Laws and Definitions - ATPL 081 — Principles of Flight

Aerodynamics is a quantitative subject: every statement about lift, drag or stability is ultimately a statement about masses, forces, pressures and speeds. This first lesson pins down those quantities, the units they are measured in, and the three laws and two flow equations that the whole of Principles of Flight keeps reusing. None of it is difficult on its own, but every later lesson assumes it, so it has to sit solidly before anything else.

Units, mass, force and weight

The exam works in SI units throughout, and several questions ask nothing more than whether you know which unit belongs to which quantity:

Mass — kilogram (kg)
Acceleration — metre per second squared (m/s²)
Force and weight — newton (N)
Velocity — metre per second (m/s)
Energy — joule (J)
Density — kilogram per cubic metre (kg/m³)
Pressure — newton per square metre (N/m²), also called the pascal (Pa)
Temperature — kelvin (K); 0 °C = 273.15 K
Wing loading — newton per square metre (N/m²): weight spread over wing area
Power — watt (W), one joule per second

Mass and weight are the pair candidates mix up, so take the definitions one at a time:

Mass — the amount of matter in a body; it does not change with location.
Force — what changes a body's state of motion; acceleration is the rate at which its velocity changes as a result.
Weight — simply one particular force: the pull of gravity on a mass.

Newton's three laws

Newton's three laws are the grammar of every force argument in this subject, and the exam wants more than the statements: it gives you a flight situation and asks which law explains it. So take them one at a time, each with the interpretation that questions are built on.

The first law (the law of inertia) says a body remains at rest, or continues at constant speed in a straight line, unless a resultant force acts on it. The key word is resultant. An airliner in steady cruise at 250 m/s has enormous forces acting on it (lift and weight in the hundreds of kilonewtons, thrust and drag in the tens), yet it neither speeds up, slows down nor turns, because those forces balance exactly and the resultant is zero. Nothing has to keep pushing a moving aircraft to keep it moving; that is the deepest habit of thought this law breaks. Turn the statement around and it becomes a diagnostic tool: the moment anything about the motion changes (the speed, or merely the direction, as in a turn at constant speed), some force must have gone out of balance first. A steady turn is accelerated flight, because velocity includes direction.

The second law quantifies what an unbalanced force does: the body accelerates in the direction of the resultant force, in proportion to that force, and in inverse proportion to its own mass. Doubling the resultant force doubles the acceleration; doubling the mass halves it. This is why the same thrust surplus accelerates a lightly loaded aeroplane noticeably harder than the same aircraft at maximum take-off mass, and why heavy aircraft need such long runways.

The third law says that whenever one body exerts a force on a second, the second exerts an equal and opposite force back on the first: forces only ever exist in pairs. The pair never cancels, because the two forces act on different bodies: that is the detail exam questions probe. Aviation runs on this law twice over. In propulsion, an engine (propeller or jet) accelerates a mass of air rearwards, and the reaction on the engine pushes the aircraft forwards: the aircraft does not push against the ground or against anything solid, only against the air it throws behind itself. In lift, a wing deflects the oncoming airflow downwards, and the reaction to that downwash pushes the wing up. The downwash is not a by-product of lift; it is the other half of the same interaction, and a wing that deflected no air downwards would generate no lift at all.

Air density

Density (symbol $\rho$ , 'rho') is mass per unit volume. Air at sea level in the International Standard Atmosphere packs 1.225 kg into every cubic metre. Aerodynamic forces come from air's mass being pushed around, so density sits inside every force equation in this subject, and it is set by pressure and temperature (plus, to a small degree, humidity: water vapour is lighter than the air it displaces, so moist air is slightly LESS dense than dry air):

Read it both ways. At constant temperature, density is proportional to pressure: compress air and it packs tighter. At constant pressure, density is inversely proportional to temperature: heat air and it expands, so a hot day means thinner air. Climbing gives you both effects at once (pressure and temperature each fall with altitude), but the pressure drop dominates, so density always decreases with altitude. Thinner air is the single root cause behind longer take-off runs, reduced engine power and higher true airspeeds that keep returning throughout the ATPL subjects.

