Well I know that the horizon blocks your view. I was trying to figure it out the starting point that gets shortened by the horizon and any lensing that might occur.
This is what I ended up with:
[FONT=Verdana, sans-serif]Line of Sight [/FONT]
[FONT=Verdana, sans-serif] The outer limit on your Line of Sight are based on your altitude due to the curvature of the Earth. Most of the time there are intervening objects that stop you from seeing very far but on the ocean you can see to the horizon. The higher you are from the water level, the farther you can see. This is why watch towers and crow's nest are built so high up. [/FONT]
[FONT=Verdana, sans-serif] In general the formula is distance in miles is approximately the square root of the height in feet. So if you are in the crow's nest of a ship about 50 ft up then you can see is about 8.7 miles. You can see the top of another ship at double that distance so about 17 miles away. Basically figure out the distance from the height in feet from sea level from the observer and the object being observed separately and then add them together. So if you had an island that had a peak at 1,000 ft then it would be visible from the horizon at sea level for 38.7 miles. Now add the height you can see from the crow's nest and you can first see it about 47 miles away! If you were in a hot air balloon and you were 1,000 ft up you could see it 77 miles away![/FONT]
[FONT=Verdana, sans-serif] If you are in a tower or a high hill you may have a line of sight that goes above a fog so you would be able to see much farther. If it is near dawn or dusk then climbing a few feet can actually change the light level as well. [/FONT]
[FONT=Verdana, sans-serif] A person can be identified as a person from about ¼ of a mile away (about long range) without any aid to vision such as a telescope. Some details can be identified from about 1/8 of a mile away (about longbow range). [/FONT]
[FONT=Verdana, sans-serif] A 1st rate was a little over 200 ft tall. It could be seen for 8 miles and identified as a ship. It could be seen for 16 miles as an object assuming the horizon didn't block it out. General details can be made out at 4 miles. [/FONT]
[TABLE="width: 100%"] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]Distance in Miles[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]General Details[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]Type of Object[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]See an Object[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]1/8 [/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]6'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]3'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]1.5'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]¼ [/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]12'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]6'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]3'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]½[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]24'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]12'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]6'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]1[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]48'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]24'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]12'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]2[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]96'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]48'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]24'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]4[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]192'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]96'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]48'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]8[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]384'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]192'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]96'[/FONT]
[/TD] [/TR] [TR] [TD="width: 25%"] [FONT=Verdana, sans-serif]16[/FONT]
[/TD] [TD="width: 27%"] [FONT=Verdana, sans-serif]768'[/FONT]
[/TD] [TD="width: 26%"] [FONT=Verdana, sans-serif]384'[/FONT]
[/TD] [TD="width: 22%"] [FONT=Verdana, sans-serif]192'[/FONT]
[/TD] [/TR] [/TABLE]
[FONT=Verdana, sans-serif]So in general, not counting the horizon: [/FONT]
[FONT=Verdana, sans-serif]Short Visual Range (-5) – Can easily identify objects. ¼ mile Detect size 3+[/FONT]
[FONT=Verdana, sans-serif]Medium Visual Range (-10) – 4 miles Detect size 5+[/FONT]
[FONT=Verdana, sans-serif]Long Visual Range (-15) – 8 miles Detect size 10+[/FONT]
[FONT=Verdana, sans-serif]Extreme Visual Range (-20) – You can see a ship or several ships and very general size but not what type of ship. 16 miles Detect size 13+. [/FONT]
[FONT=Verdana, sans-serif] So if you are in a crow's nest about 50 ft up then you can see about 8.7 miles. That means that you can see objects at long range at best. You have no chance of seeing objects at Extreme Range since you can't see over the horizon. [/FONT]
[FONT=Verdana, sans-serif] To spot something from a distance is 10 + size – range penalties. Characters have a +5 to spot something that is moving. They have a +5 to spot something in a fairly empty view, such as on the ocean. [/FONT]