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While I agree with Roy that GPS measurement is far better than any method that isn’t objective, and “apples-to-apples”, it still leaves much to be desired. First, it measures ground speed, while in our application I think that water speed is more appropriate. Also, the error factors compromise it for distances as short as those typically for board surfing. A typical long ride where I surf is probably on the order of 100 yards (certainly less than 200). Best case GPS postition accuracy with Selective Availability turned off is 3 meters, call it 10 feet. Typical accuracy, according to Wikipedia http://en.wikipedia.org/…l_Positioning_System is more like 50 feet. I see no justification to assume offsetting errors at starting and ending positions (there may indeed be reasons to assume that, but I have not found them), So, if the assumption is, on average, a 50 foot error in measuring a 300 foot ride, that’s ~17% slop inherent in the system, without accounting for any errors introduced by variations between devices or users. To be really meaningful, we would need a log of enough GPS speed measurements from the same approximate ride (and ideally, the same GPS receiver chip set) to do standard deviation and other statistical assurance calculations. I’d much rather spend that effort on some repeatable way to measure water speed…
-Samiam
I disagree. From the standpoint of making a section, it is the speed “over the bottom” that counts. Imagine viewing a breaking wave with a progressing curl as viewed from above (e.g. by looking downward from a hovering helicopter). Imagine that a surfer catches the wave and maintains a fixed distance relative to the curl. Start a stopwatch when the surfer is at some particular location (call it point “A”). Stop it when he passes some later point (say “B”). The distance he travels from point A to point B, divided by the elapsed time, gives his speed “over the bottom”, not the “speed through the water”. If the component of his speed parallel to the crest of the wave matches the speed of progress of the curl along the crest he maintains his position relative to the curl; if it is greater, he moves away from the curl; if it is less, he gets overtaken by the curl.
On the other hand, if you had a surfboard with a lot of drag, and were trying to make the drop at Teahupoo, it’s conceivable that you could end up with the slope of the wave nearly vertical and getting nowhere (at least until you got overtaken by the curl). That’s a situation with a high speed "through the water (impellor-based speed), but near zero speed “over the bottom” (GPS speed).
On another tack…
The guys in NZ that build artificial surf breaks have made extensive measurements of the angle that the path of surfers make relative to the crest of the wave (see: The Science of Surfing and Surf Breaks"). The smaller this angle, the faster the surfer is going (relative to the rate of progression of the wave toward shore). The minimum angle that they have measured is a bit over 30 degrees, increasing to around 45 degrees for larger waves (where skin friction would be expected to make a greater contribution to the total drag). If the speed of progression of the wave toward shore is Vw and the path angle is 30 degrees, then the speed of the surfer “over the bottom” is:
Vs = Vw /sin (30 deg) = 2 * Vw
If he is staying at the same position relative to the curl of the wave, the rate of progression of the curl along the crest of the wave is:
Vc = Vw/tan(30 deg) = 1.73 * Vw
For larger waves, where the path angle is closer to 45 deg, the corresponding speeds would be.
Vs = 1.41 * Vw
Vc = Vw
For a beach with a nearly constant bottom slope, the speed of progression of a wave as it progresses toward shore is about:
Vw = square-root ( g * (0.75 H +h))
where:
g = 32.2 ft/sec^2
H = height of the wave
h = depth of the water
The ratio between the height of the wave and the depth of the water at the breaking point depends on a number of factors, but typically ranges between 0.8 and 1.2. For the purposes of illustration, I’ll assume a factor of 1.0. Let’s also assume a wave height, H, of 30 feet. Then the speed of progression toward shore (i.e. over the bottom) becomes:
Vw = square-root( 32.2 * (22.5 + 30)) = 41.1 ft /sec
For a path angle of 45 degrees, and assuming that the wave peels at a speed such that the surfer stays at the same position relative to the curl of the wave, his speed would be:
Vs = 1.414 * 41.1 ft/sec = 58.1 ft/sec = 39.6 mph
…(and the speed (over the bottom) would actually be expected to be a bit slower due to factors not considered here).
This speed is comparable to a speed claimed by Roy. So let’s do a similar calculation to see what the path angle would be to achieve this speed. Roy claimed wave sizes that ranged up to 1.5x, so let’s assume a height of 9 feet. That would give a wave speed, Vw, of 22.5 ft/sec (15 mph). The path angle associated with the speed (over the bottom) reported by Roy would then be about:
tan(path-angle) = 22.5/58.1 = 0.387
path-angle = 21 degrees
By way of comparison, as I recall, the smallest path angle that was measured in the surf break design surveys was 33 degrees, so this is a significant difference. Hence I would recommend that Roy make contact with the NZ group (e.g. K.P. Black) to make them aware of the inadequacy of their data set for the design of artificial waves. Since they are also based in NZ, and presumably “neutral” observers, perhaps this would motivate them to visit Roy during one or more surf sessions and make similar path angle and speed measurements.
With regard to time-series…
It would be nice to have the time-series of Doppler based speeds over the course of a ride on a wave. Unfortunately, the inexpensive (and most compact) GPS’s that are presently commonly used to measure surfer (and windsurfer) speeds do not record the Doppler-based observations–only the sequence of times and the spatial locations. The Velocitek S10 that that is the theme of this tread (or its predecessor) does record time-series of (apparently) Doppler based speeds, and hence would help answer some of the present uncertainties. Unfortunately it costs about 3 times as much as a Garmin Gecko 201 (and two Zip-Lock bags) or 2.3 times as much as the Gecko and an Aqua-Pak. For a variety of factors differentiating surfing from windsurfing, combined with the probable errors in position data (and “mapping” onto a finite sized grid in the GPS’s internal calculations) , I do not recommend reconstituting surfing speed estimates from the time and position time-series data that are recorded by the inexpensive GPS’s presently used for most surf speed measurements.