Evaluate the cavitation behaviour of a marine propeller from ship speed, RPS, diameter and expanded area ratio. The tool reports the Thoma number σ, thrust-loading coefficient τ_c, Burrill chart limit and Keller-formula recommended EAR in real time, so you can see the design margin for container, LNG and naval vessels.
Parameters
Ship speed V_s
knots
Propeller diameter D
m
Rotational speed n
rps
rps = rpm / 60
Pitch ratio P/D
Blade number z
Merchant ships use 4–5 blades, LNG and naval vessels often 5–7
Shaft immersion depth h
m
Depth of the propeller shaft centre below the waterline
Expanded area ratio EAR
Total expanded blade area / disc area. 0.55–0.85 is typical
Sketches a stern view of the propeller with flow, blade sections and cavities. Red sheets show back-side cavitation; white filaments show tip-vortex cavitation.
V_0.7R is the resultant velocity at the 0.7-radius section (axial inflow combined with blade rotation), A_P is the projected area and T is thrust. Read the τ_c limit from the Burrill chart and use Keller to size the minimum EAR.
$$V_{0.7R}=\sqrt{V_a^{2}+(0.7\,\pi D n)^{2}},\quad p_\infty = p_{atm} + \rho g h,\quad V_a = (1-w)\,V_s$$
w is the wake fraction (this tool uses the merchant-ship representative value 0.25), h the shaft immersion depth and V_s the ship speed.
Marine Propeller Cavitation Design — Thoma Number and Burrill Chart
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People say a ship propeller "loses performance once cavitation starts" — what is actually happening on the blade?
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Roughly speaking, on the blade's back side (suction side) the local pressure drops to the vapour pressure p_v of the surrounding water, and the water locally "boils". At 20 °C sea water that point is about 2,340 Pa. Bubbles then form, travel downstream and collapse violently. That collapse causes (1) thrust loss, (2) hull-pressure pulses and stern vibration, (3) deep "erosion" pits on the blade surface, (4) extra noise, and (5) a major loss of acoustic stealth on naval vessels — all at once.
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So the design indicator that says "how close are we to cavitating" is the Thoma number σ? When I raise the ship speed on the left, σ drops fast.
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Exactly. σ = (p_∞ − p_v)/(½ρV²) — basically "available pressure margin normalised by dynamic pressure". Increasing speed or RPS makes V² larger and pushes σ down. Sinking the propeller deeper (larger h) increases p_∞ and pushes σ back up — that is why submarines are quiet deep but loud near the surface. Container ships sit around σ ≈ 0.2–0.3; high-speed naval vessels drop below 0.1. With the defaults of this tool (20 kn, 6 m diameter, 2.5 rps, 5 m immersion) you should read about σ ≈ 0.254.
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OK, low σ means cavitation. What is the "Burrill chart" then?
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An empirical chart from L.C. Burrill (1943), distilled from a huge set of cavitation-tunnel tests. The horizontal axis is σ at 0.7R, the vertical axis is the thrust-loading coefficient τ_c = T/(A_p · ½ρV²). Limit curves are drawn for "0%, 2.5%, 5%, 10%, 20% back cavitation". If your design point (σ, τ_c) sits below the chosen limit it is acceptable. Merchant ships usually target about 5% back cavitation (τ_c ≈ 0.20); naval vessels keep to 2.5% (τ_c ≈ 0.10) for acoustic reasons. CFD has taken over the detail, but Burrill is still the go-to first cut in early design.
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If a design is about to cavitate, what do I change first? Drop the RPS?
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Dropping n does work, but it also drops thrust, so it is not a stand-alone fix. The first move in practice is to "increase the EAR". EAR = total blade area / disc area; raising it lowers τ_c per unit area and pushes the design point under the limit. Keller's empirical formula EAR_min = (1.3+0.3z)·T/((p−p_v)·D²) + K gives you a target. K = 0.20 container, 0.10 tanker, 0.15 LNG, 0.30 ferry, 0.00 naval. If that is still not enough you grow D (within draft limits), add a blade (4 → 5 → 6 — also reduces vibration), or finally fit an energy-saving device (CRP, Mewis Duct, pre-swirl stator) to clean up the inflow and raise V_a.
