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The additive constant for the tacheometer is
A) f/i
B) i/f
C) f/d
D) f+d
f+d
In tacheometric surveying, the distance D between the instrument station and the staff station is given by the equation D=k⋅s+C, where k is the multiplying constant and C is the additive constant. The additive constant C represents the distance from the optical center of the objective lens to the center of the instrument (vertical axis), which mathematically equals (f+d).
In tacheometric surveying, the distance D between the instrument station and the staff station is given by the equation D=k⋅s+C, where k is the multiplying constant and C is the additive constant. The additive constant C represents the distance from the optical center of the objective lens to the center of the instrument (vertical axis), which mathematically equals (f+d).
D=k⋅s+C — Tacheometric distance equation
k=if — Multiplying constant
C=f+d — Additive constant
The tacheometer operates on the principle of similar triangles. Rays passing through the objective lens converge at the principal focus and form an image on the reticle; the distance from the objective to the principal focus is f, and the distance from the objective to the trunnion (vertical) axis is d. Summing these two fixed internal distances yields the total additive offset (f+d).
The multiplying constant k=if is typically designed to be equal to 100.
The additive constant C=f+d usually ranges from 30 cm to 45 cm for external focusing telescopes.
By inserting an internal anallatic lens between the objective lens and eyepiece, the additive constant C is reduced to zero (0).
Allows direct determination of horizontal distances without chaining/taping.
Increases speed of surveying in rough or hilly terrains.
Requires constant non-zero adjustment factors (C) if an anallatic lens is absent.
Accuracy drops at long sight distances compared to direct precision chaining.
Preparation of topographic maps and contouring.
Location surveys for roads, railways, and reservoirs in hilly regions.
Option A (f/i) represents the multiplying constant (k) of the tacheometer.
Option B (i/f) is the reciprocal of the multiplying constant.
Option C (f/d) is an incorrect geometric ratio with no physical significance in tacheometry.
D is correct — The additive constant of a tacheometer is given by f+d, where f is the focal length of the objective lens and d is the distance from the objective lens to the vertical axis of the instrument.
Remember that for a standard tacheometer fitted with an internal anallatic lens, the additive constant becomes 0 and the multiplying constant becomes 100, simplifying the distance formula to D=100⋅s.