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Equivalent airspeed

Equivalent airspeed (EAS), denoted as V_E, is the speed at which an aircraft would generate the same dynamic pressure in the International Standard Atmosphere at sea level as it does in its actual flight conditions at a given altitude and air density.^[1] It represents a standardized measure of airspeed that accounts for variations in air density, making it independent of altitude for assessing aerodynamic forces.^[2] According to Federal Aviation Administration (FAA) regulations, EAS is the calibrated airspeed corrected for adiabatic compressible flow effects specific to the flight altitude.^[3] EAS is calculated using the formula V_E = V_T \sqrt{\frac{\rho}{\rho_0}}, where V_T is the true airspeed (TAS), \rho is the local air density, and \rho_0 is the standard sea-level air density (approximately 1.225 kg/m³ or 0.002378 slugs/ft³).^[1] This relationship holds across all flight regimes, from subsonic to supersonic speeds, providing a consistent basis for performance analysis.^[1] In practice, EAS is derived from indicated airspeed (IAS) by first correcting for instrument and position errors to obtain calibrated airspeed (CAS), then adjusting for density altitude effects.^[2] The significance of EAS in aviation lies in its direct correlation to dynamic pressure, which governs lift, drag, and structural loads on the aircraft.^[2] Unlike TAS, which increases with altitude for constant dynamic pressure, EAS remains unchanged, allowing pilots and engineers to use sea-level calibrated charts for stall speeds, maneuvering limits, and fuel efficiency without altitude-specific adjustments.^[4] This standardization is essential for flight planning, aircraft certification, and ensuring safe operations across varying atmospheric conditions.^[3]

Definition and concepts

Definition of equivalent airspeed

Equivalent airspeed (EAS) is the hypothetical airspeed at sea level in the International Standard Atmosphere (ISA) that would generate the same incompressible dynamic pressure as the actual flight condition at any altitude or speed.^[5] This measure standardizes the assessment of aerodynamic forces, such as lift and drag, by referencing conditions where air density is constant, independent of the varying atmospheric effects encountered in flight.^[2] EAS assumes incompressible flow and standard sea-level air density (ρ₀ ≈ 1.225 kg/m³ at 15°C).^[2] Unlike true airspeed (TAS), the actual speed relative to undisturbed air, or indicated airspeed (IAS), the uncorrected cockpit reading, EAS focuses on dynamic pressure equivalence under idealized low-speed conditions.^[5] The concept emerged in the 1930s–1940s amid advances in high-speed aerodynamics, as aviation pushed beyond the limitations of IAS for performance standardization at higher altitudes and speeds.^[6] By 1946, the National Advisory Committee for Aeronautics (NACA) had formalized nomenclature for airspeeds, including EAS, to support consistent engineering and operational analyses.^[6] Units for EAS are typically knots (kt) or meters per second (m/s), aligning with international aviation standards.^[5]

Dynamic pressure equivalence

Dynamic pressure, denoted as q, represents the kinetic energy per unit volume of the airflow relative to an aircraft and is given by the formula q = \frac{1}{2} \rho V^2, where \rho is the local air density and V is the true airspeed.^[5]^[2] This quantity directly influences the magnitude of aerodynamic forces acting on the aircraft. Equivalent airspeed (EAS) normalizes dynamic pressure to standard sea-level conditions, where air density is \rho_0 = 1.225 \, \text{kg/m}^3 in the International Standard Atmosphere (ISA), allowing q to be expressed equivalently as q = \frac{1}{2} \rho_0 V_E^2, with V_E being the EAS.^[7]^[2] By maintaining a constant dynamic pressure through EAS, aerodynamic forces such as lift and drag—which are proportional to q via the relations L = C_L q S and D = C_D q S (where C_L and C_D are lift and drag coefficients, and S is wing area)—can be compared across different altitudes and densities as if the aircraft were operating at sea level.^[5] This equivalence ensures that performance characteristics dependent on these forces remain consistent in analysis, regardless of atmospheric variations.^[2] The concept relies on the incompressible flow assumption, where air density is treated as constant along streamlines, which is valid for low Mach numbers typically below M < 0.3.^[5]^[2] At higher Mach numbers, compressibility effects introduce density variations that require corrections, but EAS continues to serve as the baseline reference for dynamic pressure.^[7] For instance, at high altitudes where air density is lower, true airspeed must increase to produce the same dynamic pressure as at sea level, yet EAS remains unchanged, preserving equivalent aerodynamic performance.^[5] Indicated airspeed provides a direct but imperfect proxy for dynamic pressure due to instrument and installation errors.^[2]

