Planing Hull Resistance Calculation The CAHI Method SNAME Greek Section 13 October 2016 P. G. Alourdas
Savitsky CAHI Methods Empirical Prismatic hulls
PLANING HULLS A Planing Hull planes (glides, skims, slides, slips) on the water surface.
Ref. 47
Ref. 48
PLANING HULLS William Froude 1872 Ref. 78 «I must admit that it had seemed to me certain that at some assignable speed the skimming action would become so perfect as to obliterate, or virtually obliterate, water resistance.»
PLANING HULL MAIN CHARACTERISTICS WB PX LCG L WL L P L OA
PLANING HULL DIMENSIONS
PLANING HULL RESEARCH Planing hull research «starts» in the 1930s (NACA, ARC). Performance of seaplanes (floats) on the water. NACA - National Advisory Committee for Aeronautics, USA ARC - Aeronautical Research Council, UK
PLANING LIFT CREATION At rest and at low forward speeds the planing hull is supported by hydrostatic lift (buoyancy). As the speed increases the high pressures resulting from the dynamic reaction on the bottom create the hydrodynamic lift.
PLANING EQUILIBRIUM Weight of the craft = Hydrodynamic Lift + Buoyancy (Hydrostatic Lift) At Equilibrium trim and wetted length are constant.
Planing begins when the water breaks cleanly away from the transom and chines.
PLANING BUOYANCY Ref. 52 Experimental data show that when the transom is dry the ratio of Actual Buoyancy (Hydrostatic Lift) to Archimedes Buoyancy is less than 1 and it is zeroed when the wetted length is less than the beam.
PLANING BUOYANCY
HYDROSTATIC & HYDRODYNAMIC LIFT COMPONENTS Ref. 45
SPEED REGIMES Pre Planing F 2.50 Semi Planing 2.50 F 4.0 Fully Planing 4.0 F Ref. 93
Planing is Lifting on the free surface.
PRESSURE DISTRIBUTION FOR 2D FLAT PLATE Ref. 42
DYNAMIC LIFT COEFFICIENT FOR 2D FLAT PLATE Ref. 34 C LS L 2 1/2V b CLS 2sin C LS 2sin[1 ( 4/ )/F 2 ]
PLANING OF 2D FLAT PLATE NON-LINEAR EFFECT Ref. 15, Ref. 34
PLANING OF 2D FLAT PLATE WAVE & SPLASH DRAG Ref. 34
ASPECT RATIO A 1/ A b/ / b
EQUATIONS FOR DYNAMIC LIFT COEFFICIENT OF A 3D FLAT PLATE Ref. 52
C LS L 0.5V 2 b 1/ 2 CLS0.0120A 1.1 o Korvin Kroukovsky CLS 0.7A Sedov 1.4 A
C LS L 2 0.5V b CLS 2.0A Foil - Wing 2.0 A CLS 0.7A Sedov 1.4 A
C LB L 0.5V 2 b 2 CLB 1/ 2 0.0120 1.1 o Korvin Kroukovsky C LB 0.7 1 1.4 Sedov
DEADRISE REDUCES LIFT
DEADRISE REDUCES LIFT Ref. 24
SHUFORD DEADRISE FUNCTION Ref. 27
DEADRISE REDUCES IMPACT PRESSURES Ref. 43
PLANING EFFICIENCY COEFFICIENT OF PLANING - ε D/ L
VARIATION OF DRAG-LIFT RATIO FOR FLAT PLATES Ref. 13
VARIATION OF DRAG- LIFT RATIO FOR PRISMATIC SURFACES Ref. 43
Ref. 42
WETTED LENGTH RATIO PRISMATIC HULL L k L 2b c L b m
WETTED LENGTH RATIO PRISMATIC HULL Lm L k Lc 2 Lk Lc btan tan
Ref. 21
Ref. 21 C V = 3.0 - F = 3.0
Ref. 16
Ref. 71
C V = 6.16 - F = 7.12 Ref. 64
C V = 6.16 - F = 7.12 Ref. 64
DRAG COMPONENTS OF PLANING HULLS Ref. 42
DRAG COMPONENTS OF PLANING HULLS D Wtan D F cos
PRISMATIC HULL DRAG CALCULATION INPUT W b LCG V OUTPUT
EQUILIBRIUM CONDITION CASE OF CONCURRENT FORCES Ref. 42
EQUILIBRIUM CONDITION GENERAL CASE Ref. 42
SAVITSKY Method Savitsky Daniel, Hydrodynamic Design of Planing Hulls, Marine Technology, Vol. 1, No. 1, October, 1964 Ref. 33