The International Standard Atmosphere

Saying 'the density at 30,000 ft' only means something if everyone agrees which atmosphere is being talked about, and the real one changes by the hour. So ICAO defined the International Standard Atmosphere (ISA): an agreed, fictitious average atmosphere that every altimeter, performance table, aerodynamic reference and exam question is calibrated against. It is not a weather forecast; it is the ruler the real atmosphere gets measured with. A real day is then described by its deviation: 'ISA +10' means 10 °C warmer than standard at every level, and performance tables are entered exactly that way.

The standard starts at sea level with 1013.25 hPa, +15 °C and 1.225 kg/m³, and stacks three names above it:

Troposphere — the lowest layer, where all weather lives and almost all flying happens. Temperature falls throughout it at a fixed lapse rate of 1.98 °C per 1,000 ft (6.5 °C per km, and near enough 2 °C per 1,000 ft for mental arithmetic).
Tropopause — where the fall stops abruptly: 36,090 ft (11 km) in ISA, with the temperature at −56.5 °C.
Stratosphere — the layer above, where ISA holds the temperature constant at −56.5 °C up to 65,617 ft (20 km): higher than anything in this syllabus flies; higher still, the stratosphere slowly warms again.

A jet cruising at 39,000 ft therefore sits just above the tropopause in air of unchanging temperature, which matters again in the high-speed lessons: the local speed of sound depends on temperature alone, so above the tropopause it stops falling.

Density follows the same staircase downwards, and two anchors are worth memorising: static pressure has fallen to half its sea-level value by about 18,000 ft, and density to half by about 22,000 ft; density loses ground more slowly because the falling temperature partly props it up. By the tropopause, density is down to roughly a third of the sea-level figure: the same wing, at the same true speed, meets a third of the air mass per second. The full physics of the real atmosphere (moisture, fronts, inversions, why the tropopause height actually varies from 25,000 ft at the poles to 55,000 ft over the equator) belongs to subject 050, Meteorology; what this lesson needs is the standard ruler and what it does to density.

Static, dynamic and total pressure

Air pushes on a surface in two distinct ways:

Static pressure — the pressure the air exerts in all directions simply by being there: the weight of the atmosphere above, felt equally on every surface, moving or not.
Dynamic pressure — exists only for moving air: it is the extra pressure you can feel when a flow is brought to rest against a surface, like the push on your palm out of a car window.

Dynamic pressure deserves a second reading: $\tfrac{1}{2}\rho v^2$ is the kinetic energy of each cubic metre of moving air. That makes $q$ a direct measure of how much energy the airflow carries, which is why every aerodynamic force in this subject scales with it, and why the airspeed indicator is, at heart, a dynamic-pressure gauge: what it displays as indicated airspeed is the aircraft's $q$ dressed up in speed units.

Bernoulli's equation ties the two pressures together. For steady, incompressible flow (a good model below roughly 200 kt), the sum of static and dynamic pressure along a streamline is constant. That sum is called total pressure, or stagnation pressure: the pressure where the flow is brought completely to rest.

One subtlety the exam likes: total pressure is constant within a flow, but it differs between systems. Two aeroplanes at the same altitude share the same static pressure, but the faster one carries more dynamic pressure, so its total pressure is higher. Each aircraft, each stream tube, has its own $p_t$ set by its own speed.

The venturi and the equation of continuity

Bernoulli tells you pressure and speed trade off; the equation of continuity tells you when speed changes in the first place. In a stream tube (an imaginary tube whose walls are streamlines, which no air crosses) the same mass of air must pass every cross-section each second. For incompressible flow that reduces to: area times velocity is constant.

Put the two equations together in a venturi (a tube with a narrowed throat) and the whole mechanism of subsonic aerodynamics appears in miniature. The throat has less area, so continuity forces the flow to speed up there; the flow has gained dynamic pressure, so Bernoulli says its static pressure must have dropped by the same amount. Faster flow, lower static pressure. The curved upper surface of a wing squeezes the streamlines above it in just this way, and the reduced static pressure on that surface is where most of the lift comes from: the subject of the next lessons.

