Face calculations provide a useful glimpse of production.  STOPECALCTM provides calculations of indicated tonnage, grade and value based on volume projections. The user has options to calculate simple length-density-weighted average grades or to utilize area-density weighting.  In the general case, area-weighting should produce more representative results.


A single face can be calculated by clicking on CALCULATE at the lower left-hand corner of the Results section.  The Calculate All option on the Header menu will calculate all faces in the selection not already designated Final.  Up to 50 intervals may be entered and calculated for a single face; that is, face calculations occur on the first 50 intervals entered.


Assumptions

STOPECALCTM makes some assumptions behind the calculations:


Unsampled material is zero grade tonnage dilution in both length-weighted (LW) and area-weighted (AW) calculations.


Volumes are based on measurements and prismatic shapes assuming no curvature.  They are approximations to be reconciled to survey by adjustment.


Area weighting of sample results is appropriate in most cases; double weighting, density with length or area weighting is always the best option.  Areas must be supplied for all faces.  Normally, these are digitized based on the photos and need only be relatively correct--units are unimportant because the areas are normalized to the actual face area by STOPECALCTM.  However, if areas are not, or can not be digitized, they must be imported as, or otherwise set equal to the sample lengths.  In this case, length and area weighting results will be identical.


Sample database is valid--no characters or negative values in assays.


User has correctly defined the economic zone by assigning one, or more contiguous assays in each face to it.  If there is a second ore lens in the face, such as at an intersection of veins, and if the development will split into two drifts to follow each vein, then the face should be split into two separate faces to facilitate volumetrics and tonnage accounting by vein.  This is also necessary if a resuing method is used for mining cuts.  


Units are ppm (g/T) for precious metals and % for other metals.  All tonnages and densities are expressed as metric units.


STOPECALCTM  uses standard weighted average formulas, expressed generally as:


Weighted Avgx = w1w2x1 + w1w2x2 ...wnwn+1xn


w = relative weight (%)                              

x = value                                                  


The formulas are equivalent to EXCEL sumproduct (w1,w2,wx) / sumproduct (w1,w2).  The denominators for calculating the relative weights in the grade and face density calculations are the products of the sum of the sample lengths (or areas) multiplied by sample densities (L x D) for length-weight calculations, or the sum of the sample areas multiplied by sample densities (A x D) for area-weight calculations.   The calculation includes an adjustment in the denominator for any positive difference between a measured (not Auto Calc'd)  face width and the total sample width.                              


AutoCalc Calculation Options

The face width can be calculated indirectly from the total length of the sample line if the AutoCalc box is checked.  In v2, this is taken as the largest 'To' value in the group of samples.  This is not always the correct option if: 1) Entire face was not sampled; 2) The face is tapered and additional dilution was taken; 3) The face is wider than the sample line, on average.


Additionally, the sample line may not be horizontal, especially for those mines where samples are taken across the vein true width. If Autocalc is checked, STOPECALCTM  corrects the face width by the cosine of the Line Dip field to convert it to horizontal width.  This ensures proper volume calculation from the face dimensions.  It does not affect the length-weighted average grade calculation for the sample line which is based on the individual sample lengths.


Face influence can be input manually or calculated with the AutoCalc option based on FaceId's specified in PrevFace and NextFace fields.  Calculated distance is derived in two steps.  First, the distances between the central coordinates of the face in question and the adjacent faces are calculated and stored (Dprev and Dnext):


Influence (I) is then calculated as

 

I = 0.5 * Dprev + 0.5 * Dnext


Face influence permits the calculation of the volume attributable to each face.  For development faces blasted and mucked individually, tonnage and grade based on Influence can't be tied directly to the rounds produced, thus round calculations will generally supplant preliminary reports based on Influence.   Where a sample line is one of a series taken across the back of a stope or the walls of a raise, the volumes based on influence will generally compose the best estimates of production.


Economic Zone Averages

Economic zone grade averages are simply weighted by length or area.  Density is constant based on the Project Setup value and no dilution is assumed.


Face Averages

Face averages comprise the economic portion (ore)  and the waste portion, weighted by their respective lengths or areas, and by their respective densities.  Face density thus normally falls between the waste and ore densities. If the face width is greater than the sampled width, the extra material is treated as waste with zero grade and waste density. It's important to fit the sampling as close to the face width as possible if there is any grade in the wall-rock in order to get the most accurate accounting of dilution grade.