A few question about speed-length principles

[AiryW]

I'm trying to get just a basic understanding of the way that ship length relates to speed and I have a few questions.  If anyone who understands this theory could clear them up for me it would be appreciated.

1) As I understand it, the length of a ship along the waterline is the primary factor in how fast it can get before it breaks the water in an inefficient fashion.  So why did they need to make battleships even longer then cruisers when cruisers had the higher speeds?  For instance the Italian Andrea Doria dreadnought class was 575 feet long before reconstruction while a Cadorna light cruiser was 555 feet.  Yet when they rebuilt the Andrea Doria's, they lengthened them to 613 feet.  Why did they need to lengthen the ship if it was already longer then the Cadorna with it's blazing fast 37 knot speed?  Or for a Japanese example the Ise class went from 683 feet to 708 feet getting longer despite already being very long and only going up to 26 knots.  Was this lengthening purely done to increase displacement?  What about with the WWII generation of fast battleships, why did they get longer not fatter?

2) Related to this, were it not for the speed would it be preferable to have the ship be shorter?  I would think shortness would mean a smaller target, especially for torpedoes, while fatness would indicate better protection.  Is this not the case?  Or would plunging fire mean that a fat ship would be an easier target to hit then a long one?

3) Was there any issue besides the length which was limiting how fast these battleships could get without changing the hull form?  Sure upgrading the machinery requires opening the hull but if they had recreated the original hull shape, would that 

4) Destroyers were faster but shorter then cruisers.  And their engine power does seem to be extremely high.  For instance a Gleaves class destroyer has 50,000 hp at 1630 tons compared to a St. Louis with 100,000 hp for 10,000 tons.  Am I correct in thinking that destroyers were overcoming a significant amount of water resistance by sheer horsepower?  If that is the case then why didn't they make the destroyers longer in order to save on expensive military grade propulsion equipment?

[oldpop2000]

Dec 23, 2018 17:30:22 GMT -6 AiryW said:

I'm trying to get just a basic understanding of the way that ship length relates to speed and I have a few questions.  If anyone who understands this theory could clear them up for me it would be appreciated.

1) As I understand it, the length of a ship along the waterline is the primary factor in how fast it can get before it breaks the water in an inefficient fashion.  So why did they need to make battleships even longer then cruisers when cruisers had the higher speeds?  For instance the Italian Andrea Doria dreadnought class was 575 feet long before reconstruction while a Cadorna light cruiser was 555 feet.  Yet when they rebuilt the Andrea Doria's, they lengthened them to 613 feet.  Why did they need to lengthen the ship if it was already longer then the Cadorna with it's blazing fast 37 knot speed?  Or for a Japanese example the Ise class went from 683 feet to 708 feet getting longer despite already being very long and only going up to 26 knots.  Was this lengthening purely done to increase displacement?  What about with the WWII generation of fast battleships, why did they get longer not fatter?

2) Related to this, were it not for the speed would it be preferable to have the ship be shorter?  I would think shortness would mean a smaller target, especially for torpedoes, while fatness would indicate better protection.  Is this not the case?  Or would plunging fire mean that a fat ship would be an easier target to hit then a long one?

3) Was there any issue besides the length which was limiting how fast these battleships could get without changing the hull form?  Sure upgrading the machinery requires opening the hull but if they had recreated the original hull shape, would that 

4) Destroyers were faster but shorter then cruisers.  And their engine power does seem to be extremely high.  For instance a Gleaves class destroyer has 50,000 hp at 1630 tons compared to a St. Louis with 100,000 hp for 10,000 tons.  Am I correct in thinking that destroyers were overcoming a significant amount of water resistance by sheer horsepower?  If that is the case then why didn't they make the destroyers longer in order to save on expensive military grade propulsion equipment?

Ships length relates to speed by the Length to Beam Ratio. The higher that number, the better the ship can move through the water. Here is a link to "The Speed and Power of Ships: A manual of Marine Propulsion " By David Taylor. Taylor is the man the David Taylor Model Ship Basin is named after. archive.org/details/speedpowerofship00tayluoft/page/n3

I am certain it does a much better job of explaining it than I can, although it get deep into it. But I think you will be able, as I was, to get good information. You can also browse through the ship design and Construction articles on Navweaps.

www.navweaps.com/index_tech/index_tech.php

It centers around a concept called Frictional Resistance. Tables show that frictional resistance is reduced, the longer the ship is. Here is a more simple explanation. marine.marsh-design.com/content/length-beam-ratio

[AiryW]

Okay so based on a quick cram, this is how I think it works:

The crucial tradeoffs relate to these three factors:
1) Head, i.e. friction along the surface, the same as the head in your plumbing system

• Cant be nullified (unless you go to a planing hull or the like)
• Falls off as speed increase
• Linear effect

2) Wave displacement, i.e. the wave formed in the water to make room for the ship

