# Magic Number for Boats = 61.8?

Discussion in 'Boat Design' started by Capt Ronrico, Jun 27, 2018.

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### Capt RonricoJunior Member

Magic Number for Boats = 61.8 ?
I stumbled on this notion while reading "The Silent War" by John Craven. Craven was the U.S. Navy's Chief Scientist during the Cold War era. The things he and his crew got up to are mind-blowing: like wire-tapping the Soviet High Command's private phone lines' underwater cables; developing the Polaris submarines; and sorting out the Thresher & Scorpion disasters.
Anyway, he mentions that if you look at an aerial photograph of any large body of water with boats on it, you will see that the wakes left behind by the boats all measure 61.8 degrees. This is true, he says, of all boats in all waters - fresh or salt - at all times of the year in all parts of the world in all non-stormy conditions. Pretty interesting, I think.
I'm pretty sure that this number has something to do with the molecular geometry of water itself. So I started thinking of 61.8 degrees as the cleavage angle for water. I simplified it to 60 degrees (for convenience - 60 deg is so familiar to work with) and started wondering if this applied directly to boat design: that is, if the included angle of the bow from tip to widest beam was 60 deg or less, would the boat be very efficient; and if the included angle were greater, would the boat be inefficient?
That is: is the design of the boat working with or against nature in terms of slicing through water? If so, then 61.8 qualifies as a magic number for hydraulics.
If true, then if you want a boat to go fast and slice through a wave, make the bow angle 60 deg or less. If you want the boat to breast an oncoming wave, make the bow angle bluffer than 60 deg, for example.
Then I started to think: this has got to be some universal fact that every boatnik but me knows and takes for granted. It must be basic to all boat design, all marine engineering.
So - finally - my question is: is it an open secret and how does it affect boat design?

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### TinkJunior Member

New to me a very interesting point I will percolate

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### Mr EfficiencySenior Member

I have always found 7 to be a lucky number, 61.8, not so much. Actually, those visible, divergent wakes don't represent a huge % of the energy expended in propelling a boat through the water.

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### HeimfriedSenior Member

The Kelvin wake angle is 39 degree (2 * 19.47°) and is known for this kind of wave pattern. Never heard about 61.8 deg.

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### SamSamSenior Member

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### rwatsonSenior Member

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### goodwilltoallSenior Member

Samsam, if you look at immediate wake right aft of transom it looks almost exact angle as you drew then trails of straight as its left behind​

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### David J RitchieJunior Member

First off interesting idea and well worth posting

regardless of 61.8% or 40% if it's fixed or dependent on hull geometry.

The point remains should the boat be built to that angle bow to stern or not?

I'm thinking not... I think that angle should be minimized as much as possible for less water drag... the only reason for it is for handling.

Where you might have something OP is you don't want to build a boat with a more obtuse angle than that or encounter resistance of your own wake!!!

If you wanted to build the widest boat possible for a given length, without that extra resistance, it would follow that angle bow to stern. That area of the triangle represents the usable normal hull space.

Now for the fun part:

What did he say happened to the Thresher & Scorpion subs?

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### JSLSenior Member

The term "1/2 angle of entrance" has been around for years ( assumes the hull is symmetrical about the centerline) referring to displacement hulls. For planing hulls you can go higher.
The wake angle in the photos is different.

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### DCockeySenior Member

Not correct. The actual angle of 38 degrees is due to the free surface in deep water, and is independent of the "molecular geometry of water" or of any other fluid. Build a deep tank with an open top, fill it with oil, alcohol or any other liquid, tow a model on the free surface and the angle will be the same.

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### DCockeySenior Member

The wake angle depends on the depth of the water relative to speed of the vessel and gravitational acceleration. The angle is approximately 38 degrees for sufficiently deep water. In very shallow water then angle approaches 90 degrees.

Froude number based on depth is U/Sqrt(d*g) where U is the speed of the vessel, d is the depth f the water and g is the gravitational acceleration (9.8 m/sec^2, 32.2 ft/sec^2).

The Kelvin wake angle applies to wakes far from a vessel. The second photo shows an angle based on the near field, but the wake is wider further from the boat.

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### DCockeySenior Member

Not that simple. Many folks have spent lots of time during the last 130 years or so looking for a simple relationship between hull geometry, wake angle and resistance.

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### David J RitchieJunior Member

really

So you are saying you could build a boat with a more obtuse angle than the wake it creates but somehow they don't collide.

how interesting

Can you please post a paper on how it actually works then

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### DCockeySenior Member

Not what I said at all. I said nothing about boats colliding with their wakes.

The wake of a boat is not created by the bow alone. Rather it is created by the entire length of the wetted portion of the boat. The effect of the wetted portion of hull is continuous. In reality there are not a few discrete waves such as a single bow wave, a single midships wave and a single stern wave; although sometimes such simplifications are sometimes used in attempts to explain basic concepts.

I don't understand the concept of a boat colliding with it's own wake. The wake originates along the entire wetted length of the boat.

Not a paper but references include:
Marine Hydrodynamics by J. N. Newman, Chapter 6, Waves and Wave Effects
Ship Resistance and Flow by Lars Larsson & Hoyte C. Raven, Chapter 5, Inviscid Flow Around the Hull, Wave Making, and Wave Resistance, and Chapter 11, Hull Design
Hydrodynamics of Ship Design by Saunders, considerable information about experimental studies and attempts to understand wave making resistance due to hull shape​

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