The Size of an Object at a Distance

What does a human head, say 1' in size, appear as when viewed from a rescue vessel 1/10th of a nautical mile away (a standard track spacing for a search pattern)? Here is the math let's make a simple model... Draw a right triangle ABC where A is the position of your eye, B (right angle) is the foot of the object, and C is the top of the object. BC=1 foot, the height of the object.

You are saying that if AB=1, then angle A, which is the resulting angle taken by the image (45° or pi/4 rad) will make the object appear 1 foot tall.

We need to assume something else, that the apparent height of the object is proportional to angle A, the angle it uses in our field of vision.

If AB = x feet, then tanA = 1/x and so the object will appear to be A/45° = arctan(1/x) / 45° feet high. For x=600 this equals arctan(1/600) / 45° = 0.002122 or about 1/471 ft.

1/471 of a ft is really small! About .03”….  Again, if you want to visualize that, chop an inch into 100 equal pieces - .03 of an inch is 3 of those slices, laid end to end.

The period at the end of this sentence is .04 of an inch…

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for a more in-depth explanation of the size of an object at a distance, please see this reference:

http://en.wikipedia.org/wiki/Angular_diameter

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