Relationships with other airspeeds

Connection to true airspeed

The relationship between equivalent airspeed (EAS) and true airspeed (TAS) is fundamentally tied to air density variations, particularly those induced by altitude changes in the atmosphere. EAS is given by the formula

V_E = V_T \sqrt{\frac{\rho}{\rho_0}},

where V_E is the equivalent airspeed, V_T is the true airspeed, \rho is the local air density, and \rho_0 is the standard sea-level air density (1.225 kg/m³).^[1] This equation arises from the equivalence of dynamic pressure at sea level to the actual flight condition, ensuring that aerodynamic forces scale consistently.^[2] The density ratio \sigma = \rho / \rho_0 decreases with increasing altitude due to the exponential decay of atmospheric pressure and density in the International Standard Atmosphere (ISA) model, which assumes a standard temperature lapse rate of 6.5°C per kilometer up to 11 km.^[8] For instance, at 5,000 feet (1,524 m), \sigma \approx 0.86, meaning that for a constant TAS, the EAS is about 93% of the TAS value.^[9] Temperature deviations from the ISA profile can further modify \sigma, but the primary effect is altitudinal, leading to a reduction in EAS for a given TAS as altitude increases—illustrating how aircraft performance, such as lift and drag, is often referenced to sea-level equivalents despite flying in thinner air.^[1] This density-driven scaling highlights the practical impact on flight: at higher altitudes, a constant TAS results in lower EAS, requiring pilots or performance calculations to adjust for equivalent sea-level conditions to predict handling and efficiency accurately. For example, at 10,000 feet where \sigma \approx 0.74, a TAS of 250 knots corresponds to an EAS of approximately 215 knots, demonstrating how altitude reduces the effective airspeed for aerodynamic computations.^[9]^[10] At higher speeds approaching transonic regimes, compressibility effects influence dynamic pressure measurement, but the core relation V_E = V_T \sqrt{\sigma} holds as the definition of EAS preserves dynamic pressure equivalence regardless of Mach number.^[10] Calibrated airspeed serves as a practical intermediate from cockpit instruments to EAS, but the theoretical link to TAS emphasizes density as the key factor.^[2]

Relation to indicated and calibrated airspeed

Indicated airspeed (IAS) is the uncorrected reading obtained directly from the aircraft's airspeed indicator (ASI), which measures the difference between pitot (total) pressure and static pressure using the pitot-static system.^[11] This raw measurement does not account for variations in atmospheric density, instrument inaccuracies, or installation errors, making it the pilot's primary cockpit reference for basic flight parameters like stall speed.^[11] Calibrated airspeed (CAS) refines IAS by applying corrections for instrument errors (inherent ASI calibration inaccuracies) and installation errors, such as position error caused by the static port's location on the aircraft, which can be influenced by factors like angle of attack or flap settings.^[11] Position error, a key component of installation error, is determined through flight testing to produce aircraft-specific calibration charts provided by manufacturers.^[11]^[12] The correction is expressed as CAS = IAS + ΔV_pos, where ΔV_pos represents the position error adjustment, ensuring CAS more accurately reflects the dynamic pressure experienced by the aircraft.^[13] Equivalent airspeed (EAS) builds on CAS by further correcting for the effects of air compressibility at the given altitude and speed, representing the airspeed at sea-level standard atmospheric conditions that would produce the same dynamic pressure as the actual flight condition.^[3] According to Federal Aviation Regulations, EAS is defined as the CAS adjusted for adiabatic compressible flow specific to the flight altitude.^[3] In low-speed flight, where compressibility effects are negligible (typically below significant Mach numbers), EAS approximates CAS closely.^[4] However, as altitude increases, density decreases, leading to higher true airspeeds for the same dynamic pressure and thus greater potential for compressibility divergence, where CAS exceeds EAS.^[4] These cockpit-derived speeds (IAS to CAS to EAS) are essential for pilots to interpret instrument readings accurately during flight operations.^[11]

