# if you can only see one degree every 69.4 miles, how is it possible to see a ship go over the earths curveture just a few miles away?

Update:

If you can only see one degree every 69.4 miles on our globe earth which is 24,000 miles in circumference, how is it possible to see a ship go over the curvature of the earth just a few miles away?

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• Who
Lv 7
12 months ago

Is a very simple calculation to work out how far way the horizon is at any height above sea level

(all you need is the height above sea level and the radius or diameter of the earth)

(have a read of some trigonometry)

• D g
Lv 7
12 months ago

Did you never wonder why countries own the water rights out two hundred (200 ) miles from shore

Because a ship cannot see land at sea level for more than 200 miles the top of the mast drops below the horizon of a tall sailing ship.

That means even with the most powerful telescope you can't see anything at the same level as you for more than 200 miles ... So a fort could not see a tall ship farther than 200 miles so it could not protect that water ....

Rt he reason is the earth curves a hundred or so feet for every 200 miles

• Tom
Lv 7
12 months ago

You cant see one degree----69.4 miles is the length of one degree (at the Equator) We can only see 12 miles or so to the horizon

• 12 months ago

Assuming no "atmospheric refraction" and a spherical Earth with radius R=6,371 kilometres (3,959 mi):

For an observer standing on the ground with h = 1.70 metres (5 ft 7 in), the horizon is at a distance of 4.7 kilometres (2.9 mi).

For an observer standing on the ground with h = 2 metres (6 ft 7 in), the horizon is at a distance of 5 kilometres (3.1 mi).

• 12 months ago

Because you are seeing a 3 dimensional object. Close view with a telescope, you see the ship go past horizon from bottom to top.

A little increase in elevation, that horizon extends.

At 300 foot above sea level, I can see the horizon near 20 miles, and ships mostly vanish out to about 25 miles.Larger ships a bit further.

Just a guess here but you get the gist.

• 12 months ago

By not keeping your eye at sea level.

The distance of visibility depends on your "height of eye" above sea level (call it H) and the height of the highest visible part of the target ship (call it T)

If heights are in feet, then the distance (D) is nautical miles is:

D = 1.1 * (√H + √T)

To use easy numbers:

If the base of the funnel of the target ship is 81 feet high and you are standing on the flying bridge at 64 feet above sea level, then you should be able to detect the funnel (perhaps with binoculars) at

D = 1.1 * (√(81) + √(64)) = 1.1 * (9+8) = 18.7 nautical miles (approx. 20 US miles or 32 km)

The line-of-sight from your eye to the funnel will be (ever-so-slightly) above the horizon.

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By the older definition, one degree alongs Earth's "spherical" surface is exactly 60 nautical miles.

Because of how microwaves hug the water surface (sea water is slightly conductive), radar will add 10% or so to that distance.

• Tom S
Lv 7
12 months ago

If I did the math right, at 69.4 miles, that 1 degree is over 1000 feet.

• 12 months ago

Earth's radius is a bit under 4,000 miles. Using Pythagoras' theorm, then for every mile in horizontal distance you see, the curvature of Earth drops about 8 inches. So, 10 miles out, about 7 1/2 feet of the ship above the waterline is hidden by the bulk of the Earth.

• 12 months ago

The Horizon at sea from a beach is 11 miles away

Ships disappear from the Bottom up

One Degree is 1/360th of the Earth's Curvature

A lot more

It is also one Nautical Mile