Semi-Displacement Hull Speed Calculator
Estimate the speed potential, target Speed-Length Ratio (S/L), and required horsepower for semi-displacement hulls engineered to climb partially over their own bow wave. While pure displacement hulls are capped at an S/L of 1.34, semi-displacement motor yachts efficiently operate across an S/L ratio range of 1.4 up to 2.5+.
Calculated Performance Profile
Hull Speed Regime Spectrum
Understanding Semi-Displacement Hull Speed
In naval architecture, traditional displacement hulls (such as trawlers and heavy sailboats) generate a bow wave and stern wave as they move through water. As vessel speed increases, the wavelength of the bow wave lengthens until it equals the vessel's Waterline Length (LWL). At this point, the boat becomes trapped in the trough between its bow and stern waves, hitting a physical threshold known as the displacement hull speed limit ($1.34 \times \sqrt{\text{LWL}}$).
Semi-displacement hulls (also known as semi-planing hulls) feature modified bottom geometry—such as flatter aft sections, hard chine rails, and spray strakes—that generate hydrodynamic lift. This lift allows the vessel to climb partially over its own bow wave, pushing into Speed-Length (S/L) ratios of 1.4 to 2.5+ without requiring the extreme power-to-weight ratios of full planing hulls.
Key Formulas Used in Hull Speed Calculations
1. Speed-Length Ratio Formula
Speed (Knots) = S/L Ratio × √LWL (Feet)
Where LWL is the waterline length in feet, and S/L is the target operating ratio.
2. Crouch's Power & Weight Formula for Semi-Displacement Hulls
Speed (Knots) = C / √(Displacement (Lbs) / Shaft HP)
Where C is Crouch's Constant (typically 150–180 for semi-displacement craft depending on hull fineness and wetted surface area). The formula outputs speed directly in knots when using standard constants (per Dave Gerr, The Propeller Handbook). Note: Gerr's original constants (C = 150–230) were calibrated for planing hulls; the values used here (150–180) are adjusted for semi-displacement performance profiles.
Hull Regime Comparison Table
| Hull Category | S/L Ratio Range | Hydrodynamic Behavior | Typical Power Need |
|---|---|---|---|
| Displacement | 0.50 – 1.34 | Fully supported by buoyancy; trapped inside bow wave trough. | Low (1–3 HP per ton) |
| Semi-Displacement | 1.35 – 2.50 | Partial hydrodynamic lift; climbs bow wave, stern stays submerged. | Moderate to High (10–25 HP per ton) |
| Full Planing | 2.50 – 4.00+ | Riding entirely on top of water surface; dynamic lift dominates. | Very High (40+ HP per ton) |
Frequently Asked Questions (FAQ)
What is a good Speed-Length (S/L) ratio for a semi-displacement motor yacht?
Most cruising semi-displacement motor yachts operate efficiently at S/L ratios between 1.6 and 2.0. At S/L 1.6, fuel efficiency remains reasonable while providing a 20% speed boost over displacement limits. Operating above S/L 2.2 requires exponential increases in fuel consumption.
Why does a semi-displacement boat consume so much fuel past S/L 1.5?
As a semi-displacement hull climbs over its bow wave, it runs in a stern-down attitude (trim angle increases). The engine must fight both wave resistance and gravity to push the vessel uphill against its own bow wave, leading to steep fuel consumption curves.
How does waterline length (LWL) affect semi-displacement speed?
Because wave speed scales with the square root of waterline length, longer hulls achieve higher top speeds at the same S/L ratio. For example, a 50 ft LWL vessel reaches S/L 2.0 at 14.1 knots, whereas a 100 ft LWL superyacht reaches S/L 2.0 at 20.0 knots.