To: Professor AndersonFrom: RJ Hojnacki, Wes Wall, Sam CarusoDate: 3/8/12Subject: 1/12th Scale NASCAR Lift and Drag Findings

Purpose: We were asked to look into the Lift and Drag forces acting on the 1/12th scale stock car model. This memo was made to report on our wind tunnel findings of the NASCAR lift and drag testing.

Findings: The wind tunnel test results showed that the lift coefficient achieved Reynold’s Number independence after a Reynold’s Number of approximately 5X105. However, the drag coefficient never seemed to achieve Reynold’s Number independence, although it seemed to be approaching Reynold’s Number independence near the upper speed constraints of the wind tunnel.

Figure 1: The lift and drag coefficients versus Reynold’s Number. The force coefficients at a Reynold’s Number of 82817 were removed from the plot (see Attachment 4 for more detail).

Since lift reached Reynold’s Number independence, beyond a Reynold’s Number of 5.0X105 the forces exerted on the model can be scaled to a full size car. I would recommend re-running the test in a wind tunnel capable of achieving higher speeds. This would provide more opportunity to confirm Reynold’s Number independence was reached for the lift coefficient and to potentially achieve Reynold’s Number independence for the drag coefficient. Additionally, I would recommend using a dynamometer with higher precision. This would significantly reduce the uncertainty in our lift and drag measurements, especially at low wind tunnel speeds.

Experiment Setup: The dynamometer was connected to a data acquisition system which was connected to the computer. Voltage readings relating to lift, drag, and air speed within the tunnel were recorded at wind tunnel speeds varying from 4.84m/s to 41.78m/s. At each speed 100 readings from each dynamometer channel were recorded and input into Excel for further analysis. (See Attachment 5)

Analysis: The lift and drag coefficients displayed in Figure 1 offer valuable insight into the aerodynamics of the stock car. The force coefficients represent the relative magnitude of the lift/drag forces on the vehicle. The lift and drag coefficients are directly related to the change in momentum of particles flowing past that object, as well as how abruptly those changes in momentum occur. Stock cars

designers use a technique called streamlining to achieve minimal lift and drag forces in order to maximize vehicle performance.

Using Figure 1, we can see that the maximum lift coefficient (CL = 0.624) occurred at a Reynold’s Number of 95890 (see Lift Coefficient 1). After LC 1, the lift coefficient decreased until reaching the Reynold’s Number 308062 (see LC 4). LC 4 was the minimum lift coefficient throughout the experiment (CL = 0.116). After this minimum value, the lift coefficient gradually increases until reaching a Reynold’s Number of approximately 5X105(see CL 7). From Reynold’s Number 5X105 to 7.15X105 (CL 7 to CL 11) the lift coefficient remained at approximately CL = 0.161. Since the lift coefficient remained stable from CL 7 to CL 11, we can conclude that Reynold’s Number independency was most likely achieved. Therefore, beyond a Reynold’s Number of 5X105, dynamic similarity exists between our model and a full size prototype. As a result, our lift forces for Reynold’s Numbers greater than 5X105 can be scaled to the lift forces a full size car would experience. Note, due to the limitations of the wind tunnel it was assumed that the lift coefficient will remain constant beyond a Reynold’s Number of 7.15X105(final data point).

The maximum drag coefficient occurs at a Reynold’s Number of 95890 (Drag Coefficient 1). From DC 1, the drag coefficient decreases and reaches its lowest point at a Reynold’s Number of 244449 (see DC 3). After this point the drag coefficient creeps up to CD = 0.26 at a Reynold’s Number of 715607 (see DC 11). Observe DC 7 to DC 11 and notice that the rate of change between points is decreasing. This lead us to believe that if the wind tunnel could produce higher wind speeds we would see convergence of the drag coefficient at a higher Reynold’s Number. Since the drag coefficient doesn’t reach Reynold’s Number independence, dynamic similarity does not exist prior to a Reynold’s Number of 7.15X105.

Generally, both the lift and drag coefficients follow a similar trend. They begin high, decrease rapidly, and then increase gradually. To offer an explanation for this we can make an analogy to flow around a sphere because we understand that behavior and it relates to our results. In laminar (low Reynold’s Number) flow around a sphere, separation occurs at the midpoint of the sphere. This leaves a low pressure area on the back of the sphere which increases the drag. As the flow becomes turbulent and gains more momentum, the separation occurs past the mid-point and the low pressure area on the back of the sphere gets small. As a result, the drag is decreased. Given that, it is possible that flow around our NASCAR model may behave similarly.

