Wave and Surfboard Speed
by Larry Goddard
There are formulas for calculating various wave characteristics, such as propagation speed and wavelength and period. But, the first thing YOU need to determine is the degree of bias in wave height observations in your locale. This is because the formulas are all based on actual, ( i.e. true, MEASURED) wave heights. You need to know the ratio of actual wave heights as compared to the estimated or reported height. The bias varies from place to place around the surfing world, and the degree and direction of the bias varies with wave heights.
Here in Hawaii, the guys on the North Shore report about 2/3 the true, total wave height, as recorded by the Waimea Bay Buoy. The guys on the South Shore report about 1/2 the true total wave height. They say they are estimating the size of the BACKSIDE of the wave. Well, that is patently ridiculous, since they are on the beach, looking at the FRONT side of the waves. They can’t see the backside of the waves, right? And they don’t ever ride the backside of a wave, so why are they attempting to describe the wave’s backside, anyway?
My own experiments around Hawaii and a few spots in California, measuring waves with a long pole, show that surfers are far off the true measure, but generally they are consistent in their bias for any given wave height range. For small waves, less than waist high, the bias gets really ridiculous. Example: when the surf is described as “flat”, why are there so many surfboards in the water? Are they merely contemplating their navels, or are they all meditating while they cool off in the water? No, of course not…they are waiting for a RIDE! Presumably on a wave. A tabletop is FLAT…and a swimming pool or a small lake might be flat, but, the ocean is never “flat”, at least not in the middle of the ocean, like where Hawaii lies.
So, the qualitative descriptor “flat” should not even be part of the surfer’s vocabulary when describing wave heights. The only number associated with “flat” is the numerical “ZERO”, which is the proper quantitative measure of an object’s size. In Hawaii, “FLAT” means “pretty small”, but not too small to be ridable. If it’s literally too small to ride, they could still be looking at waves nearly a foot high. But they are NOT zero height! So, how big are the waves in your area when it’s reported as “flat”? If you go out with a yardstick and actually MEASURE the waves, especially the really tiny ones that look like only inches high, you will be surprised at how far off the surfers are in estimating small waves. If “flat” is actually 1 or even 2 ft, then how big is it when they call it “1 foot”?
The direction of the bias reverses when the waves reach Waimea size. The reversal seems to occur somewhere between 20 and 25 feet. Over that, and the wave heights are reported as increasingly higher than they really are as the waves get larger.
The percentage of “uncertainty” in estimating wave heights seems to be constant, at about 20% of the wave height. Surfers will give a wave height report to within the nearest foot when waves are 4, 5, or 6 ft. or, about head high. And they will give an estimate to within 2 ft for waves in the 8, 10, or 12-ft range or about double-overhead. The next step up will be reports of 12, 15, or 18 ft, for waves in the triple-overhead range, i.e. 3 ft out of 15 ft, or 20% again. Then, finally, we see reports for large waves given in 5-foot increments, or 20, 25, 30 ft, which again follows the rule of 20% uncertainty. For truly Giant waves, 40, 50, 60 ft, the 20% rule seems to hold roughly, using 10 foot increments, or about 20% of 50 feet.
The depth of water in the surf lineup where the waves break is about 1.282 to 1.284 times the true, total wave height (measured vertically from the bottom of the trough to the crest of the about-to-break wave). Or, conversely, the true wave height is about 0.78 times the water depth when the wave is about to break. If a surfer on the north shore says a wave is 10 feet, it is probably actually 15 ft, with maybe 12 1/2 ft of it above sea level. The wave appears to be “double-overhead”, so the surfboard is 10 feet down from the lip as the rider trims across the wave. The surf observer then is reporting only about 4/5 of the actual ridable wave face, or about 80% of the 12 1/2 feet that looks like the part of the wave that’s steep enough to be ridable. The trough is about 1/6 of the total wave height, but it is not ridable, or even reachable, being located about 3 or 4 wave-heights out in front of the top of the wave, or a couple wave-heights out in front of the apparent “bottom” of the wave.
