Speed Over Ground

The Need for Speed

Passage Maker - - Contents - Robert Reeder

In our last in­stall­ment we dis­cussed the ba­sic tech­niques of ocean and coastal dead reck­on­ing, which is de­ter­min­ing our lo­ca­tion based on our course and speed since the time of an ear­lier known po­si­tion. In this in­stall­ment we will dis­cuss how to ob­tain our boat speed in the ab­sence of GPS.

SPEED OVER GROUND VER­SUS SPEED THROUGH THE WA­TER

GPS speed, mean­ing Speed Over Ground (SOG), is a mea­sure of our to­tal speed over the sur­face of the earth, re­gard­less of how that speed was ac­com­plished, whether from our own propul­sion, wind, cur­rents, or any other source. Speed Through the Wa­ter (STW) is only the speed of your boat rel­a­tive to the mov­ing medium of the wa­ter.

For ex­am­ple, imag­ine that you are float­ing in a bar­rel in three knots of tidal cur­rent. Your SOG would read 3.0 knots, but your STW, how­ever de­rived, would (al­ways) be zero, no mat­ter how fast the cur­rents are run­ning. For dead reck­on­ing (and many other nav­i­ga­tion ap­pli­ca­tions) we must use STW rather than SOG, so even with an op­er­a­tional GPS, we need to be able to de­rive our STW. Above: A Nordic 40 at speed. In or­der to de­ter­mine your speed through the wa­ter, you want to be up to speed be­fore you pass your first mea­sured mark. Here are sev­eral means of de­ter­min­ing Speed Through the Wa­ter.

DST TRANSDUCERS

For a cruis­ing trawler, the sim­plest so­lu­tion is to have an elec­tronic trans­ducer that tells us our STW. There are stand-alone speed transducers, but for a few hun­dred dol­lars you can get

an all-in-one depth, speed, and sea­wa­ter tem­per­a­ture trans­ducer. There re­ally isn’t much more to say about this one; it’s plug-and-play, com­pletely in­de­pen­dent of GPS, and a su­perb in­vest­ment for any cruis­ing boat.

HULL SPEED

For a full-dis­place­ment (non-plan­ing) hull, the for­mula for boat speed in knots is 1.34 x the square root of the wa­ter­line length in feet, or 2.43 x the square root of the wa­ter­line length in me­ters. For ex­am­ple, the wa­ter­line length of my boat is 25 feet, so the square root of that is 5, which is mul­ti­plied by 1.34, equalling a hull speed of 6.7 knots. Which is about right.

Hull speed is es­sen­tially the the­o­ret­i­cal max­i­mum speed that a dis­place­ment-hull ves­sel can make; things like draft, hull shape, and clean­li­ness will de­ter­mine how much power is nec­es­sary to at­tain that the­o­ret­i­cal speed.

For pur­poses of nav­i­ga­tion, this is

use­ful only when run­ning at full speed, but it is a good start­ing point and max­i­mum for con­sid­er­ing the fol­low­ing tech­niques.

MEA­SURED MILE

Once upon a time, heav­ily trav­eled shore­lines were dot­ted with Mea­sured Miles for de­ter­min­ing a ves­sel’s speed.

They were drawn as two par­al­lel sets of range-marker tow­ers on shore, set pre­cisely one nau­ti­cal mile apart. A ship ran the dis­tance be­tween the two sets, and from that was able to de­ter­mine their Speed Made Good (SMG) for the du­ra­tion of that mile. In or­der to cor­rect for the ef­fects of cur­rents, the ship would run back and forth along the mea­sured mile sev­eral times, and then di­vide the to­tal time of the runs by the num­ber of runs. This gave the skip­per a best es­ti­mate of STW at a given shaft rpm. For our pur­poses, one run on each leg is suf­fi­cient; the more runs we do, the more the speed of the cur­rent will change, so we will ac­tu­ally start to lose ac­cu­racy by try­ing to col­lect too much data.

If you hap­pen to be near one of the re­main­ing Mea­sured Miles, by all means take ad­van­tage of it. Oth­er­wise, any par­al­lel sets of nat­u­ral or ar­ti­fi­cial ranges will work. They don’t even have to be an even mile, as long as you know the ac­tual dis­tance be­tween.

For this ex­am­ple, my nat­u­ral ranges were a charted road and a wharf, both of which hap­pen to run due north and south, per­pen­dic­u­lar to a har­bor chan­nel which runs due east and west. The two ranges are al­most pre­cisely one nau­ti­cal mile apart, which is ideal for this ex­am­ple, but you may or may not be so for­tu­nate in the real world.

