# Further Maths and Simulation (SC2153)

Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
Assignment submission date: 28th February 2018
Assignment feedback: 21st March 2018
You must attempt all questions and show all working.
Please state if you are rounding numbers, and include units where applicable.
1: The admittance, 𝑌, in a circuit is given by
𝑌 =
1
𝑍
where 𝑍 is the impedance of the circuit. If Z = 150 − j22, find 𝑌.
5 marks
2: By applying Kirchoff’s laws on a circuit, the following mesh equations were obtained:
18𝐼1 + 𝑗12𝐼1 − 𝑗25𝐼2 = 200
20𝐼2 + 𝑗40𝐼2 + 15𝐼2 − 𝑗25𝐼1 = 0
Determine, in polar form, the primary and secondary currents, 𝐼1and 𝐼2 respectively,
through the circuit.
12 marks
3: If 6𝑥
2 + 3𝑦
2 + 𝑧 = 1, find the rate at which 𝑧 is changing with respect to 𝑦 at the
point (3, 5, 2)
4 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
4: The stream function, 𝜓 (𝑥, 𝑦),has a circular
function shape as shown, and is related to the
velocity components 𝑢 and 𝑣 of the fluid flow by
𝑢 =
𝜕𝜓
𝜕𝑥 and 𝑣 =
𝜕𝜓
𝜕𝑦
a) If 𝜓 = 𝑙𝑛√𝑥
2 + 𝑦
2, find 𝑢 and 𝑣.
b) The flow is irrotational if 𝜓 satisfies Laplace’s equation,
𝛿
2 𝜓
𝛿𝑥2 +
𝛿
2𝜓
𝛿𝑦2 = 0
Determine if the flow is irrotational.
15 marks
5: Determine the force, F, which has a magnitude of 64kN in the direction of the vector
𝐴𝐵 where A = (2, 4, 6) and B = (6, 3, 4).
8 marks
6: An object is dropped and its position vector, r, is given by
𝑟 = (𝑡
5 − 2𝑡
2
)𝑖 + (7𝑡
3 − 6𝑡
2
)𝑗
a) Find the velocity, 𝑣, and the acceleration, 𝑎.
b) What is the angle between 𝑣 and 𝑎 when 𝑡 = 2?
12 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
7: If 𝛷 = 𝑥𝑧
2 + 3𝑥𝑦
2 + 𝑦𝑧
2

a) Determine grad 𝛷 at the point (3, 5, 1).
b) Find the direction from the point (1, 1, 0) which gives the greatest rate of
increase of the function of 𝜙.
9 marks
8: Consider a two-storey building subject to earthquake oscillations as shown:

Oscillations
The period, T, of natural vibrations is given by 𝑇 =
2𝜋
√(−𝜆)
where 𝜆 is the eigenvalue of the matrix A.
Find the period(s) if A = (
−30 10
10 −20)
10 marks
The equations of motion are
expressed as
𝑥̈= 𝐴𝑥
𝑤ℎ𝑒𝑟𝑒 𝑥 = (
𝑥1
𝑥2
)
𝑥1
𝑥2
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
9: Below is a screenshot of a mathematical function written in MATLAB, along with its
corresponding vector diagram.
What does this code do? Explain with respect to each line in the code and the figure
shown.
10 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
10:
a) Model Q6 using MATLAB. Include a screenshot of the code and explain what
each line of code is doing.
b) Give two advantages of MATLAB over manual calculations and support your
15 marks
Total available marks – 100

# Need help-Wind Turbine Investigation

Need help-Wind Turbine Investigation

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The following experiment enables you to:

• Measure the energy in the wind.
• Assess a commercially available wind turbine in an environmental wind tunnel.
• Determine the power curve of a wind turbine and obtain cut-in speeds
• Calculate the coefficient of performance of a turbine
• Calculate the Solidity and Tip-speed ratio.
• See how the energy is converted stored and utilised.
• Examine the Beaufort wind scale.

Introduction:

The power available to a wind turbine is the kinetic energy passing per unit time in a column of air with the same cross sectional area A as the wind turbine rotor, travelling with a wind speed U0. Thus the available power is proportional to the cube of the wind speed. See the figure below.

