Exact and approximated solutions to the critical ship speeds in canals
Delefortrie, G.; Verwilligen, J.; Vantorre, M.; Lataire, E. (2024). Exact and approximated solutions to the critical ship speeds in canals, in: Schonees, J.S. (Ed.) Proceedings of the 35TH PIANC WORLD CONGRESS 2024, Cape Town, South Africa, 29 April – 03 May 2024. pp. 649-654
In: Schonees, J.S. (Ed.) (2024). Proceedings of the 35TH PIANC WORLD CONGRESS 2024, Cape Town, South Africa, 29 April – 03 May 2024. PIANC: Brussels. ISBN 978-2-87223-041-9. 1636 pp., more
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Document type: Conference paper
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| Keywords |
Canals
Harbours and waterways > Ship motion > Fairway and harbour design
Mathematics
Proof
Simulations
Speed
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| Abstract |
A sailing ship displaces water and this amount of water needs to return along the hull. When the environment is confined, as in a channel or canal, the water is squeezed in the gap between the ship and the canal boundaries, increasing the return flow. The available space for the water to return is expressed as the blockage ratio ?, which is the ratio of the cross sectional area of the ship and the cross section of the canal.
With increasing ship speed the necessary return flow will no longer be met and the water will start to accumulate in front of the ship. At this point the flow condition starts to change, which is commonly referred to as the (first) critical speed. In the 1950s, critical speeds as a function of the blockage ratio were solved graphically, but afterwards elegant goniometric formulations of these critical speeds as a function of the blockage were established. Nevertheless, the appropriate proofs could not be traced back in literature. Because of the importance of the speed ranges, and their relationship with squat and resistance of ships navigating in canals, the present paper provides not only a proof of these goniometric relationships, but also introduces approximated solutions. |
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