Physics Report

Title of the Report

A. Partner, B. Partner, and C. Partner

Abstract

The report abstract is a short summary of the report. It is usually one paragraph (100-200 words) and should include about one or two sentences on each of the following main points:

1. Purpose of the experiment 2. Key results 3. Major points of discussion 4. Main conclusions

Tip: It may be helpful if you complete the other sections of the report before writing the abstract. You can basically draw these four main points from them.

example: In this experiment a very important physical effect was studied by measuring the dependence of a quantity V of the quantity X for two different sample temperatures. The experimental measurements confirmed the quadratic dependence V = kX2 predicted by Someone’s first law. The value of the mystery parameter k = 15.4 ± 0.5 s was extracted from the fit. This value is not consistent with the theoretically predicted ktheory = 17.34 s. This discrepancy is attributed to low efficiency of the V -detector.

1. Introduction

This section is also often referred to as the purpose or plan. It includes two main categories:

Purpose: It usually is expressed in one or two sen- tences that include the main method used for accomplish- ing the purpose of the experiment.

Ex: The purpose of the experiment was to determine the mass of an ion using the mass spectrometer.

Background and theory: related to the experiment. This includes explanations of theories, methods or equa- tions used, etc.; for the example above, you might want to explain the theory behind mass spectrometer and a short description about the process and setup you used in the experiment. It is important to remember that report needs to be as straightforward as possible. You should comprise only as much information as needed for the reader to un- derstand the purpose and methods. Your should also pro-

vide additional information such as a hypothesis (what is expected to happen in the experiment based on the theory) or safety information. The main focus of the introduction mainly focuses on supporting the reader to understand the purpose, methods, and reasons for these particular meth- ods.Purpose of the experiment

Example:

Calculation of the pressure coefficient Cp

From the lectures notes, Cp can be obtained by the eq. (1)

−Cp = P −P∞

1 2 ∗ρ∗U

2 ∞

(1)

Where P and P∞ are respectively the local pressure and the atmosphere pressure far away. U∞ is the wind velocity

Preprint submitted to supervisor April 16, 2020

 

 

of the wind tunnel.

Calculation of the lift coefficient CL

First, the expression for the pressure force acting nor- mal to the chord line is given in the lecture notes as eq.(2),

Cn = ∮ Cp(−n̂∗ ŷ)dl, (2)

with Cp the coefficient of lift and n̂ the unit normal vector pointing out of the surface, ŷ is the unit vector in the direction normal to the chord line. dl is the length of an infinitesimal line element. Similarly, the axial component can be express as eq.(3)

Ca = ∮ Cp(−n̂∗ x̂)dl, (3)

2. Method

This is a short (half a page or so) passage in your report which should include the experimental process exactly as it was done in the laboratory. The procedure should be written in paragraph form. You should not copy the lab manual. It is possible that the experiment you have done has slightly difference procedures than in the manual. You should not include any results (things happened during the procedure). A good rule of thumb for complete but brief experimental procedures is to provide enough information so that the reader of your report would be able to repeat the experiment.

A first offset measurement was taken with the pressure scanner, sample at 800 Hz for 10 seconds , while matlab was taking an offset measurement. After the offset measur- ment done , the wind tunnel VFD RPM was set to reach the target U∞ within ±0.5m/s. For each of the following α= [-8 -6 -4 -2 0 2 4 6 7 8 9 10 11 12 13 14 16 18], the same procedure was repeated :

The turntable was set to the right angle of attack (as shown in fig.(1)). Then the dynamic pressure and the tem- perature were taken (1000 Hz for 30 seconds for pressure, and 14 Hz for 10 seconds for the temperature).

While Matlab was taking the data , the pressure scan- ner was run to take measurement at 800 Hz for 60 seconds. After changing the angle, a break of 5 seconds was taken in order to fully settle the flow into a steady state before taking the next set of measurements.

The post-experiment calculations were realized with Matlab. First, the pressure offset was computed in order to get the right pressure measurement. With the 2 off- set measurements and the getfiledate.m Matlab code, the time of each offset has been taken. A linear interpolation was realized to get the offset at any time.

The pressure points were linked to the corresponding measurement value of the scanner and the time of each measurement was obtained with the getfiledate.m code. The new pressure were finally taken by subtraction of each corresponding time offset to the measurement pressure for every angle of attack.

The lower and upper Cp values were computed with eq.(1). The denominator in the eq.(1) (P − P∞) corre- spond to the new pressure calculated by subtraction of the offset . As the pressure points does not surround the airfoil entirely, the Cp curves had to be closed by interpo- lation of the data points using piecewises cubic Hermite polynomials (PCHIP) for the last three points to estimate a value for the trailing edge. An example of a Cp curve for a certain angle of attack is shown in fig.(5).

Next, the CL values for each angle of attack were com- puted using eq.(6). The coordinate system used in eq.(6) is shown in fig.(2). fig.(5) shows the resulting plot of this calculation.

