Week 2 Memo Drag and Lift Coefficients

Evan States, Zacarie Hertel, Eric Robinson

3/6/2013

“I affirm that I have carried out my academic

endeavors with full academic honesty.”

Signed Electronically,

Evan States, Zac Hertel, Eric Robinson

1

TO: Professor Anderson

FROM: Evan States, Zacarie Hertel, Eric Robinson – Students

DATE: March 8, 2013

SUBJECT: Lift and Drag on a Mercedes-Benz CLK Touring Car

Purpose:

This memo reports the results of our experiments to find the coefficients of drag and lift

on a 1:12 scale model Mercedes CLK Touring Car. Our model was mounted on a dynamometer

in the wind tunnel which measured both the drag and lift forces that the acted on the car at wind

speeds ranging from 0 to 42 m/s. The coefficient of drag from our experiments ranged from 2.0

(+/- .169) at a wind speed of 13.0(+/- .387) m/s to .75(+/- .050) at a wind speed of 42.4 (+/- .634)

m/s. The coefficient of lift from our experiments ranged from .414 to .281 with a wind speed of

6.25 m/s and 19.6 m/s respectively. We found that both of these numbers were dependent upon

Reynolds’ number until a certain point, roughly 3.0x105, at which point the data becomes

independent of Reynolds’ number.

Setup:

Drag is the force that acts opposite to the path of the vehicle’s motion, while lift is the

force that acts on a vehicle normal to the road surface that the it on. We analyzed the lift and

drag coefficients of a scaled Mercedes CLK (information on the scaled model is listed in

Appendix 9) at 12 specific wind tunnel motor frequencies on the surface of the vehicle. The

model was pre-mounted to a dynamometer in the wind tunnel and a pressure transducer was

connected to the Pitot probe for wind velocity calculations. Data was taken with a computer data

acquisition system with 3 input channels. The first related to pressure, the second related to lift

force and the third related to drag force.

Summary:

Data from each of the three input channels were measured with a Static Pitot Probe at 12

different motor frequencies, ranging from 10 Hz to 54 Hz; these frequencies represent wind

speeds from 6.25 (+/- .677) m/s to 42.4 (+/- .634) m/s. The data tables for the velocity

calculations are in Appendix 5. These results closely match our results from previous

experiments in the wind tunnel.

The coefficient of lift on the Mercedes CLK ranged from .414 (+/- .196) at a simulated

velocity of 6.25 (+/- .197) m/s to .281(+/- .026) at 19.6 (+/- .391) m/s. The coefficients of drag

range from 2.0 (+/- .169) at a wind speed of 13.0(+/- .387) m/s to .75(+/- .050) at a wind speed of

42.4 (+/- .634) m/s. This data is shown in detail in Appendices 1 and 3, and is explained

2

extensively in Appendices 2 and 4. Detailed results are shown visually in Figure 1. Note that as

the Reynolds’ Number increases, the coefficients approach a constant state. This represents how

at a certain velocity, the coefficients are no longer a function of Reynolds’ Number.

When we reflect upon these numbers, we find that both the lift and drag coefficients are

not what we expected. One would think a high performance sports car would generate high down

force, whereas our car is experiencing lift. Also, a drag coefficient of 2.0 is quite high, and even

the lowest drag coefficient value of .75 is still too high for a high performance sports car. Upon

completion, we expected to see drag coefficient values of between 0.3 and 0.5. One possible

explanation of the distortion of our coefficients was the orientation of how our vehicle was

mounted in the wind tunnel. The nose of the Mercedes was pointing slightly up in the air

meaning the car was on an angle. This could have increased the frontal area, or forced some air

underneath the car, which would have further distorted the results.

Conclusion:

The values that were obtained from the experiment seem unreasonable, comparing more

to those of a blunt object than an aerodynamically tuned sports car. While the calculated

uncertainties in these values may be low, there are other issues that are not taken into account in

the uncertainty analysis, for example the angle at which the car was mounted would significantly

swing the data. The current results cannot be deemed valid, especially without another set of

values to compare them to. We recommend completing the experiment again, paying close

attention to how the vehicle is mounted in the wind tunnel. If you have any further questions or

concerns, please contact our group at statese@garnet.union.edu.

Figure 1 – Demonstrates how the coefficients of lift and drag varied with an increasing

Reynolds’ Number. The Reynolds’ Number increases linearly with the changing wind speed.

