How far away is the horizon??

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Originally Posted by weeds

There's a calculator? We actually that somebody must have sorted a formula for working it out....

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In the days when "real" maths was taught in school:angel::wasntme:, we learned in yr 8 ("Form 2" as it was called in those days) that as a rough approximation, the distance to the horizon in nautical miles was 1.2 x the square root of your height above the water measured in feet.... thispost reminded me that this was one of those days I actually paid attention:eek::D

so say 2m approximates to 6 feet, and the square root of 6 is 2.5, thus 2.5 x 1.2 = 3 nautical miles which multiplied by 1.8 to convert to km = approx 5.4 km

just goes to show you can learn something useful on this forum every day!! So as Billy Connelly would say...stay awake and pay attention;)

the issue of refraction and total internal reflection is really interesting because due to atmospheric conditions, light is actually internally reflected off upper layer. This phenomenon is most evident travelling the Hay plains west of Narranderah at night... while cruising at 120kmh one night some 30 yrs ago I dipped the lights for oncoming traffic: it took 10 minutes before the traffic passed. Assuming they were cruising at similar speeds, that was a closing speed of 240kmh or 4km /min...thus 40km separation at first sighting. It was a coolish night and I'm assuming the lights were being reflected and refracted between narrow layers of air/water vapour...amazing!

From the Oxford companion to ships and the Sea,

HORIZON from Greek horos, 'a boundary', horizo 'form a boundary', 'limit'.

1. The line which limits an observers view of the surface of the Earth and of the visible heavens. In astronomical navigation three meanings must be distinguished:
a. The visible horizon, that which is actually seen.This however is affected by the dip of the horizon which depends on the refraction of light by the atmosphere and the observers height above above the sea.
b. The sensible horizon, the true horizon at sea level at the observers position on the Earths surface, corrected for dip; it is the projection on the celestial sphere of a plane tangential to the Earths surface at that point.
c. The rational horizon, this is the projection on the celestial sphere of a plane parallel to the sensible horizon but passing through the centre of the Earth instead of tangential to its surface. In measuring the altitude of a heavenly body considered as infinately distant , the radius of the Earth is insignificant, and normally the sensible and rational horizons coincide. For some some purposes, however, they must be distinguished.

Simple really. However your friends may have been close, for the layman, the visible horizon depends on the height it is observed from. and the refraction of light. Next time you are at the beachfront, look to Moreton, we know how far it is away, then check the horizon at different times of the day, on clear days and sunny, and then cloudy days. Look to the gap between Moreton & Redcliffe. Bob

All I know is that it must be a loooooooooooooooooog loooooooooooooooog way because no matter how far or how long I drive towards it, I never seem to get there. :wasntme:

Somewhere way back in my primary school days,we were told that the horizon across water at a height of 6 feet was 14 miles,also that at WW11 crows nest height it was 40 n/miles.

Cape vessels anchored up here are 5-7km out.
From the beach at the waterline they are visible to the water itself.

Lots of equations around to approximate but that calculator that was linked earlier is as good as any. The horizon at sea is going to be as close to any of these equations. The topography of the ground will be the limiting factor unless out on a flat plane.

d= square root of 17 x h, where d is in km and h in meters is what i was taught, that I remember, in some course somewhere in my educational journey. For the 2 metres it works out to about 5.8 km which is close to the web link answer.

Relates to a puzzle we used to ask new starters at the airport.

When you can see 3 or 4 aircraft on approach to the runway (particularly at night) which one was the closest?
Invariably they picked the one lowest in the sky, when it generally was the one highest in the sky. The others being higher above the ground but lower on the local horizon.


Martyn

Standing on the beach with the water lapping at your feet, a person 6' tall can see 3 miles, regards Frank.

Agree with Hoges,

I always used 1.17*sqrt of your height in feet above sea level to give the answer in nm (used it mainly when flying).

Never considered it from sea level, but working it out..

1.17*sqrt6=2.866nm
*1.852nm = 5.3 km.

So a smidge over 5km for a 6 foot bloke on the waterline.

edit - Tanks and I were posting at the same time and looks like we agree.... :BigThumb:

The earth drops away at a rate

h = d^2 / 2R

d = distance from origin
R = radius of earth ~6375 km (near enough for the bush) depends on topography and bearing you are looking at.

so

d h
100 m 1 mm
500 m 20 mm
1 km 80 mm
5 km 2 m
50 km 200 m

this agrees with what was said before that you can see ~5km with your eyes 2m above sea level.