If you go out on a small day, say less than head high, and measure the depth of water where the wave begins to feather and break, you can calculate the size of the wave motion by holding the stick (or a bamboo pole) so it touches the bottom as the wave trough, then the crest pass by. Note the difference of the water surface motion as it goes up and down the pole. You can measure the true wave height to the nearest inch if you’re diligent and careful (and patient!). Compare the wave height to the depth at the point where the wave begins to break. This will vary depending on how rapidly the bottom is rising.
If the bottom slope is gentle, like Waikiki, where the bottom slope might be only 1 in 100 (i.e., the bottom rises only 3 ft per hundred yards, and it’s 9ft deep at 300 yards out from the beach),the wave height will be close to the theoretical, or maybe a little less. So, I might expect 7 ft waves in 9 feet of water (note that 7/9 = .777…). However, the bottom surrounding the lineup is probably closer to 10 feet (as at Cunha’s, where I surf a lot, and snorkle a lot looking for lost swim fins). So, the wave height near or surrounding the actual shallowest spot of 9 ft (where the wave first begins to feather) would be closer to say 7.5 or 7.8 ft. If you take 2/3rds of that true wave height, you will get 5.0 or 5.2 ft for the apparent wave height, which I call the “Surf Report Height”. That works for the North Shore surfers. The guys on the South Shore only report about 60 to 70% of the front-side height (i.e., what they think the back side height of the ridable portion of the wave might be. They call head high waves about 3 1/2 ft, and that’s about 70% of 5 feet, or about .47 to .56 yimes the true total height…roughly half the actual height.
The guys on the Gulf Coast, as well as many of the Northern California, Oregon and Washington seem to use “Slant Height”, which is only half the vertical height (as for a 30-60-90 degree right triangle, where the hypotenuse is half the vertical size of the short side.)Where the bottom slope is steep, the waves can break in water considerable shallower than normal. Think Pipeline, or Teahupoo in Tahiti. Extremely dangerous. A wipeout at the latter spot on a big day can kill you! A 12 foot wave breaking in the Makaha Bowl lands in about 10 feet of water (measured personally, on a day when it was breaking…it was low tide).
Anyway, if you can determine the true wave height of the waves of interest, then you can use the following formulas to calculate the wave speed and minimum surfboard speeds needed to make the wave. Note that most “good” surf spots have a bottom slope of about 1 in 30 in the area just outside of the lineup. That seems to be the “sweet spot” for nice, curling waves.
Here are the formulas I will use:
1) Water depth, d = H / 0.78
where H = true total wave height (about 1.5 X Surf Report ht)
2) Wave speed, ft/sec, V = square root of (g X d)
where g =32.16 (accell. of gravity)
3) Wave Speed, in MPH = (15 / 22) X (Wave Speed, ft/sec)
4) Minimum Surfboard Speed, MPH = (Wave Speed, MPH) / (Cosine of Angle of ride)
where straight-off = 0 degrees
Note: a typical ride angle for a point break might be about 30 – 45 degrees, with the faster point breaks approaching 60 degrees. A place like Maalaea Bay on a 6 ft SE swell, would be a bit too fast for most surfers to make. Only a fast skegless Paipo board, like Harry Akisada’s, could make the wave all the way down the line. Surfboards get picked off after a short run, then the next guy drops in on the freight-train wave, and goes as far as HE can…
So, here it is, in table form:
|Surf Report Height
||True Wave Height
||Water Depth ft
||Wave Speed ft/sec
||Wave Speed MPH
|Surf Report Height
||Surfboard Speed, MPH vs. Ride Angle
Note that the 1/4-mile ride at Makaha Point Break on a big west swell takes about 24 seconds to ride from the point lineup past the Bowl to the channel, which is 55 ft/sec for the breaking wave, or about 37.5 MPH. If that is a 30 ft wave (25 ft without the trough), then the ride angle of that makeable wave calculates to be 50.25 degrees. Fast. indeed! the wave peels off at 1.564 times the wave propagation speed going straight in. Sunset Beach on a big west swell is faster than that, tho’…; I don’t know how much faster. Waimea Bay is about as fast as Makaha Point Break, if you catch the wave from “behind” the boils at the Bay.