Radius for Sphere-Cone Body Shape Calculator

✖The Radius of Curvature is the reciprocal of the curvature.ⓘ Radius of Curvature [R_curvature]			+10% -10%
✖Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M_r]			+10% -10%

✖Radius is a radial line from the focus to any point of a curve.ⓘ Radius for Sphere-Cone Body Shape [r]

⎘ Copy

👎

Formula

✖

Radius for Sphere-Cone Body Shape

Formula

`"r" = "R"_{"curvature"}/(1.143*exp(0.54/("M"_{"r"}-1)^1.2))`

Example

`"2633.783mm"="15235mm"/(1.143*exp(0.54/("1.4"-1)^1.2))`

Calculator

LaTeX

Reset

👍

Download Hypersonic Flow Formula PDF

Radius for Sphere-Cone Body Shape Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius = Radius of Curvature/(1.143*exp(0.54/(Mach Number-1)^1.2))
r = R_curvature/(1.143*exp(0.54/(M_r-1)^1.2))
This formula uses 1 Functions, 3 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Radius - (Measured in Meter) - Radius is a radial line from the focus to any point of a curve.
Radius of Curvature - (Measured in Meter) - The Radius of Curvature is the reciprocal of the curvature.
Mach Number - Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Radius of Curvature: 15235 Millimeter --> 15.235 Meter (Check conversion here)
Mach Number: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = R_curvature/(1.143*exp(0.54/(M_r-1)^1.2)) --> 15.235/(1.143*exp(0.54/(1.4-1)^1.2))

Evaluating ... ...

r = 2.63378254179889

STEP 3: Convert Result to Output's Unit

2.63378254179889 Meter -->2633.78254179889 Millimeter (Check conversion here)

FINAL ANSWER

2633.78254179889 ≈ 2633.783 Millimeter <-- Radius

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Hypersonic Flight Paths Velocity of Altitude Map » Radius for Sphere-Cone Body Shape

Credits

Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 9 Hypersonic Flight Paths Velocity of Altitude Map Calculators

Forces Acting Perpendicular to Body on Flight Path

Go Lift Force = Weight*cos(Angle of Inclination)-Mass*(Velocity^2)/Radius

Pressure Ratio of Blunt-Nosed Cylinder (First Approximation)

Go Pressure Ratio = 0.067*Mach Number^2*sqrt(Drag Coefficient)/(Distance from X-Axis/Diameter)

Forces Acting on Body along Flight Path

Go Drag force along flight path = Weight*sin(Angle of Inclination)-Mass*Velocity Gradient

Radial Coordinate of Blunt-Nosed Cylinder (First Approximation)

Go Radial Coordinate = 0.795*Diameter*Drag Coefficient^(1/4)*(Distance from X-Axis/Diameter)^(1/2)

Blunt-Nosed Radial Coordinate Flat Plate (First Approximation)

Go Radial Coordinate = 0.774*Drag Coefficient^(1/3)*(Distance from X-Axis/Diameter)^(2/3)

Radius for Cylinder-Wedge Body Shape

Go Radius = Radius of Curvature/(1.386*exp(1.8/(Mach Number-1)^0.75))

Radius for Sphere-Cone Body Shape

Go Radius = Radius of Curvature/(1.143*exp(0.54/(Mach Number-1)^1.2))

Radius of Curvature for Cylinder Wedge Body Shape

Go Radius of Curvature = Radius*1.386*exp(1.8/(Mach Number-1)^0.75)

Radius of Curvature for Sphere Cone Body Shape

Go Radius of Curvature = Radius*1.143*exp(0.54/(Mach Number-1)^1.2)

Radius for Sphere-Cone Body Shape Formula

Radius = Radius of Curvature/(1.143*exp(0.54/(Mach Number-1)^1.2))
r = R_curvature/(1.143*exp(0.54/(M_r-1)^1.2))

What is a shock wave?

The shock wave, a strong pressure wave in an elastic medium such as air, water, or a solid substance, produced by supersonic aircraft, explosions, lightning, or other phenomena that create violent changes in pressure.

How to Calculate Radius for Sphere-Cone Body Shape?

Radius for Sphere-Cone Body Shape calculator uses Radius = Radius of Curvature/(1.143*exp(0.54/(Mach Number-1)^1.2)) to calculate the Radius, The Radius for sphere-cone body shape formula is defined as the ratio of the radius of curvature of the shock of the body to the 1.143 time exponent of the inverse of Mach number at infinity raise to 1.2. Radius is denoted by r symbol.

How to calculate Radius for Sphere-Cone Body Shape using this online calculator? To use this online calculator for Radius for Sphere-Cone Body Shape, enter Radius of Curvature (R_curvature) & Mach Number (M_r) and hit the calculate button. Here is how the Radius for Sphere-Cone Body Shape calculation can be explained with given input values -> 2.6E+6 = 15.235/(1.143*exp(0.54/(1.4-1)^1.2)).

FAQ

What is Radius for Sphere-Cone Body Shape?

The Radius for sphere-cone body shape formula is defined as the ratio of the radius of curvature of the shock of the body to the 1.143 time exponent of the inverse of Mach number at infinity raise to 1.2 and is represented as r = R_curvature/(1.143*exp(0.54/(M_r-1)^1.2)) or Radius = Radius of Curvature/(1.143*exp(0.54/(Mach Number-1)^1.2)). The Radius of Curvature is the reciprocal of the curvature & Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Radius for Sphere-Cone Body Shape?

The Radius for sphere-cone body shape formula is defined as the ratio of the radius of curvature of the shock of the body to the 1.143 time exponent of the inverse of Mach number at infinity raise to 1.2 is calculated using Radius = Radius of Curvature/(1.143*exp(0.54/(Mach Number-1)^1.2)). To calculate Radius for Sphere-Cone Body Shape, you need Radius of Curvature (R_curvature) & Mach Number (M_r). With our tool, you need to enter the respective value for Radius of Curvature & Mach Number 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 Radius?

In this formula, Radius uses Radius of Curvature & Mach Number. We can use 1 other way(s) to calculate the same, which is/are as follows -

Radius = Radius of Curvature/(1.386*exp(1.8/(Mach Number-1)^0.75))

Home

FREE PDFs

🔍 Search