Planimetric Technique Volumes between two successive contours are obtained by trapezoidal formula and taking into account the frustum Upper most layer, i.e., frustum of pyramid: Vb h An An 1 An An 1 Trapezoidal volume is obtained by: Vb h An An 1 For successive trapezoids: Vb Notations: Vb = bulk volume, acre-f An = area of lower isopach line, acre An+1 = upper isopach line, acre h = contour interval, f h A0 A1 A2 An An htopavg An Convention: When the ratio between successive areas 0.5, use trapezoidal formula Ao = area of zero isopach, acre htopavg = avg thickness of top layer Volume Estimation using Planimeter: Example from Craft & Hawkins Contour Area Acres Ratio of areas h A0 450 A1 375 83 A2 303 80 A3 231 76 A4 154 67 A5 74 48 A6 0 Eqn Used V, ac-ft n/a Map Scale 1” = 1000 ft sq in = 22.96 acres Volume Estimation using Planimeter: Example from Craft & Hawkins Contour Area Acres Ratio of areas A0 450 A1 375 83 A2 303 A3 h Eqn Used V, ac-ft Trap 2063 80 Trap 1695 231 76 Trap 1335 A4 154 67 Trap 963a A5 74 48 Pyr 558b A6 0 Pyr 99c a: V = 5/2 (231+154) = 963 ac-ft n/a b: = 5/3 (154+74+ [154 x 74]^0.5) = 558 ac-ft c: = 4/3 x 74 = 99 ac-ft Map Scale 1” = 1000 ft sq in = 22.96 acres ...2 Volume Estimation using Planimeter: Example from Craft & Hawkins Contour Area Acres Ratio of areas... 76 A4 154 67 A5 74 48 A6 0 Eqn Used V, ac-ft n/a Map Scale 1” = 1000 ft sq in = 22.96 acres Volume Estimation using Planimeter: Example from Craft & Hawkins Contour Area Acres Ratio of areas