surf wave energy vs ski wave energy

[chrislandy]

I just did some interesting man maths over on TT, so I thought I'd share the results!

 

1 pass of a surf boat can have approximately 120x the energy of 1 pass of a ski boat.

 

No wonder lake bed and shore erosion is a hot topic!

 

 

[unksskis]

Can you link to the formula?

[Than_Bogan]

Quick google search suggests the energy scales with the square of the height. So you are estimating the surf wave is 11x taller?

Or does the period also increase proportionally? In that case it would grow by the cube, so you'd be estimating 5x increases in those parameters?

[chrislandy]

The equation is

 

Energy per wave = 1/2 x Mass of wave x frequency squared x Amplitude squared

 

This is what I wrote in TT:

 

The amount of energy a wave has is the square of the frequency multiplied by the square of the amplitude (multiplied by a few effective constants). This basically means a wave that is only a little larger in size (amplitude) has much more energy than just the increase in height. Same for the frequency, the more often the wave (or wake) the more energy and thus more potential damage can be caused. The depth of the water, lake floor profile and distance (dissipation) also have an effect on the mass of the wave, and hence the amount of energy it has.

 

To put this in perspective may get a bit mathsy, but I'll give it a go...(ignoring the constants) - I also used photos online for estimating the number of "major" waves and the area under the curve to estimate mass

 

This is a bit overslimplistic and some bits will be wrong, but not by so much that it would skew the answer too much.

 

Ski / tube wake: Say 0.2m (8") wave, 1 second wavelength (1Hz), 0.0313 mass and 5 major waves

0.2^2 x 1^2 x 0.0313 x 5 = 0.0063

 

Surf wake: Say 0.9m (3ft) wave, 1.5s wavelength (0.6667Hz) 0.2114 mass and 10 major waves

0.9^2 x 0.6667^2 x 0.2114 x 10 = 0.7611

 

So a wakesurf pass could be said to have 121x the energy of a ski or tube pass. Get that wave above a metre in amplitude and the ratio rockets.

 

[Horton]

I am not smart enough to tell if you are including speed in your calcs. I can tell you that a wake boat at surf speed does a lot less damage than the same boat at wake board speed.

[chrislandy]

@Horton, yes, the speed is included in the frequency and "mass" as it's looking at energy. I was more comparing to ski speed and wake size rather than wakeboard - it's kind of the worst case, big high energy wave AND high velocity.

 

@sgregg just sent me some figures from an Australian study, which at around 100ft from the boat has "similar" figures for maximum wave energy - mine is 3x higher, but I assumed a 36" wave and they measured a 28.5" wave and I didn't allow for any dissipation of energy. If they'd measured at 50ft, it'd be closer I reckon.

[ReallyGottaSki]

A even moreso worse case is any inside corner where the energy and height concentrates and builds a bigger wave than first layed down. Find oneself there, thats people go seriously wtf

[Than_Bogan]

This is not my area of expertise, but several web sources give the same formula, which (ignoring constants) is just TH^2, i.e. linear in the period and quadratic in the height.

 

I do not see the mass entering into these formulae independently.

 

You also observed twice as many waves, so using your measurements I think I'm getting H ratio 4.5, T ratio 1.5, and quantity ratio 2, for a total energy factor of 4.5^2 * 1.5 * 2 = 60ish.

 

Very possible I'm totally wrong, but seemed worth a try.

 

Anyhow that's still a LOT.

[jpwhit]

Where did the wave heights come from? Did you make some measurement? They don't seem to match my impression of the various wave heights I see at my dock.

[rbuss4]

This has been studied before, and if I remember correctly; calculations show that once the wave travels 100' or more; the additional energy is lost

[Than_Bogan]

@rbuss4 That is very interesting, but 100' being enough does not mesh with my experience at all, so I'd be interested to read a study producing that number.

[gsm_peter]

Would not the amount of gas consumed per distance/pass describe the energy?

