179172760 Conveyor Design Draft Xls

The values are not linked with anywhere….. 2 4 R= 40 m 3 7 6 5 10 m 500 m CONVEYOR PROFILE

8

1 9

m

2

CONVEYOR DESIGN by IS - 11592 : 2000

Material : Bottom Ash

Lump Type Lump Size Type

Flowability / Material Characteristic

Maximum Lump Size : 300 mm

Capacity C : 960 TPH

Bulk Density of Material ρ : 0.800

Input Data & Calculation:

Width of Belt B : 1200 mm As per IS 11592, Table 3

Lump Size Factor : 4

Air Bone Factor : 0

Abrasiveness Factor : 2

Speed Factor : 6

Belt Speed V : 3 m/s As per IS 11592, Table 6

Angle of Inclination δ : 14 ° As per IS 8730, Table 3

Angle of Surcharge ψ : 25 ° As per IS 8730, Table1

Angle of Repose : °

Slope Factor K : 0.91 As per IS 11592, Table 9

Maximum Capacity of a Belt C : 439.56 t/h

Corresponding Values:

Maximum Belt Capacity C : 464 t/h

Trough Angle λ : 20 ° As per IS 11592, Table 10

Belt Width B : 1200 mm

Cross Sectional Area A : 0.129 As per IS 11592, Table 7

Selected Belt Width B : 1.2 meter

Actual Belt Speeds V : 2.84 m/s

Belt Type : t/m3 KL K_AB KAS K_V Where, KV = ( KL + KAB + KAS ) Over 35 and up to 40 (for ρ=1.0 t/m3_{, V=1.0 m/s, K=1.00)} m2 Coal Uniform Size

Sized, in permissible Range Average Flowing

CONVEYOR DESIGN by IS - 11592 : 2000

Peripheral Force on the Drive Pulley : 17822 N

Main Resistance R : 2717 N

Artificial friction coefficient f : 0.02

Conveyor length (distance between centers) L : 100 m Mass of revolving idler parts along the carrying : 15 kg/m side of the conveyor per meter

Mass of revolving idler parts along the return : 15 kg/m side of the conveyor per meter

Mass of belt per meter : 7.7285 kg/m

Mass of handled material on conveyor : 93.912 kg/m per meter

Slope angle of conveyor from horizontal line in δ : 14 ° the moving direction

Secondary Resistance : 2164 N

Inertial and frictional resistance at the loading : 757.21 N point and in the acceleration area between the

Handled material and the belt

Volumetric Capacity Q : 0.3333

Q= A.V.K

Handled material conveying speed : 0 m/s

component in the direction of belt motion

Frictional resistance between handled material : 258.38 N and the skirt plates in the acceleration area

(V+V0) 2

Interskirt Plate Width : 0.8 m

Acceleration length in loading area : 0.7648 m

Coefficient of friction between material : 0.6 and belt

Coefficient of friction between material : 0.5 and skirt plate

Wrap Resistance between belt and pulley : 610.47 N not to be calculated for drive pulley

Rw = 9B 140+0.01. t for fabric carcass belt

B D

Rw = 12B 200+0.01. t for steel cord belt

B D

Average Belt Tension in the Pulley : 17115N 3E-005

Belt thickness t : 0.1 m T_E T_E = (R + R_S + R_SP1 + R_SP2 + R_SL) R = f . L . g. [ m_c + m_r + (2 m_B + m_G). Cosδ] m_c m_r m_B m_G m_G = 1000.ρ.Q / V R_S R_S = R_a + R_ska + R_w + R_b R_a R_a = Q . 1000 . ρ . ( V - V₀ ) m3_/s V₀ R_ska R_ska = μ2.Q2.1000ρ.g.

l

l

l

Pulley Bearing Resistance : 537.53 N not to be calculated for driving pulley d

D

Shaft diameter inside diameter d : 0.15 m

Pulley diameter D : 0.5 m

Vectorial sum of the two belt tensions : 35835N 1E-010

acting on the pulley and of the forces

due to the mass of the revolving parts of the pulley

Special Resitance : 1886 N

Resistance due to idler tilting : 1.5099 N

In case of carrying idlers equipped with three equal length rollers

A constant : 0.5

coefficient of friction between carrying : 0.35 idlers and belts

Angle of tilt of the idler axis with respect i : 2 ° to a plane perpendicular to the

longitudinal axis of the belt

Length of installation equipped with : 0.5 m tilted idler

Resistance due to friction between Handled : 84.491 N material and skirt plates

Length of installation equipped with : 1 m skirt plates excluding

Frictional resistance due to belt cleaners : 0.048 N Area of contact between belt and belt : 0.1 cleaner

