Velocity in Accelerated Flight Calculator

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✖The Radius of Curvature is the reciprocal of the curvature.ⓘ Radius of Curvature [R_curvature]			+10% -10%
✖Mass of Aircraft is the total mass of the plane at any phase of its mission.ⓘ Mass of Aircraft [m]			+10% -10%
✖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.ⓘ Lift Force [F_L]			+10% -10%
✖Thrust denotes the force exerted by the engine to propel an aircraft forward.ⓘ Thrust [T]			+10% -10%
✖Thrust angle is defined as the angle between thrust vector and flight path (or flight velocity) direction.ⓘ Thrust Angle [σ_T]			+10% -10%
✖Flight path angle is defined as the angle between horizontal and the flight velocity vector, which describes whether the aircraft is climbing or descending.ⓘ Flight Path Angle [γ]			+10% -10%

✖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.ⓘ Velocity in Accelerated Flight [v]

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Formula

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Velocity in Accelerated Flight

Formula

`"v" = ("R"_{"curvature"}/"m"*("F"_{"L"}+"T"*sin("σ"_{"T"})-"m"*"[g]"*cos("γ")))^(1/2)`

Example

`"60.3747m/s"=("2600m"/"20kg"*("200N"+"700N"*sin("0.034rad")-"20kg"*"[g]"*cos("0.062rad")))^(1/2)`

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Velocity in Accelerated Flight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2)
v = (R_curvature/m*(F_L+T*sin(σ_T)-m*[g]*cos(γ)))^(1/2)
This formula uses 1 Constants, 2 Functions, 7 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Velocity - (Measured in Meter per Second) - 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.
Radius of Curvature - (Measured in Meter) - The Radius of Curvature is the reciprocal of the curvature.
Mass of Aircraft - (Measured in Kilogram) - Mass of Aircraft is the total mass of the plane at any phase of its mission.
Lift Force - (Measured in Newton) - 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.
Thrust - (Measured in Newton) - Thrust denotes the force exerted by the engine to propel an aircraft forward.
Thrust Angle - (Measured in Radian) - Thrust angle is defined as the angle between thrust vector and flight path (or flight velocity) direction.
Flight Path Angle - (Measured in Radian) - Flight path angle is defined as the angle between horizontal and the flight velocity vector, which describes whether the aircraft is climbing or descending.

STEP 1: Convert Input(s) to Base Unit

Radius of Curvature: 2600 Meter --> 2600 Meter No Conversion Required
Mass of Aircraft: 20 Kilogram --> 20 Kilogram No Conversion Required
Lift Force: 200 Newton --> 200 Newton No Conversion Required
Thrust: 700 Newton --> 700 Newton No Conversion Required
Thrust Angle: 0.034 Radian --> 0.034 Radian No Conversion Required
Flight Path Angle: 0.062 Radian --> 0.062 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = (R_curvature/m*(F_L+T*sin(σ_T)-m*[g]*cos(γ)))^(1/2) --> (2600/20*(200+700*sin(0.034)-20*[g]*cos(0.062)))^(1/2)

Evaluating ... ...

v = 60.3746968438799

STEP 3: Convert Result to Output's Unit

60.3746968438799 Meter per Second --> No Conversion Required

FINAL ANSWER

60.3746968438799 ≈ 60.3747 Meter per Second <-- Velocity

(Calculation completed in 00.004 seconds)

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Credits

Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Sai Venkata Phanindra Chary Arendra

Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

Sai Venkata Phanindra Chary Arendra has verified this Calculator and 300+ more calculators!

