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Velocity in Accelerated Flight Formula

GoVelocity of aircraft at given rate of climb Formula

GoVelocity of Aircraft for given Excess Power Formula

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Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time. Check FAQs

v = {(\frac{R curvature}{m} \cdot (F L + T \cdot \sin (σ T) - m \cdot [g] \cdot \cos (γ)))}^{\frac{1}{2}}

v - Velocity?R_curvature - Radius of Curvature?m - Mass of Aircraft?F_L - Lift Force?T - Thrust?σ_T - Thrust Angle?γ - Flight Path Angle?[g] - Gravitational acceleration on Earth?

Velocity in Accelerated Flight Example

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Here is how the Velocity in Accelerated Flight equation looks like with Values.

Here is how the Velocity in Accelerated Flight equation looks like with Units.

Here is how the Velocity in Accelerated Flight equation looks like.

60.3747 = {(\frac{2600}{20} \cdot (200 + 700 \cdot \sin (0.034) - 20 \cdot 9.8066 \cdot \cos (0.062)))}^{\frac{1}{2}}

60.3747m/s = {(\frac{2600m}{20kg} \cdot (200N + 700N \cdot \sin (0.034rad) - 20kg \cdot 9.8066m/s² \cdot \cos (0.062rad)))}^{\frac{1}{2}}

60.3747 = {(\frac{2600}{20} \cdot (200 + 700 \cdot \sin (0.034) - 20 \cdot 9.8066 \cdot \cos (0.062)))}^{\frac{1}{2}}

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Velocity in Accelerated Flight Solution

Follow our step by step solution on how to calculate Velocity in Accelerated Flight?

FIRST Step Consider the formula

v = {(\frac{R curvature}{m} \cdot (F L + T \cdot \sin (σ T) - m \cdot [g] \cdot \cos (γ)))}^{\frac{1}{2}}

Next Step Substitute values of Variables

∴

v = {(\frac{2600m}{20kg} \cdot (200N + 700N \cdot \sin (0.034rad) - 20kg \cdot [g] \cdot \cos (0.062rad)))}^{\frac{1}{2}}

Next Step Substitute values of Constants

∴

v = {(\frac{2600m}{20kg} \cdot (200N + 700N \cdot \sin (0.034rad) - 20kg \cdot 9.8066m/s² \cdot \cos (0.062rad)))}^{\frac{1}{2}}

Next Step Prepare to Evaluate

∴

v = {(\frac{2600}{20} \cdot (200 + 700 \cdot \sin (0.034) - 20 \cdot 9.8066 \cdot \cos (0.062)))}^{\frac{1}{2}}

Next Step Evaluate

∴

v = 60.3746968438799m/s

LAST Step Rounding Answer

∴

v = 60.3747m/s

Velocity in Accelerated Flight Formula Elements

Variables

Constants

Functions

Velocity

Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity

Radius of Curvature

The Radius of Curvature refers to the radius of the curved path an aircraft follows while climbing.

Symbol: R_curvature

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Curvature

Mass of Aircraft

Mass of Aircraft is the total mass of the plane at any phase of its mission.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Aircraft

Lift Force

The Lift Force, lifting force or simply lift is the sum of all the forces on a body that force it to move perpendicular to the direction of flow.

Symbol: F_L

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Lift Force

Thrust

Thrust denotes the force exerted by the engine to propel an aircraft forward.

Symbol: T

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Thrust

Thrust Angle

Thrust angle is defined as the angle between thrust vector and flight path (or flight velocity) direction.

Symbol: σ_T

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Thrust Angle

Flight Path Angle

Flight Path Angle is defined as the angle between horizontal and the flight velocity vector, which describes whether the aircraft is climbing or descending.

Symbol: γ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Flight Path Angle

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Velocity

Go Velocity of aircraft at given rate of climb

v = \frac{RC}{\sin (γ)}

Go Velocity of Aircraft for given Excess Power

v = \frac{P excess}{T - F D}

Other formulas in Climbing Flight category

Go Rate of Climb

RC = v \cdot \sin (γ)

Go Flight path angle at given rate of climb

γ = a \sin (\frac{RC}{v})

How to Evaluate Velocity in Accelerated Flight?

Velocity in Accelerated Flight evaluator uses Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2) to evaluate the Velocity, The Velocity in Accelerated Flight refers to the speed of the aircraft as it undergoes changes in speed or direction to achieve specific flight objectives, it is typically measured as the airspeed of the aircraft, which is the speed of the aircraft relative to the surrounding air. Velocity is denoted by v symbol.

How to evaluate Velocity in Accelerated Flight using this online evaluator? To use this online evaluator for Velocity in Accelerated Flight, enter Radius of Curvature (R_curvature), Mass of Aircraft (m), Lift Force (F_L), Thrust (T), Thrust Angle (σ_T) & Flight Path Angle (γ) and hit the calculate button.

FAQs on Velocity in Accelerated Flight

What is the formula to find Velocity in Accelerated Flight?

The formula of Velocity in Accelerated Flight is expressed as Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2). Here is an example- 4.585787 = (radius_of_curvature_eom/20*(200+700*sin(0.034)-20*[g]*cos(0.062)))^(1/2).

How to calculate Velocity in Accelerated Flight?

With Radius of Curvature (R_curvature), Mass of Aircraft (m), Lift Force (F_L), Thrust (T), Thrust Angle (σ_T) & Flight Path Angle (γ) we can find Velocity in Accelerated Flight using the formula - Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2). This formula also uses Gravitational acceleration on Earth constant(s) and , Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Velocity?

Here are the different ways to Calculate Velocity-

Velocity=Rate of Climb/sin(Flight Path Angle)
Velocity=Excess Power/(Thrust-Drag Force)

Can the Velocity in Accelerated Flight be negative?

No, the Velocity in Accelerated Flight, measured in Speed cannot be negative.

Which unit is used to measure Velocity in Accelerated Flight?

Velocity in Accelerated Flight is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity in Accelerated Flight can be measured.

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Velocity in Accelerated Flight Formula

​GoVelocity of aircraft at given rate of climb Formula

​GoVelocity of Aircraft for given Excess Power Formula

Velocity in Accelerated Flight Example

Velocity in Accelerated Flight Solution

Velocity in Accelerated Flight Formula Elements

Other Formulas to find Velocity

Other formulas in Climbing Flight category

How to Evaluate Velocity in Accelerated Flight?

FAQs on Velocity in Accelerated Flight

Variable Name

GoVelocity of aircraft at given rate of climb Formula

GoVelocity of Aircraft for given Excess Power Formula