Here’s an excerpt from an article I wrote in1999, about hull speed.
~~~~~~~~~~
The Math
Caution! Part 1 gets technical. If you want to skip it, you can go right to Part 2 of this article.
Heavy boats with a large displacement to length ratio (D/L>240) must push a lot of water aside and they create big waves. They are restricted to the theoretical hull speed limit that is defined by the propagation of waves.
The above equation for a displacement hull can be rearranged, 1.34 = Hullspeed/(LWL^0.5), so that the 1.34 represents the ratio of speed to the square root of LWL.
So, the speed/length ratio for displacement hulls is 1.34. If a boat exceeds its theoretical displacement hull speed, the S/L ratio must increase. A semi-displacement hull has a S/L ratio of 1.45 or greater. A planing hull has a S/L greater than 3.0.
But just how fast can a monohull boat be expected to go? It all depends on displacement -- more specifically on the D/L ratio (i.e., how heavy the boat is compared to the LWL). Naval architect Dave Gerr worked out the relationship, one of the great accomplishments in modern naval engineering. (David Gerr: Nature of Boats, McGraw-Hill; Offshore, Dec. 94, pp 29-33)
D/L ratio = D[in long tons, 2240 pounds]/(0.01 x LWL)^3.
S/L ratio = 8.26 /(D/L ratio)^0.311
The formulas show that lower displacements permit higher speeds without actually planing. Everyone is familiar with Anthony Deane's original formula for heavy displacment hulls, and people are slow to catch that non-planing boats go faster than Deane's formula predicts, despite our observations that boats sometimes do go faster than they're supposed to.
That's probably because most folks divide boats into two categories - planing vs. displacement. The difference between the two is visually obvious. However, most small sailboats don't get up an obvious plane, but nevertheless, they DO go faster than a displacement hull of similar LWL. Many sailboats fit into this category -- the semi-displacement hull
We can re-write the equations to make the math easier, and then we can solve them in a step-wise manner:
Eq #1: D/L=(weight/2240)/(0.01 * LWL)^3
Eq#2: S/L = 8.26/(D/L)^0.311
Eq#3: Hullspeed = S/L * LWL^0.5
Equation 3 looks very familiar -- it's just like the traditional hullspeed formula, but the constant is no longer 1.34. In Equation 3, the S/L ratio replaces the constant allows us to take the displacement and water-line length of the boat into account.
~~~~~~~
Comments by Dave Gerr
from the Trailer Sailor Bulletin Board, where I initially posted this information
Posted By: Dave Gerr
Date: 9/22/99 9:15pm
In Response To: (deleted)
Hi Folks:
Glad my somewhat more sophisticated hull speed formula has been of interest. It has proven quite accurate over the years and across many kinds of boats. The old rule-of-thumb, “simply 1.34 x the square root of the WL in feet” really isn’t accurate. The multiplier “1.34” is really a function of D/L ratio. That’s what my formula is all about. Keep in mind, though, that my rule describes the top hull speed that a hull MAY achieve without planing.
Three things here:
1) You need lots of power (wind for sailors, obviously) or you don't go faster, regardless.
2) Many hulls that have low D/L ratios do have faster hull speeds before planing, but if--at the same time--the hull has some planing characteristics, it may well start to plane--at least to some degree--before taking advantage, as it were, of it's higher non-planing hull speed.
3) There are lots of small sailboats that do a little of both in heavy air (in the right conditions). In other words, they get up on plane a bit, and they also take advantage of their higher non-planing hull speed at the same time for a small but noticeable double boost.
Hope this is helpful. We're swamped with work here, so I may not have time to answer more, but I'll try and peek in occasionally.
Cheers, Dave
~~~~~~~~~~
The Math
Caution! Part 1 gets technical. If you want to skip it, you can go right to Part 2 of this article.
Heavy boats with a large displacement to length ratio (D/L>240) must push a lot of water aside and they create big waves. They are restricted to the theoretical hull speed limit that is defined by the propagation of waves.
The above equation for a displacement hull can be rearranged, 1.34 = Hullspeed/(LWL^0.5), so that the 1.34 represents the ratio of speed to the square root of LWL.
So, the speed/length ratio for displacement hulls is 1.34. If a boat exceeds its theoretical displacement hull speed, the S/L ratio must increase. A semi-displacement hull has a S/L ratio of 1.45 or greater. A planing hull has a S/L greater than 3.0.
But just how fast can a monohull boat be expected to go? It all depends on displacement -- more specifically on the D/L ratio (i.e., how heavy the boat is compared to the LWL). Naval architect Dave Gerr worked out the relationship, one of the great accomplishments in modern naval engineering. (David Gerr: Nature of Boats, McGraw-Hill; Offshore, Dec. 94, pp 29-33)
D/L ratio = D[in long tons, 2240 pounds]/(0.01 x LWL)^3.
S/L ratio = 8.26 /(D/L ratio)^0.311
The formulas show that lower displacements permit higher speeds without actually planing. Everyone is familiar with Anthony Deane's original formula for heavy displacment hulls, and people are slow to catch that non-planing boats go faster than Deane's formula predicts, despite our observations that boats sometimes do go faster than they're supposed to.
That's probably because most folks divide boats into two categories - planing vs. displacement. The difference between the two is visually obvious. However, most small sailboats don't get up an obvious plane, but nevertheless, they DO go faster than a displacement hull of similar LWL. Many sailboats fit into this category -- the semi-displacement hull
We can re-write the equations to make the math easier, and then we can solve them in a step-wise manner:
Eq #1: D/L=(weight/2240)/(0.01 * LWL)^3
Eq#2: S/L = 8.26/(D/L)^0.311
Eq#3: Hullspeed = S/L * LWL^0.5
Equation 3 looks very familiar -- it's just like the traditional hullspeed formula, but the constant is no longer 1.34. In Equation 3, the S/L ratio replaces the constant allows us to take the displacement and water-line length of the boat into account.
~~~~~~~
Comments by Dave Gerr
from the Trailer Sailor Bulletin Board, where I initially posted this information
Posted By: Dave Gerr
Date: 9/22/99 9:15pm
In Response To: (deleted)
Hi Folks:
Glad my somewhat more sophisticated hull speed formula has been of interest. It has proven quite accurate over the years and across many kinds of boats. The old rule-of-thumb, “simply 1.34 x the square root of the WL in feet” really isn’t accurate. The multiplier “1.34” is really a function of D/L ratio. That’s what my formula is all about. Keep in mind, though, that my rule describes the top hull speed that a hull MAY achieve without planing.
Three things here:
1) You need lots of power (wind for sailors, obviously) or you don't go faster, regardless.
2) Many hulls that have low D/L ratios do have faster hull speeds before planing, but if--at the same time--the hull has some planing characteristics, it may well start to plane--at least to some degree--before taking advantage, as it were, of it's higher non-planing hull speed.
3) There are lots of small sailboats that do a little of both in heavy air (in the right conditions). In other words, they get up on plane a bit, and they also take advantage of their higher non-planing hull speed at the same time for a small but noticeable double boost.
Hope this is helpful. We're swamped with work here, so I may not have time to answer more, but I'll try and peek in occasionally.
Cheers, Dave