Worksheet 24
Name: Zyra Anne May Hapin
Year & Section: BSCE 3A
Date Submitted: 12/08/22
Solve the following problems:
1. Assuming that the hauling capacity of the locomotive is one-fourth of the load on
the driving wheels, what would be the maximum permissible train load that a
locomotive with four pairs of driving wheels of a 22.86 t axle load each can pull on a
level broad gauge track at a speed of 90 km/h. What would be the reduced speed of
the train if it has to ascend a gradient of 1 in 300 with the same train load.
o Solution:
Hauling power of the locomotive = 4 × 22.86 × 0.2 = 18.288 𝑡𝑜𝑛𝑛𝑒𝑠
𝑊 × 0.01184 = 18.288 𝑡𝑜𝑛𝑛𝑒𝑠
𝑊 = 1544.59 𝑡𝑜𝑛𝑛𝑒𝑠 ≅ 𝟏𝟓𝟒𝟓 𝒕𝒐𝒏𝒏𝒆𝒔
18.288 = 1544.59(0.0016 + 0.000008𝑉 + 0.0000006𝑉 2 )
𝑉 = 87.02 𝑘𝑚/ℎ
𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑠𝑝𝑒𝑒𝑑 = 90 − 87.02 = 𝟐. 𝟗𝟖 𝒌𝒎/𝒉
2. Determine the gradient for a BG track when the gradient resistance together with
curve resistance due to a 2.99° curve is equal to the resistance due to ruling gradient
of 1 in 300? Determine the resistance when an 7.96° curve is provided on an MG line
and a train with a total weight of 918.45 t is passing over it.
o Solution:
𝑊
𝑊
+ 0.0004 × 2.99 × 𝑊 =
300
𝑆 = 467.67
∴ 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑓𝑜𝑟 𝑎 𝐵𝐺 𝑡𝑟𝑎𝑐𝑘 𝑖𝑠 𝟏 𝒊𝒏 𝟒𝟔𝟖
𝑆
918.45
918.45
468
𝑅
+ 0.0003 × 7.96 × 918.45 =
𝑅 = 221.01
∴ 𝑇ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑠 𝟐𝟐𝟏
3. Determine the weight in tons that the locomotive can pull on a straight level track if
a BG locomotive has three pairs of driving wheels with an axle load of 21 t and the
locomotive is running at a speed of 120 km/h. Determine also the weight of the train if
it can able to haul on a 2° and a 1 in 100 gradient.
o Solution:
Hauling power of the locomotive = 3 × 21 × 0.2 = 12.6 𝑡𝑜𝑛𝑛𝑒𝑠
Total resistance of train = 0.011272𝑊
12.6 = 0.011272𝑊
𝑊 = 1117.81 𝑡𝑜𝑛𝑛𝑒𝑠 ≅ 𝟏𝟏𝟏𝟖 𝒕𝒐𝒏𝒏𝒆𝒔
Weight of train
1
12.6 = 𝑊(0.0016 + 0.00008(120) + 0.0000006(120)2 +
+ 0.0008)
100
𝑊 = 411.23 𝑡𝑜𝑛𝑛𝑒𝑠 ≅ 𝟒𝟏𝟐 𝒕𝒐𝒏𝒏𝒆𝒔