Distance between swell lines?

[phil osofer]

Stood on the hill overlooking Kirra on Friday 17th June and was trying to work out the length of the ride from the take off at Snapper to the groyne at Kirra.
The wave period was about 14 seconds and I counted 10 lines over this distance, and it took exactly 2 minutes for a line of swell to travel this distance.
Twice in the past when the period was 9 seconds I counted 17 lines.
So if these swells have slowed down to a speed of 18 kilometres per hour and the time traveled takes 2 minutes then the distance over the 10 swell lines is .6 of a kilometre, and if it is a 45 degree peel angle then the ride is .85 kilometres long.
So the distance between swell lines with a 14 second period would be .6 of a kilometre divided by 9 gaps[between 10 lines] equals 66 metres.
Does this seem right?

[phil osofer]

Yes that's correct.
Swell speed formula is C=1.56 x T where C is the wave speed in metres / second and T is the wave period in seconds.
A 14 second period swell in the open ocean is traveling at 21.8 metres/sec or 1,310 metres/minute or 78,624 metres/hour[say 78kph]
A 9 second period swell in the open ocean is travelling at 14 metres/sec or 842 metres /minute or 50kph.
When swells get closer to the coast they start to feel the bottom and this reaction acts like a brake and they become slower as the sea depth decreases.
Also longer period swells feel the bottom earlier.
My observation at Snapper Rocks is that the swell breaks in a depth twice the wave face size and the white water travels to shore at about 18kph.
So a 14 sec swell slows down by 60kph and a 9 sec by 32kph ,hence why 14 sec swell packs more punch is comparable to braking in a car at a faster speed.

[Dolphin63]

Mr Osofer,

If you want to estimate the length of ride there, your best first pass technique is to pull out a street directory or map and scale it (say 1200 m from Snapper to Big Kirra Groyne by my reckoning).

If you're trying to work out velocity, in shallow water, wave period virtually drops out. Period still affects the breaking intensity though.
Shallow water theory is OK for velocity near the breakpoint and inside it.

Shallow water linear wave theory: c = (g*d)^0.5
where c is velocity (m/s), g is 9.81 m/s/s, d is local water depth.
More correctly, Shallow water solitary wave theory: c = (g*(H+d))^0.5, H is wave height.

Local wavelength (gap) is: L = c*T
where T is period

My observation at Snapper Rocks is that the swell breaks in a depth twice the wave face size

The generally accepted typical value is 1.28, with the absolute upper limit in onshore pus of about 1.8. You may be overestimating the water depth or more likely underestimating the real wave face height. Remember, these equations rely on the real face (or even the real back, which is the same height) for input.

Peel angle has been measured for Burleigh and old Kirra at 40 degrees.
90 being a non-closeout straighthander (fathander?) and 0 being a total straightline closeout. Don't know of measurements for Superbank, so use 40 deg for now.

For a true 2 m wave face, breaking d would be ~2.5 m, giving a straight shoreward wave velocity of c = 5 m/s by linear and 6.6 m/s by solitary.
Add surfer peel angle (40 deg) and you get
average surfer speed = c*(1/sin40)
= ~8 to 10 m/s, or 29 to 36 km/hr

The upper numbers are more correct (solitary wave theory).
So say the surfer potentially travels at 10 m/s for the 2 minutes Mr Osofer measured (120 s) and you get a ride length of 1200 m, which is what the map says!

Best to add any tough guy correction factors here, but I've wasted enough time already, so you can add your own.

[One Mile Point]

i could have not been bothered trying to figure it out

[Hunter]

keep this stuff coming, I love learning about the science of waves!