Equipment

The equipment is provided by Marlec and the following information is from their web page but has been modified slightly for this labsheet.

The Rutland 913 is designed for marine use on board coastal and ocean going yachts usually over 10m in length. This unit will generate enough power to serve both domestic and engine batteries on board.
The Rutland 913 is a popular sight in marinas, thousands are in use worldwide, boat owners like it’s clean, aerodynamic lines and its quiet and continuous operation. Without doubt this latest marine model accumulates more energy than any other comparable windcharger available, you’ll always see a Rutland spinning in the lightest of breezes!

• Low wind speed start up of less than 3m/s
• Generates 90w @ 37m/s, 24w @ 20 m/s
• Delivers up to 250w
• Modern, durable materials for reliability on the high seas
• SR200 Regulator – Shunt type voltage regulator prevents battery overcharge

Theory:

During this experiment you will make use of the following equations to calculate key parameters

Key formulae

Energy in the wind E = (watts)

Swept area of rotor A=πR2

Electrical power output P=VxI (watts)

Coefficient of performance

Tip speed ratio

R is the rotor radius (m)

ρ is air density say 1.23 kg/m3

Uo is the wind speed (m/s)

V is voltage (volts)

I is current (amps)

ω (rads/sec) is the angular velocity of the rotor found from

where N is the rotor speed in revs/min

Procedure:

Step 1         Ensure that everything is setup for you and switch on the tunnel.

Step 2         Adjust the wind speed and let it stabilize

Step 3         Measure the wind speed, voltage and current

Step 4         If available measure the rotor speed with the stroboscope.

Repeat steps 2 – 4 for other wind speeds up to a maximum of 10m/s if achievable.

Gather your data by completing tables 1 and 2

 Wind speed Uo  (m/s) Beaufort number Effect on land Output voltage V (volts) Output current I (amps) Rotor speed N (revs/min)

Table 1 measured data

Calculate the following

 Rotor radius use a ruler to measure from center to tip of turbine R = Swept area A=πR2 A = Blade area = blade area + hub area do your best! = Solidity = blade area / swept area. =

Table 2 measured data

Now analyse your data by completing table 3.

 Energy in the wind Electrical power Coefficient of performance Tip speed ratio E =  (watts) P = V x I   (watts) P/E (or column 2 /column 1)

Now present your results in graphical format to give you a better understanding of the data you have gathered and analysed.

Use excel and the x-y scatter chart for this.

Graph 1

Plot the values Uo (x-axis) against P (y1-axis) and E (y2-axis).

Graph 2

Plot the values of Uo (x-axis) against Cp (y-axis).

What conclusions do you draw?

How efficiently are you converting the kinetic energy in the wind into electrical energy that is stored chemically in the batteries?

Write up the laboratory formally and submit to turnitin. Please ensure presentation is clear and quote fully any references.

### The Beaufort Wind Speed Scale

Beaufort
Number
Wind Speed at 10m height Description Wind Turbine
effects
Effect on
land
Effect at
Sea
m/s
0 0.0 -0.4 Calm None Smoke rises vertically Mirror smooth
1 0.4 -1.8 Light None Smoke drifts; vanes unaffected small ripples
2 1.8 -3.6 Light None Leaves move slightly Definite waves
3 3.6 -5.8 Light Small turbines start – e.g. for pumping Leaves in motion; Flags extend Occasional breaking crest
4 5.8 -8.5 Moderate Start up for electrical generation Small branches move Larger waves; White crests common
5 8.5 -11.0 Fresh Useful power Generation at 1/3 capacity Small trees sway Extensive white crests
6 11.0 -14.0 Strong Rated power range Large branches move Larger waves; foaming crests
7 14.0 -17.0 Strong Full capacity Trees in motion Foam breaks from crests
8 17.0 -21.0 Gale Shut down initiated Walking difficult Blown foam
9 21.0 -25.0 Gale All machines shut down Slight structural damage Extensive blown foam
10 25.0 -29.0 Strong gale Design criteria against damage Trees uprooted; much structural damage Large waves with long breaking crests
11 29.0 -34.0 Strong gale Widespread damage
12 >34.0 Hurricane Serious damage Disaster conditions Ships hidden in wave troughs

Supplementary Theory

The power available to a wind turbine is the kinetic energy passing per unit time in a column of air with the same cross sectional area A as the wind turbine rotor, travelling with a wind speed u0. Thus the available power is proportional to the cube of the wind speed.