Derivation and formulas

Incompressible flow approximation

The incompressible flow approximation provides a foundational method for calculating equivalent airspeed (EAS), assuming air density remains constant along streamlines and compressibility effects are negligible. This simplification is valid for low-speed flight where the Mach number is below approximately 0.3. The dynamic pressure q, which represents the kinetic energy per unit volume of the airflow, is equated between the actual flight condition and a hypothetical sea-level condition. Specifically, q = \frac{1}{2} \rho \, \text{TAS}^2 = \frac{1}{2} \rho_0 \, \text{EAS}^2, where \rho is the local air density, TAS is the true airspeed, \rho_0 is the sea-level standard density (1.225 kg/m³ in the International Standard Atmosphere, or ISA), and EAS is the equivalent airspeed. Rearranging this equality gives the core incompressible relation:

\text{EAS} = \text{TAS} \times \sqrt{\frac{\rho}{\rho_0}} = \text{TAS} \times \sqrt{\sigma},

where \sigma = \rho / \rho_0 is the density ratio.^[2] To derive this step by step, begin with the definition of dynamic pressure from Bernoulli's equation under incompressible, inviscid flow: q = P_0 - P_s = \frac{1}{2} \rho V^2, where P_0 is the stagnation (total) pressure measured by a pitot tube, P_s is the static pressure, and V is the local flow speed (TAS in undisturbed air). For the same dynamic pressure at sea-level standard conditions, q = \frac{1}{2} \rho_0 \, \text{EAS}^2. Equating the expressions and solving for EAS yields the formula above. The density ratio \sigma is obtained from atmospheric models like the ISA, which uses the hydrostatic balance equation \frac{dp}{dh} = -\rho g (where p is pressure, h is altitude, and g is gravitational acceleration) integrated with the ideal gas law \rho = p / (R T) ( R is the specific gas constant for air). In the troposphere (up to 11 km or about 36,000 ft), assuming a constant temperature lapse rate \lambda = -0.0065 K/m, the pressure ratio \delta = p / p_0 = (T / T_0)^{-g / (\lambda R)}, where T_0 = 288.15 K and p_0 = 101325 Pa are sea-level values. Then, \sigma = \delta \times (T_0 / T), providing a simplified means to compute \sigma from altitude via ISA tables or equations. This relation allows EAS to be determined directly from TAS and altitude without needing direct density measurements.^[1] This approximation has key limitations: it holds accurately only for Mach numbers M < 0.3, beyond which compressibility causes density changes in the flow, leading to errors exceeding 2% in dynamic pressure calculations; it also neglects the adiabatic compression effects within the pitot-static system, which are minor at low speeds but require corrections at higher Mach numbers. In practice, calibrated airspeed (CAS) serves as the starting point for computing EAS under this model, with position and instrument errors already accounted for in CAS.^[2] For illustration, consider a numerical example using ISA conditions. At 20,000 ft (approximately 6,096 m), the density ratio \sigma \approx 0.533. If the TAS is 300 knots, then \text{[EAS](/page/EAS)} = 300 \times \sqrt{0.533} \approx 300 \times 0.730 = 219 knots. This demonstrates how EAS decreases relative to TAS with increasing altitude due to the drop in air density, maintaining equivalence in dynamic pressure for performance assessments.^[14]

Compressible flow corrections

In compressible flow regimes, particularly at Mach numbers above approximately 0.3, the incompressible approximation for dynamic pressure becomes inaccurate due to air's density variations, necessitating corrections to derive equivalent airspeed (EAS) from calibrated airspeed (CAS).^[15] The pitot-static tube measures total pressure p_t and static pressure p_s, related by the isentropic flow equation \frac{p_t}{p_s} = \left(1 + \frac{\gamma - 1}{2} M^2 \right)^{\gamma / (\gamma - 1)}, where \gamma = 1.4 for air and M is the Mach number based on true airspeed V and local speed of sound a.^[15] This equation accounts for adiabatic compression in the pitot tube, enabling computation of CAS as the airspeed that would produce the measured pressure ratio under standard sea-level conditions using the same compressible relation: p_t - p_s = p_{SL} \left[ \left(1 + \frac{\gamma - 1}{2} \left( \frac{V_{CAS}}{a_{SL}} \right)^2 \right)^{\gamma / (\gamma - 1)} - 1 \right], where p_{SL} and a_{SL} are sea-level static pressure and speed of sound.^[15] To obtain EAS from the measured pressures, first compute the true dynamic pressure q using the compressible relation:

