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
  • Recognize how measurement accuracy affects flight calculations
  • Apply suitable precision when performing aviation computations

🧠 Concept

Physics describes the real world using measured quantities.
Each measurement has:

  • Magnitude (how much)
  • Unit (what kind)

⚙ Base Quantities and SI Units

The International System Of Units (SI) is a metric system used in science providing a complete metric system for units of measurement and is based on the following fundamental units. Not all units have been included due to 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 fundamental 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 Application

Measurement Aviation Unit Conversion
Distance Nautical Mile (NM) 1 NM = 1852 m
Altitude 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 / time m/sÂČ â€”
Force mass × acceleration N (kg·m/sÂČ)
Pressure force / area Pa (N/mÂČ)
Energy force × distance J (N·m)

💡 Prefixes

Prefix Symbol Multiplier
giga G ×1,000,000,000 (or 10^9)
mega M ×1,000,000 (or 10^6)
kilo k ×1,000 (or 10³)
centi c ×0.01 (or 10^{-2})
milli m ×0.001 (or 10^{-3})
micro ” ×0.000001 (or 10^{-6})
nano n ×0.000000001 (or 10^{-9})

âœłïž Accuracy and Precision

Although the terms accuracy and precision are often used together, they describe two different ideas:

Term Meaning Aviation Example
Accuracy How close a value is to the true or accepted value Altimeter reading compared to true altitude
Precision How consistent repeated measurements are Multiple readings of fuel flow on the same engine

 

✅ Accuracy = closeness to truth
✅ Precision = consistency between measurements

✈ Pilot Application

In aviation instruments:

  • The altimeter may be precise (stable readings) but inaccurate (mis-set QNH).
  • A fuel flow meter might give readings with ±0.2 L/h variation (precision), but the total fuel burned must still match tank quantity (accuracy).

âœłïž Significant Figures (s.f.)

Significant figures indicate the number of digits that carry 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 s.f. (4 and 5)
3.60 3 s.f. (trailing zero counts after decimal)
1200 2 s.f. unless written as 1.20 × 10³
5.678 4 s.f. all non-zero digits
0.0700 3 s.f. zeros after decimal and digits count

 

🧠 Rule Summary

1ïžâƒŁ Leading zeros → not significant
2ïžâƒŁ Zeros between digits → significant
3ïžâƒŁ Zeros after a decimal → significant
4ïžâƒŁ Trailing zeros in a whole number → ambiguous (use scientific notation)

✅ Example:

1200 = 2 s.f.
1.200 × 10³ = 4 s.f.

âœłïž Rounding to Significant Figures

To round to a given number of significant figures:

1ïžâƒŁ Identify the significant digits.
2ïžâƒŁ Look at the next digit — if ≄ 5, round up; if < 5, round down.

Original Rounded to 3 s.f. Rounded to 2 s.f.
12.348 12.3 12
0.07649 0.0765 0.076
2845 2850 2800

 

✅ Example:

3.45678 (5 s.f.) → 3.46 (3 s.f.)

✈ 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’s no benefit in quoting more digits than the measurement allows.

âœłïž Decimal Places vs Significant Figures

Concept What It Refers To Example
Decimal Places (dp) Number of digits after the decimal point 12.345 → 3 dp
Significant Figures (s.f.) Number of meaningful digits from first non-zero digit 12.345 → 5 s.f.

 

✅ Use decimal places when the decimal structure matters (e.g., money, pressure)
✅ Use significant figures for measured quantities and scientific accuracy

âœłïž Combining Values in Calculations

When combining numbers:

  • Addition/Subtraction: Round to the fewest decimal places
  • Multiplication/Division: Round to the fewest significant figures

đŸ§© Example 1 — Addition

12.34+1.2 = 13.54 → 13.5

(rounded to 1 decimal place, since 1.2 has only one dp)

đŸ§© Example 2 — Multiplication

3.5×4.67 = 16.345 → 16

(2 s.f. result, since 3.5 has 2 s.f.)

âœłïž Errors and Measurement Uncertainty

Every measurement has some degree of uncertainty.
A value is usually written as:

Measured value ± Error

Example:

2500 m±20 m

This tells you the range of possible true values: 2480 m – 2520 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.

âœłïž Examples of Correct Precision in Aviation

Quantity Example Correct Precision
Airspeed 118.5 kt 1 decimal place
Altitude 6,500 ft nearest 50 or 100 ft
Pressure 1013.25 hPa 2 decimal places
Fuel Quantity 63.4 L 1 decimal place
Weight 1230 kg 3 or 4 s.f.

 

✅ 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.

💡Appropriate Precision Example

Instrument display → 63.4 L

Pilot report → 63 L

Do not record 63.421 L — this implies false accuracy

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