We can see that the power achieved is highly dependent on the wind speed. Doubling the wind speed increases the power eightfold but doubling the turbine area only doubles the power. Thus optimising the siting of wind turbines in the highest wind speed areas has significant benefit and is critical for the best economic performance. Information on power production independently of the turbine characteristics is normally expressed as a flux, i.e. power per unit area or power density in W/m2. Thus assuming a standard atmosphere with density at 1.225kg/s :

Wind speed m/s     Power W/m squared               5.0                76.6              10.0               612.5              15.0              2067.2              20.0              4900.0              25.0              9570.3

The density of the air will also have an effect on the total power available. The air is generally less dense in warmer climates and also decreases with height. The air density can range from around 0.9 kg/m3 to 1.4kg/m3. This effect is very small in comparison to the variation of wind speed.

In practice all of the kinetic energy in the wind cannot be converted to shaft power since the air must be able to flow away from the rotor area. The Betz criterion, derived using the principles of conservation of momentum and conservation of energy gives a maximum possible turbine efficiency, or power coefficient, of 59%. In practise power coefficients of 20 – 30 % are common. The section on Aerodynamics discusses these matters in detail.

Most wind turbines are designed to generate maximum power at a fixed wind speed. This is known as Rated Power and the wind speed at which it is achieved the Rated Wind Speed. The rated wind speed chosen to fit the local site wind regime, and is often about 1.5 times the site mean wind speed.

The power produced by the wind turbine increases from zero, below the cut in wind speed, (usually around 5m/s but again varies with site) to the maximum at the rated wind speed. Above the rated wind speed the wind turbine continues to produce the same rated power but at lower efficiency until shut down is initiated if the wind speed becomes dangerously high, i.e. above 25 to 30m/s (gale force). This is the cut out wind speed. The exact specifications for designing the energy capture of a turbine depend on the distribution of wind speed over the year at the site.

Performance calculations

Power coefficient Cp is the ratio of the power extracted by the rotor to the power available in the wind.

It can be shown that the maximum possible value of the power coefficient is 0.593 which is referred to as the Betz limit.

where

Pe is the extracted power by the rotor

V¥ is the free stream wind velocity (m/s)

A is area normal to wind         (m2)

ρ is density of the air              (kg/m3)

The tip speed ratio (l) is the ratio of the speed of the blade tip to the free stream wind speed.

where

w is the angular velocity of the rotor (rads/sec), and

R is the tip radius (m)

This relation holds for the horizontal axis machine which is the focus of these notes.

The solidity (g) is the ratio of the blade area to the swept frontal area (face area) of the machine

Mean chord length is the average width of the blade facing the wind.

Swept frontal area is pR2

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Need help-Wind Turbine Investigation

# Need help-CSE423 – Individual summary report

Need help-CSE423 – Individual summary report
This report is worth 10% of your grade.  The individual report describes your personal contributions to the capstone project. Late submissions will be penalized 10%.  Use the SafeAssign link on Blackboard to submit your work.
The report is to be in your own words.  Copying content from other sources, including other team member, is not acceptable.  The report will be checked against other students’ reports to verify unique content and wording.
Use Times New Roman 12pt with 1.5 line spacing. The following outline should be used for the report. You may need to deviate slightly, depending on the nature of your project.
1. Cover Page a. Title b. Class name c. Team name d. Brief project description (maximum 20 words)  2. Table of Contents (with page numbers) 3. Description of the overall project a. Work completed b. Defining the best of the work accomplished 4. Reflection on the team a. Evaluation of the success of the work produced by the team as a whole b. How things can be improved c. Moving forward next semester (goals and plans) 5. Summary of your contributions a. Work on team presentation b. Work on reports c. Work on product d. Work on team management (meeting minutes, etc.) 6. Reflection on your work a. Evaluation of the success of the work produced by you b. How you can be improved c. Lessons learned d. Moving forward next semester (goals and plans) 7. Conclusion

