Lab notebooks and technical reports

A measurement that is not recorded properly is a measurement that has to be made again. Worse, a result reported without its conditions, uncertainty and method can mislead whoever relies on it. Engineering labs therefore insist on two kinds of writing: the lab notebook, a running record made at the bench while the work happens, and the technical report, a structured document written afterwards that presents the results and the reasoning to someone who was not there. This last lesson covers both, along with fitting data to a model, presenting graphs and tables, and the habits that make your records trustworthy. It ends with Leo's report on the controller prototype tests.

At the end of the term, Amara asks Leo to write up the verification of the pedestrian controller's prototype boards: the supply, the LED drivers, the input conditioning and the temperature sensing, with the results of the chamber test. The report will go to the design team, to Cedarline's quality records and, eventually, to the municipal customers who buy the controller.

The lab notebook

A lab notebook records what you did, what you observed and what you thought at the time, in the order it happened. It is written during the work, not reconstructed afterwards from memory. Each entry starts with the date and a short statement of purpose, lists the equipment used with model and serial or asset numbers and calibration due dates, sketches the circuit or setup with the measurement points marked, and then records the readings directly, with units, as they are taken. Observations and surprises go in too, along with the reasoning behind each decision: 'reading drifted for 2 min after power-up; waited until stable before recording' is the kind of note that explains an odd result months later.

Many organizations, including Cedarline, use an electronic notebook or a version-controlled project folder instead of paper, which makes it easy to attach scope captures, data files and scripts. The principles are the same. Entries are never deleted or overwritten: a mistake is struck through or marked as superseded, with the correction beside it, so that the record shows what really happened. In research and product development, notebooks can also serve as evidence of when an idea was conceived or a test performed, which is another reason to date entries and keep them complete.

Fitting data to a model

Much lab analysis consists of comparing measurements with a model: a straight line through voltage and current that gives a resistance, an exponential decay that gives a time constant, a calibration curve that relates a sensor's output to temperature. The standard method for a straight line y = mx + b is least squares, which chooses the slope and intercept that minimize the sum of the squared vertical distances between the points and the line. It also gives the uncertainty of the slope and intercept from the scatter of the points, and the residuals, the differences between the data and the fitted line, which should look like random noise if the model is right.

Always plot the residuals. A curve in the residuals means the model is wrong, for example a resistor heating as the current rises so that its resistance increases. One point far from the others suggests a recording error or a real event worth investigating; it should be checked, not silently deleted. The coefficient of determination, R², is often quoted, but a value of 0.999 does not prove the model is right: a slightly curved relationship can still give a very high R². The residual plot tells you more.

# Least-squares line through the LED driver's current-sense data, with slope uncertainty
import math, statistics as st
# Programmed LED current setpoint (mA) and measured sense voltage (mV)
x = [50, 100, 150, 200, 250, 300, 350]
y = [111.2, 221.6, 333.4, 443.1, 555.6, 664.9, 777.3]
n = len(x)
sx, sy = sum(x), sum(y)
sxx = sum(v * v for v in x); sxy = sum(a * b for a, b in zip(x, y))
m = (n * sxy - sx * sy) / (n * sxx - sx ** 2)
b = st.mean(y) - m * st.mean(x)
res = [yi - (m * xi + b) for xi, yi in zip(x, y)]
s_res = math.sqrt(sum(r * r for r in res) / (n - 2))
s_m = s_res * math.sqrt(n / (n * sxx - sx ** 2))
s_b = s_res * math.sqrt(sxx / (n * sxx - sx ** 2))
ss_tot = sum((yi - st.mean(y)) ** 2 for yi in y)
r2 = 1 - sum(r * r for r in res) / ss_tot
print(f"slope m = {m:.4f} +/- {s_m:.4f} ohm (mV per mA), intercept b = {b:.2f} +/- {s_b:.2f} mV, R^2 = {r2:.6f}")
print("residuals (mV):", ", ".join(f"{r:+.2f}" for r in res))

slope m = 2.2194 +/- 0.0028 ohm (mV per mA), intercept b = -0.00 +/- 0.62 mV, R^2 = 0.999992
residuals (mV): +0.23, -0.34, +0.50, -0.77, +0.76, -0.91, +0.52

The fit gives a slope of about 2.219 Ω, which is the sense resistor's effective value including any gain error in the driver's current setting, in close agreement with the four-wire measurement of 2.218 Ω in lesson 8. The intercept is essentially zero, 0.0 ± 0.6 mV. The residuals scatter between about −0.9 and +0.8 mV, alternating in sign with no curve, so the straight-line model fits. Leo reports the slope with its uncertainty and includes the residual plot in an appendix.

Graphs and tables that communicate

A good graph shows the data, not the decoration. Label both axes with the quantity and its unit, for example 'LED current (mA)'. Plot measured data as markers, and draw fitted models or theory as lines, so the reader can see which is which. Show error bars when the uncertainty is significant relative to the scale. Choose logarithmic axes when the data span several decades, as frequency responses and thermistor curves do. Start the vertical axis at zero when the reader will compare magnitudes; do not, when the interest is in small variations around a large value. Give every graph and table a number and a caption that says what it shows, and refer to it in the text. Tables are better than graphs when the reader needs exact values; graphs are better for trends and comparisons.

Structure of a technical report

A technical report follows a structure that lets different readers find what they need quickly. A manager may read only the summary; a designer will read the results and discussion; someone repeating the test will need the method in full. Write the summary last, after you know what the results mean.

In engineering practice in Canada, reports that carry engineering judgement are often reviewed and authenticated by a professional engineer, and the reasoning has to stand on the page. Leo's report will be checked by Amara and approved by Daniel Fortin, a P.Eng., before it goes into Cedarline's quality records.

Writing style for technical reports

Technical writing aims to be clear, specific and honest. Use numbers instead of adjectives: 'the ripple was 0.21 V RMS, within the 0.5 V limit' rather than 'the ripple was low'. State results with uncertainties and units, rounded consistently, as lesson 2 described. Use the past tense for what was done and the present tense for what is generally true. Distinguish clearly between what you measured, what you calculated and what you assumed. Report problems and anomalies rather than hiding them: a test that partly failed, an instrument that drifted, a point that did not fit. A reader can work with an honest limitation, but cannot work with a result that was quietly adjusted. Cite data sheets and standards by name and edition, and credit any data, figures or code that are not your own.

Integrity in measurement

The value of everything in this course depends on honesty. Record the readings you actually got, not the ones you expected. Do not discard data because it is inconvenient; if a point is excluded, say which and why. Do not copy results from another group or from a previous year's report. Do not adjust a calibration factor until the result matches the answer you wanted. In industry, falsified test results can put unsafe products into public use, and in a traffic controller they could put pedestrians at risk. Professional engineering codes of ethics in both Canada and the United States treat honest reporting of results as a basic duty, and universities treat fabricating or falsifying data as serious academic misconduct.