How does reduced pulley effort change rope travel?
Engineering calculators (Beta)
Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
上の固定滑車と下の動滑車を見分けます。荷物を支えているロープはこの例では2本です。
mは荷物と動滑車の合計です。nは滑車の個数ではなく、支えるロープの本数です。
荷と動滑車を合わせた質量 m
100 kg
荷を支えるロープ本数 n（1・2・4）
2
滑車系全体の効率 η
90 %
荷の上昇距離 h
1,000 mm
荷の上昇速度 v
0.1 m/s
荷の上向き加速度 a
0 m/s²
引く力が減る分、引くロープは長くなります。荷がh上がると、この例のロープは2h動きます。
Fpull · 引く力（損失込みの概算）
544.814 N
引くロープの移動量
2,000 mm
引くロープの速度
0.2 m/s
Distinguish the top fixed pulley and lower moving block. Two rope strands support the load here.
m includes the load and moving block. n counts supporting strands, not pulley wheels.
Mass of load and moving block m
100 kg
Supporting rope strands n (1, 2 or 4)
2
Overall reeving efficiency η
90 %
Load lift distance h
1,000 mm
Load upward speed v
0.1 m/s
Load upward acceleration a
0 m/s²
Reduced effort requires more rope travel. Raising the load by h moves 2h of rope in this example.
Fpull · Pulling force including estimated loss
544.814 N
Rope pulling distance
2,000 mm
Rope pulling speed
0.2 m/s
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
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2. Example inputs
Mass of load and moving block mWhat goes here?
This is mass, including fixtures or loads that move with it where required. Kilograms describe mass; newtons describe force.
100 kg
Supporting rope strands n (1, 2 or 4)What goes here?
Match the field symbol to the diagram and check dimensions, specifications or operating conditions. Replace example numbers with your actual conditions.
2
Overall reeving efficiency ηWhat goes here?
The fraction of input delivered as useful output. η=80% means 0.8 with 20% loss. Check whether the input unit is percent or fraction.
There is no universal recommended efficiency. Use curves or measurements at the actual load, speed and temperature. For a combined train, use consistent input/output boundaries and ηtotal=η1×η2…; do not count losses twice.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
90 %
Load lift distance hWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
1,000 mm
Load upward speed vWhat goes here?
Distance travelled per time. Check whether the field asks for initial, final or constant speed.
0.1 m/s
Load upward acceleration aWhat goes here?
Change in velocity per time. Check signs for acceleration along travel versus deceleration.
0 m/s²
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Pulling force including estimated loss
544.814 N
Rope pulling distance
2,000 mm
Rope pulling speed
0.2 m/s
More supporting strands reduce ideal effort but increase rope travel. Count supporting strands in the diagram, rather than pulley wheels.
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
Vertical lifting in the illustrated 1-, 2- or 4-strand arrangement. n counts load-supporting strands, not pulley wheels. Strands are parallel, inextensible and do not slip. η is overall reeving efficiency, not efficiency per wheel. a is instantaneous upward acceleration and must exceed −g. This does not size fixed supports, ropes, bearings, dynamic load factors or holding brakes.