# Physics 211L- Lab#5: NEWTON’s SECOND LAW OF MOTION

Physics 211L- Lab#5: NEWTON’s SECOND LAW OF MOTION

Physics 211L

Peter Webb

September

Lab#5: NEWTON’s SECOND LAW OF MOTION

Abstract:

In this lab we are Verifying Newton’s 2nd Law of motion, we are also finding the acceleration using the derived equations  and which are both derived with the free body diagrams on the attached paper. We used a computer with logger pro, Rotary motion sensor (RMS), and rolling cart with wired force probe, cart track, table clamp, long rod, 5 gram and 10 gram masses.

Our results showed that the force acting on an object is proportional to the mass. This is shown when we increase the mass from 5g to 10g the force measured and the theoretical force nearly doubled as well. This proves Newton’s 2nd law of motion. Possible reasons for error would be caused by neglecting friction and the track not being perfectly straight and level.

Procedure:

The first thing we did is cleaning the track and wheels to make sure that the motion is smooth; we recorded the mass of the cart including the force probe which was 650.6 g and the mass of the string which was 3.3 g, then we added mass to the cart so that the total mass was equal to 1 kg .We used the RMS and the force gauge to collect data on Logger Pro. The force gauge was attached to the cart this combined weight became “M” and the weight hanging off the end of the RMS was “m”. The data collected from Logger Pro from both the force gauge and the RMS are shown below in Table 1 along with the comparison to the theoretical values with percent error and standard deviation for the 5g tests. The data collected from Logger Pro from both the force gauge and the RMS are shown below in Table 2 along with the comparison to the theoretical values with percent error and standard deviation for the 10g tests.

Data Tables and Plots/Results and error analysis:

Table 1:

 Test # Force Measured (N) Force Std dev. Force Theoretical (N) Force ∆% Acceleration Measured (m/s^2) Accel Std dev. Acceleration Theoretical (m/s^2) Acceleration ∆% 1 .046 .014 .049 6.12% .083 .004 .078 6.41% 2 .046 .006 .049 6.12% .056 .006 .078 28.21%

Table 2:

 Test # Force Measured (N) Force Std dev. Force Theoretical (N) Force ∆% Acceleration Measured (m/s^2) Accel Std dev. Acceleration Theoretical (m/s^2) Acceleration ∆% 1 .090 .007 .084 7.14% .106 .004 .156 32.05% 2 .088 .007 .084 4.76% .114 .009 .156 26.92%

Trial 1:

Velocity vs time graph

Force vs time graph

Trial 2:

Velocity vs time graph

Force vs time graph

Physics 211L- Lab#5: NEWTON’s SECOND LAW OF MOTION

Trial 3:

Velocity vs time graph

Force vs time graph

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[The roadway intersection at Birch Avenue and Leroux Street has the same intersection geometry as other nearby intersections in downtown Flagstaff, Arizona. Leroux Street is a two-way road with stop control at the intersection of Birch Avenue. Birch Avenue is an uncontrolled, two-lane one-way road with heavier average daily traffic.] [According to a network screening conducted by the City of Flagstaff, the intersection of Birch Avenue and Leroux Street has an estimated collision rate of 2.1 collisions per every million entering vehicles. This estimated collision rate is greater than the industry standard acceptable collision rate of 1.0 collisions (or less) per million entering vehicles. Due to a collision rate of 2.1, the City of Flagstaff has identified Birch Avenue and Leroux Street as the most dangerous intersection within the network screening study limits.] [If Birch Avenue and Leroux Street do not undergo the redesign process, the intersection will continue experiencing a high collision rate that could potentially cause economic and physical harm to intersection users.] [This preliminary proposal report outlines the strategy that the Traffic Engineering Team, or Team, will use to redesign the intersection to improve its overall safety. Within acceptable safety limits, the Team will also optimize traffic efficiency. The Team will make a primary and secondary redesign recommendation in a final report.] To choose appropriate design recommendations, the Team reviewed the guidelines of the traffic engineering industry and the City of Flagstaff’s standards and policies. The Team will collect data on the current state of the intersection of Birch Avenue and Leroux Street and will analyze the data to assess the intersection’s current conditions. The Traffic Engineering Team will conduct a warrant analysis to mitigate the City of Flagstaff’s legal liability and will conduct a cost analysis to meet the City’s budgetary needs. Finally, the Team will choose appropriate primary and secondary redesign recommendations to submit to the City of Flagstaff. Some early design concepts for the intersection’s traffic control device are an all-way stop, a roundabout, or a traffic signal.