It can not be 100 times difference??

[chrislandy]

@gsm_peter different measurement of energy, that's energy input to push the boat through the water (or over the water) rather than the portion of energy that makes it to shore.

 

I was talking to a hydraulics specialist last week (aeronautical engineer and water flow lecturer) he gave a good example of energy input. Take a narrowboat (canal boat), back in olden times, it took one horse to tow a canal boat, so why does it take a 40hp engine to do the equivalent work? - and no the major losses are not all down to losses in the engine, drive train or prop.

[unksskis]

[gsm_peter]

@chrislandy

Still have hard time to understand. Please educate me?

 

Assume for a minute that air and heat energi losses are zero.

All remaining energi will go into push the boat through the water.

There are no other energi available that can go into increase the wakes!

 

The wakes loses a tiny bit of energy into heat while traviling.

The remaining energy will be used to 'destroy' the shore line.

Type moving gravel and sand etc.

 

[chrislandy]

@gsm_peter Keeping with the narrowboat example, it is a non planing hull, similar to a ski / wake / surf boat travelling at 10ish mph.

 

The majority of the energy is used pushing the water in front of the boat. This is exemplified in the narrowboat, when going through a tunnel / under a bridge it actually stops by itself then carries on. Apparently, this is because the water thats being pushed infront of the boat is resisted by the wingwalls of the bridge and pushes back, stopping the boat, until the forces are redistributed and the boat can carry on.

 

It's similar to surf boat, it's pushing water out of the way so the vast majority of the energy goes into the water, whereas a ski boat doing is planing so the majority of the energy is used pushing the boat OVER the water rather than THROUGH it, the normal force to the hull is downward rather than forward. Thats the reason you can back off the throttle once you're on the plane as it takes less energy to keep it on the plane.

 

Essentially, when non planing, a significantly higher amount of energy is put into the water than when planing, hence the larger and higher number of wakes when not planing.

[NameUnavailable]

The funniest argument I have heard over the years at our lake is that your jump boat goes 35mph and our wakeboard boat only goes 22mph so we don't do as much damage as you...I ask with your theory what happens when they have drag boat races that must tear the hell out of the shore lines? 100+mph

This is about mass...like getting tackled by a 100 lb guy vs a 250 lb guy.

I did not know the increased number of waves that was mentioned earlier with the surfboat. Interesting stuff..Thanks

[skibrain]

In terms of energy input between displacement and planing hulls, I think it’s telling that surf boats commonly turn 3,000 - 3,600 rpm at 11 mph.

[BraceMaker]

Regardless of the science of waves - one thing is very clear.

 

Boats are bigger - waves are bigger. Unless you can convince the consumer that they want smaller boats....

 

 

 

[ReallyGottaSki]

Fat chance

 

 

[jcamp]

Beef. It's what's for dinner.

[Than_Bogan]

@ReallyGottaSki Wow! Is that the genuine data from the CDC? That's incredible if so!

[ReallyGottaSki]

@Than_Bogan seems legit . I know huh?

And latest numbers are 198/170 (avg for all over 20 years old)

[Edmund]

Here is a summary of the 2015 report upon which the video @unksskis posted is based. It analyzed the waves of a Nautique G-23 at various speeds and distances.

 

And here is the full report.

[rbuss4]

@edmund and @unksskis- Thank you for sharing. That is the study I remembered seeing before. The University of MN is also planning to undertake a study of this, and is crowdfunding for it now. https://minnpost.com/greater-minnesota/2020/07/new-u-of-m-research-could-make-waves-in-fight-over-wakesurfing/

[Than_Bogan]

Cool! Nothing like some measured data to help along our knowledge! Thanks @Edmund for digging this up!