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And the final design check is the cavitation tunnel test?
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Yes. Depressurised model tests at MARIN, SVA Potsdam, KRISO, NMRI and similar labs are still the gold standard, and the Burrill estimate is what you compare against. Increasingly, OpenFOAM (interPhaseChangeFoam, Schnerr-Sauer model) and Star-CCM+ also predict cavitation numerically. The modern workflow combines Wageningen B/AU/MAU series charts with CFD plus tunnel validation.
Frequently Asked Questions
The Thoma (cavitation) number σ is the non-dimensional ratio of available pressure margin to dynamic pressure: σ = (p_∞ − p_v)/(½ρV²). For marine propellers the reference velocity is the resultant velocity V_0.7R at the 0.7-radius blade section, and p_∞ includes atmospheric pressure plus hydrostatic pressure from the shaft immersion depth. A smaller σ means cavitation is more likely; sinking the propeller deeper or lowering the RPS raises σ and suppresses cavities. Container ships typically operate at σ ≈ 0.2–0.3, while a naval vessel at high speed can fall below 0.15.
The Burrill chart (1943) plots the local cavitation number σ_0.7R on the x-axis against the thrust-loading coefficient τ_c = T/(A_p · ½ρV²) on the y-axis, with empirical limit lines drawn for each allowable back cavitation percentage. Merchant ships are typically designed to about 5% back cavitation (τ_c limit ≈ 0.20), while naval vessels at high speed target 2.5% (τ_c limit ≈ 0.10). If the design point (σ, τ_c) is below the chosen limit curve it is acceptable. It is still routinely used in early-stage design to pick the expanded-area ratio (EAR) or propeller diameter D before model tests.
The Keller formula gives the minimum expanded-area ratio that keeps cavitation within an acceptable range: EAR_min = (1.3 + 0.3·z) · T / ((p − p_v) · D²) + K, where z is blade number, T thrust [N], D diameter [m] and K a vessel-type constant. Typical K values are 0.20 (container), 0.10 (tanker), 0.15 (LNG carrier), 0.30 (ferry) and 0.00 (naval). This tool shows the result as 'Recommended EAR' so you can compare it directly to the EAR currently being designed.
Tip-vortex cavitation (TVC) is the thin, rope-like cavity that forms in the low-pressure core of the vortex shed from each blade tip. Because TVC develops at a lower σ_TVC than the 0.7R local σ, it is difficult to eliminate entirely on merchant ships under normal operation. The consequences are (1) hull-pressure pulses and secondary noise, (2) reduced acoustic stealth on naval and submarine platforms, and (3) impact on the rudder. Mitigation uses Kappel/CLT blade tips, tip plates, pre-swirl stators and energy-saving devices such as the Mewis Duct. Modern practice manages — rather than eliminates — TVC.
Real-World Applications
Merchant-ship (container, tanker, bulker) design: At the preliminary design stage, designers feed power, ship speed and estimated thrust into the Burrill chart and Keller formula to fix the required EAR, then pick pitch ratio P/D and open-water efficiency η_O from a Wageningen B-series chart. Checking early that this tool's "recommended EAR" matches the designed EAR — and that τ_c sits around 80 % of the Burrill limit — avoids the expensive shock of discovering excess cavitation only at the model test.
Vibration and noise control on LNG carriers and PCTCs: LNG cargo tanks impose strict limits on stern-induced hull pressure, and car carriers must protect their stowed vehicles from vibration. These vessels typically use 5–6 blades and EAR of 0.70–0.85 to suppress cavitation-driven high-frequency excitation. Switching the vessel selector to LNG or ferry in this tool yields a larger K, and therefore a higher recommended EAR, for exactly this reason.
