Physics – Units and Measurements
🎯 Learning Objectives
By the end of this lesson, students will:
- Understand physical quantities and units
- Convert between common aviation measurement systems
- Use prefixes (kilo-, milli-, etc.) and scientific notation
- Understand the difference between accuracy and precision
- Identify significant figures (s.f.) in a number
- Understand how measurement accuracy affects flight calculations
- Use appropriate precision when performing aviation calculations
🧠 Concept
Physics describes the real world using measured quantities.
Each measurement has:
- Magnitude (how much)
- Unit (type)
⚙️ Base Quantities and SI Units
The International System of Units (SI) is a metric system used in science that provides a comprehensive set of units of measurement and is based on the following base units. Not all units have been included due to their irrelevance to the EASA syllabus:
| Quantity | Symbol | Unit | Symbol |
|---|---|---|---|
| Length | (l) | meter | m |
| Mass | (m) | kilogram | kg |
| Time | (t) | second | s |
| Temperature | (T) | Kelvin | K |
| Electric current | (I) | ampere | A |
Almost all other SI units can be derived in terms of one or more of the base units.
| Quantity | Symbol | Unit | Symbol |
|---|---|---|---|
| Frequency | Hz | Hertz | Hz |
| Energy | J | Joule | J |
| Force | F | Newton | N |
| Pressure | P | Pascal | Pa |
| Power | W | Watt | W |
| Electric Charge | Q | Coulomb | C |
| Potential Difference | V | Volt | V |
| Capacitance | C | Farad | F |
✈️ Aviation App
| Measurement | Aviation Unit | Conversion |
|---|---|---|
| Distance | Nautical Mile (NM) | 1 NM = 1,852 m |
| Elevation | Feet (ft) | 1 ft = 0.3048 m |
| Speed | Knot (kt) | 1 kt = 0.514 m/s |
| Pressure | hectopascal (hPa) | 1 hPa = 100 Pa |
⚙️ Derived Quantities
Some quantities are combinations of base units:
| Quantity | Formula | Unit | Derived Unit |
|---|---|---|---|
| Speed | distance / time | m/s | — |
| Acceleration | change in speed over time | m/s² | — |
| Force | mass × acceleration | N | (kg·m/s²) |
| Pressure | force / area | Pa | (N/m²) |
| Energy | force × distance | J | (N·m) |
💡 Prefixes
| Prefix | Symbol | Multiply |
|---|---|---|
| giga | G | ×1,000,000,000 (or 10^9) |
| mega | M | ×1,000,000 (or 10^6) |
| kilo | k | ×1,000 (or 10³) |
| cent | c | ×0.01 (or 10^(−2)) |
| million | m | ×0.001 (or 10^(−3)) |
| microphone | µ | ×0.000001 (or 10^(−6)) |
| nano | n | ×0.000000001 (or 10^(−9)) |
✳️ Accuracy and Precision
Although the terms " accuracy " and "precision " are often used together, they refer to two different concepts:
| Term | Meaning | Aviation Example |
|---|---|---|
| Accuracy | How close a value is to the true or accepted value | Altimeter reading compared to actual altitude |
| Precision | How consistent repeated measurements are | Multiple fuel flow readings on the same engine |
✅ Accuracy = closeness to the truth
✅ Precision = consistency between measurements
✈️ Pilot Application
In aviation instruments:
- The altimeter may be accurate (consistent readings) but incorrect (incorrectly set QNH).
- A fuel flow meter may have a reading variation of ±0.2 L/h (precision), but the total amount of fuel burned must still match the amount in the tank (accuracy).
✳️ Significant Figures (s.f.)
Significant figures refer to the number of digits that convey meaningful information about the precision of a measurement.
All digits except leading zeros are considered significant.
| Example | Number of Significant Figures | Notes |
|---|---|---|
| 0.0045 | 2 n. | (4 and 5) |
| 3.60 | 3 n.d. | (trailing zeros after the decimal point) |
| 1200 | 2 n. | unless written as 1.20 × 10³ |
| 5.678 | 4 n. | all non-zero digits |
| 0.0700 | 3 n.d. | number of zeros after the decimal point and total number of digits |
🧠 Rule Summary
1️⃣ Leading zeros → not significant
2️⃣ Zeros between digits → significant
3️⃣ Zeros after a decimal point → significant
4️⃣ Trailing zeros in a whole number → ambiguous (use scientific notation)
✅ Example:
1,200 = 2 s.f.
1,200 × 10³ = 4 s.f.
✳️ Rounding to Significant Figures
To round to a specified number of significant figures:
1️⃣ Identify the significant digits.
2️⃣ Look at the next digit — if ≥ 5, round up; if < 5, round down.
| Original | Rounded to 3 decimal places | Rounded to 2 decimal places |
|---|---|---|
| 12.348 | 12.3 | 12 |
| 0.07649 | 0.0765 | 0.076 |
| 2845 | 2850 | 2800 |
✅ Example:
3.45678 (5 significant figures) → 3.46 (3 significant figures)
✈️ Pilot Application
A flight distance of 123.47 NM might be rounded to 123 NM if the navigation accuracy (GPS or VOR) is only ±0.5 NM.
There is no point in providing more digits than the measurement allows.
✳️ Decimal Places vs. Significant Figures
| Concept | What It Means | Example |
|---|---|---|
| Decimal Places (dp) | Number of digits after the decimal point | 12,345 → 3 decimal places |
| Significant Figures (s.f.) | Number of significant digits from the first non-zero digit | 12,345 → 5 n.d. |
✅ Use decimal places when the decimal structure is important (e.g., currency, pressure)
✅ Use significant figures for measured quantities and scientific accuracy
✳️ Combining Values in Calculations
When combining numbers:
- Addition/Subtraction: Round to the fewest decimal places
- Multiplication/Division: Round to the fewest significant figures
🧩 Example 1 — Addition
12.34 + 1.2 = 13.54 → 13.5
(rounded to one decimal place, since 1.2 has only one decimal place)
🧩 Example 2 — Multiplication
3.5 × 4.67 = 16.345 → 16
(2 significant figures in the result; since version 3.5 has 2 significant figures)
✳️ Errors and Measurement Uncertainty
Every measurement has some degree of uncertainty.
A value is usually written as:
Measured value ± Error
Example:
2,500 m ± 20 m
This indicates the range of possible true values: 2,480 m – 2,520 m.
✈️ Pilot Application
When reading aircraft instruments:
- Airspeed Indicator (ASI): ±2 kt
- Altimeter: ±20 ft
- Fuel gauge: ±1 L
Understanding these tolerances helps you interpret readings safely.
✳️ Examples of Correct Precision in Aviation
| Quantity | Example | Correct Precision |
|---|---|---|
| Airspeed | 118.5 kt | 1 decimal place |
| Elevation | 6,500 ft | within 50 or 100 feet |
| Pressure | 1013.25 hPa | 2 decimal places |
| Fuel Quantity | 63.4 L | 1 decimal place |
| Weight | 1,230 kg | 3 or 4 bedrooms |
✅ Use the same level of precision as your measuring instrument.
Reporting 1230.457 kg would be meaningless if your scale only measures to ±0.5 kg.
💡Example of Appropriate Precision
Instrument display → 63.4 L
Pilot report → 63 L
Do not record 63.421 L — this implies false accuracy
