Defining Midship

Hi all. I'm deep into tweaking a canoe design, and I'm starting to get a little hung up on the numbers. I've been running John Winters' KAPER performance prediction on the design, and noticed I need to adjust my Cp downward a bit. But I've also noticed how defining your midship can have a significant effect on this coefficient. I'm concerned about how meaningful the Cp is, or how accurately it describes the hull form depending on the section chosen.

My max beam, max draft, and max sectional area do not align (at least longitudinally.) I have been using the max beam as midship, but the max sectional area is slightly forward of this. Between these two sections there's a fairly significant difference between the resulting calculation for prismatic.

Can anyone suggest the best location for defining midship...or at least choosing the best section location to calculate Cp for the most accurate depiction? I'm not concerned with "legal" definitions. I just want the form coefficients to be meaningful.

Thanks,

Tim

 

Hi Tim,

There is only one definition for the midship location. It is half way between the aft perp and fwd perp, in otherwords, it is half the waterline length.

 

Hi Tim, Ad Hoc is right, midship is the half of the LWL.
But for CP calculations you use the maximal sectional area, whatever its placement. This placement is generally somewhere 46 % (very uncommon excepted in very old designs) to 54 % of LWL on a sail boat.
It's a static measure with the boat straight on its waterlines. Meaningful but not accurate on a sail boat which oscillates.
You should try to put the static maximal sectional area at 52%, a placement used in a lot of sail boats.

Dynamically with the heeling, the placement will move (not very much on canoe boats). Longitudinally you can use the Bonjean's curves. It's also the first stage to get the lateral and longitudinal righting moments.

 

My understanding is the standard definition for prismatic coefficient is based on the maximum section area. But for ships it is sometimes defined as based on the midships area, apparently with an assumption that the midships region is parallel sided and the section area is constant in that region.

John Winters is the original author of KAPER, and in his Shape of the Canoe he defines prismatic coefficient as:

CP — Prismatic coefficient (Figure 5)-- The underwater volume of the hull divided by the volume of a solid having the same length and cross section as that of the hull at its largest section. The CP has a major impact on wave making resistance. CALPX=∇
where AX = the area of the largest section​

So it looks like you should use maximum area.

Do you know which version of KAPER you are using? The original version by John Winters did not include Cp. He then revised it for Sea Kayaker magazine to include Cp. Matt Brose has since made several revisions and put it into an Excel spreadsheet which seems to be fairly widely distributed. John Winters in the Kaper Information portion of the Shape of the Canoe CD is less than enthusiastic about Brose's modifications and extensions.

 

Keep in mind the limitations of KAPER. It was originally based on a regression of the test results from 36 hulls, and has since been modified in various ways. The accuracy of KAPER may be less than the differences you are concerned about with different locations of CP. I don't know of any studies of the accuracy of the various versions of KAPER.

John Winters has suggested that Michlet rather than KAPEER should be used as the primary analysis tool for kayak design:

Today I no longer use KAPER except as a rough tool in the early stages of a design because New Wave Systems provides it with their Nautilus® design software where it is convenient. For accuracy and for development of unique hull shapes I prefer a true CFD (Computational Fluid Dynamics) program such as Leo Lazauskas’s Michlet. This program is now available from Leo at ( http://www.cyberiad.net/michlet.htm ) He uses Grigson’s method of predicting skin friction which seems an improvement over the ITTC 1997 curve and, because it computes the forces over thousands of points on a hull it has much greater accuracy and can better cope with wide variations in hull shape.​

from: KAPER
A Performance prediction Formula for Kayaks and Canoes
By John Winters

 

Thanks guys. Ok, I see midship is a specific dimension, and Cp need not relate.

DCockey, I have a fairly recent version KAPER...came with my copy of Winter's e-book several months ago.

Ok, so what is still bugging me about these form coefficients is this:

Cp taken at max sectional area. Cm, Cb is supposed to depict area/volume in relation to max draft & beam. But all three are supposed to have a mathematical relationship to one another. If max beam, draft & sectional area don't align longitudinally, their relationships don't work. Well, I guess they're numbers to give you an idea of what's going on, and so more theoretical anyway. Before I got back to this thread, I started working with the section at the LCB, which is very, very close to max sectional area, but more accurately reflects max beam/draft (which are aft of max section).

Anyway, I'll go recalculate and see what the difference is.

 

Some questions:

1) How much does you design look like the designs KAPER was based on?

2) How accurate do you think KAPER is? (This is different than precision.)