[phil osofer]

Regarding wave breaking depth.
When the Byron waverider bouy reads 3m the actual wave height is 2m.That is a standard rule of thumb for east swell direction, that the wave height will be 2/3 of the bouy reading.
So when the formula says a 1m wave breaks in 1.28 depth and my observation was a .64 wave will break in 1.28 depth I'm not factoring in the the extra 1/3 the bouy is reading. If I did then a .96[.64+.32]m wave would break in 1.28 m depth.
Wave speed.
Tony Butts approximate wave speeds[using bouy size] just before breaking are,1m wave 13kph,2m wave 18kph, 3m wave 23kph.
Distance between Swell lines.
If the length of the ride is 1.2 and not .85, and it takes 2 minutes at an average peel angle of 40 degrees then the straight distance to shore is .85 kilometres.Divide the 850 metres by the 9 gaps [between the 10 swell lines] equals 94 metres between swell lines.
Speed the surfer is travelling at.
If the curl travels 1.2 k's in 2 min's then it travels .6 k in 1minute or 36 kph. So if the surfer is just trimming [not turning] just ahead of the curl then the surfer is travelling at 36kph.
This particular day with this combination of 2m wave size, east direction and 16 sec period it was almost possible to get a single ride the whole way.The wave was a full on down the line speed run i.e. no cutbacks. The surfers track was more like a sine wave,a good choice of line was to aim down the face at about a 70 degree angle to the swell line[remember the surfer gains more accelleration at this moment if the least amount of the right rail is in the water][less drag] then as late as possible starts a bottom turn, and so gets maximum extension/accelleration out onto wave face.
If you straighten out a sine wave it is 1/2 more the straight distance[start of sine wave to end of sine wave],so it could be possible for the surfer to travel 1/2 the distance again. 1.2+.6=1.8 kilometres.
If the surfer travels 1.8k's in 2 minutes then the speed the surfer is travelling is 54kph.
But does it really feel that fast?

[macca202]

hmmm i think he's saying that when you go down the line on a wave, although you thing your going straignt, relative to the water you are actually moving in a curved line, so although relative to the land you may be moving at a certain easily measurable speed, but relative to the water you are traveling a bit faster. If thats the case, then i don't buy that you can measure that just using the dimensions of a sine wave, well atleast not on a supersucky wave.....

[oldman]

Yeah Wanto,

I'm pretty sure Phil baby is talking about the pumping action being the sine wave. If it is agreed that the distance is 1.2 km, he is saying the sine wave would mean you would actually travel up to 1.8 km, due the effect of straightening out a sine wave. So yeah, it is the up and down movement over the wave, which is what you do if you really want to crank up the speed.

54 kmh sounds a bit fast but you might go close to that. 36 kmh seems a bit slow for what is a fast barrelling down the line wave.

[Dolphin63]

are you from asr ltd dolphin?

No! There are some big egos there and the missus says Raglan is too cold.

As for distance between swell lines. I didn't answer it directly as I thought most surfers would be interested in length and speed. I did say:

Local wavelength (gap) is: L = c*T

So if for this case, if you accept c = 6.6 m/s (24 km/hr) and T = 14 s, then the gap or distance or local wavelength is 92 m.

When the Byron waverider bouy reads 3m the actual wave height is 2m.That is a standard rule of thumb for east swell direction, that the wave height will be 2/3 of the bouy reading.

Interesting observation. I presume you're talking about the Hsig. Between the booeey and the break, waves change through refraction (bending), diffraction, shoaling (an increase, or decrease in height due to depth changes), and frictional losses. It's quite complex and dependent on at least height, period and direction. Refraction can cause focussing at some spots in some conditions. I have seen east coast Oz cases where Hsig of 1.2 m can give breaking faces of 3 m in some circumstances.

I did meet Tony Butt's co-author Paul Russell, and said:
"Nice book, but ya chickened out on wave height measurement."
PR said: "We couldn't agree on it, so agreed to leave it out"

[macca202]

Yeah Wanto,

I'm pretty sure Phil baby is talking about the pumping action being the sine wave. If it is agreed that the distance is 1.2 km, he is saying the sine wave would mean you would actually travel up to 1.8 km, due the effect of straightening out a sine wave. So yeah, it is the up and down movement over the wave, which is what you do if you really want to crank up the speed.