• Can be nullified if the bow and stern waves cancel each other out
• Would be much larger then head if not nullified
• Nullification means it will be smaller then head on all but the very fastest ships if competently built
• Increases as the speed increases because the volume of water displaced per second increases

3) Cavitation
, i.e. if the water stops having a laminar flow

• Caused by water pressure falling too low, can be avoided nearly completely
• Pressure decreases as water speed relative to the hull increases

        Water speed relative to the hull increases as beam increases due to conservation of mass

        For this reason the fatter and farther from the bow a point in the ship is, the more likely cavitation is

• Pressure decreases as head increases and water speed stays the same, i.e. along the length of the ship
• Wave displacement "solves" cavitation by making the laminar flow happen through a larger volume

So, battleships and cruisers didn't need to get longer because they were at the speed limit of their lengths, they were reconstructed because even a sufficiently long ship will still have wave displacement and a reconstructed bow allowed for a more efficient displacement.  This came at the cost of increasing head but because speed reduces head, it's possible this would still be a net gain even without engine power increases.

Destroyers dont need to get longer because that would increase head more then it would improve the wave displacement.  The problem is that for a fixed density, mass and surface area follows the square-cube law.  Thus a 2000 ton destroyer has half the wet surface as a 8000 ton light cruiser despite only having a quarter of the weight.  Destroyers cant get shorter to reduce head because in addition to having horrible sea handling at high speeds that would create cavitation as the fast water slammed into to fat midship, forcing a new, inefficient wave form.  This is why a destroyer needs such a higher power-mass ratio then a light cruiser.  And this is how the Italians were able to make such fast cruisers with the Condottieri, making something that resembles an enlarged destroyer means a very favorable power-surface ratio.

[oldpop2000]

Dec 24, 2018 10:24:27 GMT -6 AiryW said:

Okay so based on a quick cram, this is how I think it works:

The crucial tradeoffs relate to these three factors:
1) Head, i.e. friction along the surface, the same as the head in your plumbing system

• Cant be nullified (unless you go to a planing hull or the like)
• Falls off as speed increase
• Linear effect

2) Wave displacement, i.e. the wave formed in the water to make room for the ship

• Can be nullified if the bow and stern waves cancel each other out
• Would be much larger then head if not nullified
• Nullification means it will be smaller then head on all but the very fastest ships if competently built
• Increases as the speed increases because the volume of water displaced per second increases

3) Cavitation
, i.e. if the water stops having a laminar flow

• Caused by water pressure falling too low, can be avoided nearly completely
• Pressure decreases as water speed relative to the hull increases

        Water speed relative to the hull increases as beam increases due to conservation of mass

        For this reason the fatter and farther from the bow a point in the ship is, the more likely cavitation is

• Pressure decreases as head increases and water speed stays the same, i.e. along the length of the ship
• Wave displacement "solves" cavitation by making the laminar flow happen through a larger volume

So, battleships and cruisers didn't need to get longer because they were at the speed limit of their lengths, they were reconstructed because even a sufficiently long ship will still have wave displacement and a reconstructed bow allowed for a more efficient displacement.  This came at the cost of increasing head but because speed reduces head, it's possible this would still be a net gain even without engine power increases.

Destroyers dont need to get longer because that would increase head more then it would improve the wave displacement.  The problem is that for a fixed density, mass and surface area follows the square-cube law.  Thus a 2000 ton destroyer has half the wet surface as a 8000 ton light cruiser despite only having a quarter of the weight.  Destroyers cant get shorter to reduce head because in addition to having horrible sea handling at high speeds that would create cavitation as the fast water slammed into to fat midship, forcing a new, inefficient wave form.  This is why a destroyer needs such a higher power-mass ratio then a light cruiser.  And this is how the Italians were able to make such fast cruisers with the Condottieri, making something that resembles an enlarged destroyer means a very favorable power-surface ratio.

This is a complex subject, but I believe you understand the issues about  speed and length. By 1935, a formula had been developed that could predict maximum speed by using the length to speed ratio. It was Speed = √1.408 (waterline length). My dad's ship, the Saratoga went from San Pedro to Pearl in 1933, averaging 33.4 knots with a maximum speed of 35.6 over 16 hours. The problem with these ships was the single rudder and high lengthtobeam or slenderness ratio as it was called. She and Lexington just could not turn fast enough and Saratoga was torpedoed twice. Later, at the David Taylor Ship Model Basin a more accurate length to speed was developed for large cruiser hulls. It was Capital ship Speed  = 1.19 √ l Waterline. Here is a sketch drawing of the three optimal waterline lengths.



The Length to Beam of the Iowa's was 7.96. As one can see, there are limitations such as turning radius, etc. I have said this many times. A ship is a balance system. Good discussion, I enjoy this kind of in depth research. BTW, one limitation on the beam is the locks of the Panama Canal, the limitation is 108 1/6 feet.