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Hopper Angles
- Thread starter flange
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If the hopper is rectangular in plan view and the slope angles are known, A and B being the angles between the sides and the horizontal plane, then the true angle between the planes of the angled sides (Theta) is ;
Theta = arccos[ -cos(A) * cos(B) ]
Explanation ;
Calculating the angle between any two planes can be done by finding the angle between the normals to the planes. Each normal line has its own direction cosines, (these are cosines of the angles between a line and X,Y and Z respectively), [i,j,k] and the equation is;
Theta = arccos[(i1*i2) + (j1*j2) + (k1*k2)]
Assuming the hopper is rectangular then most of the above cancels out as some of the i and j values are zero. If the hopper is, for example, hexagonal in plan view then all i,j and k values may be used.
Be careful with the signs of the angles, or you will be getting the supplementary angle to the one you're after.
Theta = arccos[ -cos(A) * cos(B) ]
Explanation ;
Calculating the angle between any two planes can be done by finding the angle between the normals to the planes. Each normal line has its own direction cosines, (these are cosines of the angles between a line and X,Y and Z respectively), [i,j,k] and the equation is;
Theta = arccos[(i1*i2) + (j1*j2) + (k1*k2)]
Assuming the hopper is rectangular then most of the above cancels out as some of the i and j values are zero. If the hopper is, for example, hexagonal in plan view then all i,j and k values may be used.
Be careful with the signs of the angles, or you will be getting the supplementary angle to the one you're after.
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