From pressures to the airspeed indicator

The pitot-static system measures exactly the quantities this lesson defined:

Pitot tube — faces the flow and brings it to rest, so it senses total pressure.
Static port — flush with the fuselage side, it senses static pressure.
Airspeed indicator (ASI) — a differential gauge between the two, and total minus static is dynamic pressure.

The instrument then displays that $q$ on a scale calibrated for ISA sea-level density, which is why the speed it shows is called indicated airspeed (IAS) rather than a true speed.

Four airspeeds build on that reading, each one correction apart, and before defining them it is worth seeing why four exist at all. The problem is that 'how fast am I going?' has three genuinely different answers, needed by three different users:

The wing — does not care about your speed over the ground or even through the air: aerodynamic forces follow dynamic pressure, so flying the aeroplane (stall margins, approach speeds, control feel) needs a q-based number.
The structure — the same: airframe load limits are really dynamic-pressure limits.
The navigator — needs the aircraft's actual speed through the air mass to plan legs and fuel.

One instrument, sensing only q, has to serve all three, so a chain of named corrections connects what the needle shows to what each user needs. That chain is the ladder below.

Indicated airspeed (IAS) is the raw reading on the dial. It is honest about one thing only: the dynamic pressure the instrument actually sensed. That turns out to be exactly what a pilot needs day to day, because the aerodynamic forces on the aircraft respond to the same $q$ the instrument does, which is why an aeroplane stalls at essentially the same indicated airspeed at any altitude, and why operating speeds are published as indicated values.

Calibrated airspeed (CAS) is IAS with the measurement's own imperfections removed. Two errors are corrected: instrument error, the small mechanical inaccuracy of the gauge itself, and position error, which arises because the static port sits in airflow disturbed by the aircraft's own body, so it never senses perfectly undisturbed static pressure. Position error changes with angle of attack and configuration (lowering flap changes the flow around the port), which is why the flight manual tables the correction rather than quoting one number.

Equivalent airspeed (EAS) removes compressibility error. At higher speeds the air no longer behaves as incompressible: it packs together as the pitot tube brings it to rest, generating extra pressure on top of the true dynamic pressure, so the instrument over-reads. EAS subtracts that surplus, making it the speed that corresponds exactly to the real $q$ : the speed aerodynamic theory actually means. Because structural load limits are at heart dynamic-pressure limits, EAS is the engineer's speed: aerodynamic and structural calculations run on it. Below roughly 200 kt and 10,000 ft the compressibility effect is negligible, which is why light aircraft ignore EAS and jets cannot.

True airspeed (TAS) is the aircraft's actual speed through the air mass, and it exposes the calibration trick from earlier: the ASI converts $q$ to a speed assuming ISA sea-level density. At altitude the real density is lower, so producing the same dynamic pressure requires moving faster through the air; TAS rises above EAS, and the gap widens with every foot of climb:

At 40,000 ft the density is roughly a quarter of the sea-level value, so the square root makes TAS about double the EAS: an airliner indicating around 240 kt up there is truly moving through the air at roughly 480 kt. Navigation and flight planning therefore run on TAS (with wind added to give groundspeed, the business of subject 061), while handling and structural limits stay with the indicated values. The instrument mechanics behind these errors get their full treatment in subject 022, Instrumentation; what this lesson fixes is the ladder itself.

What the exam asks

Questions from this lesson are short and unforgiving about definitions. This overview follows the learning objectives one by one. Expect to:

Match quantities to their SI units, and define mass, force, acceleration and weight: keeping mass and weight strictly apart

State Newton's three laws and identify which one a given flight situation illustrates

Explain what air density is, name the properties that set it, and predict its response to pressure and temperature changes using the equation of state both ways

Define static, dynamic and total pressure; state the dynamic-pressure formula and compute q from density and speed (watch the units: speed in m/s)

Read dynamic pressure as the flow's kinetic energy per volume and connect it to what the ASI senses

State Bernoulli's equation, and apply it together with continuity to venturis and stream tubes: qualitatively and numerically

Recognise that total pressure is constant within one flow but differs between systems (two speeds, two total pressures)

State which pressures feed the pitot tube, the static port and the ASI

Define IAS, CAS, EAS and TAS in the correct correction order, with the correct correction between each pair