Coefficient of friction between belt and : 0.6 belt cleaner

Resistance due to friction at the discharge plough : 1800 N

Scraping factor : 1500 N/m

Slope Resistance : 11055 N

Lift of conveyor between loading end and H : 12 m dicharge end : : : : : : : : : : : : : : : R_b R_b=0.005 R_v R_v R_sp R_sp = (R_sp1+R_sp2) = (R_i + R_sk + R_bc + R_p ) R_i R_i = g.C_i.μ₀.L_i (m_B+m_G) cos δ. sin i C_i μ₀ L_i R_sk R_sk = μ2.Q2.1000ρ.g.

l

l

: :

CONVEYOR DESIGN by IS - 11592 : 2000

Φ

Peripheral Force on the Drive Pulley : 17822 N Minimum Slack Side Tensile : 8204.12 N

1

Maximum Peripheral Force : 21386.38 N

Drive Coefficient ξ : 1.2 See IS-11592, Table 15 Coefficient of friction between drive pulley and belt μ : 0.35 See IS-11592, Table 16

Angle of Wrap Φ : 3.67 radian 210 °

: 5191.077 N 8S

Pitch of carrier idler or idler spacing on carrying : 1 m side of the conveyor

Minimum Tensile force to limit the Belt Sag(Return Side) : 592.0756 N 8S

Pitch of return idler or idler spacing on return : 1.5 m side of conveyor

Maximum Allowable Belt Sag S : 0.024 S= h_{a adm}

Minimum Force required in slack side T2 : 8204.12 N

Tension of Tight Side T1 : 26026.11 N

Average Belt Tension at the pulley Tavg : 17115.11 N Vectorial sum of the two belt tensions acting on the Rv : 35835 N

pulley and of the force due to the mass of the revolving parts of the pulley

δ : 14⁰

Ѳ : 30 ⁰

Weight of Pulley Wp : 5000 N

Maximum Operating Belt Tension : -9617.87 N ξ -1 T₁ T₂ 30⁰ T_E T_E T_2min T_{2 min}≥ T_{E max} eμΦ _{- 1} T_{E max} T_{E max}= ξ . T_E

Minimum Tensile force to limit the Belt Sag(Carrying Side) Tmin

T_min≥ Pc (mB+mG) g P_c T_min T_min≥ Pr.mB.g P_r ={ (T₁ * cos(δ) + T₂ * Cos (Ѳ) )2 _+(T 1 * sin(δ) + T2 * sin ( ) + WѲ p )2 }1/2 T_max Tmax = T1 = TE eμΦ _{- 1}

Table 3: Maximum Lumps Sizes in relation to Belt Width

Belt Width Maximum Lump Size Uniform Size Unsized

300 75 100 1 400 75 100 2 450 75 125 3 500 100 150 4 600 125 200 5 650 125 230 6 750 180 300 7 800 180 330 8 900 200 380 9 1000 260 430 10 1050 280 460 11 1200 360 530 12 1350 380 660 13 1400 380 680 14 1500 410 750 15 1600 410 800 16 1800 460 900 17 2000 500 1020 18

Table 4: Lump Size Factor

6 4 0

Material Lump Size

<10 mm 0 4 ₁ Granular <25mm 1 0 2 2 0 3 3 0 4 Lump Size

Factor Air Bone Factor Fine Grain to dust Sized and Unsized <20 percent of maximum permissible lump size Sized, <60% in permissible Range Quantity of largest Lump is <60 percent of maximum permissible lump size

Unsized 4 0

5

4 0

6

Table 5: Abrasiveness Factor

16 2 Non Abrasiv Cereal 1 1 Grains 2 Wood 3 Chips 4 Wood Pulp 5 Fullers Earth 6 Flue Dust 7 Soda Lime 8 Char 9 Loam 10 Sand 11 Ground 12 Gravel 13 2 14 Slate 15 Coal 16 Salt 17 Sand stone 18 Abrasive Slag 3 19 Spar 20 21 Pellet 22 Iron Ores 4 23 Tacontie 24 Jaspar 25 26 Flint Rock 27 Glass cullet 28 Granite 29 Traprock 30 Largest lump does not exceed maximum permissible lump size Sized, in permissible Range Largest lump does not exceed maximum permissible lump size Abrassiven

ess MaterialType of Abrasiveness Factor

Mildly Abrasive Run of bank sand and gravel Limestone Concentrates Very Abrasive Heavey Mineral

Pyrites 4 31 Sinter 32 Coke 33 IS 8730 : 1997

Table 1: Class based on Flowability, Angle of Sucharge and angle of repose

22 4 25 Over 35 and up to 40

Class Flowability Material Characteristic

1 5

Very Free Flowing -uniform size

-Very small round particle -very wet

-or very dry -like silica sand -cement

-wet concrete, etc.