To find the uncertainty in the force coefficients, we considered the uncertainty in velocity, the uncertainty in force measurements, and the uncertainty in density (See Attachment 3). The average uncertainty in the lift/drag coefficients were CL ± 0.024 and CD ± 0.067. The error bars on Figure 1 show the percent uncertainty for each force coefficient. For both the lift and drag the uncertainty decreased as Reynold’s Number increased (see Attachment 4).This is what we would expect because at low wind tunnel speeds the lift and drag forces are very small, especially with regards to the dynamometers precision. As the forces became larger (i.e. at higher wind tunnel speeds) the percent uncertainty reduced significantly.

Conclusion: From the provided force coefficient data we reached a few conclusions. The lift coefficient converges at approximately CL = 0.161 and therefore reaches Reynold’s Number independence. This statement is limited by the speeds achievable with our wind tunnel. The drag coefficient does not reach Reynold’s Number independence, but it does seem to be converging prior to reaching the top speed of the wind tunnel. If our wind tunnel had the ability to produce higher speeds I predict that the drag coefficient would reach Reynold’s Number independence. Next time this test is done a dynamometer with higher precision should be used because of the relative magnitude of forces on this streamlined stock car design. If you need any further assistance in any way feel free to contact us at NASCAR_labteam@gmail.com

Attachments:

1,2 - All Data for Lift, Drag, and Wind Tunnel Velocity3 - Uncertainty Analysis for Lift and Drag Coefficients4 - Explanation for the Removal of Data for Reynold’s Number 828175 - Experimental Setup and Schematic

Attachment 1Table 1: All Calculated Lift Results

Data Point Label Reynold's Number Velocity Uncertainty Lift Force Lift Coeffi cient UncertaintyCL # Re V δV FL CL δCL

82817 4.84 0.771 0.19 0.462 0.2191 95890 5.60 0.474 0.34 0.624 0.0742 176372 10.30 0.382 0.52 0.285 0.0403 244449 14.27 0.356 0.59 0.168 0.0304 308062 17.99 0.364 0.64 0.116 0.0215 369669 21.58 0.390 1.00 0.125 0.0196 428999 25.05 0.425 1.54 0.143 0.0167 487720 28.48 0.466 2.12 0.152 0.0148 545954 31.88 0.510 2.74 0.157 0.0149 603775 35.25 0.556 3.47 0.163 0.01410 660036 38.54 0.602 4.19 0.165 0.01311 715607 41.78 0.648 4.81 0.161 0.012

Table 1 includes all the relevant results computed from the dynamometer readings at various wind tunnel speeds.

Table 2: Raw Experimental Lift Data

Avg. Volt STDEV. Volt % STDEV. Volt STDEV. F(N) Avg. F(N) δF(N)0.008 0.001 7.73% 0.007 0.185 0.1010.020 0.001 3.97% 0.010 0.335 0.1020.035 0.001 3.43% 0.015 0.519 0.1040.041 0.003 8.43% 0.042 0.586 0.1300.046 0.004 7.75% 0.043 0.645 0.1320.075 0.005 6.83% 0.062 0.998 0.1590.119 0.006 4.80% 0.070 1.539 0.1710.167 0.007 3.92% 0.080 2.120 0.1880.218 0.008 3.68% 0.098 2.738 0.2190.278 0.011 3.78% 0.128 3.468 0.2740.338 0.011 3.16% 0.130 4.195 0.2780.389 0.011 2.93% 0.138 4.813 0.294

Raw Lift Data

Table 2 contains additional raw data that was necessary for the calculations made to get the values in Table 1.

Attachment 2Table 3: All Calculated Drag Results

Data Point Label Reynold's Number Velocity Uncertainty Drag Force Drag Coeffi cient UncertaintyCD # Re V δV FD CD δCD

82817 4.84 0.771 0.03 0.30 0.7191 95890 5.60 0.474 0.05 0.32 0.2572 176372 10.30 0.382 0.06 0.11 0.1373 244449 14.27 0.356 0.04 0.04 0.0864 308062 17.99 0.364 0.09 0.06 0.0595 369669 21.58 0.390 0.15 0.07 0.0476 428999 25.05 0.425 0.39 0.13 0.0347 487720 28.48 0.466 0.61 0.16 0.0298 545954 31.88 0.510 0.95 0.20 0.0249 603775 35.25 0.556 1.31 0.23 0.02210 660036 38.54 0.602 1.70 0.25 0.02111 715607 41.78 0.648 2.14 0.26 0.022

Table 3 includes all the relevant results computed from the dynamometer readings at various wind tunnel speeds.

