Determination of distances using thousandths. Tourist tips

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Determination of distances using thousandths. Tourist tips

Tourist tips

One way to measure distances according to the angular size of the object is to define them using "thousandths". This method is as follows.

The circle contains 360°. Each degree is divisible by 60', and each minute by 60", i.e. the circle contains 21' or 600".

To obtain the simplest relationship between linear and angular quantities, it is necessary to divide the circle into 6000 equal parts, called "thousandths". In this case, the angular values will be measured not in degrees, minutes and seconds, but in "thousandths".

"Thousandth" - the value of the central angle of the circle, based on the chord, the length of which is equal to 0,001 of the length of the radius (taking into account that at small angles and large radii of the circle, the values of the chord and arc can be equated).

An angle of one "thousandth" in normal degree measurement is equal to 360º / 6000 = 0°.06=3'6=216" and is denoted 0-0,1 "thousandths", or 1-6000.

The angle at 30 "thousandths" is denoted by 0-30, at 123 "thousandths" - 1-23, etc. If in the formula L \u1000d L * P / N replace L \uXNUMXd XNUMX, H \uXNUMXd U (angle of view), then you get the relationship between the angular and true magnitudes of an object and the distance to it

D \u1000d XNUMX x P / U

There is always a sufficient number of improvised measures, the value of which in "thousandths" can be seen in the figures or calculated by yourself.

Hand and fingers in "thousandths"

The angular value, or goniometric "price", of fingers, a fist, a matchbox, a match, a pencil, a twenty-kopeck coin, a sleeve and other improvised objects in "thousandths" is determined in the following way.

The length of the observer's outstretched arm (measured during self-control) is taken, that is, the distance in millimeters from the observer's eye to the object at hand, which can be measured with a thread. Then the value of this improvised object is measured in millimeters and divided by the length of the outstretched arm.

Arm length measurement

The number of thousandths in the decimal fraction obtained from this division gives the goniometric "price" of the chosen item in "thousandths".

Example. The width of an ordinary matchbox is 37 mm. If we take the length of the outstretched arm as 600 mm, then the goniometric "price" of the width of a matchbox will be equal to 37/600 \u0,061d 61, i.e. 0 "thousandth", or 61-XNUMX.

These measures should be used as follows: taking a penny in an outstretched hand, we look to see if it closes the height of the railway booth along its diameter. If the height of the booth is known to us (4 m), then this means that we see it at an angle of 0-25. We find the value of one "thousandth" (4/25 = 0,16 m). Therefore, the distance to the booth will be 0,16x1000=160 m.

Determination of the distance by the height of the object

Determination of distance by the length of an object

Example. It is necessary to measure the distance to the house, the length of which is known and is 40 m. We determine its angular value. Let's say it turned out 50 "thousandths". Then the distance to the house D \u100d P * 40 / Y \u1000d (50 x 800) / XNUMX \uXNUMXd XNUMX m

If the angular value of an object in "thousandths" is measured with a match or a ruler with divisions into millimeters, it must be removed from the eyes by 500 mm (50 cm), then a division of 1 mm will be equal to 1/500, or 2/1000, i.e. .two "thousandths" (0-02).

Author: A.E. Menchukov

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