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25-Nav-A2 Hydrodynamics of Ships (I)_ Resistance and Propulsion · Undated paper

Question 3 of 10: ITTC'78 Resistance Extrapolation to Full Scale

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — May 2019 — 16-Nav-A2 Hydrodynamics of Ships I: Resistance and Propulsion. Three-hour, closed-book exam; a data sheet, a Wageningen B4-55 propeller chart and a Burrill cavitation chart are supplied. Format: Questions 1–8 are compulsory (attempt all eight), then one of Questions 9 or 10. All ten are solved below for completeness.

Reference texts: Larsson & Raven, Ship Resistance and Flow (SNAME) — model-scale resistance testing, Froude/Reynolds scaling, boundary-layer estimates and the ITTC 1978 performance-prediction method; Lewis (ed.), Principles of Naval Architecture, Vol. II — Resistance, Propulsion and Vibration (SNAME) — propeller geometry, wave-pattern interference, open-water B-series design and wake-induced blade loading; Carlton, Marine Propellers and Propulsion (Butterworth-Heinemann) — Wageningen B-series charts, the Burrill back-cavitation criterion and open-water model testing.

Question 3: ITTC'78 Resistance Extrapolation to Full Scale (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. $L_M=6.0$ m, $L_S=180$ m ($\lambda=30$); ship design speed $V_S=11.8$ m/s; model total resistance $R_{TM}=119.0$ N at the Froude-corresponding model speed; form factor $k=0.20$; ship wetted surface $S_S=9{,}460\ \text{m}^2$; $C_A=C_{AA}=0$. Model test in freshwater at 15 °C ($\nu=1.139\times10^{-6}\ \text{m}^2/\text{s}$, $\rho=999\ \text{kg/m}^3$); full-scale prediction in saltwater at 15 °C ($\nu=1.188\times10^{-6}\ \text{m}^2/\text{s}$, $\rho=1025\ \text{kg/m}^3$).

QuantityValue
Scale ratio $\lambda=L_S/L_M$30
Ship speed $V_S$11.8 m/s
Model resistance $R_{TM}$119.0 N
Form factor $k$0.20
Ship wetted surface $S_S$9,460 m²

Find. Full-scale ship total resistance $R_{TS}$ at $V_S=11.8$ m/s.

Approach. Get the Froude-corresponding model speed and wetted area from the scale ratio, form $C_{TM}$ from the measured force, subtract the model's own ITTC-57 friction line (times $1+k$) to isolate the Froude-scalable residuary coefficient $C_R$, then rebuild the ship's total coefficient from the ship-scale friction line plus $C_R$.

  1. Froude-corresponding model speed and wetted area. $$V_M=\frac{V_S}{\sqrt\lambda}=\frac{11.8}{\sqrt{30}}=2.154\ \text{m/s},\qquad S_M=\frac{S_S}{\lambda^2}=\frac{9460}{900}=10.51\ \text{m}^2.$$
  2. Model friction coefficient (ITTC-57, freshwater). $$R_{n,M}=\frac{V_ML_M}{\nu_{fw}}=\frac{(2.154)(6.0)}{1.139\times10^{-6}}=1.135\times10^{7},\qquad C_{FM}=\frac{0.075}{(\log_{10}R_{n,M}-2)^2}=0.00294.$$
  3. Model total coefficient and residuary coefficient. $$C_{TM}=\frac{R_{TM}}{\tfrac12\rho_{fw}S_MV_M^2}=\frac{119.0}{0.5(999)(10.51)(2.154)^2}=0.00488.$$ $$C_R=C_{TM}-(1+k)C_{FM}=0.00488-1.20(0.00294)=\boxed{0.00136}.$$
  4. Ship friction coefficient (ITTC-57, saltwater). $$R_{n,S}=\frac{V_SL_S}{\nu_{sw}}=\frac{(11.8)(180)}{1.188\times10^{-6}}=1.788\times10^{9},\qquad C_{FS}=\frac{0.075}{(\log_{10}R_{n,S}-2)^2}=0.00143.$$
  5. Ship total resistance coefficient and force (ITTC'78, no roughness/air terms). $$C_{TS}=(1+k)C_{FS}+C_R=1.20(0.00143)+0.00136=0.00307.$$ $$R_{TS}=C_{TS}\cdot\tfrac12\rho_{sw}S_SV_S^2=(0.00307)(0.5)(1025)(9460)(11.8)^2=\boxed{2{,}074\ \text{kN}}.$$
QuantityResult
Model residuary coefficient $C_R$0.00136
Ship friction coefficient $C_{FS}$0.00143
Ship total coefficient $C_{TS}$0.00307
Full-scale ship resistance $R_{TS}$≈ 2,074 kN (2.07 MN)