2 10

Free Flowing -rounded -dry polished -medium wight -like whole grain -beans 3 20 Average Flowing -irregular -granular or lumpy -medium weight -anthracite coal -cotton-seed meal -clay, etc. 4 25 Average Flowing -bituminous coal -stone

-most ores, etc

5 30 Over 40 Sluggish Sluggish -irregular -stringy -fibrous -interlocking -like, wood chips -bagasse

-tempered foundry sand, etc. Very Abrasive Surchage Angle Angle of Repose (degree) Over 0 and

up to 20 Very free flowing

Over 20 and up to 30 FlowingFree Over 30 and up to 35 Average Flowing Over 35 and up to 40 Average Flowing

Table 6: Maximum Recommended Belt Speed (m/s) Belt Width in mm up to 500 600 to 650 750 to 800 950 to 1050 1200 to 2000 1 2.5 3 3.5 4 4.5 2 2.3 2.75 3.2 3.65 4.12 3 2 2.38 2.75 3.15 3.55 4 2 2.38 2.75 3.15 3.55 5 1.65 2 2.35 2.65 3 6 1.65 2 2.35 2.65 3 7 1.45 1.75 2.05 2.35 2.62 8 1.45 1.75 2.05 2.35 2.62 Lump Size Lump Type 300 280 0.93 11 1050 1200 Uniform Size 1 300 300 1.0 Unsized 7 750 800 Belt Width 1200 Speed Factor: 6

Velocity 3 For belt size above 2000mm 2.5m/s velocity has been considered.

Belt Type

Fabric Carcass Belt 1

Steel Cord Belt Speed Factor

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Table 7: Maximum Section of the Handled Maaterial in M2 for Triple Roller Troughed Belt

1200 25 20 0.129

Trough Angle in Degree

20 25 30 35 40 45 500 0 0.009 0.012 0.013 0.015 0.017 0.018 10 0.014 0.016 0.18 0.019 0.021 0.022 20 0.018 0.02 0.022 0.023 0.024 0.025 30 0.023 0.025 0.026 0.027 0.028 0.029 650 0 0.018 0.022 0.026 0.029 0.032 0.034 10 0.026 0.029 0.033 0.036 0.038 0.04 20 0.034 0.037 0.04 0.043 0.045 0.046 30 0.042 0.045 0.048 0.05 0.052 0.053 800 0 0.027 0.034 0.04 0.045 0.05 0.054 10 0.04 0.046 0.051 0.056 0.06 0.063 20 0.053 0.059 0.063 0.067 0.071 0.073 30 0.067 0.072 0.076 0.079 0.082 0.084 1000 0 0.047 0.058 0.067 0.076 0.083 0.089 10 0.067 0.077 0.085 0.093 0.099 0.105 20 0.087 0.096 0.104 0.111 0.116 0.12 30 0.109 0.117 0.134 0.129 0.134 0.136 1200 0 0.07 0.085 0.099 0.112 0.123 0.132 10 0.098 0.113 0.126 0.137 0.146 0.154 20 0.129 0.142 0.153 0.163 0.171 0.176 30 0.16 0.172 0.182 0.19 0.196 0.2 1400 0 0.098 0.12 0.139 0.157 0.171 0.184 10 0.138 0.158 0.175 0.191 0.204 0.214 20 0.179 0.197 0.213 0.22 0.237 0.245 30 0.221 0.238 0.253 0.264 0.272 0.277 1600 0 0.13 0.159 0.185 0.208 0.228 0.244 10 0.182 0.209 0.233 0.253 0.27 0.283 20 0.236 0.261 0.282 0.3 0.314 0.324 30 0.293 0.315 0.334 0.349 0.36 0.366 1800 0 0.167 0.203 0.237 0.266 0.292 0.313 Belt Width

