Start with the symptom, not the propeller
The complaint is always the same: the throttle goes forward, the wake gets bigger, the fuel flow climbs — and the GPS barely moves. The reflex purchase is a new propeller, and it is frequently the wrong one, because a slow boat can be slow for three unrelated reasons: the hull may be against a physical wall, the engine may not carry enough power for the weight, or the prop may genuinely be delivering less than it should. Each has its own number, and the numbers are cheap to run before any money changes hands.
This guide runs them in diagnostic order. First the speed-length ratio, which says which physics your hull is currently living under. Then Crouch’s formula, which says what speed your power-to-weight ratio can buy a planing hull at all. Last, propeller slip, which is the prop’s own testimony — computed from nothing more than a tachometer reading and a GPS speed. A wrong conclusion at any step sends you shopping in the wrong store, so resist skipping ahead.
The bow-wave trap: 1.34 times the square root of the waterline
A hull moving through water drags a wave system along with it, and waves of a given length can only travel so fast. As the boat accelerates, its bow wave stretches — until, at a speed of about 1.34·√LWL knots, the wave is exactly as long as the waterline itself. The boat is now sitting in the trough of a wave of its own making, bow up on one crest, stern down behind the other, and going faster means climbing uphill on its own bow wave. Drag rises steeply; the last knot before this point can cost more power than all the previous ones combined. For a 25 ft waterline that wall stands at 1.34 × √25 = 6.7 knots — about 7.7 mph.
Two clarifications keep this number honest. The length that matters is the waterline length, not the length overall — overhangs and swim platforms do not lengthen the wave system, and on many sailboats LWL runs 10–20% shorter than LOA. And hull speed is a soft guidance point, not a law: light, slender, easily driven hulls routinely exceed it, while heavy ones struggle to reach it. Treat 1.34·√LWL as the economical cruise ceiling of a conventional displacement hull, and treat pushing past it as a decision to pay disproportionately for every increment.
First test: which regime is the hull in?
Normalize any speed by the waterline and you get the speed-length ratio, S/L = V/√LWL — the number that says which rulebook applies. Below about 1.34 the hull runs in displacement mode, fully supported by buoyancy. From 1.34 to just under 2.9 it is semi-displacement: partly wave-bound, partly lifted, with power demand rising fast. At about 2.9 and above the hull is planing, carried mostly by dynamic lift — the regime framing in Dave Gerr’s Propeller Handbook, with the caveat that the edges are guidance, and published sources place the planing transition anywhere from 2.5 to 3.0 depending on hull form.
This is the test that catches the most expensive misdiagnosis. Take a boat asked to do 10 knots on a 25 ft waterline: S/L = 10/√25 = 2.0, deep in the semi-displacement band and far past the 1.34 hull-speed point. If that boat is a heavy displacement trawler, no propeller and no plausible repower will make 10 knots economical — the hull itself is the ceiling. Our hull speed calculator bands any speed-and-waterline pair into its regime, which is worth thirty seconds before blaming any other component.
Second test: what Crouch says your power can buy
For a hull that genuinely planes, the ceiling moves from waterline length to power-to-weight, and the standard estimate is Crouch’s empirical formula: V = C/√(Δ/SHP), with displacement in pounds, shaft horsepower, and a hull-type constant C. As Gerr formulates it in the Propeller Handbook (pp. 15–17) the answer is in knots, with C = 150 for average runabouts, cruisers, and passenger vessels, 190 for high-speed runabouts and very light high-speed cruisers, and 210 for race boat types. A 3,000 lb runabout with 100 shaft horsepower and C = 150 works out to 150/√30 = 27.39 knots, or 31.52 mph.
The formula’s square root is the economics lesson. Because speed scales with √(SHP/Δ), doubling the horsepower multiplies speed by only √2 ≈ 1.41, and doubling speed requires four times the power-to-weight ratio — which is why stripping weight is worth as much per pound as adding power is per horsepower. Two cautions: the vast majority of ordinary planing craft rate C at or barely above 150, so be honest before flattering your hull with 190; and if you have trial data for a sister hull, back-calculate C = V·√(Δ/SHP) and use that instead of a preset. Where the weight sits matters too — trim and ballast placement are a stability question (metacentric height) as much as a speed one.
Third test: prop slip, the propeller’s testimony
A propeller of pitch P would, if it advanced like a screw in wood, move the boat P inches per revolution. Real water yields, so boat speed in mph is (RPM ÷ gear ratio) × pitch × (1 − slip) ÷ 1056, where 1056 is pure unit conversion — 63,360 inches per mile divided by 60 minutes per hour — and slip is the fraction by which the boat falls short of the geometric advance. Slip is not a defect: a blade is a foil and must run at an angle of attack to make thrust, so every working prop slips. The diagnostic question is only whether the number is typical. Run it from a wide-open-throttle GPS pass: a sterndrive at 5000 RPM through a 2.0:1 drive with a 19-inch prop has a zero-slip ceiling of 2500 × 19 ÷ 1056 = 44.981 mph, so a measured 39.6 mph means about 12% slip.
Now read the result against the bands. A properly propped planing hull at wide-open throttle typically runs 10–15% slip — the convention Mercury Racing teaches — while displacement hulls legitimately run far higher: Gerr’s Propeller Handbook gives typical values from about 26% for heavy powerboats at 9–15 knots up to 45% for auxiliary sailboats under 9 knots, and heavy planing cruisers often sit between the bands. A planing hull showing slip well above its band is the one case where the propeller (or the load it is dragging) really is the suspect; a slip inside the band with a disappointing speed points the inquiry back at power, weight, or the hull. Our propeller sizing calculator solves the relation four ways — speed, slip, pitch, or RPM.
The unit trap that fakes a miracle prop
Marine speed arithmetic runs in two currencies, and confusing them corrupts every test above. A knot is 1.15078 statute mph — about 15% bigger — and the formulas here are unit-specific: Crouch’s constants as Gerr publishes them give knots (older texts print the same formula with constants meant for mph), while the 1056 slip formula gives statute mph. Calibrate a custom Crouch C, or a slip figure, with a GPS reading in one unit and inputs in the other, and you will carry a 15% error into every future prediction.
The slip check has a built-in lie detector for exactly this. A boat cannot outrun the zero-slip speed its prop geometry implies, so if the measured speed beats (RPM ÷ gear ratio) × pitch ÷ 1056, the conclusion is not a miracle propeller and not negative slip — it is bad data. The usual culprits, in order: the gear ratio is not what you think (check the drive model, not the engine brochure), the GPS was reading knots while you entered mph, the tachometer over-reads, or the prop was re-pitched at some point and no longer matches its marking. Fix the data, rerun the three numbers, and only then decide what the boat actually needs.