Physics lab report
Title of the Report
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A. Partner, B. Partner, and C. Partner
Abstract
The report abstract is a short summary of the report. It is usually one paragraph (100-
2
00 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 September 9, 2019
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
Introduction
Method
Results
Discussion
Conclusion
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| |
Har
m |
onic
|
Number n
Frequency o
| f |
Vibrator f(Hz)
| L |
ength of String Ln(m)
Hanging mass m(kg) |
(fL/n)^2 |
(Hz.meter)^2
| →原数据 |
Harmonic |
f L m (fL/n)^2
|
| 7 |
170 |
0.79 |
| 0.07 |
|
| 3 |
| 6 |
8.092
7
1
|
| 5 |
3
0.
|
| 81 |
2
0.07
31
|
| 4 |
.
99 |
1
|
| 50 |
4
6
| 130 |
0.97 |
| 0.09 |
44
|
| 1.7 |
00
6 99
|
|
|
| 1.1
| 55 |
0.09
363.18830625 |
5
|
| 95 |
1.155 |
|
|
| 0.1 |
1
48
|
|
|
| 1.5 |
83
5 95 1.155 0.11
481.583025 |
4 81
| 1.148 |
| 0.13 |
540.423 |
4 81 1.155 0.13
547.03362
| 65 |
625
3
| 75 |
| 0.95 |
4
|
|
| 0.15 |
568.823 |
3 65 1.155 0.15
626.250625 |
2 55
| 0.943 |
| 0.17 |
672.495 |
2 50 1.155 0.17
833.765625 |
1 50
| 0.588 |
| 0.19 |
864.360 |
1 50
0.656 |
0.19
1075.84 |
| 10.624712 |
| 0.0841542857 |
→原数据
| Stretch Amount (m) |
|
|
| Tension (N) |
| Average Time(sec) |
| Average Velocity (m/s) |
V^2
(m^2/s^2) Tension (N)
Stretch Amount (m) Tension (N)
| Time1(sec) |
Time2(sec) |
Average Time(sec) Average Velocity (m/s)
|
| V^2(m^2/s^2) |
0.1
|
|
| 0.8 |
0.95
6.0141052632 |
36.1694621163 |
0.8
0.1 0.8
|
|
|
|
| 1.3 |
3
| 1.39 |
|
| 1.36 |
4.201 |
| 17.649 |
0.15 1
| 1.32 |
4.4040909091 |
19.3960167355 |
1
0.15 1
| 1.43 |
|
| 1.2 |
5
1.34 |
4.338 |
| 18.821 |
| 0.2 |
1.3
| 1.31 |
5
4.4968821293 |
20.2219488846 |
1.3
0.2 1.3 1.31 1.32
| 1.315 |
4.497 |
| 20.222 |
| 0.25 |
1.5
1.345 |
4.470929368 |
19.9892094139 |
1.5
0.25 1.5
| 1.24 |
1.41 |
1.325 |
4.538 |
| 20.597 |
| 0.3 |
| 1.6 |
1.25
4.89072 |
23.9191421184 |
1.6
0.3 1.7 1.2 1.36
| 1.28 |
4.776 |
| 22.811 |
Tension (N) V^2(m^2/s^2)
0.8 17.649
| slope |
1 18.821
| 5.2202 |
1.3 20.222
1.5 20.597
| 1/slope |
1.7 22.811
1.355 |
| 0.1915635416 |
1.36
| v2 是纵轴 |
1.37 |
| error3 |
error4 |
T 是横轴 |
1.39
| 0.1752364517 |
0.0477 |
1.38 |
(fL/n)^2 (Hz.meter)^2 |
7.0000000000000007E-2 0.09 0.11 0.13 0.15 0.17 0.19 368.09163265306125 441.70027777777773 481.58302500000002 540.42300899999998 568.82249999999988 672.49455624999985 864.3599999999999
m
(fL/n)^2
V^2(m^2/s^2)
0.8 1 1.3 1.5 1.7 17.648648118512114 18.821351949209173 20.221948884615941 20.59721156852973 22.811071508789055
T tension
V^2
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-
2
00 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 ∗ U2∞
(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 March 4, 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 xc ≈ 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
Introduction
Method
Results
Discussion
Conclusion
