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    Re: Scale a small area plotting sheet?
    From: Peter Hakel
    Date: 2016 Mar 2, 01:33 +0000
    Speaking of graph paper, a while back I did a little exercise - here is the summary:

    Peter Hakel

    From: Frank Reed <NoReply_FrankReed@fer3.com>
    To: pmh099@yahoo.com
    Sent: Tuesday, March 1, 2016 3:08 PM
    Subject: [NavList] Re: Scale a small area plotting sheet?

    Bill Lionheart, you wrote:
    "Is the idea to print them out for the Lat and Long that you expect to sail before you set off? I have not had much luck with a printer on the boat. Isn't that where the ones with just a compass rose and you draw your own scale win?"
    Well, they work for any longitude, and if you're going to pre-print, I recommend not setting a longitude, equivalently using 0° for the central longitude. And you really don't need to print out many possibilities for most voyages. Consider sailing from Martinique in the Lesser Antilles at latitude 15° N to Mystic, Connecticut at latitude 41.3° N. The scaling factor is cos(lat). We would probably like to get the scaling factor to the nearest percent. That is, if the actual scaling factor for my latitude is 0.832, I could comfortably use a plotting chart with a scaling factor of 0.83. In latitudes outside the tropics, this implies a different plotting scale for roughly every degree of latitude (eventually approaching every 34' of latitude at very high latitudes). From roughly 10° to 22°, it's approximately every two degrees of latitude. So for that fairly long voyage from Martinique to Mystic, you would need about 24 distinct scaling options. You could estimate how long you're going to be in each latitude band, but certainly five sheets per degree should be sufficient... let's call it ten to be safe. That yields 240 sheets of paper, and probably 50 to 80% will end up in the recycle bin when you're done. If you carry generic plotting sheets, you'll use the same number of plotting sheets, but at the end you can put the leftovers back on the shelf. Really not much difference unless you're worried about wasting paper and printer ink. And that's for quite a long ocean voyage. Not many people have such options these days. For most modern yachting, you know you'll be sailing during a particular period of time in a specific region of the globe. 
    I now jump up on a soapbox... Gather ye round!
    Plotting sheets and plotting generally are a damn nuisance. Paper and ink and storage are expensive today, while computation is dirt cheap. Even if you have plotting sheets, unless you're a hardcore celestial navigation enthusiast, it can even be difficult to set aside tabletop space for careful plotting on a modern sailing vessel (credit to Herber Prinz for emphasizing this point over the years). Custom-printed scaled "Mercator" [sic] plotting sheets can also be lost or forgotten at home. They are a weak link in the chain. All of this argues in favor of so-called "Sumner lines" which are simply lines of position drawn from two points on the line rather than an azimuth and intercept. They're much easier to plot and cross for a fix since scaling doesn't matter. You can plot on common graph paper. Even two sheets of lined notebook paper crossed and taped together can be used for plotting. It's much easier than all the fiddling that goes with standard scaled plotting sheets. Note that you have to work out the advancing of lines by a short computation rather than plotting, but that's  a minor disadvantage today (unless you're allergic to calculators). This is how I teach modern celestial navigation.
    Frank Reed
    Conanicut Island USA

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