The first 2 Drag Coefficient data points have been omitted due to the extreme uncertainty

associated with them. This uncertainty can be seen in Appendices 1 and 3.

0

0.5

1

1.5

2

2.5

0 2 4 6 8

Co

eff

icie

nt

Re x 100000

Lift Coef.

Drag Coef.

3

Appendices:

1. Coefficient of Lift Data Tables

2. Coefficient of Lift and CL Uncertainty Calculations

3. Coefficient of Drag Data Tables

4. Coefficient of Drag and CD Uncertainty Calculations

5. Velocity Data Tables and Calculations

6. Equations Used

7. Setup, Experimental Procedure, and Tasks

8. Car Data

9. References

Appendix 1: Coefficient of Lift Data Tables

Table 1 below shows the data found in the lab experiment. The equations and methods used are explained in depth on the next

page. One thing to note while looking at Table 1and Figure 2, is as the velocity of the wind increased, the lift force on the car also

increased, however their relationship is non-linear. The data from Table 2 is used in Figure 3 which shows the relationship between

the coefficient of lift and Reynolds’ Number. Notice that at a Reynolds’ Number of about 3x105 the lift coefficient approaches a

constant of about .3. This signifies the point at which the Coefficient of Lift is no longer dependent upon Reynolds Number.

0

2

4

6

8

10

0 10 20 30 40 50

Lift

Fo

rce

(N

)

Wind Velocity (m/s)

Figure 2

Frequency (Hz) 10 14 18 22 26 30 34 38 42 46 50 54

Velocity (m/s) 6.255 9.625 12.972 16.328 19.651 22.988 26.272 29.570 32.868 36.129 39.295 42.445

Uncertainty in Velocity 0.677 0.466 0.387 0.362 0.391 0.397 0.437 0.471 0.516 0.562 0.608 0.654

Lift Force (N) 0.241 0.436 0.755 1.143 1.618 2.236 2.952 3.760 4.706 5.901 7.207 8.676

Uncertainty Lift F (N) 0.101 0.103 0.104 0.121 0.124 0.119 0.124 0.146 0.148 0.215 0.187 0.206

Frequency (Hz) 10 14 18 22 26 30 34 38 42 46 50 54

Coefficient of Lift 0.414 0.316 0.301 0.288 0.281 0.284 0.287 0.289 0.292 0.303 0.313 0.323

Uncertainty CL 0.196 0.081 0.046 0.034 0.026 0.020 0.018 0.017 0.016 0.017 0.016 0.016

Reynolds' Number 93992.5 144647.5 194936.1 245380.3 295312.3 345460.8 394805.2 444374.8 493927 542943.8 590517.4 637852.3

Viscosity (kg/ms) 1.98E-05

0

0.2

0.4

0.6

0.8

0 1 2 3 4 5 6 7Li

ft C

oef

fici

ent

Re

x 100000 Figure 3

Table 2

Table 1

Appendix 2: Coefficient of Lift Calculations with Uncertainties

Firstly, the average of the 100

voltage data points at each frequency

was found, and then the standard

deviation and the percent standard

deviation. Next, we took the averages

and used the calibration curve shown

in Figure 4 to the right to calculate the

lift force on the car at each of the

motor frequencies. Then, using

equation (1) in Appendix 6, we

calculated the coefficient of lift at each of

the motor frequencies. The coefficient of

lift at each of the subsequent motor frequencies can be viewed in Appendix 1, on the previous

page. The next step in our calculations was to calculate the uncertainties in both the lift force on

the car and the car’s coefficient of lift. The former calculation was completed using equation (9)

with the standard deviation of the lift force, and the uncertainty in the lift coefficient was found

using equation (10).

One trend that we have noticed in multiple experiments now, is that as the velocity of the

wind in the tunnel decreases, so too does the accuracy of our data. In other words, the uncertainty

rises as the velocity decreases, this is why in Figure 3 the uncertainties decreases as the

Reynolds’ Number increases.

As mentioned in the memo, the values of our lift data seem high. One would think that a

high performance race car such as this would produce immense down force in order to

strengthen cornering ability; however we observed a tendency for the car to lift off of the surface

on which it is driving. This is most likely caused by the angle at which the car was mounted in

the tunnel. This angle would affect our lift data by forcing more air under the car than over it,

thereby pushing the car up off of the road surface.

