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INSTRUMENT CONSTANT. The
distance from the center of the instrument to the principal focus is the instrument
constant. Usually, this
constant is determined by the manufacturer of the instrument. You should find it stated on the inside of the instrument box.
Externally focusing telescopes are manufactured so that the instrument constant may be considered equal to 1. For internally focusing telescopes, though, the objective in the telescope is so near the center of the instrument that the instrument constant may be considered as zero. This, as you will learn in the following discussion of stadia reduction formulas, is a distinct advantage of internally focusing telescopes. Most modem instruments are equipped with internally focusing telescopes. STADIA REDUCTION FORMULAS. In stadia stadia reduction formulas.Stadia Formula for Horizontal Sights. For aWrite ks for the stadia distance and (f + c) for the instrument constant. Then the formula for computing horizontal distances when the sights are horizontal becomes the following: Where: h = horizontal distance from the center of the k = stadia constant, usually 100 s = stadia interval f +c = instrument constant (zero for internally f= focal lengths of the lens c = distance from the center of the instrument to Figure 8-4.-(A) Angle of elevation and (B) angle of depression. The instrument constant is the same for all readings. Suppose that you are using an externally focusing instrument with an instrument constant of 1.0. If the stadia interval is 1 foot, then the horizontal distance is as follows: h = (100)(1) + 1 = 101 feet.If the stadia interval is 2 feet, the horizontal distance is as follows: h = (100) (2) + 1 = 201 feet.Now suppose that you are using an internally focusing instrument. In this case, the instrument constant is zero and can be disregarded. This is the advantage of an internally focusing telescope. So, if the stadia interval is 1 foot, the horizontal distance is simply the stadia distance which is 100 feet. For a stadia reading of 2 feet, the horizontal distance is 200 feet. Horizontal distance usually is stated to the nearest foot. Occasionally on short distances (under 300 feet), it maybe specified that tenths of a foot be used. Stadia Formulas for Inclined Sights. -Most often angle of elevation. If the line of sight is depressed below the horizontal, the vertical angle is an angle of depression. In either case, you find the horizontal and vertical distances by using the following formulas:These two expressions are called the stadia formulas for inclined sights in which h = horizontal distance v = vertical distance h= stadia distance a= vertical angle f +c= instrument constant Refer to figure 8-5 for clarification of the terms in the stadia formulas for inclined sights. Figure 8-5.-Stadia Intervalinclined sight. Figure 8-6.Ground elevations: (A) Telescope raised and (B) telescope depressed. |
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