Dead Reckoning

[pabrides]

I was playing with some math today figuring out the best way to use my E6-B flight computer for marine applications.   Somehow my mind went to log lines and sand timers. 

I got the idea that with todays watches, all of which incorporate a second hand, working a log contrary to the old way, which took counting knots to determine speed after a certain time, typically 28 or 30 seconds, a predetermined length of log line might easily be timed to determine speed. 

The following is a list reflecting time in seconds vs speed in knots for a log line extending 60ft:

1 kt   35.5 sec
2       17.8
3       11.8
4       8.9
5       7.1
6       5.9
7       5.1
8       4.4

So you take a fishing line 60 feet long on a cuban rig fishing spool.   Attach a log device to throw into the water which pulls the line.  Throw the log into the sea and start your timer.  When the line pulls taught stop the timer.  Determine your speed over the water using the chart above.  If the spool is held any more than 4 or 5 feet off the water accuracy may suffer.  With high cockpits a longer line would be better; just refigure the knots vs time table.

The math is thus:

1knot = 6076ft ÷ 3600s = 1.6878ft/s

You could have a log line 6076 feet long and spool it off for 3600 seconds which would tell you your speed is 1 knot.  But there's a better, faster way.

60ft of line ÷ multiples of 1.6878 gives time in seconds

Ex: 
60 ÷ 1.6878 = 35.5s for 1 knot
60 ÷ (2 × 1.6878) = 17.8s for 2 knots ...  etc.

You can help me out here and let me know if I got the figures wrong.  Any length of line would do beyond a certain minimum.   I took 60 because in an emergency 10 arms spread would about equal 60ft.  You can kinda sense here that line length doesnt get critical until you reach the higher speeds.

Have fun and give it a try next time you're out on the lake and dont forget to tell us what happened.

Cheers

[P.Rutherford]

That is a good method but between the time the line pays out and goes taught could be a lot.

I was reading in a book, don't remember the title, but in the 1500's aboard ships certain crew members were designated as the hour glass turners- they turned the sand hour glass over and said various prayers at that moment.  

Plenty are the mariners and navigators upon the advent of Loran or GPS let their sextants become dusty...and for good reasons too- time in shipping is money.

Not to disregard your method but here's one I've used extensively to calculate boat speed.  It can be used, loosely, to determine time.  The file's attached.

Paul

[pabrides]

As long as the boat has forward speed of at least a knot my log line method will take no longer than 35 seconds.  But at the cruise speed of a midsized yacht,  say 7 knots, the line will fully extend in only 5.1 seconds.

Ive seen your pdf and its just fine, but it takes two people; one to drop the chip and one to time it's passing the stern.    My line method can be accomplished from the cockpit solo and more closely simulates the original log line proceedure that took three people or more. 

Anyway, its just something to have fun with while at sea. If you want accuracy you have gps - but for the sheer love of marine history we have sextants, compasses, and log lines.

Cheers

[pabrides]

@Paul.

I was intrigued with your Dutch log trick in ascertaining boat speed. I'm very fond of slide rules (SR) in general but especially in how they may be applied to marine use. SRs have been used on ships since about 1620; well before the advent of electronics.

I copied the following from a text which describes how to use a SR to easily calculate boat speed. But what's more the user can do this for any length boat going any speed. The quote is paraphrased:

"Calculate Boat speed with a Dutch Log In the event your knotmeter fails. You may determine your boatspeed by putting the right index on C over .5925 on D Move the cursor over the C-scale value of the LOA of your boat in feet. Without moving the cursor further, adjust the slide until the number of seconds that passed for a chip of wood to move from the bow to the stern is under the cursor. Read the boatspeed under the C index. "

Just replace the LOA with log line length and this works for my log line idea in the original post.

I've tried the math with my SR and it works fine. In cases such as this an SR is much faster to use than a electronic calculater. Imagine, if you will, sitting on the pier watching a boat charge through the channel. By estimating its length, and timing it's passing of some marker on the water or opposite shore, one could calculate its speed quickly. Or already knowing its speed one could calculate its length. All by timing its passing.

BTW - .5925 is the inverse of 1.6878, so you multiply instead of divide using the decimal number.

Cheers