Quiet design for naval vessels and submarines: Self-radiated cavitation noise dominates a ship's acoustic signature and degrades own-ship sonar performance. Naval architects push the "cavitation inception speed" (CIS) as high as possible using 7-blade skewed propellers, ducted pump-jets and pre-swirl stators. Design σ is around 0.10–0.15 and the allowable τ_c is roughly half that of a merchant vessel. Select "Naval vessel" here to see the limit tighten.
Pre-screening for CFD and model tests: Before running an OpenFOAM interPhaseChangeFoam (Schnerr-Sauer model) or Star-CCM+ cavitation simulation, this kind of chart-based estimate tells you how far the design point sits from the Burrill limit. Feeding a clearly over-loaded design into CFD wastes compute; the same holds for depressurised tunnel test series (MARIN T32, SVA UT, KRISO LCT, NMRI LCT). This first-cut tool helps prune candidates.
Common Misconceptions and Pitfalls
The biggest misconception is the assumption that "cavitation must be eliminated completely". In reality almost every commercial propeller cavitates to some degree, and the design goal is to keep it inside an acceptable window. Up to about 5 % back-sheet cavitation, with no erosion and thrust loss under 3 %, is usually fine. Tip-vortex cavitation in particular cannot be fully removed on merchant ships — the realistic goal is to manage its vibration and noise impact, not to make it disappear.
Second, "if σ stays high enough, the propeller is safe". σ is computed with the 0.7R reference velocity V_0.7R, which is an approximation; the real blade-surface pressure depends on local σ_min, not on σ_0.7R. At the same σ_0.7R, a high P/D and low skew design can have a much larger leading-edge suction peak, with local σ_min 30 – 50 % below σ_0.7R. The Burrill chart absorbs this on average; for unusual blade sections or operating conditions you still need a CFD check of the local σ distribution.
Third, "just push EAR up and you are safe". Increasing EAR does improve cavitation margin, but at a cost: (1) tighter inter-blade water passages raise viscous drag and lower open-water efficiency (typically 2 – 4 % loss going from EAR 0.55 to 0.85), (2) thinner blades increase structural stress, and (3) more blades increase manufacturing cost and tolerance demands. Keller's formula gives the minimum required EAR; for efficiency you usually stop 5 – 15 % above that minimum. Blindly oversizing EAR and ending up with a quiet but fuel-thirsty ship is a common pitfall in practice.
How to Use
Enter ship speed (knots) and propeller diameter (metres)—typical container ships use 8–12 m diameter props at 15–22 knots.
Input propeller RPM and pitch-diameter ratio (P/D typically 0.8–1.2 for cargo vessels).
The simulator calculates local velocity at 0.7R blade station, Thoma cavitation number σ, thrust loading τ_c, and compares against Burrill's empirical limit to predict inception.
Worked Example
Container ship: 18 knots, propeller D = 8.5 m, N = 110 RPM, P/D = 1.0. At 0.7R station, V_0.7R ≈ 9.2 m/s; Thoma number σ ≈ 0.68. Calculated thrust τ_c = 0.42 exceeds Burrill limit of 0.38 at this speed—cavitation inception likely. Increasing pitch-diameter ratio to 1.1 reduces blade loading, lowering τ_c to 0.35 and mitigating cavitation. Recommended expanded area ratio (EAR) per Keller method: 0.72.
Practical Notes
Higher ship speeds and shallow water lower σ dramatically; bulk carriers operating in estuaries require P/D ≤ 0.9 to stay below Burrill limits.
Thrust loading τ_c increases nonlinearly with RPM—reducing revolutions by 10 % often prevents cavitation erosion without significant speed loss.
Propeller material (Ni-Al-bronze vs. composite) determines erosion tolerance; use EAR ≥ 0.70 for bronze props in cavitating regimes.