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Airspeed describes an aircraft's motion relative to the surrounding air. When the kinematic magnitude is intended, it is the true airspeed,It differs from groundspeed whenever wind changes the relative motion. A ground-station velocity alone cannot establish the aerodynamic airspeed.^[ref]

An airspeed instrument normally infers motion from pressure. At low Mach number, for an aligned Pitot-static tube in the regime of the Bernoulli equation,Here $p_0$ is stagnation pressure, $p$ is static pressure and $\rho$ is air mass density. For a stipulated difference of $245\mathrm{Pa}$, $\rho =1.225kg/{\mathrm{m}}^3$ gives $V=20m/s$; the same difference at $0.6125kg/{\mathrm{m}}^3$ gives $28.28m/s$. The instrument senses a pressure difference, so interpreting its reading requires a density model and an instrument calibration.^[ref]

Indicated airspeed is the displayed reading before instrument and installation corrections. Calibrated airspeed includes those corrections. True airspeed expresses actual motion through the air, rather than simply relabeling either reading. The FAA distinguishes these quantities in its instrument chapter.^[ref]

The square-root calculation above assumes an appropriate low-speed stopping relation. At appreciable Mach number, compressibility changes that relation; a blocked passage or displaced static pressure source introduces a different measurement problem. Report which airspeed convention and corrections accompany a performance curve. Comparing speeds without that information can confound a change of air mass density with a change in the aircraft's loading. Functioning ports and known corrections are part of the inference, not extra measurements of groundspeed.

The glide angle is the inclination of a descending flight path below the horizontal. A positive $\gamma$ will denote descent here. For aerodynamic reasoning it is important to specify motion relative to the air: a steady wind can change the ground track without changing the air-relative glide angle at the same operating condition.

For a steady unpowered descent, resolve gravitational weight perpendicular and parallel to the air-relative velocity. With lift normal to that velocity and drag opposing it,The still-air horizontal distance per unit height lost is therefore $L/D$. NASA's description connects this geometry with a historical observation: the Wright brothers flew parallel to a dune slope, letting the slope provide an estimate of the flight-path angle.^[ref]

For an original constant-velocity model, set $L/D=20$ and airspeed $V=25m/s$. Then $\gamma =\arctan (1/20)\approx 2.8624{}^{\circ }$, horizontal air-relative speed is $u=V\cos \gamma \approx 24.9688m/s$, and downward speed is $w=V\sin \gamma \approx 1.24844m/s$. In still air, a stipulated $1000\mathrm{m}$ height loss corresponds to $20\mathrm{km}$ horizontally.

If a constant horizontal wind component $U_w$ is positive along the direction of travel, the ground-frame horizontal speed is $u+U_w$. With no vertical wind and $u+U_w>0$,A $10m/s$ headwind makes that ratio about $11.9900$; a tailwind of the same magnitude gives $28.0100$. All three cases retain the same air-relative angle and sink rate. Their groundspeeds and ground-frame path angles differ.

This distinction separates a measured ground trajectory from an aerodynamic lift-to-drag ratio. Estimating the latter from height and horizontal travel requires accounting for air motion and identifying the steady portion of the trajectory.

A glider sink polar relates a glider's steady downward speed relative to the air to its true airspeed, for specified loading, configuration and atmospheric conditions. Write it as $w(V)>0$ with downward motion positive. Some plots instead put descent below the horizontal axis; the sign convention must accompany the curve. The minimum sink speed and best glide speed select different points on this same performance relation.^[ref]

The curve is a measurement or model of performance, rather than a drawing of the flight path. At steady speed, its horizontal air-relative component is $u=\sqrt{V^2-w^2}$. Thus time per height lost is $1/w$, while horizontal distance per height lost is $u/w$. The best glide speed article derives the tangent construction and an original parabolic drag polar example; those results need not be recomputed to interpret a measured polar.

A useful extension is glider ballast scaling. Suppose the gravitational weight changes from $W$ to $\alpha W$ at unchanged air mass density and geometry, and suppose the same lift coefficient and drag coefficient remain applicable. At corresponding steady glide conditions, the lift-to-drag ratio and glide angle are unchanged. Since $L=\rho V^{2}S{C}_L/2=W\cos \gamma$,For an original stipulated point $V_1=25m/s$ and $w_1=0.80m/s$, increasing gravitational weight by $25\%$ gives $V_2\simeq 27.95m/s$ and $w_2\simeq 0.8944m/s$. The corresponding distance-to-height ratio is unchanged, but the same height is lost sooner. This scaling assumes the aerodynamic coefficients transfer; changes of Reynolds number, surface condition or trim can invalidate it. The FAA illustrates the loading-dependent displacement of glider polars.^[ref]

To measure a polar, record steady true airspeed and height change at several operating points while documenting configuration and loading. Ground-relative descent $s$ includes vertical motion of the air: with upward air velocity $u_z$, $s=w-u_z$. For example, an air-relative sink of $1.5m/s$ in air rising at $0.5m/s$ appears as $1.0m/s$ ground-relative descent. Repetition can reveal variability, but one trajectory cannot separate these two contributions without additional information. A measured groundspeed is likewise not automatically the horizontal component of the air-relative polar.

Groundspeed is the magnitude of an aircraft's horizontal velocity relative to the ground. It determines travel time along a ground track, whereas aerodynamic lift and drag depend on motion relative to the air. Let ${\mathbf{v}}_{g,h}$ and ${\mathbf{v}}_{a,h}$ be the horizontal ground-relative and air-relative velocity vectors, and let ${\mathbf{w}}_h$ be the horizontal wind velocity:For climbing or descending flight this horizontal convention distinguishes groundspeed from the magnitude of the full three-dimensional ground-relative velocity.^[ref]

In an original horizontal-flight example, an airspeed of $50m/s$ directed due north and a wind blowing east at $15m/s$ give ${\mathbf{v}}_{g,h}=(15,50)m/s$ in east/north coordinates. Thus $V_g=\sqrt{2725}\approx 52.20m/s$, with the track about $16.70{}^{\circ }$ east of north. Adding scalar speeds would wrongly give $65m/s$.