10 0.233 0.268 0.298 0.324 0.346 0.363 20 0.302 0.334 0.361 0.384 0.401 0.414 30 0.374 0.403 0.427 0.446 0.46 0.468 2000 0 0.207 0.253 0.294 0.331 0.362 0.388 10 0.29 0.332 0.37 0.403 0.429 0.45 20 0.376 0.415 0.448 0.476 0.49 0.514 30 0.465 0.501 0.53 0.554 0.571 0.581 2200 0 0.257 0.311 0.363 0.408 0.446 0.478 10 0.357 0.408 0.455 0.494 0.527 0.552 20 0.461 0.508 0.549 0.584 0.61 0.629 30 0.569 0.613 0.649 0.677 0.697 0.71 2400 0 0.303 0.368 0.428 0.482 0.528 0.566 10 0.423 0.484 0.539 0.586 0.625 0.656 20 0.547 0.604 0.653 0.694 0.725 0.748 30 0.677 0.729 0.772 0.806 0.83 0.845 2600 0 0.36 0.439 0.51 0.573 0.628 0.672 10 0.502 0.575 0.64 0.695 0.741 0.777 20 0.648 0.716 0.774 0.822 0.859 0.885 30 0.801 0.863 0.914 0.953 0.982 0.999 2800 0 0.413 0.505 0.585 0.66 0.721 0.774 10 0.578 0.663 0.727 0.803 0.885 0.897 20 0.749 0.827 0.894 0.95 0.993 1.025 30 0.928 0.998 1.063 1.104 1.137 1.158 500 0.018 650 0.034 800 0.053 1000 0.087 1200 0.129 1400 0.179 1600 0.236 1800 0.302 2000 0.376 2200 0.461 2400 0.547 2600 0.648

Table 8: Maximum Section B of the Handled Material in m2 fro Two Equal Idler Troughed Belts and for the Flat Belts

..

Two Idler Troughed Belts Trough Angle

Flat Belt 15 20 25 300 0 10 0.001 20 0.002 30 0.004 400 0 0.005 0.007 0.009 10 0.008 0.01 0.011 0.002 20 0.01 0.012 0.013 0.005 30 0.014 0.015 0.016 0.008 500 0 0.01 0.012 0.015 10 0.014 0.017 0.019 0.004 20 0.018 0.021 0.023 0.009 30 0.023 0.025 0.027 0.014 650 0 0.017 0.023 0.027 10 0.025 0.03 0.037 0.008 20 0.033 0.038 0.041 0.016 30 0.042 0.045 0.048 0.025 800 0 0.027 0.036 0.042 10 0.039 0.047 0.053 0.013 20 0.052 0.059 0.064 0.026 30 0.065 0.071 0.076 0.04 1000 0 0.044 0.057 0.069 10 0.064 0.076 0.86 0.021 20 0.084 0.095 0.104 0.042 30 0.106 0.116 0.123 0.065 1200 0 0.066 0.085 0.102 10 0.095 0.112 0.127 0.03 20 0.125 0.14 0.153 0.062 30 0.156 0.17 0.181 0.095 1400 0 Belt Width (mm) Surchage Angle

10 0.042 20 0.086 30 0.132 1600 0 10 0.56 20 0.114 30 0.175

Table 9: Slope Factor K Table 10: Maximum Capacity of a Belt Conveyor in tonnes/hour

14 0.91 25 439.56 1200

Trough Angle in Degree

2 1 20 25 4 0.99 500 0 35 43 6 0.98 10 51 58 8 0.97 20 67 74 10 0.95 30 84 90 12 0.93 650 0 56 80 14 0.91 10 94 107 16 0.89 20 123 135 18 0.85 30 153 165 20 0.81 800 0 100 123 21 0.78 10 145 168 22 0.76 20 192 212 23 0.73 30 241 260 24 0.71 1000 0 172 209 25 0.68 10 242 277 26 0.66 20 315 348 27 0.64 30 392 421 28 0.61 1200 0 252 307 29 0.59 10 355 407 30 0.56 20 464 511 30 576 619 1400 0 352 432 10 497 569 20 644 709 30 795 857 1600 0 468 572 10 655 752 20 849 939 30 1054 1134 1800 0 601 731 Conveyor

Inclination Factor KSlope Belt Width

10 839 965 20 1087 1202 30 1346 1451 2000 0 745 911 10 1044 1195 20 1359 1494 30 1674 1803 1 2 500 0 67 74 650 0 123 135 800 0 192 212 1000 0 315 348 1200 1 464 511 1400 1 644 709 1600 1 849 939 1800 1 1087 1202

