Abstract
Racing catamarans use aerodynamic alleviation concept which in existing extreme ground effect significantly enhances the performance. Beside design measures, controlling strategies may be employed as convenient solutions to improve the performance and address concerns regarding poor stability in these crafts. Being of substantial importance for a racing catamaran to reach the final speed as soon as possible, this study attempts to find the optimal form of changing the drive angle (as control variable) to minimize its acceleration time. In this regard, a mathematical model is developed for forward acceleration phase of these catamarans based on empirical and theoretical methods. Then the formulation and solution algorithm for the time-optimal problem are described according to an indirect method. Results for a representative racing craft have been presented in uncontrolled and controlled conditions. Problem in controlled condition has been solved without and with a predefined constraint regarding stability margin. Optimal controlling of the drive angle without stability constraint during the acceleration results in 40 % reduction in time required to reach the speed of 110 kn and 14 % reduction in resistance at this speed in comparison to the uncontrolled case. Addition of the stability constraint changes optimal solution for drive angle and causes craft trim angle follow a decreasing trend at higher speeds.
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References
Shipps PR (1976) Hybrid ram-wing/planing craft—today’s raceboats, tomorrow’s outlook. In: AIAA/SNAME Advanced Marine Vehicles Conference, no. AIAA 76-877. Arlington, Virginia, 20–22 Sept 1976
Bate J (1994) Performance analysis and prediction of high speed planing craft. Ph.D. thesis, University of Plymouth
Yengejeh MA, Amiri MM, Mehdigholi H, Seif MS, Yaakob O (2015) Numerical study on interference effects and wetted area pattern of asymmetric planing catamarans. Proc Inst Mech Eng Part M J Eng Marit Environ. doi:10.1177/1475090215586638
Xu L, Troesch AW (1999) A study on hydrodynamics of asymmetric planing surfaces. In: Proceedings of FAST’99, vol 99, pp 471–481
Ward TM, Goelzer HF, Cook PM (1978) Design and performance of the ram wing planing craft KUDU II. In: AIAA/SNAME Advanced Marine Vehicles Conference
Kallio JA (1978) Results of full scale trials on two high speed planing craft (kudu II and kaama). Tech. Rep. DTNSRDC/SPD-0847-01, David W. Taylor Naval Ship Research and Development Center
Reif TH, Geunther DA (1978) A comparative study of the aerodynamics and hydrodynamics of a tunnel hull boat. J Hydronaut 12(4):166–168
Reif TH (1985) A wind tunnel study of the aerodynamics of a tunnel boat hull with consideration of ground effect. High Speed Surf Craft 24(2):29–33
Nangia RK (1987) Aerodynamic and hydrodynamic aspects of high speed water surface craft. Aeronaut J R Aeronaut Soc 91(906):241–268
Doctors LJ (1997) Analysis of the efficiency of an ekranocat: a very high speed catamaran with aerodynamic alleviation. In: International Conference on Wing in Ground Effect Craft (WIGs 97), RINA ed
Morch HJB (2003) Aerodynamic properties of a high speed offshore racing catamaran. In: Proceedings of 7th International Conference on Fast Sea Transportation, Ischia, Italy, 7–10 Oct 2003
Russel J (2007) Secrets of tunnel boat design. Aeromarine Press, Cambridge
Williams AGW (2008) Aerodynamic forces on high-speed multihulled marine vehicles. Ph.D. Thesis, Cranfield University
Chaney CS, Matveev KI (2014) Modeling of steady motion and vertical-plane dynamics of a tunnel hull. Int J Naval Archit Ocean Eng 6(2):323–332
Rozhdestvensky KV (2000) Aerodynamics of a lifting system in extreme ground effect. Springer Science & Business Media, Berlin
Martin M (1978) Theoretical determination of porpoising instability of high-speed planing boats. J Ship Res 22(1):32–53
Matveev KI (2012) Modeling of longitudinal motions of a hydroplane boat. Ocean Eng 42:1–6
