Semi Major Axis of Elliptic Cylinder given Surface to Volume Ratio Calculator

Formula Used:

\[ a = \frac{LSA}{\pi \times b \times \left( \left( \frac{RA}{V} \times h \right) - 2 \right)} \]

Lateral Surface Area (LSA):

m²

Semi Minor Axis (b):

Surface to Volume Ratio (RA/V):

1/m

Height (h):

Semi Major Axis (a):

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1. What is the Semi Major Axis of Elliptic Cylinder?

The Semi Major Axis of an Elliptic Cylinder is the longest radius of the elliptic face, extending from the center of the elliptic face along the major axis to the furthest edge-point. It is a fundamental parameter in defining the geometry of elliptic cylinders.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a = \frac{LSA}{\pi \times b \times \left( \left( \frac{RA}{V} \times h \right) - 2 \right)} \]

Where:

\( a \) — Semi Major Axis (m)
\( LSA \) — Lateral Surface Area (m²)
\( b \) — Semi Minor Axis (m)
\( \frac{RA}{V} \) — Surface to Volume Ratio (1/m)
\( h \) — Height (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the semi major axis of an elliptic cylinder using its lateral surface area, semi minor axis, surface to volume ratio, and height.

3. Importance of Semi Major Axis Calculation

Details: Accurate calculation of the semi major axis is crucial for determining the geometric properties of elliptic cylinders, which is essential in various engineering and architectural applications involving elliptical shapes.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, square meters for area, and 1/meter for surface to volume ratio). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between semi major and semi minor axis?
A: The semi major axis is the longest radius of the ellipse, while the semi minor axis is the shortest radius perpendicular to the major axis.

Q2: When might this calculation be undefined?
A: The calculation becomes undefined when the denominator equals zero, which occurs when (RA/V × h) = 2.

Q3: What are typical applications of elliptic cylinders?
A: Elliptic cylinders are used in various engineering applications including structural components, fluid containers, and architectural designs where elliptical shapes are preferred.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the input parameters, assuming precise measurements.

Q5: Can this formula be used for other elliptical shapes?
A: This specific formula is designed for elliptic cylinders and may not apply directly to other elliptical geometries.