Table 10: Maximum Capacity of a Belt Conveyor in tonnes/hour Table 11: Mximum Capacity of a Belt Conveyor in tonnes/hours

1 20 464

Trough Angle in Degree

30 35 40 45 15 50 56 62 67 300 0 65 70 75 79 10 80 85 89 92 20 96 100 103 105 30 93 106 116 125 400 0 21 119 130 139 146 10 30 146 156 163 169 20 40 174 182 188 192 30 50 144 163 180 194 500 0 36 186 203 217 229 10 53 229 244 255 265 20 67 274 287 296 302 30 84 243 274 301 323 650 0 64 308 336 359 378 10 96 374 339 417 432 20 121 446 464 482 489 30 151 357 403 443 475 800 0 99 453 493 525 554 10 143 551 587 615 633 20 188 655 684 705 720 30 236 500 565 615 662 1000 0 161 630 687 734 770 10 232 767 792 853 882 20 304 911 950 979 997 30 381 666 749 820 878 1200 0 238 839 911 972 1019 10 342 1015 1080 1130 1166 20 450 1202 1256 1296 1317 30 561 853 957 1051 1127 1400 0 Belt Width (mm) Surchage Angle

Two Idler Troughed Belts Trough Angle

1073 1166 1245 1307 10 1299 1382 1443 1490 20 1537 1605 1656 1685 30 1058 1191 1303 1397 1600 0 1332 1451 1544 1620 10 1613 1713 1793 1850 20 1908 1994 2055 2091 30 3 4 5 6 80 85 89 92 146 156 163 169 229 244 255 265 374 339 417 432 551 587 615 633 767 792 853 882 1015 1080 1130 1166 1299 1382 1443 1490

Table 11: Mximum Capacity of a Belt Conveyor in tonnes/hours Flat Belt 20 25 5 10.5 15.8 27 33 36 41 10 45 49 20.5 55 58 31 46 55 61 69 17 76 83 34 92 98 52 83 98 109 123 30 137 148 60 165 175 93 129 154 171 193 47 214 233 95 258 274 146 208 248 275 310 75 344 374 154 417 443 235 306 367 403 457 111 504 551 225 612 651 345

Two Idler Troughed Belts Trough Angle

153 311 475 201 410 630

CONVEYOR DESIGN by IS - 11592 : 2000

Peripheral Force : 17822 N

Operating Power Requirement on Drive Pulley : 50.606 kW

1000

Absorbed Power : 53.866 kW

+

1000 1000

Wrap resistance between belt and pulley for drive pulley : 610.47 N

Pulley bearing resistance for drive pulley : 537.5 N

Motor Output Power (shaft) : 56.701 kW

PM =

Efficiency of various trasmission element : 0.95 See IS-11592 table 12

Additional power required due to tripper : 79.169 kW

+

1000 1000

Number of trippers : 5

Factor for extra power for each tripper β : 0.1 See IS-11592 table 13or14

T_E P_DP P_DP = TE . V P_A P_A = TE . V ( Rwd + Rbd )V R_wd R_bd P_M P_A η₁ η₁ P_a P_a = TE . V _(1+n tβ) ( R_wd + R_bd )V n_t

CONVEYOR DESIGN by IS - 11592 : 2000

Idler Spacing (Normal Circumstances) : 1200 mm See IS:11592, Table 17

For Carrying Side

Belt Sag for Considered Idler Spacing S : 0

S = For Return Side

Belt Sag for Considered Idler Spacing S : 0

S =

Minimum Tensile force on Belt between Spacing : N

Selected Idler Spacing is Safe

Transition Distance x : m

x = 0.707y E 1/2

Vertical Distance Between Belt Rise or y : m

lowers during transition

y = ₃ When pulley is in line with _{top centre idler roller} y = _{3 When pulley is elevated}

Belt Modulus E : 500 N/mm

Induced Belt Edge Stress in the Transition : N/mm See IS:11592, Table 18 : : : : : : : : : : : : : : : : : : P_c (m_B+m_G) g 8.Tmin P_{r .} m_B .g 8.T_min T_min ΔT B sinλ B sinλ ΔT

CONVEYOR DESIGN by IS - 11592 : 2000

See IS:11592, Table 17

CONVEYOR DESIGN by IS - 11592 : 2000

Selection Of Belt

Factor of Safety Factor of Safety: : 10

Full Thickness Tensile Strength of Belt : -96178.6626 N

*Select the Belt Type

Selectecd Belt : Belt Type

Belt Thickness t : m

Grade of Cover Thickness : N17

Conveyor Carrying Side Thickness : 2.5 mm

Belting Pulley Side Thickness : 1.0 mm

Elevator Carrying Side Thickness : 1.5 mm

Belting Pulley Side Thickness : 2.5 mm

:

