Resistance Components: Frictional & Residuary

Why total calm-water resistance is always split into two parts that obey different physical laws.

Marine EngineeringResistance & PoweringFree preview
⏱️ About 14 min

A towing tank measures the total drag force on a scaled ship model — but that single number can't just be scaled up to predict the full-size ship's resistance. It first has to be split into two pieces that scale by completely different rules.

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The big idea: Total calm-water resistance splits into frictional resistance (viscous drag on the wetted hull, governed by the Reynolds number) and residuary resistance (wave-making and eddy/form drag, governed by the Froude number) — the split matters because model-to-ship scaling treats the two completely differently.
🎯 By the end, you'll be able to
  • State the two-component split of total resistance: RT = RF + RR
  • Compute the Reynolds number for a ship hull
  • Use the ITTC 1957 model-ship correlation line to estimate the frictional resistance coefficient CF
  • Explain why frictional and residuary resistance must be treated separately when scaling from model to ship
📎 Helpful to know first

Two Resistances, Two Physical Causes

A ship moving through calm water experiences a single measurable drag force, but naval architects always split it into two components with different physical origins:

  • Frictional resistance RF — viscous shear drag from water flowing over the wetted hull surface. It depends on wetted surface area, speed, and the fluid's viscosity, and is governed by the Reynolds number.
  • Residuary resistance RR — mainly wave-making resistance (energy shed into the ship's own bow and stern wave pattern), plus eddy-making and form drag. It is governed by the Froude number (covered in the next lesson).

For most displacement hulls at normal speeds, frictional resistance is the larger share, but residuary resistance grows sharply — and can dominate — as speed approaches the hull's wave-making limit.

\[ R_T = R_F + R_R, \qquad C_T = C_F + C_R, \qquad C_T = \frac{R_T}{\tfrac{1}{2}\rho S V^2} \]
S is the wetted surface area (m²), ρ is water density in kg/m³ — note the fluid-dynamics form of ρ here, not the t/m³ used for Δ = ρ∇ in Module 2's mass-based displacement equation.

The Reynolds Number & the ITTC 1957 Line

Frictional resistance is governed by the Reynolds number, which compares inertial to viscous forces in the boundary layer:

\[ Re = \frac{VL}{\nu}, \qquad C_F = \frac{0.075}{(\log_{10} Re - 2)^2} \]
V is speed (m/s), L is waterline length (m), ν is kinematic viscosity (m²/s). The second equation is the ITTC 1957 model-ship correlation line, the standard formula for CF used throughout naval architecture.
A single stacked bar showing total resistance RT split into a larger frictional resistance RF segment and a smaller residuary resistance RR segmentRFRRRT = RF + RR
At normal displacement speeds, frictional resistance is usually the larger share of the total — but residuary resistance grows sharply at higher Froude numbers (next lesson).
📝 Worked example: A ship has waterline length L = 180 m and speed V = 7.5 m/s in seawater (ν = 1.19 × 10⁻⁶ m²/s, ρ = 1025 kg/m³). Its wetted surface area is S = 4500 m². Find the Reynolds number, the frictional resistance coefficient CF, and the frictional resistance RF.
  1. Re = VL/ν = (7.5 × 180)/(1.19 × 10⁻⁶) = 1350/1.19 × 10⁻⁶ ≈ 1.1345 × 10⁹
  2. log₁₀(Re) ≈ 9.0544, so (log₁₀ Re − 2) = 7.0544
  3. CF = 0.075/(7.0544)² = 0.075/49.765 ≈ 0.001507
  4. RF = ½ρSV²CF = 0.5 × 1025 × 4500 × 7.5² × 0.001507 = 129,726,562.5 × 0.001507 ≈ 195,510 N
✓ Re ≈ 1.13 × 10⁹; CF ≈ 0.001507; RF ≈ 195.5 kN
✏️ Practice: A ship has waterline length L = 140 m and speed V = 6.2 m/s in seawater (ν = 1.19 × 10⁻⁶ m²/s). Find the frictional resistance coefficient CF using the ITTC 1957 line.
Solution
  1. Re = VL/ν = (6.2 × 140)/(1.19 × 10⁻⁶) = 868/1.19 × 10⁻⁶ ≈ 7.294 × 10⁸
  2. log₁₀(Re) ≈ 8.8630, so (log₁₀ Re − 2) = 6.8630
  3. CF = 0.075/(6.8630)² = 0.075/47.10 ≈ 0.001592

Why Residuary Resistance Can't Be Computed the Same Way

Unlike frictional resistance, residuary resistance has no equivalent closed-form formula — wave-making is a complex free-surface phenomenon that depends on hull form in ways that resist simple analytical treatment. In practice, residuary resistance is found experimentally, from towed-model tests, and the Froude number is the key to making those model tests meaningful for full-scale prediction — the subject of the next lesson.

Check your understanding

1. Frictional resistance RF is primarily governed by:
Frictional resistance is viscous drag on the wetted hull surface, and the Reynolds number (inertial vs. viscous forces) governs it via the ITTC 1957 line.
2. Residuary resistance RR is mainly caused by:
Residuary resistance is dominated by wave-making (plus eddy-making/form drag), which scales with the Froude number rather than the Reynolds number.
🔎 Related lessons
Froude Scaling & Model Testing
✅ Key takeaways
  • Total resistance splits as RT = RF + RR: frictional (viscous, Reynolds-number-governed) and residuary (wave-making/eddy, Froude-number-governed)
  • The ITTC 1957 line CF = 0.075/(log₁₀Re − 2)² is the standard formula for estimating frictional resistance coefficient
  • Residuary resistance has no simple closed-form formula and is found experimentally from model tests
➡️ Model tests measure total resistance on a small scaled hull — next we see how Froude's law of comparison makes that measurement meaningful for predicting the full-scale ship.
Want to test yourself on this? Try the Marine Engineering Aptitude test →