Most efficient waterline length?

As far as designing ships go, how do you go about finding the most efficient waterline length for a ship, for a particular speed?

I have been looking at warships, ocean liners, cruise ships, etc. and the SLRs (speed-length ratios) vary widely from one ship type to another. I would think it would be wiser to use the shortest possible hull length for maximum speed. But I think it depends more on the type of ship and what the speed requirements are, and then finding a hull that gives the most optimal result across all speeds.

Capital ship (warships) formula for top speed: 1.20 x square root (waterline length)

Merchant ship formula for top speed: 1.23 x square root (waterline length)

Here are a three examples I have looked into in depth:

Iowa Class Battleships:

Design max. speed: 33 knots (SLR = 1.125)
Maximum speed by formula: 34.9 knots
Waterline length: 860 ft

SS United States Ocean Liner:

Design max. speed: 37.3 knots (SLR = 1.216)
Maximum speed by formula: 37.7 knots
Waterline length: 940 ft

and this is my ship derived by looking at the trend above...

MS Canada - my own ship

Design max. speed: 32 knots (SLR = 1.156)
Maximum speed by formula: 34 knots
Waterline length: 765 ft

 

The design of any boat is dictated far more than just its length. This is even more so of warships.

There is stability...in terms of seakeeping and statical/damage stability to consider. Then there is the powering..and the amount of fuel it must carry...and then the crew, the accommodation and the weaponry, the stores the am munitions etc etc.

There is no one size fits all. The design must satisfy the SOR. The result, is..well, what it is...that which satisfies the SOR, cross the board from speed to length to capital costs to maintenance and through life costings.

 

There is not a more efficient waterline length. They are however, efficient speeds for every hull. These speeds are usually even multiples of the square root of the waterline is knots or close to it.

 

All coeffcient ratios are multiplied by sq root of wl length. Ergo, n all cases, greater wl length will result in greater hull speed. longer is better, but other factors like cost, locks and docks, ect, determine max length

 

One that will get you on a plane so waterline length goes out the door