 

That said, the Newburyport study (from my home state -- go Mass!) summary appears to be rather speculative. My interpretation is that they actually measured the energy of both wind and surf wakes, but then they assume that the total energy hitting the shore is what dictates shore damage. That could be true, of course, but it wouldn't be my hypothesis, and it deserves further testing. My hypothesis is that single, high-energy events reshape the shore in a fundamentally different way than repeated, low-energy events that happen to sum to the same total.

 

Maybe the planned MN study will more directly measure shore impact?

[chrislandy]

@Than_Bogan you are correct.

 

100 taps with a hammer don't cause the same damage as one big blow

[ReallyGottaSki]

Indeed, can assume same energy overall. As you predict the same energy over shorter time equals higher power peaks within that period.

[Edmund]

@rbuss4 @Than_Bogan There is a long story behind the scenes, but the short version is...

 

The reason I had the links to that wave study handy is that last fall I was on a task force to decide whether or not to ban wake surfing on our (the city's) lake. I used the study to justify my vote to ban them, and tried to persuade others. Our lake is not even 400ft wide in most places, but we do have a short stretch that is between 400 and 500ft. Even so, my neighbors and I often face surfing happening within 75ft of our docks and shoreline, and sometimes within 50ft. The task force vote (close to 50/50) went the other way because most did not want to take away some of the other property owners' big toys. Also, if you are having a wake surfing study/demonstration performed and you are not in complete control of all of the variables, then PM me and I will tell you my experience when the task force members were at my dock as observers. [Yes, this is the short version :D ]

[DW]

Ski tug weights appear to have more than matched the slope of the human weight chart.

[The_MS]

Pandas for everyone

[S1Pitts]

I am glad to see this thread and learn that there are studies being done. One thing I have noticed about surf waves is that not all brand boats are the same. These studies should use multiple mfg and models.

The other uncontrolled activity I see on our lake is these larger boats are not only using the designed ballast tanks but also adding the old school fat sacs and loading more than probably is the recommended people/weight to produce what we have named death waves.

It is sad but I just don't see this ever going away.

[unksskis]

What happens to the manufacturers in 5 years when wakesurfing becomes restricted or even outlawed? Hopefully its make more ski boats and not runabouts/out of business. They can't control these studies by the State. Now is an important time to differentiate ski boat wakes vs surf boat wakes and their different erosion impacts.

[The_MS]

We need to have a Nerd/Geek looking Panda

[unksskis]

@The_MS who are your posts directed to?

[The_MS]

Probably @chrislandy for the thread start but after reading your last post it may make sense to figure it out. I would just like to see a Nerd/Geek panda so we can use it when needed. I just think there are to many variables to figure in on the wave deal.

[vtmecheng]

@chrislandy what did you assume for the wave mass in each case?

 

Edit: should have asked how you determined the wave mass

[2Valve]

@ReallyGottaSki Not so sure the average female's weight is 167 (2010). :( At least not in my neck of the woods....

[Horton]

I just moved this thread into the section that can only be seen by registered members. I cannot bear to be judged by the greater public for this thread. :-)

[chrislandy]

@vtmecheng that was the easy bit, ignoring the density of water (as its the same for both big and little waves) I used the area under the curve of the wave shape.

 

For that, rather than mess around trying to calculate a wave form then integrating to find the area, I simply plotted the a series of 10 or so peak & troughs at the wavelength in my CAD program, used a spline line to form a curve between the points, then measured the area under the middle wave, then multiplied it by a unit width to create the volume - hence this is the mass used. I believe this underestimates the mass considerably as there is a function of depth which effects the wave energy. Some of the research on wave energy (for renewables) use the wave amplitude, others a nominal depth, others use the depth to the bed if its a lake.

 

@Horton does this qualify for a nerd panda? I can't believe I've been a member for nearly 6 years and not got at least one panda yet! I feel like I'm missing a rite of passage

 

[Than_Bogan]

Must ... acquire ... nerd panda ...

[Horton]

I have awards for the Nerds that I have just not unveiled. meh.

[Horton]

If we can get off the Nerd track here is some anecdotal data.

