Calculating Power for Displacement Boats

[Jeremy Harris]

Originally Posted by Willallison

I don't know anything about the Freeship Kaper methods, but I would have been surprised if any of those gave you sensible results... as Alik suggests, your hull is well outside normal parameters. Michlet would surely have been a better bet...

Define normal. Surely this depends on your sphere of reference, doesn't it? For me, normal is light weight open river boats of around 15 to 20ft LOA, designed to operate in speed limited sheltered waters with human, sail or very low power mechanical propulsion. I was merely illustrating exactly the point you make, that some methods (like Gerr) don't work well when applied to inappropriate hull shapes. Other methods (like Kaper/Winters) do work acceptably well for hulls like this.

The Kaper method in Freeship gives pretty good results for canoe-like hulls, which this one very much resembles (waterline length around 5.15m, waterline beam around 0.9m, draft around 0.15m at max displacement, fairly symmetrical wetted area, like a heavy canoe). Michlet gives exactly the same figures as Freeship (better than 1% correlation), so I very strongly suspect that they use the same method.

Jeremy

[Willallison]

Originally Posted by Jeremy Harris

Define normal. Surely this depends on your sphere of reference, doesn't it? ....Jeremy

Fair point...poor choice of words on my part
Interesting that Kaper and Michlet give such similar numbers. Does Freeship give application limits for Kaper, or alternatives for use with hulls that lie outside the typical Michlet parameters? Or perhaps they've been clever and the program selects the best method depending on the input parameters...

[Alik]

Originally Posted by Jeremy Harris

Sure, and you can rest assured that I carefully checked...

I suggest for Your boat flow will be significantly laminar; so using common friction extrapolator can give wrong result.

[Jeremy Harris]

Freeship lets you choose the method for resistance calculations, either the Delft yacht series or the Kaper method. It does trap user errors to some degree by not giving results if an inappropriate method is selected.

Freeship allows hull files to be exported in a form which Michlet can use, which makes life a bit easier for those who want to cross check results. In my case, the hull form is so canoe-like as to fit well with the Kaper/Winters method, for other hull forms the correlation may not be as good I'd guess.

Overall, Freeship is an very useful tool, IMHO, and a useful educational aid for those new to boat hull design, as it allows pretty quick "what if" changes to be made and the impact analysed and understood. I can't vouch for its accuracy on bigger, heavier, hulls though, as I've only used it for light displacement boats.

Jeremy

[Jeremy Harris]

Originally Posted by Alik

I suggest for Your boat flow will be significantly laminar; so using common friction extrapolator can give wrong result.

No way! The overhead canopy with the solar panels, the associated narrow diameter support struts and the exposed upper torsos of the crew will all have a fairly high Cd and these make up over half of the exposed frontal area. I agree that the hull itself will have a fairly low Cd, but when I modelled the air drag I factored in the CdA for each component.

Frictional air drag is so small as to be pointless to calculate, virtually all the drag is form drag from the bluff, relatively high CD things sticking up into the airflow. Virtually all of these things (except the small exposed hull frontal area) will be close to the critical Reynolds Number in a 10kt breeze and have entry angles that will promote early boundary layer separation.

Jeremy

[Alik]

Originally Posted by Jeremy Harris

No way! The overhead canopy with the solar panels, the associated narrow diameter support struts and the exposed upper torsos of the crew will all have a fairly high Cd and these make up over half of the exposed frontal area. I agree that the hull itself will have a fairly low Cd, but when I modelled the air drag I factored in the CdA for each component.

Frictional air drag is so small as to be pointless to calculate, virtually all the drag is form drag from the bluff, relatively high CD things sticking up into the airflow. Virtually all of these things (except the small exposed hull frontal area) will be close to the critical Reynolds Number in a 10kt breeze and have entry angles that will promote early boundary layer separation.

Jeremy

I meant hydrodynamical resistance, not air...

[Jeremy Harris]

Originally Posted by Alik

I meant hydrodynamical resistance, not air...

