1. Senior Member
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## wave speed?

This morning I was messing around on the "Windy" app, and noted 10' waves every 8 seconds offshore of Neah Bay, Wa. while in Eastern Lake Michigan the app reported 6' waves every 5 seconds. I wondered what the relative wave speeds and steepness might be, but quickly got in over my head in equations when searching the topic online. Has anyone come across graphs &/or a simple way to deduce wave speed? (In both cases I think I got the data far enough offshore that they would be considered deep water waves) Obviously we are also dealing with the difference between fresh and salt water.

Ken

2. ## Re: wave speed?

Waves in my part of the Atlantic are *normally running at about 10-12 knots. This estimate from years of running home downsea at ~22 knots boat speed and observing.

*Normal means, say, 2'-4" seas, six second period and winds 15 kts or less and no storm nearby. A hurricane in mid-Atlantic may not affect the weather but can generate larger, faster moving waves, for example.

Kevin

3. ## Re: wave speed?

Originally Posted by kbowen
In both cases I think I got the data far enough offshore that they would be considered deep water waves
the waves in neah bay began their journey 6000 miles away and bounded over the deepest ocean on earth before piling up on the west coast

the waves in lake michigan coalesced twenty or so miles off the coast of wisconsin and then traveled a mere 100 more miles across the lake

big difference in how the two waves were generated and evolved
Last edited by Paul Pless; 10-16-2021 at 12:00 PM.

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## Re: wave speed?

In oceanography, the equation you are seeking is for "celerity". Dont have it ready to hand tho, sorry.

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## Re: wave speed?

rough formula... in deep water, the speed (in knots) at which a train or set of waves moves thru the water = 1.5x the wave period (in seconds) so a set of waves with an average period of 10 seconds would be 15 knots

individual waves within the set would move faster than that, new waves are constantly forming at the back of the set, moving their way through to the front and then petering out and the process is constantly repeats itself across thousands of miles of ocean with very little energy loss until ideally it becomes perfect clean surf breaking on a California beach

6. ## Re: wave speed?

Wave celerity - The speed at which an individual wave advances or “propagates” is known as the wave celerity. For a deepwater wave the celerity is directly proportional to the wave period, T. The formula for deepwater celerity, Co, is Co =1.56T m/sec
So for Lake Michigan your speed is 7.80 m/s

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## Re: wave speed?

Originally Posted by Peerie Maa
So for Lake Michigan your speed is 7.80 m/s
Does your formula also apply to fresh water?

Ken

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## Re: wave speed?

I believe In deep water wave speed is purely a function of wave length. This is why boats have a hull speed.

9. ## Re: wave speed?

Originally Posted by kbowen
Does your formula also apply to fresh water?

Ken
Yes, or it would include a density function.

10. Senior Member
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## Re: wave speed?

Originally Posted by Peerie Maa
Yes, or it would include a density function.
Ok, I hear what you are saying, but I just moved from Chicago to Port Townsend, Wa. and my initial impression squares with what is often mentioned in other accounts: That waves in fresh water get up taller and closer together for a given wind velocity than in the sea.

11. ## Re: wave speed?

Lots of factors will affect wave speed, especially water depth, fetch, and how long the wave was forming. For mature ocean waves, the formula is like the "hull speed" formula: 1.3 times the square root of distance crest to crest in feet yields wave speed in knots. Give or take.

Factors matter. For example, shoaling will increase wave height and slow wave speed. Juvenile seas are not so high but can be steep, close crest to crest, and slow. And lets not even get to barometric pressure.

Correctly estimating wave height from a boat is hard. In another thread I gave a method that involves known sight lines. Wave speed is even harder unless you have good instrumentation, can climb on the wave's back, and take that a ways.

12. ## Re: wave speed?

Originally Posted by kbowen
Ok, I hear what you are saying, but I just moved from Chicago to Port Townsend, Wa. and my initial impression squares with what is often mentioned in other accounts: That waves in fresh water get up taller and closer together for a given wind velocity than in the sea.
Originally Posted by Ian McColgin
Lots of factors will affect wave speed, especially water depth, fetch, and how long the wave was forming. For mature ocean waves, the formula is like the "hull speed" formula: 1.3 times the square root of distance crest to crest in feet yields wave speed in knots. Give or take.

