Hullspeed calculations for larger vessels?

Hello all. I teach a high school physics class in Philadelphia. I'm trying to make connections between physics and the real world including sailing.

One of the more interesting connections I've found involves hullspeed. Since the general equation seems pretty simple: Theoretical Hullspeed = 1.34 x LWL^1/2 this would seem to lend itself to a high school physics class. (Not too hard, just quantitative enough to give learners a sense that they're really doing something without blowing them out of the water with euler equations and stuff)

Questions:
1. Can this equation be used in thinking about ships in the age of sail and shortly thereafter? For example, does it make sense to use it in a lesson regarding topsail schooners in the Revenue Service -VS- barbary pirates between 1790 and 1812? The Independence Seaport Museum has a great lifesize model of a schooner I'd like to use and a learning space.
2. Is the connection between V = fλ and Theoretical Hullspeed = 1.34 x LWL^1/2 solid enough to explore in a physics class setting?

 

As I understand it, hull speed is rooted in observations. It is not a hard and fast rule or "physics" but a reflection of averages.

In essence it captures a common point at which the development of a boat's wave system matches it's length at the waterline and the displacement hull boat has to push uphill against its own waves to go any faster.

What ever makes the wave system stronger -- bluff bows, broad beam relative to length, deep draft -- exasperates this and the reverse is true (fine bow, narrow beam, shallow draft reduce the strength of the wave system).

As for the wave system and it's different components, there is an online discussion I'll link to which may help explain the different components of same: http://www.ivorbittle.co.uk/Article...he bulbous bow for my site This one again.htm

This may help you design your lesson.

 

I agree with Rurudyne. It is not based on physics and it is only a rule of thumb. Even the 1.34 constant varies as some would use 1.1. Other books use 90% of the length, not 100%.

Predicting speed is based on so many factors and that is where physics come in, to a certain extent, as most formulae are made to fit based on averages of tests.

 

Hello Jgerstemeier

Welcome to the forum.

Before delving into your answer further...what age group are the students you teach...to provide a measure of their current understanding of maths and physics. Since to answer your question, it can be either very basic with a lot of generalisations, or, rather more detailed and with lots of maths added in.

 

Actually I think this could be a great high school level physics example. Start with the basic formula, which as mentioned was derived by observation. Then use it to segway into a deeper examination of the same phenomina. It's a great example of how a ball park number (1.34) upon deeper research turns into a much more refined equasion (1.34 is no longer a constant but a variable, based on the l/b of the vessel).

In the same way that Newton works for a gun, but you need relatively to get a space craft to Mars.

You could also get into ways to 'cheat' physical rules by exploring bulbous bows, but that's more engineering.

 

Actually, Newtonian physics can put a spacecraft in Mars. The speeds will not be high. They also work for calculating vessel speeds. At high school math and physics level there probably won't be any calculation of turbulence or laminar flow. They may be given values for friction and wave resistance on different hull shapes.

 

Speed-length ratio is only one of many ratios and the value of 1.34 is sort of a benchmark based on wavelength & perhaps a guideline limit for average 'displacement' hulls... whatever they are. It is one of many ratios that are inter-related. Another ratio is displacement/ length ratio where low figures could achieve an S/L of over 1.34 and high figures (big, heavy boats) have difficulty. There are lots of good books (ie: Nature of Boats by Dave Gerr) and stuff on line.

 

Reminded me: Sponberg's The Design Ratios

https://www.theamya.org/my/downloads/my165/THEDESIGNRATIOS.pdf

 

Even if hull speed were a fact the question of POWER remains , as to weather you can get there in a 10K breeze or need 35K to do so.

Fat heavy boat,light long narrow boat , acres of sail or barely enough to move in a gale?