CALCULATION OF EMERGENCY BRAKING DISTANCE OF LOADED BOXN RAKE

By; M.K.De, Lecturer/C&W/IRIMEE

FIG. : 8.45

A B C D E

Force/BC = (/4)d2 x PBC

d = 355 mm, PBC = 3.8 kg/cm2

Resistance offered by spring = 125 kgf/BC

Effective force (K)= (/4)d2 x PBC - 125 = 3644 kgf = 3600 kgf (rounded)

620

335

497

458

i = (458/497) x 12 = 11.05

Total braking force (FBB) = (Ki – 12 Q)x η

η = Rigging efficiency = 0.9

Q = force of SAB

(FBB) = (3600 x 11.05 – 12 x 200)x 0.9 = 33642 kgf

Total brake block force /wagon (FBB) = 33642 kgf

Total brake force of locomotive = 79150 kgf

Coefficient of friction loco brake block = 0.084

Coefficient of friction wagon brake block = 0.15

Weight of locomotive = 118800 kg

Gross weight/wagon = 81280 kg

Number of wagons/rake = 58

Weight of the train = 4714240 kgf

Effective moving load, considering 5% additional load for rotating inertia

= 1.05X4714240 = 5074692 kgf

Specific rolling resistance for loco (SRRL)

= 2.16 + 0.011V + 0.00038V2 kgf/ton, where V is in KMPH

Specific rolling resistance for wagon (SRRW)

= 0.64 + 0.011V + 0.000073V2 kgf/ton, where V is in KMPH

SRRL100 = 7.06 kgf/ton

Total rolling resistance for loco at 100 kmph = 7.06 X 118.8 = 839 kgf

SRRW100 = 2.47 kg/ton

Total rolling resistance for wagon at 100 kmph = 2.47 X 4714.240 = 11644 kgf

Loco braking force = 79150 X 0.084 = 6651 kgf

Wagon braking force = 33642 X 58 x 0.15 X 0.85 = 248783 kgf

Total retarding force = 839 + 11644+ 6651 + 248783 = 267917 kgf

Maximum retardation = (267917 X 9.81) / 5074692 = 0.518 m/s2

Average retardation = 0.518 / 2 = 0.259 m/s2

Free running time (t1) = 5 s

Free running distance (S1) = (100 X 5) / 3.6 = 139 m

Brake development time (t2) = 21 s

Distance traveled during brake development period (S2), using relation, S = ut – ½ ft2

= 27.78 X 21 – ½ X 0.259 X 212 = 526.27 m

Speed at the end of brake development period, using relation, V = u – ft,

= 27.78 – 0.259 X 21 = 22.341 m/s = 80.4 kmph

Total rolling resistance for loco at 80.4 kmph using relationship at = 654 kgf

Total rolling resistance for wagon at 80.4 kmph using relationship at = 9410 kgf

Total retarding force at 80.4 kmph = 654 + 9410 + 6651 + 248783 = 265498 kgf

Distance traveled to stop after brake development period

= ½ x (4833040 X 22.342) / (265498 X 9.81) = 463 m

Retardation = (265498 X 9.81) / (5074692) = 0.513 m/s2

Time taken to stop after brake development period (t3), using relation, V = u – ft,

= 22.341 / 0.513 = 44 s

Total braking distance = S1 + S2 + S3 = 139 + 526 + 463 = 1128 m

Total stopping time = t1 + t2 + t3 = 5 + 21+ 44 = 70 s

Thank you