To keep a due-north track in the same wind, the aircraft must instead supply an air-relative westward component of $15m/s$. At the same airspeed, its northward component becomes $\sqrt{50^2-15^2}\approx 47.70m/s$, so the on-track groundspeed is smaller than the airspeed. The required wind correction angle is $\arcsin (15/50)\approx 17.46{}^{\circ }$ west of north. Heading and track are distinct directions.

Timed positions from a ground-based tracker estimate groundspeed, not airspeed. Inferring the latter also needs the wind velocity. Conversely, a Pitot-static tube does not measure travel over the ground. The same distinction explains why a headwind changes the ground range of a steady glider without changing its air-relative glide angle.

Indicated airspeed is the airspeed read directly from an indicator before correcting its instrument and installation errors. It is a displayed measurement, not automatically the aircraft's true airspeed or groundspeed. A conventional Pitot-static tube supplies total and static pressure through separate connections; the indicator converts their difference into a speed reading.^[ref]

A simple low-Mach number instrument model uses a standard reference mass density ${\rho }_0$ and the sensed difference $q_I$:This formula describes the stipulated ideal scale; real instrument errors need separate characterization. In particular, using ${\rho }_0$ does not assert that local air has that mass density.

For an original error example, let the actual total-minus-static difference be $245\mathrm{Pa}$, but suppose the static connection reads $12\mathrm{Pa}$ too high while the total-pressure connection is correct. Then $q_I=233\mathrm{Pa}$. With ${\rho }_0=1.225kg/{\mathrm{m}}^3$, the model shows $19.50m/s$ instead of $20.00m/s$. A positive error in one input has become a negative error in the difference. At lower pressure differences, the same offset has a larger fractional effect on the indicated speed.

A pressure-bench check can apply known differences to the instrument and test its zero and scale. It cannot alone characterize static-pressure position error caused by the ports' location on the flying aircraft. Calibrated airspeed accounts for the established instrument and installation corrections. A blocked port is another failure mode: treating every discrepancy as a correctable constant offset would conceal a changing or trapped pressure signal. The FAA specifically identifies obstruction and instrument deterioration as causes of incorrect indications.^[ref]

True airspeed is the magnitude of an aircraft's velocity relative to the surrounding air,It determines the relative motion used in aerodynamic models, while groundspeed concerns horizontal travel over the ground. Indicated airspeed and calibrated airspeed describe stages in a pressure-instrument reduction, rather than another reference frame.^[ref]

For an aligned low-Mach number pressure measurement in the regime of the Bernoulli equation,An equivalent airspeed uses the same dynamic pressure with a standard reference mass density, $V_{\mathrm{EAS}}=\sqrt{2q/{\rho }_0}$. HenceOnly where the low-speed pressure relations justify $V_{\mathrm{CAS}}\simeq V_{\mathrm{EAS}}$ may calibrated speed be substituted in this last expression without a separate compressibility correction.

For an original low-speed example, use $V_{\mathrm{CAS}}\simeq 30m/s$, ${\rho }_0=1.225kg/{\mathrm{m}}^3$ and ambient $\rho =0.800kg/{\mathrm{m}}^3$. The corrected difference is approximately $551.25\mathrm{Pa}$, giving $V_{\mathrm{TAS}}\simeq 37.12m/s$. At a fixed pressure difference, halving ambient mass density increases the inferred true airspeed by $\sqrt{2}$, rather than doubling it. This follows from the square-root dependence, not a wind correction.

Obtaining the ambient mass density can require independent static pressure and thermodynamic temperature measurements, with a suitable equation of state. For fixed $q$, a small relative density error changes the inferred speed by approximately $\delta V/V=-\delta \rho /(2\rho )$. Wind information is needed separately to predict the ground track. A single ground-travel speed cannot supply all of these quantities. The pressure inference also depends on clear passages and valid stopping-flow assumptions.^[ref]

The wind correction angle is the difference between the aircraft heading and the desired ground track needed to compensate for a crosswind. A heading points the vehicle; a track describes horizontal travel over the ground. In the horizontal model here, the air-relative velocity is aligned with the heading. Wind-direction statements below specify where the air moves, not the meteorological direction it comes from.^[ref]

Let $V$ be true airspeed, let $w_{\parallel }$ be wind along the desired track, and let $w_{\perp }$ be wind to its right. Define a positive correction $\delta$ as heading right of the track. Cancelling cross-track velocity and projecting along the track givesFor the branch with a nonnegative along-track air-relative component,The condition $|w_{\perp }|\le V$ permits crosswind cancellation, but forward progress also requires $V_g>0$.

In an original example, take $V=40m/s$, wind $8m/s$ rightward and $12m/s$ opposite the intended track. Then $\delta \simeq -11.54{}^{\circ }$ and $V_g\simeq 27.19m/s$. A constant-condition $100\mathrm{km}$ ground leg takes about $61.29\min$. With the same headwind, a rightward component of $39m/s$ can still be cancelled, but $\sqrt{40^2-39^2}-12\simeq -3.11m/s$: the resulting track-line motion is backward.

The calculation assumes a uniform horizontal wind and a steady true airspeed. Ground-position measurements can test the resulting groundspeed; they cannot determine the correction from air-relative speed alone without wind information. Wind variation and a difference between heading and air-relative velocity require a fuller vector model.