3) How much do the KAPER results vary when you change the input parameters by the amounts you are concerned about?

4) How do the variations in 3) compare to the estimated accuracy in 2)?

5) Will you be able to detect differences of the magnitude you are concerned about?

6) What are the consequences of "If max beam, draft & sectional area don't align longitudinally, their relationships don't work."

 

Remember that KAPER is based on regression, not on fundamental physics. And it has had various adjustments made since the regression.

 

Just make sure you're using the correct definitions. How they relate is unique to your hull shape.

 

Winters complicates matters because he says to use the beam and draft at the section of maximum area for the sectional coefficient. For the block coefficient he says to use the beam and draft of the hull, presumably the extreme beam and draft. On a ship with parallel mid-section this doesn't make a difference, but with a kayak it's quite possible to have maximum beam at a location other than the maximum area section, and likewise for the maximum area. The consequence is the simple relationships between the various coefficients are not always exact with those definitions.

The question is; what are the consequences? Obviously the boat doesn't know which definitions were used. It may affect analysis results slightly when but I doubt the analysis accuracy is such that it matters.

 

It depends upon how much faith and wisdom you put into coefficients of hull form, and their sensitivity to the “holy grail”.

If the maximum beam is clearly at say 5% aft of midships, it is obvious what the Cwp is using the formula above. But when looking at Cm, your first question will be …er….the max beam is aft of midships, so shouldn’t I use that, and not the B at midships? Well if your draft T (max) at midships and 5% aft are the same, what is the difference, none, ergo it must be the same at midships and 5% aft. But if the max B is 5% aft, then the max T will not be the same. The result will inform you how the hull shape is proportioned, fwd to aft.

For example. If the aft end was a block 1x1 (B x T)…but just aft of midships the B reduced and the draft reduced by say 10%, the Cm would have a value of Am/ (0.9x0.9) = 1.23Am. If just the beam was reduced by 10% & the draft the same, Am/(0.9x1.0) = 1.11Am. If the same were true but now 5% Fwd, that values would still be the same, but the change in lines from the max B and T to the bow would create a more bluff bow as the waterlines going fwd would have less distance to converge and also create a high angle of entry. So, how are the other coeff’s changed as a result?

It really doesn’t matter what values you arrive at, so long as your consistent with them. If you place “meaning” into every single coefficient you’ll go around in circles. Since while these coeff’s can be exactly defined, they are not necessary linked directly to each other in the sense that you think…ie resolve them all at once and hey presto out pops the holy grail.

So, coeff’c are simply for you that once you have a hull, and worked out what each coeff is, next time you create a hull, you can compare the 2 in a rational “systematic” manner. Then evaluated what differences in performance there is between the 2. Then draw another ascertain the coeff’s again and repeat the performance. After a while you will notice subtle changes have subtle effects on performance. But you also need to recognise that a change in one parameter for one type of hull does not translate to another type of hull nor Fn it is operating at. Thus don’t get bogged down with coeff’s, they are what they are and many other aspects influence performance, not just what its coeff’s are.

Having said all that, the only coefficients I bother with is the location of the LCB, transom/draft ratio, L/B and L/D ratio. The Cwp, Cm etc etc, are what they are and do not drive the hull shape I require.

 

And that in turn depends on how much faith you have in the analysis formula which uses those coefficients, or other source for them. Hence my questions about accuracy of the analysis, sensitivity of analysis to variation in coefficients, etc several posts above.

Some folks in the sea kayak world seem to view differences in predicted resistance from KAPER or the Brose-Taylor formulas on the order of several percent as significant. I'm very skeptical.

Then there are potential differences in the boat as built and used vs the design which was analysed: Displacment, CG location, water density and viscosity (both dependent on salinity and temperature), shape, etc. And then factor in wind and waves.

 

The boats we deisgn are commerical boats. As such an important factor is the power...ie the engine and how we deliver that power.

In this case, how much importance is placed upon the person rowing..their weight, their influences on rowing when hungry (lighter) to after a big meal (heavier), their endurance (power delivery over time) and the the efficiency of their strokes and the type of paddles they use (ie the PC) etc?...these have a much greater influence than using a certain Cm or Cwp coeff, just as the type of engine and how that power is delivered. It is all the same, just different a method of delivery.

 

My post was about sea kayak design and some of the analysis methods commonly used in their design. How accurate do you find commercial vessel resistance prediction which has had much more development than that for sea kayaks?

It looks like we are in agreement about how much emphasis to put on the coefficients for sea kayak design.

 

Michlet is not CFD.