Prismatic Coefficient Calculator with Solution

Prismatic Coefficient Formula:

\[ C_p = \frac{V}{A_m \times L} \]

Prismatic Coefficient (C_p):

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1. What is Prismatic Coefficient?

Definition: The prismatic coefficient (C_p) is a dimensionless value that represents the ratio of the actual underwater volume of a ship's hull to the volume of a prism with length equal to the ship's length and cross-sectional area equal to the ship's maximum underwater cross-section.

Purpose: It's a key parameter in naval architecture that helps determine the hull's efficiency and resistance characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_p = \frac{V}{A_m \times L} \]

Where:

\( C_p \) — Prismatic coefficient (dimensionless)
\( V \) — Displaced volume (m³)
\( A_m \) — Midship section area (m²)
\( L \) — Length (m)

Explanation: The formula compares the actual underwater volume to the theoretical prism volume formed by the midship section extended along the ship's length.

3. Importance of Prismatic Coefficient

Details: The prismatic coefficient affects a ship's resistance, speed potential, and fuel efficiency. Lower values (0.55-0.65) are typical for slow ships, while higher values (0.70-0.80) are for faster vessels.

4. Using the Calculator

Tips: Enter the displaced volume in cubic meters, midship section area in square meters, and length in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical prismatic coefficient range?
A: Most ships range between 0.55 and 0.85, with cargo ships around 0.70-0.80 and high-speed vessels up to 0.85.

Q2: How does prismatic coefficient affect performance?
A: Higher C_p generally means better performance at high speeds but worse at low speeds. Lower C_p is more efficient for slow-moving ships.

Q3: What's the relationship with block coefficient?
A: Prismatic coefficient equals block coefficient divided by midship section coefficient (C_p = C_b/C_m).

Q4: How do I measure midship section area?
A: It's the underwater cross-sectional area at the midship (widest) section of the hull.

Q5: Why is precision important in this calculation?
A: Small changes in C_p can significantly affect resistance and power requirements, so we display 6 decimal places.