD below:

The drag force at 100 km/h on the model car should be in the previous table. Calculate the drag force inthe real car that your model car represents using the scale factor you got earlier. Show the calculationsbelow and put the result in the table. Record other desks results too.

Calculate the drag force at 100 km/h for the real car:

The Drag Coefficient and the Drag Force of Different Cars

Drag Force at 100 km/h( N )Make, Model and

Year of the CarDrag Coefficient CD

Model car Real car


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Part 4: Real-world meaning of results

Given the CD, we can compare the forces and energy cost of different cars at different speeds. To relatethe drag force to energy cost, recall that:

The work done by the drag force: dFW D=

The work done against the drag force: dFW D=

where dis the distance traveled. The latter is the energy cost due to the drag force. To keep thingssimple, we will assume that the car is moving along a straight, flat highway going at constant speed for100 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%

Todays gas price = $1.43/L.

First, lets 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 andCD is constant (and is the same as your model car). When calculating thefuel 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 Doneagainst Drag

(J)

Fuel used due toDrag(L)

Cost of Fuel useddue to Drag

($)

80

90

100

110

120

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?


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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 theCar

DragCoefficient

Drag Force(N)

Work Done toOvercome Drag

(J)

Fuel used toOvercome Drag

(L)

Cost of Fuel toOvercome Drag

($)

Consider the drag alone, what shape of the car is most economic? Why are not all cars made in thisshape?

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