Factors matter. For example, shoaling will increase wave height and slow wave speed. Juvenile seas are not so high but can be steep, close crest to crest, and slow. And lets not even get to barometric pressure.

Correctly estimating wave height from a boat is hard. In another thread I gave a method that involves known sight lines. Wave speed is even harder unless you have good instrumentation, can climb on the wave's back, and take that a ways.
Wind blowing on one part of a sea or large lake will generate waves of all sizes and wave length. The longer faster waves will arrive at an observer before the shorter slower waves. If there was a storm close to the observer and one far away, the observer will see a mix of waves from the two storms, and if there are islands out there waves will also be reflected or diffracted. Which is why measuring sea states is such fun.
On the topic of wave height/sea state observers tend to focus on the highest wave heights in a sea, so oceanographers refer to Significant Wave Height to define the sea. That is theaverage height of the highest one-third of all waves measured, which is equivalent to the estimate that would be made by a visual observer at sea.
If an observer reports a six-foot wave height sea state, the oceanographer can convert that to a spectrum and calculate the total entrained energy of the wave system.

13. ## Re: wave speed?

Is the purpose being to work out what wave state you'll go out in? Because that's down to boat size / comfort and how much they can bridge the chop or be in or out of sync with the wave.
Brings to mind a wonderful sail on a 50 ft (35 ft waterline) boat upwind in shallow water in a typical 3 or 4 ft chop, the Tamaki straight( one of the recent America's Cup courses) up front were small boats at perhaps half or 2/3 our speed, pitching away their boat speed. Bucketing.
As we caught them up they turned out to be 3 or 4 Townson 32 yachts, not small at all and a boat renowned for windward ability and performance. They just weren't in sync with the waves presented that day, a few ft more in w/l and overhangs and we slid on through near flat.

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## Re: wave speed?

Originally Posted by John B
Is the purpose being to work out what wave state you'll go out in?.
Indirectly: When I was younger I crewed on a variety of plastic sloops in 'round-the-buoy races out of Chicago. I was always struck that in going upwind they all had a rhythm that was essentially out of sync with the waves: They would ride one wave fine, ride the next one and overshoot in height and on the third or fourth they would butt head into the next wave. Then they would start the whole process over again. Of course all these production boats were designed for the predominant salt-water market and I wondered if there might be a design that would stay in sync with the waves? So a huge part of my motivation for building a traditional Mackinaw boat has been to find out if the old timers may have found a better rhythm? I haven't sailed my Mackinaw enough in big enough water to be ready to weigh-in on that question, however I can say that the fine lines aft definitely lift less with a passing wave and therefore are less likely to lever the bow down into the coming wave. It is also striking that as this boat approaches hull speed it doesn't drag a big quarter wave behind it. The bluff bow definitely makes itself known, but the water leaves the stern much flatter than other boats I have sailed.

So my essential question is differences between fresh and salt water waves?

Ken

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## Re: wave speed?

Originally Posted by kbowen
Indirectly: When I was younger I crewed on a variety of plastic sloops in 'round-the-buoy races out of Chicago. I was always struck that in going upwind they all had a rhythm that was essentially out of sync with the waves: They would ride one wave fine, ride the next one and overshoot in height and on the third or fourth they would butt head into the next wave. Then they would start the whole process over again. Of course all these production boats were designed for the predominant salt-water market and I wondered if there might be a design that would stay in sync with the waves? So a huge part of my motivation for building a traditional Mackinaw boat has been to find out if the old timers may have found a better rhythm? I haven't sailed my Mackinaw enough in big enough water to be ready to weigh-in on that question, however I can say that the fine lines aft definitely lift less with a passing wave and therefore are less likely to lever the bow down into the coming wave. It is also striking that as this boat approaches hull speed it doesn't drag a big quarter wave behind it. The bluff bow definitely makes itself known, but the water leaves the stern much flatter than other boats I have sailed.

So my essential question is differences between fresh and salt water waves?

Ken
I'm no expert, but I would think that the shape of the body of water, its orientation to the wind, openness to the ocean or not, and currents, would make a much bigger difference in wave forms than the small difference in density between salt and fresh water. To take but one variable, bodies of salt water very often are tidal, and tide running against a wind can generate a nasty chop. But some areas have a greater tidal range and/or variety of landforms that exacerbate this; others do not.

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