# Definition of bow entry angle

Discussion in 'Hydrodynamics and Aerodynamics' started by laukejas, Nov 13, 2018.

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### laukejasSenior Member

Hi, guys,

While trying to include a KAPER resistance algorithm in a software that I'm developing, I confronted a problem with one of the measurements required for the formula: bow entry angle. Despite researching this for a while, I cannot find a clear definition of how that angle is measured. In most waterplane shapes, the part near the bow has a curve, and therefore, the location which you choose for measuring can change the result drastically - the closer you measure to the bow, the higher that angle is. Measuring, say, "as close to the bow" is also ambiguous, because the forebody curve can transition into bow edge rounding seamlessly, with no clear distinction. At the very tip, the entry angle can be 180°... Half an inch back, it can be 90°... Few inches back, it can be 20°... And decreasing as you go. So where do you measure?

It seems to me that the most logical way to go about it is to choose the point where the waterplane beam is the highest, draw a straight line to the tip, and then measure the angle between that line and the centerline, like shown in this sketch:

(This, of course, is the half angle. The light green part is the hull plan view, and the dark green is the waterplane area)

This way, ambiguity is eliminated. But I am not sure if this is the accepted or correct way of measuring that entry angle. There are plenty of posts about what is the best angle of entry on numerous forums on the internet, but the definition of it seems to be one of these "common knowledge" things, and no one really explains it :/

Can anyone shed some light on this, please?

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### Mr EfficiencySenior Member

I'd say the place to measure the angle would be at the bow, if the radiusing of the stem wasn't there, and the stem was sharp enough to cut your hand on (only joking).

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### laukejasSenior Member

Yeah, only "if"... Most stems do have some sort of rounding. If it's obvious where that rounding terminates, you can measure right after that, but sometimes, the front end of the hull might have a shape like this:

And it can be really, really difficult to tell where exactly does the stem rounding terminate, and the normal curvature starts. It's hard enough to do intuitively, and for my case, I need to find a solution that a computer could figure out on it's own. There must be an official definition of this entry angle, right? I am surprised that I'm unable to find it anywhere.

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### DCockeySenior Member

KAPER was developed by John Winters to estimate the resistance of canoes and sea kayaks. John Winters Page http://www.greenval.com/jwinters.html It is based on regression, not physics. Matt Brose later modified KAPER.

John Winters defined the entry angle as (from KAPER file on "The Shape of the Canoe" CD):
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.
Winters created KAPER for use with canoes and sea kayaks where the waterline usually has low curvature aft of any rounding at the stem. For such hull shapes the angle tangent to the waterline will be relatively constant for a range of several percent of waterline length aft of the stem. The difference in KAPER results due to using the angle at 3% vs 5% of LWL should be small compared to the overall uncertainty of the KAPER predictions.

If it is not relatively constant then the hull shape is probably one which is outside the intended range of KAPER.

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### laukejasSenior Member

Thank you for your reply, I do not have that resource that you quoted. Tangent line makes sense, but if the stem has a round, or a smooth transition from the round to the chine curve, then it the tangent line method would produce wildly inaccurate results... How would you draw a tangent line on the bow sketch that I included in my previous reply?

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### DCockeySenior Member

How much of the bow has that shape? If the shape is confined to a few percent of the waterline then just go aft of that shape. But if that shape extends for most of the bow then the shape is outside the intended range of KAPER.

In the image below A has a sharp end and just use the tangent at the end. B and C have rounded ends with the rounded parts only very near the end of the waterline. I'd use a tangent to the waterline at perhaps 5% of the LWL. Small differences in location will be insignificant. D has a rounded ends which extend for a large portion of the length. I would not use KAPER with this shape.

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### laukejasSenior Member

Well, that's the thing, the difference between these bow shapes are easy to dinstinguish for a person, not so much for a software. Anyway, the D shape is what I had in mind with my previous illustration.

What are some alternatives to KAPER, then? I am trying to work out an algorithm that would work both for a kayak and an oil tanker, with everything in between (of course, different methods could be used for different types of vessels, but I don't know of any algorithm except KAPER).

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### DCockeySenior Member

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### DolfimanSenior Member

My personal theory : if you have an analytical definition of the waterline curve, let'say y(x), the x point where you can use the tangential method to determine a significant half angle entry is where the curvature 1/R is minimum (up to zero if you have a local flat just before the rounded stem end), 1/R being equal to : y" / (1 + y'^2)^(3/2).
In most cases, when approaching the stem, the curvature 1/R decreases, then a minimum (up to zero), then an increase due to the rounded of the stem. It is where there is the minimum that you can have your significant half angle. If the waterline is pointy without any roundness, that gives the very end. If you have an inflexion point (giving also a zero of the 1/R function), it is there to evaluate the entry angle.

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When it becomes asymptotic to the direction of flow..

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### RAraujoSenior Member - Naval Architect

You could use the definition in DnV "DNVGL-ST-0111 - Assessment of station keeping capability of dynamic positioning vessels":

which seems reasonable to me...

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### DCockeySenior Member

What if the maximum curvature is amidships as in the example below?

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### DolfimanSenior Member

From your figure, I understand your question as "if the curvature is constant", i.e. An arc of circle : then, it is the fore end to consider of course. If the line is made of 2 arc of circle, a small curvature becoming a great curvature due a rounded stem, it is the fore end of the small curvature.
In general, whatever the curvature in the midship zone, either zero (flat : the cargo ship case) or maximum (the sailing yacht case), what counts is what happens to 1/R when you progress to the stem and where is the minimum.
The only case which causes problem is the one where the notion of entry angle is not relevant (for me) : if the 1/R continuously increases from the midship up to the stem end, for example an arc of ellipse. In that case, what means an entry angle ?

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### DCockeySenior Member

In the example above the curve is not a circular arc. The curvature is maximum at the ends and decreases to the center.

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### DolfimanSenior Member

Good point, my "theory" does not work there. That said, this angle is for me just an output data among others, and I don't use it in any regression formulas, for the residuary drag of sailing boats I follow the Larson-Eliasson formulations based on the Delf series models ("Principles of Yacht Design" second edition 2000, there more recent editions since).

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