# Visibility questions

Hello. 2 questions, one of which I think is a math problem and the other of which is technical and has to do with airplanes.

1. I am standing somewhere on the earth where the terrain is perfectly level for literally as far as the eye can see. I have some kind of binoculars or other optical device that allows me to see basically forever. How far away will my 6-foot tall friend have to be before I cannot see him due to the curve of the earth?

2. What do pilots mean when they talk about “10 miles” visibility, etc (i.e. at such times it often seems like you can see a lot further than 10 miles).

Thanks!
Jeremy L

This calculator http://www.ringbell.co.uk/info/hdist.htm indicates that the distance to the horizon for a viewing height of 5.5 feet, I figure my eyes are about 6" lower than the top of my head, is 2.9 miles. It also calculates that for 6’, the distance is 3 miles. So if you count the top of your friends head to your eyes, it looks to be 5.9 miles.

Someone else will soon appear to answer the second part.

That’s so cool. I was just thinking about that, as I was staring at a large fishing boat on the horizon of Lake Huron last week. Sometimes you forget you’re standing on a sphere. It makes me wonder what the difference is, in degrees of plumb, by comparing the two at six miles apart. I could probably figure out the math, but I’m lazy. Yet, it’s cool to think about; we’re all standing at different angles to each other. Why, some people are walking upside down compared to me (of course, it looks the other way around to them. Ahhh, relativity.)

Presumably that is the same question as “How many degrees of latitude is 6 miles?”

Quick and rough calculation - assuming the earth is a sphere.

The circumference is 24,880 miles.

6/24880 x 360 = 0.0868 degrees, or about 5.2 seconds of arc.

(One degree latitude is about 69 miles; longitude degrees obviously vary.)

I found this definition of flight visibility, attributed to the US DoD:

“The average forward horizontal distance from the cockpit of an aircraft in flight at which prominent unlighted objects may be seen and identified by day and prominent lighted objects may be seen and identified by night.”

Huh, I did not know that. Cool.

Visibility for aviation is measured in statute miles (5,280 feet), whereas other distances in aviation are measured in nautical miles (6,000 feet).

Other countries have different methods. Australia uses nautical miles for distance, feet for altitude, and kilometres/metres for visibility.

Of particular use in aviation, one degree of latitude is very close to 60 nautical miles, which means a minute of latitude is equal to 1 nm. The latitude markings can therefore be used as a 1:1 ruler.

A nautical mile was originally *defined *as one minute of latitude. Not just “very close”, but equal, by definition. It has since been redefined as 1852 metres exactly, which happens to be about 0.999 minutes - close enough to make no difference in practice.

I’m not going to work it out either, but I’ll mention an interesting fact: the Humber Bridge in England, one of the longest suspension bridges in the world, has its two main towers 1410m or 4626 ft (a little under a mile) apart. The towers are 36mm (about an inch and a half) further apart at the top than at the bottom, due to the curvature of the earth.

Yes I know. It used to be equal, now it is very close. Would you have preferred I said “very very close”? ;). I’m sure if I’d said “equal” someone would have piped up to explain that it is not quite equal.

Steady on, there. I wasn’t arguing with you. I was pointing out that the “very close” was more than just a coincidence. Some people reading this thread might not have known that, so I clarified the point. No offence intended.

None taken, the was added in an attempt to tone down my post.