Carter WE (1961) Effects of ground proximity on the aerodynamic characteristics of aspect ratio 1 airfoils with and without end plates. Technical report, NASA
Matveev K, Kornev N (2013) Dynamics and stability of boats with aerodynamic support. J Ship Prod Des 29(1):17–24
Collu M (2008) Dynamics of marine vehicles with aerodynamic surfaces. Ph.D. Thesis, Cranfield University
Irodov RD (1970) Criteria of longitudinal stability of ekranoplan. Technical Note of the Central Hydro-Aerodynamical Institute (TSAGI), vol 1, no 4 (in Russian)
Kornev N, Kleinsorge L, Migeotte G (2010) Dynamics and stability of racing boats with air wings. Int J Aerodyn 1(1):28–51
Gu P, Gundersen R, Kalvik AO, Salvesen R, Karimi HR, Ottestad M (2011) Data gathering and mathematical modeling for pitch stabilization of a high speed catamaran. Model Identif Control 14(3):149–158
Kim SH, Yamoto H (2004) An experimental study of the longitudinal motion control of a fully submerged hydrofoil model in following seas. Ocean Eng 31:523–537
Kim SH, Yamoto H (2004) On the design of a longitudinal motion control system of a fully- submerged hydrofoil craft based on the optimal preview system. Ocean Eng 31:1637–1657
Bai J, Kim Y (2010) Control of the vertical motion of a hydrofoil vessel. Ships Offshore Struct 5(3):189–198
Clavounos PDS, Thomas B, Ulusoy T (2006) Optimal ship maneuvering and seakeeping by linear quadratic gaussian regulatros. In: 26th Symposium on Naval Hydrodynamics Rome, Italy, 17–22 Sept 2006
Milandri GS (2006) Seakeeping control of HYSUCATs. Master’s Thesis, University of Stellenbosch, Stellenbosch, South Africa
Salarieh H, Ghorbani MT (2011) Trajectory optimization for a high speed planing boat based on Gauss pseudospectral method. In: 2nd international conference on control, instrumentation and automation (ICCIA), pp 195–200, 27–29 Dec 2011
Xi H, Sun J (2006) Feedback stabilization of high-speed planing vessels by a controllable transom flap. IEEE J Ocean Eng 31(2):421–431
Karimi MH, Seif MS, Abbaspoor MA (2015) study on vertical motions of high-speed planing boats with automatically controlled stern interceptors in calm water and head waves. Ships Offshore Struct 10(3):335–348
Yengejeh MA, Mehdigholi H, Seif MS (2015) Planing craft modeling in forward acceleration mode and minimization of time to reach final speed. Ships Offshore Struct 10(2):132–144
Troesch AW (1992) On the hydrodynamics of vertically oscillating planing hulls. J Ship Res 36:317–331
Katayama T, Ikeda Y (2000) Characteristics of hydrodynamic forces acting on rapidly accelerated planing craft from rest. In: Proceedings of the fourth international conference on hydrodynamics (ICHD 2000), 7–9 Sept, 2000; Yokohama (Japan), pp 235–240
Savitsky D (1964) Hydrodynamic design of planing hulls. Mar Technol 1:71–95
Liu CY, Wang CT (1979) Interference effect of catamaran planing hulls. J Hydronaut 13(1):31–32
Faltinsen OM (2005) Hydrodynamics of high-speed marine vehicles. Cambridge University Press, New York
Gallington RW, Miller MK (1970) The RAM-wing: a comparison of simple one dimensional theory with wind tunnel and free flight results. AIAA Paper 70-971, AIAA guidance, control and flight mechanics conference, Santa Barbara, CA, Aug 1970
Tuck EO (1979) A nonlinear unsteady one-dimensional theory for wings in extreme ground effect. J Fluid Mech 98(part 1):33–47
Matveev KI (2013) Aero-hydrodynamic aspects of power-augmented ram wings. J Ship Res 57(2):86–97
Payne PR (1995) Contribution to planing theory. Ocean Eng 22(7):699–729
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Yengejeh, M.A., Mehdigholi, H. & Seif, M.S. A mathematical model for acceleration phase of aerodynamically alleviated catamarans and minimizing the time needed to reach final speed. J Mar Sci Technol 21, 458–470 (2016). https://doi.org/10.1007/s00773-016-0368-z
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DOI: https://doi.org/10.1007/s00773-016-0368-z