Boat Wake

[Keeping Up]

A question on University Challenge last night, was "In deep water, what is the angle of the wake left by a boat, relative to its direction of travel?". The answer was given as 39 degrees.

 

This intrigued me, even though of course a canal is not "deep water", because intuitively I would have expected it to vary with the speed of travel and maybe also according to the shape of the boat; but when I thought about it I realised that no, it always looks about the same.

 

I tried to look it up, and came across this intriguing page (look near the bottom for the statement about the 39 degrees).

[matty40s]

well that was worth reading just for this photo.

 

[Batavia]

Like you I am amazed that the angle is constant, as I had always assumed that it would be a function of velocity, similar to a supersonic shock wave, where, if I remember correctly, the half angle is sin-1 (Mach No).

 

Chris G

 

 

 

[Doorman]

Certainly makes you think a little more when out cruising after reading about the science of waves.

[sueb]

I thought someone had died

[TNC]

I thought someone had died

 

We had one in Ireland, when a local boater died.

[blackrose]

A question on University Challenge last night, was "In deep water, what is the angle of the wake left by a boat, relative to its direction of travel?". The answer was given as 39 degrees.

 

I missed it last night - did anyone actually get it right? It's amazing what they know.

 

I'm also surprised that the hull shape doesn't influence the angle. I guess if I had a square shaped bow the wake would still be 39 degrees.

[Keeping Up]

I missed it last night - did anyone actually get it right? It's amazing what they know.

 

I'm also surprised that the hull shape doesn't influence the angle. I guess if I had a square shaped bow the wake would still be 39 degrees.

 

No, they guessed at 45 degrees which is not all that far out.

[Doorman]

We had one in Ireland, when a local boater died.

 

Ah, an Irish wake.

 

Nowhere else do they celebrate a person's life better than in Ireland.

[homer2911]

What a shame though, that for most people, their life only gets celebrated when they're dead. I've learned so many interesting things about people I've known - at their funeral.

[Old git]

I missed it last night - did anyone actually get it right? It's amazing what they know.

 

I'm also surprised that the hull shape doesn't influence the angle. I guess if I had a square shaped bow the wake would still be 39 degrees.

 

Its the same for ducks swimming too ! 39degrees.

[Top cat]

So why is it 39 degrees regardless of boat size or speed ? Is it something to do with Froudes number ?

 

TC

[RLWP]

Apparently not. If you can say Froude number with confidence, you'll understand the entry on Wikipedia: http://en.wikipedia.org/wiki/Wake

 

Richard

[nicknorman]

Its the same for ducks swimming too ! 39degrees.

I think it's the same for migrating birds such as geese. By flying in the V formation they are riding the waves of the bird in front, thus reducing the effort required. Pity the poor one at point of the V!

[Old git]

I think it's the same for migrating birds such as geese. By flying in the V formation they are riding the waves of the bird in front, thus reducing the effort required. Pity the poor one at point of the V!

 

Do they change position like cyclists in the peloton or penguin in a storm stood in a pack so all taking turns in easier or warmer positions ?

[RLWP]

Do they change position like cyclists in the peloton or penguin in a storm stood in a pack so all taking turns in easier or warmer positions ?

 

Yes

 

Richard

[Doorman]

What a shame though, that for most people, their life only gets celebrated when they're dead. I've learned so many interesting things about people I've known - at their funeral.

 

In some cases yes, that's quite true. Depending on the humility of a particular person and whether they are introvert or extrovert, you may never get to know them that well in order to celebrate their life or achievements in the living years.

 

A local man in our village passed away recently and it was only at his funeral did people learn that as well as a heavyweight boxer, he was an accomplished violinist. A most unusual combination for such a big guy like him.

 

Sorry, way off topic.

 

Mike

[Top cat]

Richard thanks for the link

Wikipedia has this to say on the angle

 

"The angle of the shock wave (theta) thus follows from simple trigonometry and can be written as,

 

Theta = arcsin(C/V)

 

This angle is dependent on V, and the shock wave only forms when V>C

In deep water, however, shock waves always form even from slow-moving sources because waves with short enough wavelengths move still more slowly. These shock waves also manifest themselves at sharper angles than one would naively expect because it is group velocity that dictates the area of constructive interference and, in deep water, the group velocity is only half of the phase velocity.

By a simple accident in geometry, all shock waves that should have had angles between 33° and 72° get compressed into a narrow band of wake with angles between 15° and 19° with the strongest constructive interference occurring at the outer edge, resulting in the two arms of the V in the Kelvin wake pattern. This can be seen easily in the diagram on the left. Here, we consider waves generated at point C by the source which has now moved to point A. These waves would have formed a shock wave at the line AB, with the angle CAB = 62° because the phase velocity of the wave has been chosen to be = 0.883 of the boat velocity. But the group velocity is only half of the phase velocity, so the wake actually forms along the line AD, where D is the midpoint on the segment BC, and the wake angle CAD turns out to be 19°. The wavefronts of the wavelets in the wake coming from the wave components in our example still maintain an angle of 62° to the AC line. In reality, all the waves with would-be-shock-wave-angles between 33° and 72° contribute to the same narrow wake band and the wavelets exhibit an angle of 53°, which is roughly the average of 33° and 72°.

