Boat Speed, Prop Pitch, Horsepower and Fuel Cost Calculator

Hull speed and power

Deep-water gravity-wave dispersion gives $V_h=\sqrt{gL_{WL}/(2\pi)}$, $Fn=V/\sqrt{gL_{WL}}$ and wavelength $\lambda_w=2\pi V^2/g$. This corresponds closely to the US Naval Academy's rounded $1.34\sqrt{L_{WL}[ft]}$ knots (EN400, Lab 7, printed page 7-3).

Crouch is used only as a planing correlation: $V[kn]=C\sqrt{SHP[hp]/m[lb]}$. The numerical coefficient follows the knots convention described by Sponberg, The Design Ratios, pp. 48–50. Mechanical horsepower and loaded pounds are converted explicitly. The default C = 150 is a starting assumption for a runabout, not a measured coefficient for the user's boat. No separate propeller-efficiency factor is applied to Crouch.

The displacement branch is $P_d=P_{ref}(V/V_{ref})^3$, calibrated to the same loaded boat. For semi-planing/Crouch, a smoothstep blend joins it to Crouch over Fn = 0.35–0.90. An additional factor is $1+H G\exp(-[(Fn-0.50)/0.15]^2)$, where G rises smoothly from zero at Fn 0.35 to one at 0.50. These transition thresholds, width and hump shape are assumptions made for this tool, not coefficients from Savitsky or a universal resistance series. The low-speed reference is preserved below Fn 0.35. The maximum demand up to the selected speed is sampled densely through the transition and refined locally; above it Crouch rises with speed squared.

Fixed-trim Savitsky option

For a prismatic planing bottom, $C_{L\beta}=mg/(0.5\rho V^2b^2)$ and $C_v=V/\sqrt{gb}$. Bisection solves $C_{L\beta}=C_{L0}-0.0065\beta C_{L0}^{0.6}$ and $C_{L0}=\tau^{1.1}(0.012\lambda^{0.5}+0.0055\lambda^{2.5}/C_v^2)$. Angles in these empirical powers are numerical degrees. Wetted keel/chine lengths use $b[\lambda\pm\tan\beta/(2\pi\tan\tau)]$.

The mean-bottom-speed correction follows Savitsky (1964), with the deadrise correction documented in OpenPlaning. Bottom friction uses the ITTC-1957 line $C_f=0.075/(\log_{10}Re-2)^2+\Delta C_f$, rather than Savitsky's original Schoenherr chart. Resistance is $R=mg\tan\tau+D_f/\cos\tau$ and delivered shaft power is $RV/\eta_p$. This is an explicitly fixed-trim adaptation: it does not solve pitching moment equilibrium. A nonpositive bottom-speed radicand or Reynolds number below one million stops the solver before friction, resistance and power. The operating point and every chart sample use the same complete applicability test; invalid quantities are gaps, without clamped physical results. No standard tables or figures are reproduced.

Propeller and fuel

For reduction G, shaft turns per second are $n_e/G$, converted from RPM. Zero-slip travel speed is pitch times shaft turns per second. Apparent slip is $1-V/V_0$; assumed slip gives $V_p=V_0(1-s)$ and required pitch $p=V/[n_p(1-s)]$. This kinematics does not implement Wageningen B-series thrust/torque polynomials, select blade area/diameter or establish propulsive efficiency.

Generic cruise burn is $Q=BSFC\,P_{engine}/\rho_f$, with explicit grams-to-kilograms conversion. Measured burn replaces it. The optional Cummins table linearly interpolates its per-engine RPM/fuel pairs (attached s3, page 1), then multiplies burn by the count of identical engines at that RPM. Hull engine-power demand is divided equally among them and compared per engine with the published 2.7-exponent demand curve. Total reference power scales by the same count. Moving time is distance divided by the actual positive ground speed; no minimum-speed substitution is made. Zero or negative progress is rejected by the input condition. Add idle fuel, multiply consumed volume by price, and add the user-entered extra-fuel fraction for loading.

• Calm, deep water; constant load, steady speed and one constant along-track current. Reciprocal runs are recommended for slip measurements.
• The default low-speed power pair, transition hump, gearbox efficiency, specific fuel consumption, fuel density, idle burn and price are illustrative user-adjustable assumptions. They are not measurements of a particular boat or live market prices.
• Displacement power is a local calibration at the entered loading; it does not scale automatically when mass changes. Recalibrate the reference point when loading changes.
• Crouch's coefficient includes the behavior of a similar hull/propulsion setup. Match its unit convention and operating regime.
• Savitsky assumes a prismatic, constant-deadrise, hard-chine monohull at a specified running trim, with wetted transom chines. The mean-bottom-speed correction and turbulent friction line are used without air, appendage or whisker-spray drag.
• Effective-to-shaft efficiency and gearbox efficiency are independent of apparent slip. Neither Crouch nor a prescribed-slip RPM sweep guarantees that an engine can attain that RPM.
• The Cummins option is only the 134 kW, 2500 RPM 6BT5.9-M M-90762 curve dated 7 November 2000, not a generic diesel curve. Multiple units must be identical, run at the entered common RPM and share the load equally. Cruise burn and reference power are summed over their count; the entered idle burn is already a total.
• Additional fuel is a fraction of predicted consumption, not a fraction of tank capacity and not a prescribed reserve rule. Cost uses any consistent user currency. Fuel-price basis is selected explicitly.

Displacement cubic estimates are local to a measured low-speed point and are flagged above Fn 0.40. The semi-planing option is flagged above Fn 1.20; its hump must be calibrated. The Crouch high-speed branch is a preliminary estimate for planing hulls, not a displacement or multihull resistance calculation.

The fixed-trim Savitsky option is restricted here to beam Froude 1–13, trim 2–15°, deadrise 0–30°, mean wetted length/beam no greater than 4, wetted keel within waterline length, nonnegative wetted chine length and turbulent wetted-bottom Reynolds number at least one million. These geometry and speed limits, a strictly positive mean-bottom-speed radicand, and the Reynolds-number limit apply to every chart point. Invalid regions are gaps in the chart. Fixed-trim planing demand does not assess whether the boat can get onto the plane.

No cavitation, ventilation, porpoising, propeller strength, shaft torque, engine RPM/load matching, motor/transom rating or regulatory compliance is established. The minimum modeled engine power has no acceleration, wave or service margin. Confirm engine choice against the boat builder's permitted rating and loading limits.

Fuel consumption depends on actual load and RPM. A fixed BSFC can underpredict low-load fuel burn. The historical Cummins curve is only valid from 700 to 2500 RPM on the specified propeller demand, and it must not be extrapolated. For multiple specified Cummins engines, the curve assumes identical units at the same RPM and equal loading. Ground speed must be strictly positive; all positive values are used as entered. Calculate outward and return legs separately when current or operating conditions differ.