Flight path angle at given rate of climb Solution

STEP 0: Pre-Calculation Summary
Formula Used
Flight Path Angle = asin(Rate of Climb/Velocity)
γ = asin(RC/v)
This formula uses 2 Functions, 3 Variables
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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)
Variables Used
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.
Rate of Climb - (Measured in Meter per Second) - The Rate of Climb (RoC) is defined as the aircraft's vertical speed – the positive or negative rate of altitude change with respect to time.
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.
STEP 1: Convert Input(s) to Base Unit
Rate of Climb: 3.71976 Meter per Second --> 3.71976 Meter per Second No Conversion Required
Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
γ = asin(RC/v) --> asin(3.71976/60)
Evaluating ... ...
γ = 0.0620357824911862
STEP 3: Convert Result to Output's Unit
0.0620357824911862 Radian --> No Conversion Required
FINAL ANSWER
0.0620357824911862 0.062036 Radian <-- Flight Path Angle
(Calculation completed in 00.004 seconds)

Credits

Created by Vinay Mishra
Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
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Verified by Chilvera Bhanu Teja
Institute of Aeronautical Engineering (IARE), Hyderabad
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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

Flight path angle at given rate of climb Formula

Flight Path Angle = asin(Rate of Climb/Velocity)
γ = asin(RC/v)

What is the purpose of zoom climb?

Zoom climbs are somewhat commonly performed by modern fighter aircraft. Zoom climbs have been used to test new aircraft designs and conduct research in different flight regimes.

How to Calculate Flight path angle at given rate of climb?

Flight path angle at given rate of climb calculator uses Flight Path Angle = asin(Rate of Climb/Velocity) to calculate the Flight Path Angle, The Flight path angle at given rate of climb is given by the inverse sine of the rate of climb and velocity of the aircraft. Flight Path Angle is denoted by γ symbol.

How to calculate Flight path angle at given rate of climb using this online calculator? To use this online calculator for Flight path angle at given rate of climb, enter Rate of Climb (RC) & Velocity (v) and hit the calculate button. Here is how the Flight path angle at given rate of climb calculation can be explained with given input values -> 0.06199 = asin(3.71976/60).

FAQ

What is Flight path angle at given rate of climb?
The Flight path angle at given rate of climb is given by the inverse sine of the rate of climb and velocity of the aircraft and is represented as γ = asin(RC/v) or Flight Path Angle = asin(Rate of Climb/Velocity). The Rate of Climb (RoC) is defined as the aircraft's vertical speed – the positive or negative rate of altitude change with respect to time & 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.
How to calculate Flight path angle at given rate of climb?
The Flight path angle at given rate of climb is given by the inverse sine of the rate of climb and velocity of the aircraft is calculated using Flight Path Angle = asin(Rate of Climb/Velocity). To calculate Flight path angle at given rate of climb, you need Rate of Climb (RC) & Velocity (v). With our tool, you need to enter the respective value for Rate of Climb & Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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