The wave components with would-be-shock-wave-angles between 73° and 90° dominate the interior of the V. Again, the waves that should have joined together and formed a wall similar to the phenomenon in sonic boom end up half-way between the point of generation and the current location of the wake source. This explains the curvature of the arcs.

Those very short waves with would-be-shock-wave-angles below 33° lack a mechanism to reinforce their amplitudes through constructive interference and are usually perceived by the naked eyes as small ripples on top of the interior transverse waves."

 

Simples

 

TC

[Pluto]

If you are interested in waves on canals, have a look at the soliton

[Keeping Up]

A few years ago I experienced something which was a little bit similar to a soliton.

 

Coming back down from the head of the Ashby, my attention was wandering as I left a relatively deep wide section to enter a narrow, shallow wooded cutting. Normally it is impossible to travel much above tickover speed through that cutting without making a wash, but on this occasion I was travelling quite fast from the open section beforehand and I simply forgot to slow down.

 

As we entered the narrow, shallow section the boat naturally started to slow down, but then my stern wave caught me up. At this point, just as I realised where I was and reached for the throttle to slow down, the stern wave lifted the back of my boat and it seemed as if I started "surf-riding" down the front of the wave (which was not breaking, I hasten to add). I soon discovered that if I kept the throttle open, this seemed to feed the wave so that it didn't die down; indeed I found I could open the throttle further and further to maintain a very large, smooth, non-breaking wace behind me - upon which the stern of the boat rose higher and higher. I estimate that I travelled about a quarter of a mile at a speed that was probably a "little bit" above the BW sped limit before my attention wavered for a few seconds and I strayed a couple of feet off the centre-line of the canal. At that point the symmetry was lost, the wave developed a breaking crest at the bank and I had to slow to my usual tickover speed.

 

I have often wondered about this phenomenon, and have tried unsuccessfully a couple of times to re-create it.

[fudd]

Richard thanks for the link

Wikipedia has this to say on the angle

 

"The angle of the shock wave (theta) thus follows from simple trigonometry and can be written as,

 

Theta = arcsin(C/V)

 

This angle is dependent on V, and the shock wave only forms when V>C

In deep water, however, shock waves always form even from slow-moving sources because waves with short enough wavelengths move still more slowly. These shock waves also manifest themselves at sharper angles than one would naively expect because it is group velocity that dictates the area of constructive interference and, in deep water, the group velocity is only half of the phase velocity.

By a simple accident in geometry, all shock waves that should have had angles between 33° and 72° get compressed into a narrow band of wake with angles between 15° and 19° with the strongest constructive interference occurring at the outer edge, resulting in the two arms of the V in the Kelvin wake pattern. This can be seen easily in the diagram on the left. Here, we consider waves generated at point C by the source which has now moved to point A. These waves would have formed a shock wave at the line AB, with the angle CAB = 62° because the phase velocity of the wave has been chosen to be = 0.883 of the boat velocity. But the group velocity is only half of the phase velocity, so the wake actually forms along the line AD, where D is the midpoint on the segment BC, and the wake angle CAD turns out to be 19°. The wavefronts of the wavelets in the wake coming from the wave components in our example still maintain an angle of 62° to the AC line. In reality, all the waves with would-be-shock-wave-angles between 33° and 72° contribute to the same narrow wake band and the wavelets exhibit an angle of 53°, which is roughly the average of 33° and 72°.

The wave components with would-be-shock-wave-angles between 73° and 90° dominate the interior of the V. Again, the waves that should have joined together and formed a wall similar to the phenomenon in sonic boom end up half-way between the point of generation and the current location of the wake source. This explains the curvature of the arcs.

Those very short waves with would-be-shock-wave-angles below 33° lack a mechanism to reinforce their amplitudes through constructive interference and are usually perceived by the naked eyes as small ripples on top of the interior transverse waves."

 

Simples

 

TC

Are you sure!? ?

[pquinn]

Ah, an Irish wake.

 

Nowhere else do they celebrate a person's life better than in Ireland.

 

and maybe their death!

[MtB]

I thought someone had died

 

I thought a boat had died

[Doorman]

and maybe their death!

 

Aye, maybe so!

[keble]

A few years ago I experienced something which was a little bit similar to a soliton.

 

Coming back down from the head of the Ashby, my attention was wandering as I left a relatively deep wide section to enter a narrow, shallow wooded cutting. Normally it is impossible to travel much above tickover speed through that cutting without making a wash, but on this occasion I was travelling quite fast from the open section beforehand and I simply forgot to slow down.

 

As we entered the narrow, shallow section the boat naturally started to slow down, but then my stern wave caught me up. At this point, just as I realised where I was and reached for the throttle to slow down, the stern wave lifted the back of my boat and it seemed as if I started "surf-riding" down the front of the wave (which was not breaking, I hasten to add). I soon discovered that if I kept the throttle open, this seemed to feed the wave so that it didn't die down; indeed I found I could open the throttle further and further to maintain a very large, smooth, non-breaking wace behind me - upon which the stern of the boat rose higher and higher. I estimate that I travelled about a quarter of a mile at a speed that was probably a "little bit" above the BW sped limit before my attention wavered for a few seconds and I strayed a couple of feet off the centre-line of the canal. At that point the symmetry was lost, the wave developed a breaking crest at the bank and I had to slow to my usual tickover speed.

 

I have often wondered about this phenomenon, and have tried unsuccessfully a couple of times to re-create it.

I feel an annual competition coming on!