Table 4: Raw Experimental Drag Data

Avg. Volt STDEV. Volt % STDEV. Volt STDEV. F(N) Avg. F(N) δF(N)0.016 0.003 17.0% 0.003 0.032 0.1000.028 0.005 17.8% 0.006 0.046 0.1010.036 0.007 18.6% 0.008 0.056 0.1010.023 0.009 38.4% 0.010 0.040 0.1020.062 0.009 14.1% 0.010 0.086 0.1020.118 0.022 18.5% 0.026 0.152 0.1120.318 0.015 4.7% 0.017 0.386 0.1060.508 0.023 4.5% 0.027 0.610 0.1140.800 0.019 2.3% 0.022 0.952 0.1091.107 0.030 2.7% 0.035 1.313 0.1221.438 0.035 2.4% 0.041 1.702 0.1291.808 0.052 2.9% 0.061 2.137 0.158

Raw Drag Data

Table 4 contains additional raw data that was necessary for the calculations made to get the values in Table 3.

Attachment 3Calculation of uncertainty in the lift coefficient

First the uncertainty in the density had to be calculated. We concluded that the uncertainty of the density was about 3% of the density, so δρ = 1.186*(0.03) = 0.03558.

Next, the uncertainty in the velocity was derived from the equation for the velocity

V=√ 2 ΔPρ (1)

Next, the percent uncertainty of the velocity had to be calculated using the equation

UV=δVV

=√( (0.5 )×( δΔPΔP ))2

+¿¿ (2)

This value was then calculated at each wind speed. The percent uncertainty in the lift coefficient was derived from the equation

CL=FL

12ρV 2 AT

(3)

Next, the equation for the percent uncertainty of the lift coefficient had to be derived, as shown

UC L=δCLCL

=√(δ FLFL

)2

+( δρρ

)2

+(2δVV

)2 (4)

In order to find the uncertainty of the lift force, the percent uncertainty in the lift force needed to be multiplied by the lift force at each wind tunnel speed.

δCCL=CC L∗√( δ FLF L )

2

+( δρρ )2

+( 2δVV )2

(5)

The calculation in equation 5 was carried out for each wind speed.

Equations 3-5 can be applied for the drag coefficient in the same way. Note that the area used for drag is the frontal area of the model rather than the area of the top of the model used for finding lift force.

Attachment 4

Figure 2: Percent Uncertainty in Lift Coefficient versus the Lift Force

Figure 2 shows the percent uncertainty in the lift force with respect to the size of the lift force. As you can observe, as the force gets bigger the percent uncertainty decreases. This is likely because the dynamometer’s precision. The highest precision the dynamometer can measure is a thousandth. Relative to a thousandth, our lift forces are quite small, therefore any fluctuation or inaccuracy in the data results in a high uncertainty.

Figure 3: Percent Uncertainty in Drag Coefficient versus the Drag Force

Figure 3 shows a similar trend. However, note the magnitude of the drag forces in comparison to the lift forces in Figure 2. Since these force measurements are even smaller on the scale of tenths (for the first few forces shown), any fluctuation in testing causes a huge uncertainty relative to the force measured. We chose not to include the points represented by the first data bars, on Figure 1, because of the large percent of uncertainty for both lift and drag.

Attachment 5Experimental setup

The NASCAR model was pre-mounted to the dynamometer in the wind tunnel so that the wheels were just touching the floor of the wind tunnel and the front of model was facing the direction of the air flow. The dynamometer was attached to a data acquisition box which was plugged into a computer. A Pitot probe was positioned in the wind tunnel and attached to a pressure transducer using Tygon tubing which was also then connected to the data acquisition box.

Then dynamometer was zeroed using the attached knobs. Results pertaining to the Pitot probe, the lift, and the drag were represented by voltages. Data was recorded while the motor was at 10 Hz (4.8 m/s) and repeated in intervals of 4 Hz up to and including 54 Hz (41.8 m/s). Care was taken to ensure that the flow in the wind tunnel was steady before taking any readings. One student watched the behavior of the car to record any suspicious movements (i.e. the front of the model tipping upwards).

Figure 4: Schematic of Experimental Setup

“We completed this assignment to our full academic honest - [RJ, Wes, Sam]”