Upvote:-2
A couple ways:
Upvote:13
The distance to horizon is approximately 3.6 sqrt(h) where h is the height of the observer in meters and the distance is in kilometers. So your 4.7 km is the distance to the horizon for a person standing on sea level. And from a 30 m tower the distance is 20 km.
Upvote:13
Here is a scale diagram of Warspite in 1918 from this post on World of Warships (only minor modifications were incorporated since Jutland so in tems of rangefinder heights this is representative). From this drawing we can take measurements, which gives the height of the rangefinder above the fire control top on the foremast is about 28m above the top edge of the boot topping (the black band around the hull approximately where the waterline would be). So the height above the water line in combat should have been within a meter or so of 28m.
This would put the geometric horizon at about 19+ km (~21 kyd). So the maximum range at which an opponent could be seen by the range finder would be maybe something like 35 km (~ 38 kyd).
But this is academic for Jutland as visibility was constrained by the weather conditions and the smoke not by the geometric horizon.
(also note the refraction will result in the horizon generally being further away than the geometrical horizon)
Added for information, the longest range hit by one underway warship on another is a toss up between Warspite's hit on Guilio Cesare during the Action off Calabria (the battle of Punta Stilo) July 1940 at ~26 kyds, and Scharnhorst on Glorious in June 1940 at about 26.2-26.5 kyds. The uncertainties in the figures make it difficult to say that the latter was definitely at a longer range than the former.
Upvote:19
Ships have masts. The 5th Battle Squadron was made up of ships that had lookout ("gunnery spotting") positions high enough to cater for the ranges of the guns.
Upvote:45
Battleships were built to engage at range. Even at that time, the rangefinding gear was fairly extensive. Concerning the HMS Barham, one of the ships in the engagement:
Barham was completed with two fire-control directors fitted with 15-foot (4.6 m) rangefinders. One was mounted above the conning tower, protected by an armoured hood, and the other was in the spotting top above the tripod foremast. Each turret was also fitted with a 15-foot rangefinder.
And from the picture you can get a good idea of the height of the conning tower above decks:
For scale note the row of sailors on deck. From the rangefinders position on top of the conning tower, the visible horizon is much farther away. Scaling the diagram found on the Wikipedia page, gives a rough estimate of 120ft above the waterline. Using the formula provided here, (if my math works out), I get a range of 21.6 km, or over 23,000 yds for a minimum range. As pointed out in the comments, the other ships superstructures will project well above the waterline as well, so the actual maximum range you could visually detect another ship would vary by circumstance including the conditions and the height of the structures on the opponent vessals..