The actual formula for horizon distance during normal daytime is:
Max_Distance[miles]=2.08 * sqrt(Observer_Height[m])
This is based on the curvature of the earth AND the refractive index of air at sea level at a certain temperature and latitude.
By combining the vision fields of the observer and the target, the maximum distance at which the target mast can be seen is:
Max_Distance[miles] = 2.08 * (sqrt (Observer_Height [m]) + sqrt (Target_Height [m]))
Judging from the Type VII dimensions, the observer's eye must've been at around 5 meters:
Heigth = 9.60 m (31 ft 6 in)
Draft = 4.72 m
Railing Height = 1.4 m
Average man = 1.7 m
Eye Height = 9.6-4.72-1.4+1.7 = 5.18 m
Which gives us a 4.8 mile horizon distance (8800 meters).
Thus, a ship with a mast of 25 meters above water would be visible at 15.1 miles (28 kilometers!).
By climbing up on the periscope you gain 5 more meters on the observer height (let's say a total of 10 meters). So:
Which gives us a 6.6 mile horizon distance (12,225 meters).
And a ship with a mast of 25 meters above water would be visible at 17 miles (31.5 kilometers!).
Of course, the real situations were very different. To actually SEE something, let alone identify it properly, it would need to be much closer. What's important is that beyond 8 kilometers you wouldn't be able to see the waterline of ANY ship. Weather conditions, funnel smoke, lighting conditions, all have a major effect.
|