q = \frac{\gamma p_s}{\gamma - 1} \left[ \left( \frac{p_t}{p_s} \right)^{\frac{\gamma -1}{\gamma}} - 1 \right],

then

V_{\text{EAS}} = \sqrt{ \frac{2 q}{\rho_0} },

where \rho_0 is the sea-level air density. This method directly provides the EAS corresponding to the actual dynamic pressure under incompressible sea-level conditions, without needing intermediate Mach number calculations.^[15] ^[2] The relation \text{EAS} = \text{TAS} \times \sqrt{\sigma} continues to hold, where TAS is obtained as \text{TAS} = M \times a after solving the isentropic equation for M, and \sigma is the density ratio at the flight altitude. For practical computations from CAS, correction charts or numerical solutions are often used, as direct analytical inversion is complex. At low Mach numbers, an approximation from binomial expansion of the isentropic relation gives V_{\text{EAS}} \approx V_{\text{CAS}} \left(1 - \frac{\gamma + 1}{4} M^2 \right), or roughly $1 - 0.225 M^2 for \gamma = 1.4, highlighting the quadratic error term in pressure rise.^[15] These corrections are critical above M = 0.3, where density variations exceed 5-10%, and are essential in transonic flight testing to accurately assess aerodynamic loads and performance without overestimating dynamic pressure by up to 20% or more. Indicated airspeed serves as the uncorrected input, but compressible adjustments ensure reliable EAS computation for structural and stability analyses.^[15]

Practical applications

In aircraft performance

In aircraft performance analysis, aerodynamic coefficients such as the lift coefficient C_L and drag coefficient C_D are primarily functions of equivalent airspeed (EAS), since the dynamic pressure q is proportional to EAS squared (q \propto \text{EAS}^2). This relationship allows for standardized calculations of key metrics like range, climb rate, and cruise efficiency using EAS-based performance charts, which normalize data to sea-level conditions regardless of actual altitude.^[16]^[17] During flight planning, EAS enables pilots and planners to interpolate from sea-level performance tables, such as those plotting power required against EAS for constant-speed propellers, ensuring accurate predictions of engine settings and fuel consumption without recalculating for varying densities.^[16]^[18] In high-altitude operations, EAS facilitates predictions of fuel burn and endurance by inherently accounting for air density effects, avoiding the need for complete true airspeed recomputations in each scenario.^[17]^[18]

Safety and handling characteristics

Equivalent airspeed (EAS) plays a critical role in defining aircraft stall characteristics, as the stall speed remains nearly constant when expressed in EAS terms. This constancy arises because the maximum lift coefficient (C_L max) is primarily a function of the dynamic pressure (q), which EAS normalizes to sea-level conditions regardless of altitude. For instance, an aircraft with a sea-level stall speed of 100 knots EAS will exhibit a similar stall speed in EAS at higher altitudes, though the corresponding true airspeed (TAS) increases to compensate for reduced air density. This property allows pilots to reference consistent stall margins across flight levels, enhancing safety during high-altitude operations.^[19] In structural integrity assessments, EAS forms the basis for evaluating gust loads and maneuver margins under regulations like FAR Part 25 and CS-25. Gust load criteria specify reference gust velocities in feet per second EAS, which decrease linearly from 56 ft/sec at sea level to 44 ft/sec at 15,000 feet to model realistic atmospheric turbulence. The V-n diagram, outlining safe combinations of airspeed and load factor, is plotted using EAS to maintain uniform dynamic pressure envelopes, ensuring the airframe withstands loads like those from vertical gusts or turns without exceeding design limits. This approach prevents altitude-dependent variations in structural stress predictions.^[20]^[21] EAS also informs handling qualities by linking control effectiveness and stability to dynamic pressure. Aerodynamic control power, such as that from ailerons or elevators, scales directly with q, so maintaining a constant EAS preserves consistent response to pilot inputs and damping of perturbations. This is vital for stability assessments, where stick force versus EAS plots reveal speed stability characteristics, aiding in the design of flying qualities that support pilot training and recovery from upsets like stalls or Dutch rolls.^[22]^[23]