CAHI Method Propulsive Performance and Seaworthiness of Planing Vessels, 1978 in Russian, Ivan Timofeevich Egorov, Michail Maksimovich Buňkov, Iuriĭ Mikhaĭlovich Sadovnikov Central Aero-Hydrodynamic Institute ЦАГИ TSAGI Ref. 79
C LB W 0.5V 2 b 2 mm/wb mlcg/b
2 V 2 C / 0.4-0.4 0.7 1.4 1 CLB 2 V 2 V 2 V 0.865 C 0.4 0.4 C ) C 0.08 (0.75 1.4 1 0.7 1.2 3-0.8 1.4 1 0.7 m FLAT PLATE EQUATIONS
] C m ) 1.35(sin [1 ] ) 0.29(sin [1 V 0.44 0.28.8 0 cos 1 cos λ cos λ 0.17 1 C ) 0.15(sin 0.3 V 0.8 PRISMATIC HULL CORRECTIONS
S b 2 cos D Wtan 0.5C F SV 2 cos
Ref. 79
mδ 5 CV = 2.0 4 CV = 2.5 CV = 3.0 CV = 4.0 CV = 5.0 CV = 6.0 CV = INF. 3 2 1 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 λ
Ref. 79
CB/τ 4 3.5 CV = 2.0 CV = 2.5 CV = 3.0 3 CV = 4.0 CV = 5.0 CV = 6.0 2.5 CV = 7.0 CV = INF. 2 1.5 1 0.5 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 λ
LIMITATIONS OF PRISMATIC METHODS Prismatic hulls (without excessive bottom warp / beam tapering) F > 2.0 ~ 2.50 Lk < 80% of LWL Ref. 39 Chines dry condition Lc < 0.0 Ref. 20 Ref. 40
V = 15.7 knots, L = 2.04 m Customs W = 60 kg, b = 0. 59 m Craft LCG = 0.81 m, β = 21.4 deg. Model C V = 3.34, F = 4.11, C = 0.29, M = 5.21 Tow point LCG - 133% of draft SAVITSKY CAHI MODEL TEST LAMDA 1.97 2.26 2.47 TRIM 3.74 3.62 2.50 D/W 0.19 0.202 0.21 DRAG (N) 111.54 119.09 124.26
V = 18.01 knots NACA W = 80 lbs, b = 16.0 in TN-509 LCG = 18.5 in, β = 20 deg. Model 29 C V = 4.64, F = 5.16, C = 0.53 Ref. 4 SAVITSKY CAHI MODEL TEST LAMDA 1.59 1.68 2.31 TRIM 4.21 3.95 4.0 D/W 0.19 0.19 0.19 DRAG (lbs) 15.12 15.17 15.20
V = 20.92 knots NACA W = 80 lbs, b = 16.0 in TN-509 LCG = 18.3 in, β = 20 deg. Model 29 C V = 5.39, F = 5.99, C = 0.53 Ref. 4 SAVITSKY CAHI MODEL TEST LAMDA 1.56 1.62 1.81 TRIM 3.46 3.32 4.0 D/W 0.21 0.21 0.20 DRAG (lbs) 16.76 16.89 16.0
D/W 0.3 USCG SERIES MODEL 5631-298 Lbs - LCG 38% DRAG WEIGHT RATIO 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0.13 SAVITSKY MODEL TEST CAHI 0.12 0.11 0.1 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 FV
TRIM DEGREES 6 USCG SERIES MODEL 5631-298 Lbs - LCG 38% TRIM 5.75 5.5 5.25 5 4.75 SAVITSKY MODEL TEST CAHI 4.5 4.25 4 3.75 3.5 3.25 3 2.75 2.5 2.25 2 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 FV
LAMDA 6 USCG SERIES MODEL 5631-298 Lbs - LCG 38% LAMDA - WETTED LENGTH BEAM RATIO 5.75 5.5 5.25 5 4.75 SAVITSKY MODEL TEST CAHI 4.5 4.25 4 3.75 3.5 3.25 3 2.75 2.5 2.25 2 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 FV
V = 25 knots USCG W = 298 lbs, b = 2.24 ft SERIES LCG = 3.8 ft, β = 25 deg. Ref. 55, 56 C V = 4.97, F = 5.73, C = 0.43, M = 5.94 Tow point LCG - 83% of draft SAVITSKY CAHI MODEL TEST LAMDA 2.39 2.76 2.69 TRIM 2.93 2.73 2.10 D/W 0.256 0.28 0.2894 DRAG (lbs) 76.55 83.42 86.24
D/W 0.56 0.54 0.52 0.5 0.48 0.46 0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26 0.24 0.22 0.2 0.18 0.16 0.14 UOS SERIES MODEL C - 243.4 N - LCG 33% DRAG WEIGHT RATIO SAVITSKY MODEL TEST 0.12 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00 CAHI FV
V = 23.43 knots UOS W = 24.81 kg, b = 0.39 m SERIES LCG = 0.66 m, β = 22.5 deg. Ref. 64 C V = 6.16, F = 7.12, C = 0.42, M = 6.86 Tow point LCG - 110% of draft SAVITSKY CAHI MODEL TEST LAMDA 2.34 2.52 2.18 TRIM 2.12 2.12 1.70 D/W 0.38 0.403 0.46 DRAG (N) 92.69 98.04 112.05
Surfury (1965), Sonny Levi Weight 4 tons, Length 11 m, 1050 HP Speed about 60 knots