This ex­am­ple is Port Canaveral, Florida, run­ning the Canaveral Barge Canal at cruis­ing rpm. My ranges are look­ing down the Mor­ton’s Salt wharf on the west­ern side of the Mid­dle Basin, and look­ing down Cruise Ter­mi­nal Drive be­hind the Dis­ney Cruises wharf. For ease, I have noted on the charts high­lighted la­bels, “Mor­tons” and “Dis­ney.”

For each run I want to be up to full cruis­ing speed be­fore I cross the first range,

For a full-dis­place­ment (non-plan­ing) hull, the for­mula for boat speed in knots is 1.34 x the square root of the wa­ter­line’s length, in feet, or 2.43 x the square root of the wa­ter­line length in me­ters.

and to re­main at that speed un­til I’m past the sec­ond range be­fore I slow and turn to run the re­cip­ro­cal course. Any watch with a sec­ond hand will work for this, but a good stop­watch or smart­phone with a stop­watch fuc­tion is re­ally help­ful. I will round my times up or down to the near­est six-sec­ond in­ter­val (tenth of a minute) to sim­plify the math.

My first run is west­bound, 8 min­utes and 12 sec­onds, or 8.2 min­utes. Us­ing the “60 D street” for­mula (60 x Dis­tance in nau­ti­cal miles / Time in min­utes and dec­i­mal min­utes = speed in knots), 60 times 1.0 nau­ti­cal miles is 60, di­vided by 8.2 is 7.3 knots.

My sec­ond run is east­bound, 6 min­utes and 36 sec­onds, or 6.6 min­utes. 60 times 1.0 = 60 di­vided by 6.6 is 9.1 knots.

Then I need to av­er­age these. 7.3 + 9.1 = 16.4 knots, di­vided by two = 8.2 knots Speed Through the Wa­ter.

The same tech­nique can be used even in open ocean, if you still have a func­tion­ing GPS. At a par­tic­u­lar rpm, record your SOG, then run the re­cip­ro­cal course and do like­wise, then av­er­age your SOGs for a rough STW. This tech­nique can be used to de­ter­mine your STW at any rpm, data which could prove valu­able in any num­ber of sit­u­a­tions.

BOAT LENGTH

This tech­nique will yield a far less ac­cu­rate STW than any of the afore­men­tioned meth­ods, but if it is all you have, it’s bet­ter than noth­ing. As you come up on a piece of drift­wood or any­thing else float­ing ( not an­chored!) in the wa­ter, us­ing a wrist­watch or stop­watch count the num­ber of

sec­onds it takes to pass the ob­ject, from bow to stern.

For ex­am­ple, my boat is 26 feet long. I see a small stick float­ing in the wa­ter ahead of me. My boat passes the stick, from bow to stern, in two sec­onds, which means I am trav­el­ing at 13 feet per sec­ond. One foot per sec­ond is 0.6 knots, muli­plied by 13 feet equals 7.8 knots STW.

1 FOOT/SEC­OND = 0.6 KNOTS

The same ex­am­ple in met­ric; my boat is 8 me­ters, and I pass the stick in 2 sec­onds, mean­ing I am trav­el­ing at 4 m/s. One me­ter per sec­ond is 1.9 knots, mul­ti­pled by four me­ters equals 7.6 knots STW.

1 ME­TER/SEC­OND = 1.9 KNOTS

Note that our de­rived speeds are not pre­cisely iden­ti­cal, be­cause 26 feet is not ex­actly 8 me­ters. Savvy nav­i­ga­tors will also note that this is a bit faster than my prob­a­ble hull speed, likely due, in part, to my in­abil­ity to mea­sure time pre­cisely in units less than sec­onds. In this par­tic­u­lar case, as­sum­ing a full-dis­place­ment hull, I would al­ways de­fault to my cal­cu­lated hull speed if it were the lower of the two.

Now, in ad­di­tion to know­ing where we are, we also have a pretty good sense of how fast we are go­ing. With apolo­gies to Heisen­berg.

Good watch.

Above: One easy way to de­ter­mine your speed through the wa­ter is with a tran­ducer that cal­cu­lates speed, like this Sim­rad B744V Depth/Speed/Tem­per­a­ture Trans­ducer. Be­low: NOAA Chart 11478 of Port Cape Canaveral, where one can eas­ily cre­ate their own “Mea­sured Mile.”

Above: The eas­i­est way to set your di­viders to a nau­ti­cal mile is to mea­sure out a minute of lat­i­tude. One minute of lat­i­tude will al­ways equal one nau­ti­cal mile.

Above: Af­ter mea­sur­ing out a nau­ti­cal mile with our di­viders from a minute of lat­ti­tude, we can find a suit­able place on our chart to run against our “mea­sured mile.” Right: We can use the “60 D Street” mnemonic to re­mem­ber the equa­tion for de­ter­min­ing our boat speed.

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