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Common Ground | Destabilizing Condition | Costs & Benefits | Main Purpose

# Peer Critique – Final Report Draft: Proposal Peer review

Proposal Peer review

Peer Critique – Final Report Draft

Read each review question before beginning your critique.  After completing the critique, assign points for each category in the table provided.

Reviewer’s Name: _________________________________________

Title of Reviewed Proposal: __________________________________

1. Briefly, summarize the main points of the design proposal (in your own words).
1. Does the overall document demonstrate proper coherency/flow? Is the information easy to follow/understand? Mention specific document sections where coherency/flow is lacking.
1. Look at the entire paper for organizational headings and evaluate the figures and tables.
1. Are the figures and tables easy to understand? Explain.
1. Do the figures and tables help clarify and make the paper more concise? Explain.
1. Reread the entire paper. Focus on the details, such as grammar, spelling, active verbs, sentence structure, vague words (or phrases), consistency, clarity, citations (in-text with footnotes or reference list), etc.
2. Mark the actual paper.
3. Make constructive suggestions for ways to improve the paper.
4. Provide any additional concerns here:
1. What are the most notable strengths of this document? What did the authors do well?
1. List the two most important things the authors should do to improve this paper during revision. Be specific.

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Companies gaining market share and increasing profit margins

In light of the economic crises of 2009, explain how companies such as General Electric (GE) are trying to gain market share and increase profit margins.

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# Industrial Engineering

Industrial Engineering

1. INTRODUCTION

The project is intended to demonstrate students’ ability to develop a new product/service idea and/or criticize an existing product/service design. Students would independently choose an existing product/service, or develop a new design idea to evaluate in terms of customers’ needs, perceptions and functionality. They are expected to perform a perceptual mapping to position it on the market and execute the house of quality step of Quality Function Deployment (QFD). Through both methods, market gaps and competitive position of the product/service as well as the voice of the customers are identified.

For the service or the service component of a product, service blueprint should be prepared. Where it is applicable, current vs. ideal process flows should be compared. Finally to assess the quality of the service, SERVQUAL survey is applied.

For a product, existing/new product is analyzed in terms of DFM, DFA and DFE. VA/VE technique is exercised where it is applicable. Improvement suggestions for the product should be made.

In addition to applying technical knowledge in a ‘real world’ project, this would demonstrate the students’ ability to conduct group research, teamwork, and report writing and project management skills.

1. PROJECT SUMMARY (SCENARIO)

The project intends to evaluate either an existing or a new product/service design offering. In both cases, the students are expected to evaluate the product/service in terms of its form, functionality and customers’ perceptions through perceptual maps and the house of quality of QFD. This process might be helpful to identify the gap existed in the market so that it may bring some new product/service ideas. Some steps you need to evaluate in phase 1 are as follows:

• Definition of the product/service
• Main characteristics of the product/service
• Differentiating factors of the product/service
• Perceptual maps
• House of quality
•  Critical analysis of the product/service  In phase 2, the students should evaluate either the service further drawing the service blueprints and assessing the service quality through SERVQUAL survey (At least 30-40 responses are required) or the product using the tools such as DFM, DFA, DFE and VA/VE. In conclusion, a comprehensive analysis of the findings should be discussed.

Report Requirements:

The report should follow the APA format and guidelines, and includes the following subsections after a cover page:

• What is the product/service you are going to evaluate?
• Why is it interesting and who would use your analysis?
• What data will you use?
• How will you collect and organize the data?