54 kmh sounds a bit fast but you might go close to that. 36 kmh seems a bit slow for what is a fast barrelling down the line wave.

i just re-read it and yeah i agree thats what he means, but its totally wrong imo. There is no way the pumping action gives the amplitude of a normal sine wave. not even close, unless they were doing real exagerated pumping, which would slow you down anyway.
Think about it, you would have to move up and down the wave a total of say 1 meter for every 3.14 meteres. that normal?

[snakes]

Regarding wave breaking depth.
When the Byron waverider bouy reads 3m the actual wave height is 2m.That is a standard rule of thumb for east swell direction, that the wave height will be 2/3 of the bouy reading. [.quote]

WTF

So when the formula says a 1m wave breaks in 1.28 depth and my observation was a .64 wave will break in 1.28 depth I'm not factoring in the the extra 1/3 the bouy is reading. If I did then a .96[.64+.32]m wave would break in 1.28 m depth.
Wave speed.
Tony Butts approximate wave speeds[using bouy size] just before breaking are,1m wave 13kph,2m wave 18kph, 3m wave 23kph.
Distance between Swell lines.
If the length of the ride is 1.2 and not .85, and it takes 2 minutes at an average peel angle of 40 degrees then the straight distance to shore is .85 kilometres.Divide the 850 metres by the 9 gaps [between the 10 swell lines] equals 94 metres between swell lines.
Speed the surfer is travelling at.
If the curl travels 1.2 k's in 2 min's then it travels .6 k in 1minute or 36 kph. So if the surfer is just trimming [not turning] just ahead of the curl then the surfer is travelling at 36kph.
This particular day with this combination of 2m wave size, east direction and 16 sec period it was almost possible to get a single ride the whole way.The wave was a full on down the line speed run i.e. no cutbacks. The surfers track was more like a sine wave,a good choice of line was to aim down the face at about a 70 degree angle to the swell line[remember the surfer gains more accelleration at this moment if the least amount of the right rail is in the water][less drag] then as late as possible starts a bottom turn, and so gets maximum extension/accelleration out onto wave face.
If you straighten out a sine wave it is 1/2 more the straight distance[start of sine wave to end of sine wave],so it could be possible for the surfer to travel 1/2 the distance again. 1.2+.6=1.8 kilometres.
If the surfer travels 1.8k's in 2 minutes then the speed the surfer is travelling is 54kph.
But does it really feel that fast?

I dunno man, but you maths sounds flawed to me

snakes

[Dolphin63]

I'm feeling like a Dr Karl wannabe here.

Think about how many reos you could fit in in an olympic pool on a down the line wave like good superbank. We'll keep it at the 2 m face wave. Maybe Wanto and Snakes can do 2, but us old cruisers may be down to one, which I'll use for now. Again the young shredders might rise 2 m on their reos, Snakes may extend it to 3 m with air and old cruisers just wiggle 1 m, but we'll say 2 m.

So your "sine wave" has a height of 2 m (or amplitude of 1 m) and a wavelength of 50 m. That's a very flat "sine" wave. I don't want to buggerise around with line integrals, but if you're adventurous you could do a simple Pythagoras triangulation on it and you'd find that the "sine" wave adds very little to the distance travelled (partly because the wave is moving shorewards quite quickly).

That said, yes, you will speed up and slow down around your average.

[Johnno]

Thanks guys I appreciate you sharing your knowledge here as this is starting to make sense.

And Dolphin63 I can listen to Dr Karl all day long.......he's a brilliant educator.

[oldman]

I appreciate your erudition fellas.

I wish I was able to follow the maths more closely though. Not having studied it for so long I can really only remember to concepts rather than the details. I used to be very good at this stuff.

I think Macca and others are right. It's a small amplitude for a sine wave and the stretch from 1.2km to 1.8 seems too much, which would bring down the calculated speed.