Estimating or Judging Distances in the Field

by Alan Sheehan BE

There are several different methods in use to judge or estimate distances in the field. Three are often referred to in Map Reading texts as the most common methods, but I will also introduce a fourth method based on what sort of detail or features you can see on common objects...

The Unit of Measure Method

This consists of using a distance which the viewer is familiar with to estimate other distances. The viewer may be familiar with how long a football field is, or an olympic swimming pool, or a cricket pitch, or a building block, etc. The idea is to visualise how many of the viewer's chosen lengths will fit into the distance to be estimated. It is useful for relatively short distances, say up to 400-500 metres. It is also usually pretty important that the viewer can see all the ground continuously from viewpoint to the object or destination.

The Appearance Method

Using this method the viewer judges the distance to an object by comparing its size with that of its surroundings. It takes a lot of practice to become expert at this, but under some circumstances this method can be extremely valuable.

A variation of this method is to measure the angle subtended by an object of known height or length. For information on how to use a handspan at arm's length to do this, refer to The Bushwalker's Guide to the Galaxy at http://www.ix.net.au/~als/impnav.htm. Another way of achieving the same result is to estimate the faction of the field of view of a pair of binoculars (if available) the object occupies, or to compare the object to the size of the sun or moon (0.5 degree).

The following table gives the distance to objects for various measured (observed) angles. A reference of 1 metre is also give so if other items of known height are observed (eg cliffline) simply mutliply the distance for one metre by the height in metres to get the actual distance.

Remember, the object's apparent size is inversely proportional to the distance away it is. ie. double the distance halves the size.

Distances (in metres) to Common Objects of a given Apparent Size in Angular Degrees

	Size of Object in degrees...	0.1	0.5	1	2	5	10	15	20	30	45	60	90
Object	Dimension of Object, m		(Same size as sun or moon)		(Width of 1 Knuckle at Arms Length)		(Width of Fist at Arms Length)	(Small handspan at Arm's Length)	(Average handspan at Arm's Length)
1 metre	1	573	115	57	29	11	6	4	3	2.0	1.3	1.0	0.8
Sheep (1m tall)	1	573	115	57	29	11	6	4	3	2.0	1.3	1.0	0.8
Car (1.5m tall)	1.5	859	172	86	43	17	9	6	4	2.9	2.0	1.6	1.1
Fence post (1.5m tall)	1.5	859	172	86	43	17	9	6	4	2.9	2.0	1.6	1.1
Short person (1.5m tall)	1.5	859	172	86	43	17	9	6	4	2.9	2.0	1.6	1.1
Tall person (2m tall)	2	1146	229	115	57	23	11	8	6	3.9	2.7	2.1	1.5
4WD (2m tall)	2	1146	229	115	57	23	11	8	6	3.9	2.7	2.1	1.5
1 floor of highrise (4m tall)	4	2292	458	229	115	46	23	15	12	7.8	5.3	4.1	3.0
Car/4WD (5m long)	5	2865	573	286	143	57	29	19	14	9.8	6.7	5.2	3.8
Small shipping container (6m long)	6	3438	688	344	172	69	34	23	17	11.7	8.0	6.2	4.5
Large shipping container (12m long)	12	6875	1375	688	344	138	69	46	35	23.4	16.0	12.4	9.0
Yellow Box (medium tree - 10-30m tall)	20	11459	2292	1146	573	229	115	77	58	39.1	26.7	20.7	15.0
Radiata Pine (tall tree - 50m tall)	50	28648	5730	2865	1433	573	287	192	145	97.6	66.8	51.8	37.6

Now... if you want a rule of thumb to remember rather than this table of numbers, it is this: an object one metre high subtends and angle of 1 degree when it is 57 metres away. So, a 10 metre tall pole that appears as high as the diameter of the moon (0.5 degree) is going to be 10 x 57 / 0.5 = 1140 metres away approximately.

The Bracketing Method Method

With this method the viewer decides on a maximum and a minimum distance that the object could be from the viewing point and than takes an average between the two distances. For example, it may be decided that a particular object is more than 200 metres away but less than 600 metres. Therefore the distance, in this case, would estimated at 400 metres.

The Visibility Method

This method is based on what you can and can't see at different distances. It is generally accepted that the resolution of the human eye is about 1 minute of arc (1/60 degree). In theory this should mean that something that subtends and angle at the eye bigger than 1 minute (of arc) should be able to be seen, and something smaller cannot. Unfortunately, it is not quite that simple. Everybodies eyes are different so some will see better than others. Lighting will affect what can and can't be seen, as well as colour, contrast, clarity of the atmosphere, air movement (heat haze, wind, etc), and even the shape of an object (lines are more easily seen than dots or spots), etc.

