Estimating Ranges at Sea

[jimp]

Sorry Whaler Friends, this should get JimH calculating. Also for those winter doldrums (a state or period of inactivity).

So in the long range planning shop of Alaska DOT&PF we got to discussing Morse code, signal flags, and semaphore - time well spent. At home I found my 1972 Edition of the Naval Training Command Boatswain's Mate 3 & 2 Rate Training Manual (NAVTRA 10121-E), I'm sure you all have a copy at home (The 1982 edition is available http://www.amazon.com/Boatswains-Traini ... B0038ZHBDS). Lots of good stuff on signaling.

But where is the Whaler connection? Page 335 - Estimating Ranges of Surface Targets. This is the stuff that 18-yr olds are using as lookouts in the fleet (USN and USCG).

QUOTE:
To estimate distances accurately, you must have a reference point whose range you know, or you must know the size of the object whose distance you are estimating. If you know both the size of the target and the range of the reference, the job is a little easier. At sea you are not likely to have a set reference point, but in daytime the horizon usually can be seen and it moves with your ship. Hence, the horizon is the logical point to use as a reference. The distance to the horizon varies with the height of eye above the water. Figure 15-20 shows approximate distances in yards to the horizon from various heights of eye (Measured in feet). For example, if your eyes are 30 feet from the waterline where you stand at your gun station, the horizon would appear to be approximately 12, 750 yards away. If height of eye is 25 feet, the range would be 11,550 yards.

The key to estimating ranges is the appearance of the main deckline in relation to the horizon. (See inset in fig. 15-20) That is, does the deckline lie above or below the horizon? If above, what percentage of the freeboard shows above and how much shows below the horizon? If the deckline lies below the horizon, try to determine the size of the space between the deckline and the horizon in relation to the amount of freeboard of the target. Is the space equal? Half as great? A third as great?

Now let's see how estimating ranges works by setting up a hypothetical (assumed) situation. We will say that the height of eye is 30 feet; therefore, distance to the horizon is approximately 12, 750 yard. Assume a target with 20 feet of freeboard. If the target is placed on the horizon, the range will be 12,750 yards. (It must be understood that all ranges are approximations) As we move the target in towards our own ship, more and more of the freeboard will be seen below the horizon and less and less above, until all of the freeboard will be below the horizon, and you will be able to see more and more water between the main deckline and horizon.

When our target reaches a position where the deckline appears to be on the horizon, the range is a third of the distance to the horizon, as shown in figure 15-20. At a range of 6375 yards it appear as though three-fourths above, or 15 feet and 5 feet respectively. At 8500 yards, half the freeboard shows below the horizon. At 2500 yards, it appears there is space between the deckline ad horizon equal to about one-fourth the freeboard or a total of 25 feet from the waterline to a line between the eye and the horizon.

Figuring ranges as explained is merely a question of proportion; this is further described in the remainder of the topic. We have here two similar triangles. A line from the EYE to the HORIZON and a line along the surface of the water form two common sides of the two triangles (fig. 1-21). A line from the EYE to the WATERLINE and the TARGET itself form the corresponding sides of the two triangles (third sides). Triangle AC is similar to triangle EBD. Therefore, ED is to AC as BD is to BC.

You can work out tables or charts yourself, with the correct height of eye and distance to the horizon and any size or sizes of target, by applying the following formula.

Height of eye above the waterline =
Height horizon appears above waterline at target

Distance of own ship from the horizon =
Distance of target from horizon (X or unknown quantity)

Example:
30 ft = 12,750 yards
20 ft X

By cross-multiplying:

30 = 12,750 yds. = 255,000 yds.
20 X 30X

X = 255,000 yds. = 8500 yards - Distance of target from horizon.
30

12,750 yards - Distance of own ship from horizon
-8,500 yards - Distance of target from horizon
4,250 yards - Range of target from own ship.

Make two or three of these charts for different sizes of targets and memorize key combinations which will serve to aid you in quickly figuring out other combinations. Then every time you have a chance to get an exact range on a ship, make an estimate and check your estimate against the radar or rangefinder. Note the size of the target and its position in relations to the horizon. Enough practice of this type beforehand will enable you to take a quick look at a target ad estimate an opening range if the need arises. At first your estimated ranges probably will not be very accurate, but practice will bring them close to accuracy. In any event, they will be much better than haphazard guesses. A salvo fired with an opening range of this sort will be close enough for spotting.
UNQUOTE

What is your height of eye aboard your Whaler? At 6.5 feet, your horizon is approximately 3.0 nautical miles away.
1.17 times the square root of your height of eye = Distance to the horizon in nautical miles