A compound weight motor can combine several falling weights through one rope and movable pulleys. The limited-fall arrangement shown here uses three equal driving weights, a balance weight and a winding drum. The calculator finds ideal rope tension and torque, then applies two optional gear-stage speed gains. Rewinding restores the gravitational energy used during descent.
Compound Weight Motor Interactive Calculator
Explore a three-weight pulley motor with an optional two-stage speed-increasing gear train. Enter the mass of each equal driving weight, drum diameter and gear gains. The balance weight is half one driving mass. Torque results use ideal, slowly moving conditions.
Equation Used
- Three equal moving-pulley driving weights and an ideal continuous rope.
- Balance weight is m/2 and remains stationary during the illustrated motion.
- The total weight includes its moving pulley and hanger; their separate masses are not added.
- The drum has a constant effective winding diameter; rope layering is neglected.
- Each gear gain is output speed divided by input speed; both external meshes reverse rotation.
- No descent speed, available drop height, power or operating duration is calculated.
Each of the three moving weights is supported by two rope strands. This gives half one weight as the ideal rope tension. The returning half of the animation represents rewinding with external work.
One rope, three moving pulley loads
Hiscox Figure 42 shows a compound weight motor with three pulley-supported weights, a drum and a tail weight. The drawing here follows that arrangement. Each driving load is supported by two rope strands. Under the ideal slow-motion assumption, the strand tension is half the force of one driving weight.
The animation chooses equal descents for A, B and C while holding the balance weight D at the same height. Each descending pulley lengthens two rope spans. Three descents of h therefore require 6h of rope to leave the drum. The rope remains continuous and tangent to the pulleys throughout the cycle.
On the return half, the drum winds the rope back and raises the weights. That motion requires external work; it is not another power-producing stroke. The two gear close-ups are an optional extension of the drum drive. The two gear-gain controls set their ideal speed ratios.
Understanding a gravity drive
The tool demonstrates how a pulley arrangement changes rope force and travel, and how a speed-increasing gear train then reduces available torque. These are useful comparisons for studying mechanical power transmission.
The model does not establish clock accuracy, equipment capacity, a guaranteed runtime or a safe hanging-weight installation. Real load sharing depends on the constraints, losses and inertia of the assembled mechanism.
Force, torque and energy
For each moving load of mass m, two equally tensioned strands give 2T = mg. The ideal rope tension is T = mg/2. With effective drum diameter D in metres, drum torque is Ï„drum = TD/2.
The gear controls are speed gains: G = r1r2. For ideal gears, output torque is Ï„out = Ï„drum/G. A larger gain produces more output rotation per drum turn and less output torque.
With three equal descents h and no motion of the balance weight, the released rope length is s = 6h. The drum receives work Ts = (mg/2)(6h) = 3mgh, equal to the potential energy lost by the three driving weights. The gear train preserves that ideal work; rewinding requires it to be supplied again.
Default calculation
Each driving load is 5 kg, giving an ideal rope tension of 24.525 N. A 60 mm effective drum diameter gives 0.73575 N·m drum torque. Two 3× speed gains give a 9× overall speed gain and 0.08175 N·m ideal output torque.
In the illustrated 100 mm descent of each driving weight, the rope payout is 600 mm and the released energy is 14.715 J. That is an energy per demonstrated stroke, not a power or runtime. A descent time has not been entered.
Increasing each driving mass doubles torque when mass doubles. Doubling drum diameter doubles torque while halving drum turns for the same rope payout. Increasing either gear gain reduces output torque by the same factor that it increases output rotation.
What this arrangement changes
Multiple moving weights allow more total gravitational energy to be stored within their individual fall distances. The pulley arrangement also increases rope travel while reducing tension relative to one directly suspended load.
More pulleys introduce additional bearing and rope losses in practice. The ideal calculator does not model those losses, transient motion or an escapement. A gear ratio changes torque and speed together; it cannot extend operating time without considering the output load and available stored energy.
Questions about the weight motor
Is the mass input the total of all three weights?
No. It is the mass of each equal driving load A, B and C, including its moving pulley and hanger.
Why is rope tension half one weight?
Two strands support each moving pulley load. In ideal slow motion their combined upward force equals that load’s weight.
Why does the rope move six times as far?
There are two changing spans for each of three equal descents, while the tail weight stays at the same height in this illustration.
Does the upward part produce power?
No. It represents powered rewinding, which restores the energy released during the fall.
Can I calculate how long the motor will run?
Not from these inputs alone. Available fall height, output demand, losses and a speed-controlling load are not specified.
Reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 25, Figure 42 (PDF page 35): compound weight motor for a limited fall.
The animation selects equal descents and a stationary tail weight to make rope-length conservation visible. The optional gear-stage close-ups use illustrative dimensions to show the selected transmission ratios.
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