Now after all that, you may be wonder what use this method is at all, but it is just as useful as any other judgement method. Below are presented some theoretical distances at which the listed objects or features should be on the limit of visibility. With a bit of practice, you can develop your own list which suits your own eyes (conduct your own calibration!) and provided you are then aware of all the other factors which can affect your "seeing" you are well on the way to being a reliable distance estimator! Even without calibrating your own eyes, the theoretical distances will probably yield a closer estimate than most people would guess without experience.

To illustrate how the system works, say we can see a peron in the distance: we can distinguish the person's head and legs from their torso but can't really distinguish their arms (though our mind tells us they are there!!!). From the table below this would indicate the person was between 500 and 700 metres away.

Theoretical Distances to Features on the Limit of Visibility

Feature	Distance
Car	7 -17.5 km*
Windows in car	3.5 km
Wheels on car	3 km
Headlights (off)	700 m
Number plate	525 m
Characters on number plate	315 m
Doorhandles	175 m
Individual Wheel nuts	90 m
Panel Joints (dark coloured vehicle)	35 m
Grooves in tyre tread	20 m
Person	1.7 - 7 km*
Head	700 m
Legs	700 m
Arms	500 m
Hands	400 m
Ears	170 m
Eyes	90 m
Fingers	90 m
Finger nails	35 m
Telegraph Pole	1 - 35 km*
Cross arm on telegraph pole	420 m - 7 km*
Insulator	350 m
Bolt on cross arm	140 m
Woodgrain	4 m
Guide posts (beside road)	3.5 km
Reflector (white, daytime)	300 m
Screw in reflector	20 m
Individual sand grains	3.5 m
Individual stones, 10mm Blue Metal (road gravel)	35 m
Individual stones, 20mm Blue Metal (road gravel)	70 m
Individual blades of grass	10 m
Individual trees (10 m tall)	35 km
Crown of Eucalypt	20 km
Tree trunk	1 - 3.5 km
Large branches	700 m
Small branches	200 m
Individual pine needles	3.5 m
Individual gum leaves	105 m
House	21 - 52 km*
Roof and Walls distinguishable	10 km
Roller door	10 km
Doors and windows	7 km
Brick chimney	2 km
Metal chimney	750 m
Individual steps	700 m
Fascia	700 m
Guttering	350 m
Corrigations in cladding	250 m
Doorhandle	250 m
Individual bricks	250 m
Individual roof tiles	100 m
Pointing between bricks (similar colour to brick)	35 m
Shoe	300 m
Sock	250 m
Wallet	300 m
Shirt or jacket	2.4 km
Tent	5 km
Sleeping bag (open)	3 km
Sleeping bag (rolled)	875 m
Trangia Stove	750 m
Karabiner	40 m
Rock hat / hard hat	600 m
Back pack	2.1 km
Cave / Rope pack	1.1km
Stretcher	2.5 km
Paling fence	5.5 km
Individual palings	350 m
Wire fence post (timber)	700 m
Steel post	150 m
Wire	11 m
Nails / wire staples	11 m
Railway Carriages	17.5 km
Wheels on railway carriage	4.2 km
Carriage windows / doors	4 km
Individual railway sleepers	900 m
Rails	560 m
Individual stones in railway ballast	175 m
Bolts in rails and fishplates	140 m

* First figure is the distance at which the feature is identifiable as that feature, the second is the distance beyond which it should not be visible.

The data in the above table assumes items of similar colour, and brightness as its surrounds. High contrast items are easier to see. For example, a light will be easier to see if turned on rather than off (obviously!) and how much so will depend on it's brightness. The joins (gaps) between the panels of a car are much easier to see on a white car than a dark coloured one, again due to the contrast of the shadows in the gaps compared to the white panels.

Lines are easier to see then dots, spots or other shapes. Consider how much easier it is to see a 10 gauge fence wire at a distance than it is to see a ball bearing of the same diameter! In fact, some scientific tests have shown the human eye can see lines 3 times thinner than it should theoretically be able to (ie about 20 seconds of arc!), though these tests were for black lines on a white page (excellent contrast).

Now for those of you who like a rule of thumb again, try this one... an object is at the limit of resolution (for the human eye) when it is 3500 times its size away. So consider a car, 1.5 metres tall, 5 metres long. You should be able to begin to resolve it as a car at 1.5 x 3500m = 5.25km away, but at 5 x 3500m = 17.5 km it should be barely visible at all. In between, it should be able to be seen as a spot but not resolved into a car (our mind will often do this for us though if the context - eg it is moving along a road - suggests it is a car).

Important Points About Estimating Distances

Remember that objects seem closer than they really are when:
• the light is bright or the sun is shining from behind the viewer;
• they are bigger then other things around them;
• there is hidden ground between them and the viewer;
• they are higher up then the viewer.

Objects seem farther away than they really are when:
• the light is bad or the sun is in the viewer's eyes;
• they are smaller than other things around them;
• the viewer is looking across a valley, or down a ravine or creek;
• the viewer is lying down;
• the object is against a dark background.

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Oberon State Emergency Service / handcrafted by Alan Sheehan / Alan Sheehan / revised April 10,2002.