< 16 Climbing Flight Calculators

Velocity in Accelerated Flight

Go Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2)

Lift in Accelerated Flight

Go Lift Force = Mass of Aircraft*[g]*cos(Flight Path Angle)+Mass of Aircraft*Velocity^2/Radius of Curvature-Thrust*sin(Thrust Angle)

Thrust in Accelerated Flight

Go Thrust = (sec(Thrust Angle))*(Drag Force+(Mass of Aircraft*[g]*sin(Flight Path Angle))+(Mass of Aircraft*Acceleration))

Drag in Accelerated Flight

Go Drag Force = Thrust*cos(Thrust Angle)-Mass of Aircraft*[g]*sin(Flight Path Angle)-Mass of Aircraft*Acceleration

Centrifugal Force in Accelerated Flight

Go Centrifugal Force = Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)

Rate of Climb of Aircraft

Go Rate of Climb = (Power Available-Power Required)/Aircraft weight

Flight path angle at given rate of climb

Go Flight Path Angle = asin(Rate of Climb/Velocity)

Velocity of aircraft at given rate of climb

Go Velocity = Rate of Climb/sin(Flight Path Angle)

Rate of Climb

Go Rate of Climb = Velocity*sin(Flight Path Angle)

Velocity of aircraft for given excess power

Go Velocity = Excess Power/(Thrust-Drag Force)

Thrust available for given excess power

Go Thrust = Drag Force+(Excess Power/Velocity)

Total Drag for given excess power

Go Drag Force = Thrust-(Excess Power/Velocity)

Excess power

Go Excess Power = Velocity*(Thrust-Drag Force)

Weight of aircraft for given excess power

Go Aircraft weight = Excess Power/Rate of Climb

Excess power for given rate of climb

Go Excess Power = Rate of Climb*Aircraft weight

Rate of Climb for given excess power

Go Rate of Climb = Excess Power/Aircraft weight

Velocity in Accelerated Flight Formula

Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2)
v = (R_curvature/m*(F_L+T*sin(σ_T)-m*[g]*cos(γ)))^(1/2)

What is the acceleration of a plane taking off?

An average commercial jet accelerates to between 120 and 140 knots prior to liftoff. To do this in 30 to 35 seconds requires a good sustained acceleration. This is something that pilots look for during a takeoff roll.

How to Calculate Velocity in Accelerated Flight?

Velocity in Accelerated Flight calculator 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 calculate the Velocity, The Velocity in accelerated flight is a function of the radius of curvature of a curved flight path. Velocity is denoted by v symbol.

How to calculate Velocity in Accelerated Flight using this online calculator? To use this online calculator 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. Here is how the Velocity in Accelerated Flight calculation can be explained with given input values -> 4.585787 = (radius_of_curvature_eom/20*(200+700*sin(0.034)-20*[g]*cos(0.062)))^(1/2).

FAQ

What is Velocity in Accelerated Flight?

The Velocity in accelerated flight is a function of the radius of curvature of a curved flight path and is represented as v = (R_curvature/m*(F_L+T*sin(σ_T)-m*[g]*cos(γ)))^(1/2) or Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2). The Radius of Curvature is the reciprocal of the curvature, Mass of Aircraft is the total mass of the plane at any phase of its mission, 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, Thrust denotes the force exerted by the engine to propel an aircraft forward, Thrust angle is defined as the angle between thrust vector and flight path (or flight velocity) direction & Flight path angle is defined as the angle between horizontal and the flight velocity vector, which describes whether the aircraft is climbing or descending.

How to calculate Velocity in Accelerated Flight?

The Velocity in accelerated flight is a function of the radius of curvature of a curved flight path is calculated using Velocity = (Radius of Curvature/Mass of Aircraft*(Lift Force+Thrust*sin(Thrust Angle)-Mass of Aircraft*[g]*cos(Flight Path Angle)))^(1/2). To calculate Velocity in Accelerated Flight, you need Radius of Curvature (R_curvature), Mass of Aircraft (m), Lift Force (F_L), Thrust (T), Thrust Angle (σ_T) & Flight Path Angle (γ). With our tool, you need to enter the respective value for Radius of Curvature, Mass of Aircraft, Lift Force, Thrust, Thrust Angle & Flight Path Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Velocity?

In this formula, Velocity uses Radius of Curvature, Mass of Aircraft, Lift Force, Thrust, Thrust Angle & Flight Path Angle. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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