Second Semi Axis of Semi Ellipsoid Calculator

Formula Used:

\[ b = \frac{3V}{2\pi a c} \]

Volume of Semi Ellipsoid (V):

m³

Bisected Axis of Semi Ellipsoid (a):

Third Semi Axis of Semi Ellipsoid (c):

Second Semi Axis of Semi Ellipsoid (b):

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1. What is the Second Semi Axis of Semi Ellipsoid?

The Second Semi Axis of Semi Ellipsoid is the length of the segment of second cartesian coordinate axis from the center of the elliptical face of Semi Ellipsoid to its boundary edge. It is one of the three principal axes that define the shape and size of a semi-ellipsoid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{3V}{2\pi a c} \]

Where:

\( b \) — Second Semi Axis of Semi Ellipsoid (m)
\( V \) — Volume of Semi Ellipsoid (m³)
\( a \) — Bisected Axis of Semi Ellipsoid (m)
\( c \) — Third Semi Axis of Semi Ellipsoid (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the second semi axis when the volume and the other two semi axes are known, based on the volume formula of a semi-ellipsoid.

3. Importance of Second Semi Axis Calculation

Details: Calculating the second semi axis is essential for understanding the complete geometry of a semi-ellipsoid. It's particularly important in engineering, architecture, and physics where ellipsoidal shapes are used in various applications such as dome structures, antenna design, and optical systems.

4. Using the Calculator

Tips: Enter the volume in cubic meters, and both the bisected axis and third semi axis in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a semi-ellipsoid?
A: A semi-ellipsoid is half of an ellipsoid, typically formed by cutting an ellipsoid through one of its principal planes.

Q2: How is this different from a full ellipsoid calculation?
A: For a full ellipsoid, the volume formula is \( V = \frac{4}{3}\pi abc \), while for a semi-ellipsoid it's \( V = \frac{2}{3}\pi abc \), hence the different formula for calculating the axes.

Q3: What are typical applications of semi-ellipsoids?
A: Semi-ellipsoids are commonly used in architectural domes, radar antennas, telescope mirrors, and various engineering structures where aerodynamic or aesthetic elliptical shapes are required.

Q4: Can this calculator handle different units?
A: The calculator uses meters for length and cubic meters for volume. You need to convert your measurements to these units before calculation for accurate results.

Q5: What if I get a negative result?
A: The second semi axis should always be a positive value. If you get a negative result, check that all input values are positive and that the volume and axes measurements are consistent.