Figure 4 – this graph shows the Dynamometer Lift Force

Calibration we used to calculate our lift forces.

Appendix 3: Coefficient of Drag Data Tables

Table 3 below shows the resultant data from the drag experiment in the lab. The equations and methods used to obtain this data

are explained in depth on the next page. Figure 4 shows the relationship between the drag force on the car and the velocity of the wind

in the wind tunnel. Notice that as seen in Figure 2, this relationship is non-linear. Figure 5 shows the relationship between the drag

coefficient and the Reynolds’ Number of the flow of air. Note that here, Reynolds’ Number independence is achieved around 4.0x105.

Frequency (Hz) 10 14 18 22 26 30 34 38 42 46 50 54

Coefficient of Drag 7.188 3.288 1.986 1.528 1.239 1.089 1.065 0.963 0.893 0.846 0.791 0.750

Uncertainty Cd 1.686 0.423 0.197 0.123 0.089 0.069 0.060 0.052 0.046 0.043 0.039 0.037

Reynold's Number 93992.5 144647.5 194936.1 245380.3 295312.3 345460.8 394805.2 444374.8 493927 542943.8 590517.4 637852.3

Viscosity (kg/ms) 1.98E-05

0

2

4

6

8

10

0 1 2 3 4 5 6 7

Co

eff

icie

nt

of

Dra

g

Re

x 100000 Figure 6

0

1

2

3

4

5

6

0 10 20 30 40 50

Dra

g Fo

rce

(N

)

Wind Velocity (m/s)

Figure 5

Table 3

Table 4

Frequency (Hz) 10 14 18 22 26 30 34 38 42 46 50 54

Velocity (m/s) 6.255 9.625 12.972 16.328 19.651 22.988 26.272 29.570 32.868 36.129 39.295 42.445

Uncertainty in Velocity 0.677 0.466 0.387 0.362 0.391 0.397 0.437 0.471 0.516 0.562 0.608 0.654

Drag Force (N) 1.174 1.271 1.395 1.700 1.997 2.402 3.067 3.515 4.025 4.606 5.097 5.637

Uncertainty Drag F 0.100 0.101 0.102 0.102 0.104 0.104 0.105 0.109 0.112 0.122 0.127 0.131

Appendix 4: Coefficient of Drag Calculations with Uncertainties

Again, the first step was to find the

average of the 100 voltage data points at

each frequency, and then the standard

deviation and finally, the percent standard

deviation. After, we used the calibration

curve shown to the right in Figure 7 to

calculate the drag forces at each of the 12

motor frequencies. From here on out, the

calculations are very similar to those used

for the lift force and coefficient

calculations. Equation (1) was used to

find the coefficient of drag, equation (9)

was used to find the uncertainty in the drag force, and equation (10) was used to calculate the

uncertainty in the coefficient of drag.

The drag forces calculated in this lab seem to be quite large, but as mentioned previously,

the car was mounted on an angle in the tunnel and that could have had a substantial effect on the

resulting data. This would have increased the frontal area, which would have greatly increased

the drag force on the car, and it also would have directed more air under the car, which would

help to explain the high lift forces shown and explained in Appendices 1 and 2.

Figure 7 – this graph shows the Dynamometer Drag Force

Calibration we used to calculate our lift forces.

Appendix 5: Velocity Data Tables and Calculations

Tables 5 and 6 show the velocity data obtained in the wind tunnel. We

calculated the pressures at each motor frequency and then used those pressures to

calculate the velocity of the wind at each motor frequency. These calculated

velocities were then in turn used for the calculations of the Reynolds’ Numbers. The

equation used to calculate the Reynolds’ Number is equation (8) in Appendix 6.

These numbers compare very directly to the velocity and pressure calculations from

last week’s report.

In order to calculate the wind velocity at each frequency, we had to first use

the calibration curve shown in figure 8 to find the average pitot probe pressures at

each frequency. Then, we used the pitot probe pressures along with the density of

the air in equation (4) in Appendix 6 to find the wind velocity of each motor

frequency. The final step of the velocity analysis was to calculate the uncertainty in

pitot probe pressure using equation (5). Lastly, we used the results from the

uncertainty in pressures to find the uncertainties in velocity using equation (7).