References

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Definition: Equivalent Air Speed - Equivalent air speed is defined by the following equation. The definition holds for all flight regimes, low speed, high speed ...
[2]
Airspeed Definitions & Measurement – Introduction to Aerospace ...
EAS is the “Equivalent airspeed,” which is the airspeed reading on an error-free ASI corresponding to a given dynamic pressure. The EAS must also be corrected ...
[3]
14 CFR 1.1 -- General definitions. - eCFR
Equivalent airspeed means the calibrated airspeed of an aircraft corrected for adiabatic compressible flow for the particular altitude. Equivalent airspeed is ...
[4]
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Equivalent airspeed. Airspeed equivalent to CAS in standard atmosphere at sea level. As the airspeed and pressure altitude increase, the CAS becomes higher ...
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The purpose of this textbook is to present the elements of applied aerodynamics and aeronautical engineering which relate directly to the problems of flying ...
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None
- **Introduction/Definition of Equivalent Airspeed**: Equivalent airspeed (Ve) is defined as the airspeed at sea level under standard conditions that produces the same dynamic pressure as the true airspeed at altitude. It is used in structural design, expressed in feet per second, and relates to true airspeed and pressure ratio (Ve = 760.9M√(p/p0)).
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Sep 6, 2019 · Calibrated airspeed is equal to true airspeed in the ... Aviation Environmental Design Tool. 3b Technical Manual. Page 8. Equivalent Airspeed.
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Over a period of nearly fifteen years Dr. Wexler led the development and formulation of the United States Standard. Atmosphere. This work is respectfully ...
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• EAS – Equivalent Airspeed. CAS corrected for compressibility effects. • TAS – True Airspeed. EAS corrected for density (altitude). 3. Page 4. Airspeed ...
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The increase in static pressure on the pitot side is equivalent to an increase in dynamic pressure since the pressure cannot change on the static side. If an ...
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(3) The air-speed error of the installation, excluding the air-speed indicator instrument calibration error, shall not exceed 3 percent or 5 mph, whichever ...
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Mar 27, 2024 · This report calculates a chart to convert CAS to EAS, using equations based on Mach number and pressure altitude, to simplify the conversion.
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In dealing with aircraft it is customary to refer to the sea level equivalent airspeed as the indicated airspeed if any instrument calibration or placement ...Missing: aviation | Show results with:aviation
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Defining Aircraft 'Speed'
This gives a value of 0.967 for the pressure correction, and this determination pf the equivalent airspeed from Ve=Vc⋅f V e = V c ⋅ f so, Ve= V e = 192.489kn.Airspeed Measurement · Equivalent Airspeed · True Airspeed
[19]
Equivalent Airspeed (EAS) | SKYbrary Aviation Safety
Equivalent airspeed (EAS) is defined as the speed at sea level, under ISA conditions, that would produce the same incompressible dynamic pressure.
[20]
[PDF] Performance 8. Level, Non-Accelerated Flight
We can observe that the stall airspeed in terms of the equivalent airspeed is a constant! ... view, the stall speed is the same on the airspeed indicator ...
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The airplane is assumed to be subjected to symmetrical vertical and lateral gusts in level flight. Limit gust loads must be determined in accordance with the ...
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[PDF] Stability and Control. Volume 1. Stability and Control Flight Test ...
for speed stability are relatively easy to examine. The stick force versus equivalent airspeed data from either test method is rlotted. Since all that is ...<|separator|>
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However, the variation of long- itudinal control force with equivalent airspeed will give us an indication of whether the stick-free stability is positive, ...
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Apr 29, 1993 · On April 29, 1993, at 1555 central daylight time, an Embraer EMB-120 RT,. Brasilia, N24706, was substantially damaged when it collided with ...