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Chord length of hypocycloid Solution

STEP 0: Pre-Calculation Summary
Formula Used
chord_length = 2*Radius 1*sin(pi/Number of cusps)
l = 2*r1*sin(pi/n)
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
Variables Used
Radius 1 - Radius 1 is a radial line from the focus to any point of a curve. (Measured in Meter)
Number of cusps- Number of cusps is defined as the the number of curves made by the small circle of hypocycloid
STEP 1: Convert Input(s) to Base Unit
Radius 1: 11 Meter --> 11 Meter No Conversion Required
Number of cusps: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = 2*r1*sin(pi/n) --> 2*11*sin(pi/3)
Evaluating ... ...
l = 19.0525588832577
STEP 3: Convert Result to Output's Unit
19.0525588832577 Meter --> No Conversion Required
FINAL ANSWER
19.0525588832577 Meter <-- Chord Length
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Lateral Surface Area of a Conical Frustum
lateral_surface_area = pi*(Radius 1+Radius 2)*sqrt((Radius 1-Radius 2)^2+Height^2) Go
Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Moment of Inertia of a solid sphere about its diameter
moment_of_inertia = 2*(Mass*(Radius 1^2))/5 Go
Moment of inertia of a circular disc about an axis through its center and perpendicular to its plane
moment_of_inertia = (Mass*(Radius 1^2))/2 Go
Moment of Inertia of a right circular solid cylinder about its symmetry axis
moment_of_inertia = (Mass*(Radius 1^2))/2 Go
Moment of Inertia of a spherical shell about its diameter
moment_of_inertia = 2*(Mass*(Radius 1))/3 Go
Moment of Inertia of a right circular hollow cylinder about its axis
moment_of_inertia = (Mass*(Radius 1)^2) Go
Moment of inertia of a circular ring about an axis through its center and perpendicular to its plane
moment_of_inertia = Mass*(Radius 1^2) Go
Top Surface Area of a Conical Frustum
top_surface_area = pi*(Radius 1)^2 Go
Area of a Torus
area = pi^2*(Radius 2^2-Radius 1^2) Go
Volume of cylinder circumscribing a sphere when radius of sphere is known
volume = 2*pi*(Radius 1^3) Go

11 Other formulas that calculate the same Output

Length of the chord intercepted by the parabola y^2=4ax on the line y = mx + c
chord_length = (4/Slope of Line^2)*((Numerical Coefficient a)*(1+(Slope of Line^2))*(Numerical Coefficient a-(Slope of Line*Numerical Coefficient c)))^(0.5) Go
Chord length for circulation developed on the airfoil
chord_length = Circulation/(pi*velocity of airfoil*sin(Angle of attack)) Go
Chord length for flat plate case
chord_length = (Reynolds number using chord length*static viscosity)/(Static velocity*Static density) Go
Chord length of astroid given radius of area
chord_length = 2*(sqrt((8*Area)/(3*pi)))*sin(pi/4) Go
Chord length when radius and perpendicular distance are given
chord_length = sqrt(Radius^2-Perpendicular Distance^2)*2 Go
Length of a chord when radius and inscribed angle are given
chord_length = 2*Radius*sin(Inscribed Angle) Go
Length of a chord when radius and central angle are given
chord_length = 2*Radius*sin(Central Angle/2) Go
Chord length of astroid given radius of perimeter
chord_length = 2*(Perimeter/6)*sin(pi/4) Go
Chord length of astroid given radius of small circle
chord_length = 2*(4*Radius)*sin(pi/4) Go
Chord Length when radius and angle are given
chord_length = sin(Angle A/2)*2*Radius Go
Chord length of astroid
chord_length = 2*Radius 1*sin(pi/4) Go

Chord length of hypocycloid Formula

chord_length = 2*Radius 1*sin(pi/Number of cusps)
l = 2*r1*sin(pi/n)

What is a hypocycloid?

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line. Any hypocycloid with an integral value of k, and thus k cusps, can move snugly inside another hypocycloid with k+1 cusps, such that the points of the smaller hypocycloid will always be in contact with the larger. This motion looks like 'rolling', though it is not technically rolling in the sense of classical mechanics, since it involves slipping.

How to Calculate Chord length of hypocycloid?

Chord length of hypocycloid calculator uses chord_length = 2*Radius 1*sin(pi/Number of cusps) to calculate the Chord Length, The Chord length of hypocycloid formula is defined as the straight line distance between two points on the curve of hypocycloid, where a = radius of large circle of hypocycloid. Chord Length and is denoted by l symbol.

How to calculate Chord length of hypocycloid using this online calculator? To use this online calculator for Chord length of hypocycloid, enter Radius 1 (r1) and Number of cusps (n) and hit the calculate button. Here is how the Chord length of hypocycloid calculation can be explained with given input values -> 19.05256 = 2*11*sin(pi/3).

FAQ

What is Chord length of hypocycloid?
The Chord length of hypocycloid formula is defined as the straight line distance between two points on the curve of hypocycloid, where a = radius of large circle of hypocycloid and is represented as l = 2*r1*sin(pi/n) or chord_length = 2*Radius 1*sin(pi/Number of cusps). Radius 1 is a radial line from the focus to any point of a curve and Number of cusps is defined as the the number of curves made by the small circle of hypocycloid.
How to calculate Chord length of hypocycloid?
The Chord length of hypocycloid formula is defined as the straight line distance between two points on the curve of hypocycloid, where a = radius of large circle of hypocycloid is calculated using chord_length = 2*Radius 1*sin(pi/Number of cusps). To calculate Chord length of hypocycloid, you need Radius 1 (r1) and Number of cusps (n). With our tool, you need to enter the respective value for Radius 1 and Number of cusps 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 Chord Length?
In this formula, Chord Length uses Radius 1 and Number of cusps. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • chord_length = sin(Angle A/2)*2*Radius
  • chord_length = sqrt(Radius^2-Perpendicular Distance^2)*2
  • chord_length = 2*Radius*sin(Central Angle/2)
  • chord_length = 2*Radius*sin(Inscribed Angle)
  • chord_length = (4/Slope of Line^2)*((Numerical Coefficient a)*(1+(Slope of Line^2))*(Numerical Coefficient a-(Slope of Line*Numerical Coefficient c)))^(0.5)
  • chord_length = Circulation/(pi*velocity of airfoil*sin(Angle of attack))
  • chord_length = (Reynolds number using chord length*static viscosity)/(Static velocity*Static density)
  • chord_length = 2*Radius 1*sin(pi/4)
  • chord_length = 2*(4*Radius)*sin(pi/4)
  • chord_length = 2*(Perimeter/6)*sin(pi/4)
  • chord_length = 2*(sqrt((8*Area)/(3*pi)))*sin(pi/4)
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