Frequency (Hz) Test 10 14 18 22 26 30 34 38 42 46 50 54

Pressure (Pa) -1.937 23.316 55.218 100.287 158.905 230.156 314.961 411.363 521.144 643.850 777.981 920.290 1073.741

Velocity (m/s) 1.803 6.255 9.625 12.972 16.328 19.651 22.988 26.272 29.570 32.868 36.129 39.295 42.445

% unc. V 1.287 0.108 0.048 0.030 0.022 0.020 0.017 0.017 0.016 0.016 0.016 0.015 0.015

Uncertainty in V (m/s) 2.321 0.677 0.466 0.387 0.362 0.391 0.397 0.437 0.471 0.516 0.562 0.608 0.654

Reynolds' Number 27093.113 93992.504 144647.471 194936.093 245380.260 295312.341 345460.763 394805.197 444374.786 493927.028 542943.807 590517.373 637852.270

Viscosity (kg/ms) 1.98E-05

Frequency (Hz) Test 10 14 18 22 26 30 34 38 42 46 50 54

Δ Pressure (inH2O) -0.008 0.094 0.222 0.403 0.639 0.925 1.266 1.653 2.095 2.588 3.127 3.699 4.316

Uncertainty Pressure (inH20) 0.020 0.020 0.020 0.021 0.021 0.024 0.021 0.023 0.021 0.022 0.023 0.025 0.026

Density (kg/m^3) 1.192 0.036Uncert. in Density

Table 5

Table 6

Figure 8

Appendix 6: Equations Used

Firstly, the two most important equations used in this lab are as follows:

(1) and

(2)

Where CL is the coefficient of lift, FL is the actual lift force the car is experiencing, CD is the drag

coefficient, FD is the drag force, ρ is the density of the air, V is the velocity of the air and AF is

the frontal area of the car. Equations 1 and 2 were used to calculate the lift and drag coefficients

of the car.

The Ideal Gas Law, which was used to calculate the density and uncertainty in density is:

(3)

Where P is the Pressure in the chamber, is the density, R is the ideal gas constant, and T is the

temperature of the air in Kelvin.

Another very important equation, integral to the calculation of the velocity of the wind is

√

(4)

Where V is the velocity of the air, is the pitot probe pressure and is the density of the air.

The Uncertainty in the pitot probe pressure was calculated using equation 5:

√ (5)

The Uncertainty in density was calculated using the following equation which was

derived from the ideal gas law is:

√

(

) (6)

The uncertainty in the velocity of the air was calculated using the equation:

√(

)

(7)

The equation used to solve for the Reynolds’Number is:

(8)

The uncertainty in the lift force is found using Equation 9 below:

√ (9)

The uncertainty in the coefficient of lift was found using:

√

(10)

The uncertainty in the drag force is found using:

√ (11)

The uncertainty in the coefficient of drag was found using:

√

(12)

1

Appendix 7: Setup, Experimental Procedure, and Tasks

Introduction:

The purpose of this week’s lab exercise is to measure the lift and drag forces acting on the radio

controlled vehicle that your group is studying. Drag is the force that acts opposite to the path of

the vehicle’s motion. It is detrimental to vehicle performance because it limits the top speed of a

vehicle and increases the fuel consumption, both of which are negative consequences for race

vehicles. Low drag vehicles usually have one or some combination of the following

characteristics: streamlined shape, low frontal area, and minimal openings in the bodywork for

windows or cooling ducts. The drag performance of vehicles is characterized by the drag

coefficient (CD) which is defined as:

(1)

Where FD is the drag force, ρ is the air density, V is the free stream velocity, and AF is the

frontal area of the vehicle. This non-dimensional coefficient allows the drag performance

between different vehicles and different setups of the same vehicle to be compared directly.

Lift is the other of the two main aerodynamic forces imposed on a race vehicle, but unlike drag,

lift can be manipulated to enhance the performance of a racecar and decrease lap times. Lift is

the force that acts on a vehicle normal to the road surface that the vehicle rides on. As its

definition implies, lift usually has the effect of “pulling” the vehicle upwards - away from the

surface it drives on. However, by manipulating the racecar geometry it is possible to create

negative lift, or down-force. Down-force enhances vehicle performance by increasing the normal

load on the tires. This increases the potential cornering force which results in the ability of the

vehicle to go around corners faster and reduce lap times. The lift of the vehicle is characterized

by the lift coefficient (CL) and is defined as:

(2)

Where FL is the lift force, AT is the area of the top surface of the vehicle (see Table 1), and the

other variables are as defined above. A negative lift coefficient means that a vehicle is

experiencing down force (Note: See last week’s lab handout for frontal and top area information

on your vehicle).