Diameter of Pulley D :

Driving Pulley and Pulley Exposed to high tension : mm

Snub Pulley in the return run under lower tension : mm

Bend Pulley for a change of Direction of the belt : mm

of less then 30° : : : : : : : : : : See IS-1891 (Part-1) Annex A See IS-1891(Part-1) Table 8 and IS 3181 for PVC Belt

Factor of Safety:

Textile Belt Textile Belt: 9 to 12.5, Generally 10 Steel Cord Belt Steel Cord Belt: 7 to 10, Generally 7

Belt Type

Textile Rubber Belt Textile Rubber: 1.0 to 3.0 mm M24

PVC Belt PVC belt: 0.8 to 1.2 mm N17

DETERMINATION OF CONVEYOR SECTIONAL AREA AS PER C.E.M.A

TYPICAL CONVEYOR CROSS-SECTION

= angle which the surface of the material assumes with the horizontal while the material is at rest on a moving conveyor belt

l = 0.371 x b + 0.25

Cross-sectional area of material on conveyor , sq. in

BELT WIDTH a b A A Belt Bulk. Dnst. Capacity l l

mm in deg. deg. sq. ft sq.m Speed m/s Te/Hr. in mm

800 32 25 20 0.6728 0.063 0.84 800 151.2151 12.12 307.90 450 18 25 20 0.1881 0.017 2 800 100.6383 6.93 175.97 500 20 25 20 0.2391 0.022 1.2 800 76.7525 7.67 194.82 600 24 25 20 0.3593 0.033 2 800 192.2602 9.15 232.51 750 30 25 20 0.5853 0.054 2 800 313.2048 11.38 289.05 900 36 25 20 0.8661 0.08 2 800 463.4721 13.61 345.59 1000 40 25 20 1.0838 0.101 1.83 800 530.6457 15.09 383.29 1050 42 25 20 1.2017 0.112 2 800 643.0621 15.83 402.13 1200 48 25 20 1.5921 0.148 1.25 800 532.4842 18.06 458.67 1350 54 25 20 2.0373 0.189 2 800 1090.21 20.28 515.21 1500 60 25 20 2.5373 0.236 2 800 1357.768 22.51 571.75 1800 72 25 20 3.7017 0.344 2 800 1980.852 26.96 684.83 2100 84 25 20 5.0852 0.472 2 800 2721.226 31.41 797.92 2400 96 25 20 6.688 0.621 2 800 3578.892 35.87 911.00

NB : Results are verified against CEMA's Publication

l₁

a = angle of surcharge , degrees

= 25 O _{for bituminous coal or lignite}

b = angle of the idler roll , degrees

b = width of belt , inches

Standard edge distance , c =0.055b + 0.9 , inches

b = l + 2m + 2c m = 0.2595 x b -1.025

A = [ 0.371b + 0.25 + (0.2595b - 1.025) cos b ] x [ ( 0.2595 b -1.025 ) sin b ]

+ (π a/180 - sin 2a / 2 ) X [ { 0.1855 b + 0.125 + (0.2595 b - 1.025 ) cos b}/ sin a ] 2

Detail Proof

As = area of surcharge , sq. in ( area ABC ) Ab = base trapezoidal area , sq. in (area AFGC) l = length , smaller edge of trapezoidal area , inch l₁ = length , larger edge of trapezoidal area , inch

j = height of trapezoidal area , inch m = slant length of trapezoidal area , inch r = radius of surcharge angle, inch

f = horizontal projection of slant side of trapezoid , inch c = edge distance , edge of material to edge of belt ,inch b = width of belt , inch

Standard edge distance c = 0.055 b + 0.9 inch

Ab = 0.5 (l + l₁) x j b = l + 2 x m + 2 X c l₁ = l + 2 x f f = m x cos b l = 0.371 x b +0.25 c = 0.055 x b + 0.9 Solving , m = 0.2595 x b -1.025 j = m x sin b

Area of whole sector (ABCD) = π x r2 _{x 2 x a /360}

Area of triangle (AECD) = r2 _{x 0.5 x sin ( 2 a)}

Surcharge area , As = r2 _{x {π x a / 180 - 0.5 x sin ( 2 a) }}

r = 0.5 x l₁ / sin a