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The multiplying constant for the tacheometer is
f/i
i/f
f/d
f+d
f/i
In a stadia tacheometer, the horizontal distance D is given by the formula D=KтЛЕs+C, where K is the multiplying constant and C is the additive constant. The multiplying constant K is the ratio of the focal length of the objective lens (f) to the stadia interval (i).
In a stadia tacheometer, the horizontal distance D is given by the formula D=KтЛЕs+C, where K is the multiplying constant and C is the additive constant. The multiplying constant K is the ratio of the focal length of the objective lens (f) to the stadia interval (i).
K=ifтАЛ тАФ Multiplying constant definition
C=f+d тАФ Additive constant definition
D=Ks+C тАФ Basic tacheometric distance equation
The tacheometric intercept s is the length intercepted on the staff by the stadia hairs. From similar triangles formed by the stadia hairs and the objective lens of the tacheometer, the ratio of the distance to the staff relative to the intercept is constant for a fixed telescope configuration, defined as K=f/i.
The constant K is typically maintained at 100 for most modern tacheometers.
The focal length f is a property of the objective lens.
The stadia interval i is the distance between the top and bottom stadia hairs on the reticle.
The multiplying constant is dimensionless since both f and i are lengths.
Allows rapid determination of horizontal distances without chaining.
Efficient for terrain where direct measurement is difficult.
Limited precision compared to EDM (Electronic Distance Measurement).
Requires stable atmospheric conditions to minimize refraction errors.
Topographic surveying
Contour mapping
Preliminary route surveys
The additive constant C=(f+d), where d is the distance from the objective lens to the vertical axis of rotation.
In anallactic telescopes, the design is modified such that the additive constant C becomes zero.
A is correct тАФ The multiplying constant K is defined by the ratio of the focal length of the objective lens to the stadia interval, expressed as f/i.
Always remember that in the distance equation D=Ks+C, K is the multiplying factor (usually 100) and C is the additive factor (usually 0 in modern anallactic instruments).
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