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The multiplying constant for the tacheometer is, generally, kept a
100
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In tacheometry, the multiplying constant (k or K) is a ratio of the focal length of the objective lens (f) to the distance between the top and bottom stadia hairs (i). It converts the staff intercept (s) into horizontal distance. For standard tacheometers, this value is intentionally fixed and kept at 100 to simplify distance calculations.
In tacheometry, the multiplying constant (k or K) is a ratio of the focal length of the objective lens (f) to the distance between the top and bottom stadia hairs (i). It converts the staff intercept (s) into horizontal distance. For standard tacheometers, this value is intentionally fixed and kept at 100 to simplify distance calculations.
K=ifтАЛ тАФ Multiplying constant
C=f+d тАФ Additive constant
D=Ks+C тАФ Horizontal distance formula for horizontal line of sight
Tacheometry is an optical method of distance measurement based on the principle of isosceles triangles, where the ratio of the distance from the vertex to the base and the base length remains constant. By designing the telescope optics such that K=ifтАЛ=100, the horizontal distance equation D=Ks+C simplifies directly to D=100s+C.
The multiplying constant (K) is generally kept at 100.
The additive constant (C=f+d) is usually kept at 0 by providing an anallatic lens in modern tacheometers.
Using an anallatic lens makes the distance directly proportional to the staff intercept (D=100s).
Eliminates the need for physical chaining or taping over rough terrain.
Provides rapid survey measurements for topographic mapping.
Significantly simplifies field office calculations when K=100 and C=0.
Precision is lower compared to precise electronic distance measurement (EDM) or invar tape chaining.
Accuracy decreases at longer sight distances due to reading errors on the staff.
Contouring and topographic surveying in hilly or rugged terrain.
Location surveys for roads, railways, and reservoirs.
The additive constant C=f+d ranges from 30┬аcm to 45┬аcm for external focusing telescopes and 8┬аcm to 20┬аcm for internal focusing telescopes.
Anallatic lens (invented by Porro) reduces the additive constant C to strictly zero.
B is correct тАФ The multiplying constant of a tacheometer is fixed at 100 to simplify the calculation of horizontal distances.
Remember that for an ideal tacheometer fitted with an anallatic lens, K=100 and C=0, reducing the distance equation to D=100s.
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