Finally, the errors in the lift coefficient were computed using eq.(9). The different variance values were given in the lab document and calculated using eq.(8). fig.(3) shows the resulting plot of this calculation.

Figure 1: Set up of the airfoil experiment

2

 

 

3. Results

In this section all the results of the experiment is re- ported, including:

Raw data- in forms of graphs or tables. Each graph, table, or figure should be labeled and titled properly. Mak- ing tables and figures is helpful when you refer to and explain each of them in the report. Make sure that you attach the appropriate units to all physical quantities.

Assume that the reader has not done the lab; so give clear definition of each symbol that is used in the re- port. (ex: âĂIJL is the length of the pendulumâĂİ.)

Important results âĂŞ It is expected to use complete sentences to communicate the main results, which also should be expended to discussion section. (Ex: âĂIJThe gravitational acceleration was calculated to be 9.98 m/sâĂİ) This enables the important results to stand out from all the calculations, tables, and figures.

Calculations Normally, one sample of each calcula- tion is necessary. For example, if the speed of an object is calculated for 6 trials, you are expected to write out calcu- lations for only one of them. However, it is important to mention that the calculation was repeated 6 times and give the average of all 6. Significant figures should be consid- ered in all calculations (see appendix of âĂIJSignificant Figure RulesâĂİ as a resource with significant figures). Again, make sure units are included in all calculations.

Example: The resulting slope of the Cl for α ∈ [−8, 8] is 6.174 rad and 6.209 rad for α ∈ [−4, 4] . This devi- ates by 0.1090 and 0.0745 respectively from the 2π value predicted by thin airfoil theory, indicating larger errors for higher AoA’s.

The max theoretical error ∆Cl was calculated to be 0.0887, and occurred at α = 16◦, which is in the stall re- gion. Outside of the stall region the max error was calcu- lated to be 0.0391, at α = 8◦

The standard deviations presented in tab.1 were used in the result above. σqinf , and σPi were found with eqn (8). However, σPi is a vector for all of the pressure ports, and will not be presented.

Figure 2: Resulting plot of ∆CL

Table 1: Value of variance σP0 σα σqinf 3.000 0.250 0.453 [Pa] [deg] [Pa]

Figure 3: Resulting plot of CL compared to experimental data

Figure 4: – Cp for α = 8◦

4. Discussion

The most important part of your report is the discus- sion section. Here you explain your results and allow your instructor to see that you have a thorough understanding of the scientific concept of the experiment and the results. In this section you also compare the expected (theoreti- cal) results with actual (experimental) ones. It is possible that your experiment turns out not exactly the way it was supposed to. Analyze and discuss why the results might have been different and try to explain why you obtained the results you did. Be specific what caused the error: faulty equipment, inaccurate measurements or calculation errors. After you have discussed the cause of the error,

3

 

 

try to suggest how to avoid the error and how to setup the experiment more effectively (ex: be more careful with measurements, use more precise equipment, etc.)

Example According to thin airfoil theory, the Cl curve for cambered airfoils should be straight for low angles of attack with a slope of ¡textit2π. It should also have a positive lift at α = 0◦. The resulting CL curve clearly follows this trend, albeit not perfectly, especially at higher AoA’s. This likely follows from the assumption of a thin airfoil, as the NREL S826 has a non negligible aspect ratio of 5 .

Furthermore, the boundary layer acts as a streamline, essentially adding some minute thickness to the airfoil flow. It would therefore experience a higher adverse pressure gradient due to the curvature, and thus earlier separation. This can also be observed in figure 4, where a high pressure gradient is starting to form already for α = 8◦ at x

c ≈ 0.2.

Furthermore, stall can be predicted to be about α = 12◦ from figure 3. This seems to fit well with previous experimental data shown in pink [2], . Larger theoreti- cal errors are expected in this region, as separation and irregular flow further complicates the theory.

The discrepancies are also likely to be due to the mea- surement errors described in the theory section. The max calculated error ∆CL is 5.93 % of the total CL.

5. Conclusion

This section is a short paragraph that includes one or two sentences. Conclusion summarizes the major result(s) of the experiment.

Example The goal of this lab was experimentally mea- sure pressure around an airfoil for different AoA’s and to compare the resulting lift data with theory. This was done with numerical integration of the pressure distrubution, while also adjusting for measurment errors. There seems to be good agreement between the lab data and theory. The resulting slope of the CL curve deviates at a maxi- mum 0.109 from thin airfoil theory outside the stall region. This is probably due to the thickness of the airfoil, as well as the measurement error in the equipment. As expected stall occurs at about α = 12◦, which can be qualitatively observed in both the CL and CP curves.

References

[1] Scanivalve: MPS4264 Miniature Pressure ScannerManual, http://www-cs-faculty.stanford.edu/˜uno/abcde.html

[2] Airfoil tools: Previous experimental data for the NREL S826, http://airfoiltools.com/airfoil/details?airfoil=s826-nr

4