Procedure

The race car body will be pre-mounted in the wind tunnel for you and the pressure transducer has

been pre-calibrated (use the same calibration that you used for the surface pressure

measurements).

You will be provided with calibration data for the dynamometer.

Setup Steps:

1. Note any experimental observations about how the car is mounted in the wind tunnel.

Note the room temperature for your density calculation.

2. Make sure that the pressure transducer output is connected to channel 1, the

dynamometer lift (blue/black, blue wire) is connected to channel 2 and the dynamometer

drag.

2

3. Check the connections on the wind tunnel pitot probe. The stagnation pressure (vertical

tap) should be connected to the “total” connection on the back of the pressure transducer

and the static pressure (horizontal tap) should be connected to the “static” tap on the back

of the pressure transducer and the pressure selector switch should be set to channel 0.

4. Start Excel and make sure the Daq software is running. Check that the data acquisition is

set to read channels 1, 2 and 3 (-10to +10V) and record 100 readings at a rate of about 6

Hz.

5. With the wind tunnel off, start the data acquisition program and read the data on channels

1, 2 and 3. Since there is no flow all three should be close to zero. Confirm this before

proceeding. If the lift and drag values are not zero (or less than .05 V) you will need to

re-zero the lift and drag system using the two brass thumb wheels mounted directly on

the dynamometer to account for the weight of your car model. DO NOT adjust the span

or zero dials for the lift or drag on the wind tunnel instrumentation box. These are the

dials that are helpfully labeled “do not touch.”

6. Set the wind tunnel speed to 10 Hz and turn on the wind tunnel.

7. Acquire and save your data. Note: a negative Lift value implies down force and a positive

Drag value implies Drag (in direction of flow).

8. Increment the wind tunnel speed by 4 Hz, and repeat step 7 until the wind tunnel speed is

54 Hz. Be sure to allow the system stabilize for a minute or so after you change each

wind speed

9. Save your output file and move to another computer to perform your data reduction.

Data Reduction

a) Convert your pressure transducer voltages to Pressure (using calibration for transducer

provided last week) and calculate wind tunnel speed for each motor frequency setting.

Check these numbers against the data you acquired two weeks ago when you calibrated

the wind tunnel.

b) Review the lift and drag calibration information (see Figure 1 and 2 below). Note: To

acquire this data we removed the dynamometer from the wind tunnel and mounted it on a

calibration test stand. We then hung calibrated weights in the range from 10 to 1000 g in

lift and drag configurations and recorded the voltage output of the dynamometer. Use the

information provided to convert your dynamometer voltage output to lift and drag forces.

The uncertainty estimate given in each figure is a combination of SLF and calibration

accuracy. You will need to add the effects of random variations in your measurements

(using the stdev) in your uncertainty analysis.

c) Calculate lift and drag coefficient at each velocity. Calculate the uncertainty in lift and

drag coefficient at each velocity and make a plot of CD and CL versus Re with error bars.

Note: For the Reynolds number you should use car length as your length scale.

Report

Prepare a memo report on the results (including the uncertainty estimates with sufficient

DETAIL in an appendix) of your lift and drag data. The intention of the memo is to relay your

results to me. Include a description of the experiment, your results and a short discussion.

Include tables of data as an attachment. Draft memo reports are due one week from the day that

you performed the lab. The final group report will be due Friday Mar 8.

3

Appendix 8: Scaled Mercedes CLK Data Sheet

MERCEDES CLK

Length = 250mm

Width = 100mm

Height = 70mm

Top Area = 250 cm2

Frontal Area = 70 cm2

Appendix 9: References

Anderson, Ann M. Race Car Aerodynamics Part 2: Lift and Drag. Union College, 2013.

Print.

Anderson, Ann M. Race Car Aerodynamics Project. Union College, 2013. Print.

Hertel, Zacarie. Aerodynamics of a Mercedes-Benz CLK - Memo 1. Union College, 2013.

Print.

Figure 9 – This is the Mercedes-Benz CLK Touring car that our

model is based off of. Our model is approximately 1/12th

the

overall size of the one shown above. Some important things to

note are that our model does not have the rear spoiler, front

spoiler nor the rear diffuser that the full scale car has, therefore

we expected our data to be slightly different that the coefficients

of the full size car.