What work do you plan to do in the project?

• Introduction to the problem: The topic of the project and problem statement,
• Description of the selected product/service,
• Objectives of the project,
• Description of the collected data
• Main characteristics of the product/service
• Differentiating factors of the product/service
• Perceptual maps
• House of quality
• Critical analysis of the product/service
• Work schedule & Gantt chart for the project showing the current progress.
• Evaluation of the product/service (service blueprint and SERVQUAL results for services, and DFM, DFA, DFE and VA/VE for the products)
• Results and Analysis
• Conclusions and Recommendations.

# Physics Experimental Results and Analysis

Physics Experimental Results and Analysis

The Discussion of Results section includes an explanation of how the collected data provide logical and reasonable support for the statement found in the Conclusion. The Discussion of Results should be clear, specific, and reasonable. It is often a lengthy section of several sentences and even paragraphs. It is an opportunity for a student to express their understanding of the clear and logical line connecting the evidence (Data section) to the verdict (Conclusion section). In the Discussion of Results section, the student writes, explains, elaborates, supports and cites evidence from the Data section. The student describes how the observations and collected data support the conclusion, citing specific examples as evidence. The student may describe what would have been observed if a contrary conclusion were to be drawn and show how those observations were not made. The student may identify data which seem inconsistent with the conclusion and explain why such data are not swaying the Conclusion in a different direction.

A Discussion of Results section sometimes includes an error analysis. In an error analysis, the student evaluates the reliability of the data. An error analysis is a response to the question “How well did I do?” Expectations or theories (found in textbooks) may be introduced and the consistency between the experimental findings and the theory is discussed. If there is an accepted answer to the question which involves a determined quantity, a percent error calculation is often performed (see bottom of page). If two values are being compared (perhaps a class average of a determined quantity and an individual lab group’s value), a percent difference calculation is often performed (seebottom of page). An error analysis will often identify specific data trials which are in error, describe the manner in which they err from the expected results and attempt to explain the cause of such errors.

here, you show that you understand the experiment beyond the simple level of completing it. Explain. Analyse. Interpret. Some people like to think of this as the “subjective” part of the report. By that, they mean this is what is not readily observable. This part of the lab focuses on a question of understanding “What is the significance or meaning of the results?” To answer this question, use both aspects of discussion:

Analysis Interpretation
What do the results indicate clearly?
What have you found?
Explain what you know with certainty based on your results and draw conclusions: What is the significance of the results? What ambiguities exist? What questions might we raise? Find logical explanations for problems in the data:
Since none of the samples reacted to the Silver foil test, therefore sulfide, if present at all, does not exceed a concentration of approximately 0.025 g/l. It is therefore unlikely that the water main pipe break was the result of sulfide-induced corrosion. Although the water samples were received on 14 August 2000, testing could not be started until 10 September 2000. It is normally desirably to test as quickly as possible after sampling in order to avoid potential sample contamination. The effect of the delay is unknown.
More particularly, focus your discussion with strategies like these:

Compare expected results with those obtained.

If there were differences, how can you account for them? Saying “human error” implies you’re incompetent. Be specific; for example, the instruments could not measure precisely, the sample was not pure or was contaminated, or calculated values did not take account of friction.

Analyze experimental error.

Was it avoidable? Was it a result of equipment? If an experiment was within the tolerances, you can still account for the difference from the ideal. If the flaws result from the experimental design explain how the design might be improved.

Explain your results in terms of theoretical issues.

Often undergraduate labs are intended to illustrate important physical laws, such as Kirchhoff’s voltage law, or the Müller-Lyer illusion. Usually you will have discussed these in the introduction. In this section move from the results to the theory. How well has the theory been illustrated?

Relate results to your experimental objective(s).

If you set out to identify an unknown metal by finding its lattice parameter and its atomic structure, you’d better know the metal and its attributes.

Compare your results to similar investigations.

In some cases, it is legitimate to compare outcomes with classmates, not to change your answer, but to look for any anomalies between the groups and discuss those.

Analyze the strengths and limitations of your experimental design.

This is particularly useful if you designed the thing you’re testing (e.g. a circuit).