Formula Explanation

The Planing vs Displacement Hull Speed Calculator uses established naval architecture principles to determine hull speed limits, power requirements, and performance characteristics based on your vessel’s specifications.

Core Speed Calculation Formulas

1. Displacement Hull Speed (Theoretical Maximum)

The fundamental formula for displacement hull speed is based on the Froude number and waterline length:

Displacement Speed = Speed Coefficient × √(Waterline Length)

Where:
- Speed Coefficient ranges from 1.34 to 2.5 based on hull type
- Waterline Length is in feet

Hull Type Coefficients:

• Displacement Hull: 1.34
• Semi-Displacement Hull: 1.5
• Semi-Planing Hull: 1.8
• Planing Hull: 2.5

2. Planing Hull Speed Potential

For planing hulls with sufficient power, the speed potential is calculated as:

Planing Speed = (Engine Power / Displacement) × 1000 × Hull Multiplier × Vessel Factor

Where:
- Engine Power in horsepower
- Displacement in pounds
- Hull Multiplier: Planing (2.0), Semi-Planing (1.5), Semi-Displacement (1.2)
- Vessel Factor: Category-specific adjustment (0.9-1.4)

Key Performance Metrics

Froude Number Calculation

The Froude number indicates the vessel’s speed relative to its length and determines the hull’s operating regime:

Froude Number = Speed (ft/s) ÷ √(Gravity × Waterline Length)

Where:
- Speed in feet per second (knots × 1.68781)
- Gravity = 32.174 ft/s²
- Waterline Length in feet

Froude Number Interpretation:

• Below 0.4: Pure displacement mode
• 0.4-0.5: Semi-displacement transition
• Above 0.5: Planing potential

Speed-Length Ratio

Speed-Length Ratio = Speed (knots) ÷ √(Waterline Length)

This ratio helps classify vessel performance characteristics and compare different hull types.

Power Requirement Estimation

Basic Power Formula

Power Required (HP) = (Displacement / 1000) × Speed³ ÷ 10 × Efficiency Factor

Where:
- Displacement in pounds
- Speed in knots
- Efficiency Factors:
  - Displacement Hull: 0.8
  - Semi-Displacement: 0.6
  - Planing Hull: 0.4

Hull Efficiency Characteristics

The calculator uses predefined efficiency values for different hull types:

• Displacement Hulls: 85% efficiency – optimized for low-speed operation with minimal wave making resistance
• Semi-Displacement Hulls: 70% efficiency – balanced performance across speed ranges
• Semi-Planing Hulls: 65% efficiency – transitional design with some planing capability
• Planing Hulls: 55% efficiency – optimized for high-speed operation with increased power requirements

Vessel Category Adjustments

Different vessel types have specific performance characteristics accounted for through adjustment factors:

Wave Drag Estimation

The calculator provides a simplified wave drag percentage based on the Froude number:

Wave Drag (%) = min(Froude Number × 50, 95)

This represents the percentage of total resistance attributable to wave making at the calculated speed.

Unit Conversion Formulas

The calculator automatically handles unit conversions using these formulas:

Length Conversions:
- Meters to Feet: value × 3.28084

Weight Conversions:
- Kilograms to Pounds: value × 2.20462
- Tons to Pounds: value × 2204.62

Power Conversions:
- Kilowatts to Horsepower: value × 1.34102

Speed Conversions:
- Knots to Feet/Second: value × 1.68781

Performance Regime Classification

Based on the calculations, vessels are classified into performance regimes:

• Pure Displacement: Froude Number < 0.4 – Efficient low-speed operation
• Semi-Displacement Transition: Froude Number 0.4-0.5 – Increasing wave making resistance
• Planing Potential: Froude Number > 0.5 – Requires significant power for planing

Practical Applications

These formulas help boat owners and designers:

• Determine realistic speed expectations for given hull forms
• Estimate power requirements for desired performance
• Understand the trade-offs between different hull types
• Optimize vessel design for specific operating conditions
• Compare performance across different vessel categories

The calculations are based on established naval architecture principles and provide practical guidance for vessel performance planning and evaluation.