 

My lake is about 8' deep. That means that a surf boat does not work great but it is just usable. When the surf boat arrived I was super unhappy and assumed that it would destroy the shoreline.

 

What I have learned is that a MasterCraft XT21 (or 22 IDK) at surf speed has much less impact on the shore then anticipated. The islands took a beating but we fixed that with concrete. At wakeboard speed the wakes are FAR more damaging. Boat speed a huge factor.

 

We had 40+ mph wind for 2 solid days that did more damage to the shore than the surf boat has ever done.

[slow]

Surf wakes are much worse than wakeboard waves on big lakes. Due to their size they can carry over a mile. 200 foot shore line restrictions do nothing. Reduced fun for skiers, paddle boarders, sailers swimmers, people trying to enjoy their beach or dock.

[vtmecheng]

@chrislandy That's honestly what I was hoping you did.

 

I'm not getting into the nerd on this one due to lake of time but do find the discussion and evaluations interesting. @Horton I can say with definite certainty that surf waves are considerably more damaging for shorelines than wakeboarding when on a lake. We first only had wakeboarding at my parents' place and it wasn't horrible. When the wakesurfing came along our shoreline degradation increased quickly and we had to increase the size of riprap and height of the shore buildup handle it.

[Horton]

@vtmecheng you mean on a big deep lake?

[Edmund]

From the 2015 WSIA Study

Shallow lake depth at the boat track was 10 ft or less.

Deep lake depth at the boat track was around 22 ft to 30 ft.

Given the same lake (shallow/deep), at no time is the wakesurf wave height lower than the wakeboard wave height within ~350 ft of the boat track.

[Horton]

@Edmund in terms of shoreline damage wave height is one factor and wave speed is another factor. A tall slow wave does less damage than a slightly smaller wave moving much faster. ( the science guys can create some perplexing formula to explain why I'm right or wrong )

 

In my experience on a private lake 8 feet deep

If you take the same boat and you go surf speed and then you go wakeboard speed the waves created while wakesurfing are far less damaging. watching those wake surf waves hit shore looks terrible but doesn't really do that much damage.

 

Let me go a step further and say that a MasterCraft ProStar makes a hysterically huge wave at exactly 8.5 miles an hour. When it gets to shore it just rolls up and rolls off because of its slow speed and shape.

 

I understand on big lakes that are much deeper all these Dynamics are different. I'm not saying surf boats are great I'm just saying in my experience on a private lake it's not as scary as we thought

[Joeprunc]

Interesting topic.

I spent the first half of my life surfing and following swells and storms to predict where to surf. The four variables that I used to predict what spots to surf were, height, period (frequency), tide, and swell angle.

 

I can tell you that the longer period swells had more driving force behind them, and were much more ideal for point breaks, where the swell had the power to wrap around the reef (more potential energy). "even if it was a small height". The longer period swells were generated from storms further away, vs the short period swells (the distance bleed height, but also allowed for a more organized swell).

These storms required a lot more potential energy to perpetuate through the ocean. Tide and angle depicted how the swell would hit the reef.

 

If you have wake surfed, think of the period as the difference between riding a fully loaded boat at 9 mph vs 13 mph. The 9 mph wake is generally taller, but has less push, where as the 13 mph wave may be smaller but the "sweet spot" is much longer. I wonder if the period between a surf, wake, and ski boat are significantly different? I think the other contributing factor of the surf wake not affecting a private lake shoreline (straight) is given the angle at which the swell contacts the shore. At slower speeds the boat wake is angle is much larger (say 45°). The surf wake bleeds off energy as the depth decreases, and as it hits the shoreline the wake slowly works down the shoreline gradually bleeding the remaining energy. If you take that same wake and change the angle to parallel to the shoreline, there is no gradual bleed and you get a hard pounding. The faster the boat travels the smaller the wake angle....maybe this has something to do why the wake boat wake is more "detrimental" to the shoreline.