Prismatic Coefficient Calculator with Radius

Prismatic Coefficient Formula:

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

Prismatic Coefficient (C_p):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Prismatic Coefficient?

Definition: The prismatic coefficient (C_p) is a dimensionless value that represents the ratio of the displaced volume of a vessel to the volume of a prism with length equal to the vessel's length and cross-section equal to the vessel's midship 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 of the vessel (m)

Explanation: The formula compares the actual underwater volume of the hull to an imaginary prism with constant cross-section equal to the midship section.

3. Importance of Prismatic Coefficient

Details: The prismatic coefficient affects the vessel's resistance, speed potential, and overall hydrodynamic 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 vessel length in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is 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, while lower C_p is better for slow-speed efficiency.

Q3: What's the relationship between C_p and block coefficient?
A: C_p = Block coefficient / Midship section coefficient. They're related but measure different hull characteristics.

Q4: How do I measure midship section area?
A: It's the underwater cross-sectional area at the midpoint of the vessel's length. For circular hulls, use πr².

Q5: Why is C_p important in hull design?
A: It helps naval architects optimize the hull form for specific speed ranges and predict resistance characteristics.