Ah...... I was confused by the part of my post you quoted, which was actually this in full: "Sure, and you can rest assured that I carefully checked all the air drag figures"

Jeremy

[DCockey]

Kaper is a popular method for estimating the resistance of sea kayaks, and was originally developed by John Winters. Sea Kayaker magazine uses a modified version to develop and publish a resistance vs speed curve for each kayak they test. (Sea Kayaker also develops and publishes resistance curves based on a Taylor series method as modified by Matt Brose.)

Winters, in an addendum to his Shape of the Canoe, describes Kaper and provides it in spreadsheet form. His comments about it's original purpose may be a good description of how many of the regression based methods should be viewed.

It was a design tool in the strict sense that it provided only relative performance figures resulting from a basic dimensional or form parameter change. For example, it would not tell if one shape gave better performance than a different shape but it would reveal the effect of varying dimensions in a design. This provides enough information for design purposes so long as a new design remains within the conventional envelope of shapes and dimensions and absolute resistance figures are unnecessary.
..........
In its original form the program used only 6 variables – waterline length (LWL), waterline beam (BWL), displacement (DISP), angle of entry (Ie), longitudinal center of buoyancy (LCB) and Block coefficient (Cb). The effect of these parameters was derived by regression analysis of thirty-six tank-tested hulls having displacement/length ratios between Cv 1.0 and 2.0. The parameter of prismatic coefficient (Cp) was not included because the formula assumed the designer would always select the ideal for his target speeds and I could find no solid evidence of any interaction between Cp and the other form factors.
...........
I offered KAPER to Sea Kayaker in 1994 and modified the formula to include a factor for Cp. I also modified the formula to make it better fit the tank test data Sea Kayaker already had by adding a “worm curve”. Although worm curves are sometimes justified they should only be used when you have sufficient data for reliability. The Sea Kayaker data was highly suspect because it ignored anomalies in the data were ignored and “smoothed” the resistance curves rather than run additional tests to attain suitable accuracy. Nevertheless, Sea Kayaker felt a need for consistency and I saw no problem so long as they were up-front about it.

The input to Kaper is described by Winters as:

LWL – This is the waterline length at the stated displacement.
EWL – This is the corrected effective waterline length determined as described in the Shape of the Canoe in the Chapter 3 – Geometry with one exception. I do not recommend correcting the stern length because the data is incomplete. Using the curve of areas alone does not accurately predict where the stern wave begins which also depends upon the slope of the buttocks and the shape of the stern. In the absence of objective tank data it is better to ignore this factor.
BWL – This is the waterline beam at the stated displacement.
H – This is the draft at the stated displacement and is not used in the formula but is included for reference.
W.S. – This is the actual wetted surface at the stated displacement.
Cp – The prismatic coefficient at the LWL waterline. Although it may make logical sense using the EWL may or may not produce accurate results. We have no tank data to confirm this.
Disp. – Self explanatory but must be in pounds.
Ie – This is the angle of entry. Actually it is ½ the angle at the waterline and is found by drawing a line starting at the bow and tangent to the waterline. The angle formed by the tangent and the centerline is the Ie.
LCB – This is the longitudinal center of buoyancy as a percentage of the waterline length aft. For example, 0.50 is amidships, 0.48 is forward of amidships and 0.52 is aft of amidships.
At/Ax – is the transom factor and is found by dividing the underwater transom area by the area of the largest section.

Winters estimate of the range of applicability of Kaper is:

I consider the following acceptable ranges;
LWL - 12’ to 24’
BWL – Not less than 7% of LWL nor more than 18% of LWL
Cp – Not less than 0.48 nor more than 0.64
Ie – Not less than 30 nor more than 100
Displacement – Not less than a Cv of 1.0 nor more than 2.0, Cv = D/L^3 where D is the displacement in long tons (2240 pounds) and L = the measured waterline length.
At/Ax – Not more than 0.05

Winters goes on to say that he now uses Michlet as his primary tool for evaluating kayak resistance, and only uses Kaper as a rough tool during the initial stages of the design process.

Shape of the Canoe CD can be ordered at http://www.greenval.com/order.html