Deflection Angle Calculator

✖The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ Specific Heat Ratio [Y]			+10% -10%
✖Mach Number ahead of shock is the Mach number over the body before a shockwave has occurred.ⓘ Mach Number ahead of shock [M₁]			+10% -10%
✖Mach Number behind shock is the Mach number over the body after a shockwave has occurred.ⓘ Mach Number behind shock [M₂]			+10% -10%

✖A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.ⓘ Deflection Angle [θ_def]

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Formula

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Deflection Angle

Formula

`"θ"_{"def"} = 2/("Y"-1)*(1/"M"_{"1"}-1/"M"_{"2"})`

Example

`"-4.444444rad"=2/("1.6"-1)*(1/"1.5"-1/"0.5")`

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Deflection Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock)
θ_def = 2/(Y-1)*(1/M₁-1/M₂)
This formula uses 4 Variables

Variables Used

Deflection Angle - (Measured in Radian) - A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.
Specific Heat Ratio - The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Mach Number ahead of shock - Mach Number ahead of shock is the Mach number over the body before a shockwave has occurred.
Mach Number behind shock - Mach Number behind shock is the Mach number over the body after a shockwave has occurred.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Mach Number ahead of shock: 1.5 --> No Conversion Required
Mach Number behind shock: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_def = 2/(Y-1)*(1/M₁-1/M₂) --> 2/(1.6-1)*(1/1.5-1/0.5)

Evaluating ... ...

θ_def = -4.44444444444444

STEP 3: Convert Result to Output's Unit

-4.44444444444444 Radian --> No Conversion Required

FINAL ANSWER

-4.44444444444444 ≈ -4.444444 Radian <-- Deflection Angle

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 20 Hypersonic Flow Parameters Calculators

Coefficient of Pressure with Similarity Parameters

Go Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2))

Pressure Ratio having High Mach Number with Similarity Constant

Go Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Mach Number with Fluids

Go Mach Number = Fluid Velocity/(sqrt(Specific Heat Ratio*Universal Gas Constant*Final Temperature))

Pressure Ratio for High Mach Number

Go Pressure Ratio = (Mach Number ahead of shock/Mach Number behind shock)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Moment Coefficient

Go Moment Coefficient = Moment/(Dynamic Pressure*Area for Flow*Chord Length)

Deflection Angle

Go Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock)

Normal Force Coefficient

Go Coefficient of Force = Normal Force/(Dynamic Pressure*Area for Flow)

Supersonic Expression for Pressure Coefficient on Surface with Local Deflection Angle

Go Pressure Coefficient = (2*Deflection Angle)/(sqrt(Mach Number^2-1))

Dynamic Pressure given Coefficient of Lift

Go Dynamic Pressure = Lift Force/(Lift Coefficient*Area for Flow)

Coefficient of Drag

Go Drag Coefficient = Drag Force/(Dynamic Pressure*Area for Flow)

Dynamic Pressure

Go Dynamic Pressure = Drag Force/(Drag Coefficient*Area for Flow)

Lift Coefficient

Go Lift Coefficient = Lift Force/(Dynamic Pressure*Area for Flow)

Axial Force Coefficient

Go Coefficient of Force = Force/(Dynamic Pressure*Area for Flow)

Drag Force

Go Drag Force = Drag Coefficient*Dynamic Pressure*Area for Flow

Lift Force

Go Lift Force = Lift Coefficient*Dynamic Pressure*Area for Flow

Mach Ratio at High Mach Number

Go Mach Ratio = 1-Hypersonic Similarity Parameter*((Specific Heat Ratio-1)/2)

Hypersonic Similarity Parameter

Go Hypersonic Similarity Parameter = Mach Number*Flow Deflection angle

Shear-Stress Distribution

Go Shear Stress = Viscosity Coefficient*Velocity Gradient

Fourier's Law of Heat Conduction

Go Heat Flux = Thermal Conductivity*Temperature Gradient

Newtonian Sine Squared Law for Pressure Coefficient

Go Pressure Coefficient = 2*sin(Deflection Angle)^2

Deflection Angle Formula

Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock)
θ_def = 2/(Y-1)*(1/M₁-1/M₂)

what is deflection angle?

Equation is the hypersonic relation for Prandtl–Meyer expansion waves; it
is an approximate relation that becomes more accurate as M1 and M2 become
larger

How to Calculate Deflection Angle?

Deflection Angle calculator uses Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock) to calculate the Deflection Angle, Deflection angle is the product of the inverse of specific heat ratio minus 1 and double the inverse change in velocity of flow usually in Mach number. Deflection Angle is denoted by θ_def symbol.

How to calculate Deflection Angle using this online calculator? To use this online calculator for Deflection Angle, enter Specific Heat Ratio (Y), Mach Number ahead of shock (M₁) & Mach Number behind shock (M₂) and hit the calculate button. Here is how the Deflection Angle calculation can be explained with given input values -> -4.444444 = 2/(1.6-1)*(1/1.5-1/0.5).

FAQ

What is Deflection Angle?

Deflection angle is the product of the inverse of specific heat ratio minus 1 and double the inverse change in velocity of flow usually in Mach number and is represented as θ_def = 2/(Y-1)*(1/M₁-1/M₂) or Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock). The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume, Mach Number ahead of shock is the Mach number over the body before a shockwave has occurred & Mach Number behind shock is the Mach number over the body after a shockwave has occurred.

How to calculate Deflection Angle?

Deflection angle is the product of the inverse of specific heat ratio minus 1 and double the inverse change in velocity of flow usually in Mach number is calculated using Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock). To calculate Deflection Angle, you need Specific Heat Ratio (Y), Mach Number ahead of shock (M₁) & Mach Number behind shock (M₂). With our tool, you need to enter the respective value for Specific Heat Ratio, Mach Number ahead of shock & Mach Number behind shock 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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