What is the pulley speed ratio formula?
For two pulleys connected by a belt: N1 × D1 = N2 × D2. Rearranged: N2 = N1 × D1/D2. The driven pulley's RPM equals the driver's RPM multiplied by the ratio of driver-to-driven diameters. If driver is smaller (D1 < D2), the driven runs slower (speed reduction). If driver is larger (D1 > D2), the driven runs faster (speed increase).
How is belt length calculated?
The open-belt formula: L = 2C + π(D1+D2)/2 + (D2-D1)²/(4C). C is the center-to-center distance between pulley shafts. The first term is the straight runs (2× distance between pulleys), the second is the half-wrap around each pulley, and the third is a correction term when pulleys differ in size. Add 5-10% slack for installation and tensioning.
What is mechanical advantage?
Mechanical advantage (MA) is the factor by which a simple machine multiplies force. For pulleys, MA equals the number of rope segments supporting the load. A 4:1 system has MA = 4, meaning 25% of the load's weight is needed to lift it. But you trade: rope pulled = MA × distance lifted. Energy is conserved.
Why is real mechanical advantage less than calculated?
Friction in pulley bearings and rope bending around sheaves consumes some force. Each pulley typically has 90-95% efficiency for quality hardware, lower (70-85%) for worn or basic pulleys. A 4:1 system with 90% efficiency per pulley has effective MA closer to 3.3:1. For critical lifts, always design with margin and factor in efficiency losses.
How does pulley size affect torque?
In belt drives, power is conserved: P = Torque × RPM, so reducing speed by ratio R increases torque by R (ideally). A 2:1 speed reduction doubles torque. This is why heavy loads use large driven pulleys (high torque, low speed) and motors use small driver pulleys (modest torque at high speed). The motor doesn't need to be high-torque if you provide mechanical reduction.
What's the difference between V-belt and timing belt?
V-belts have trapezoidal cross-section that wedges into matching grooves — high friction, cheap, slip slightly under load (1-3%). Timing belts have teeth that mesh with toothed pulleys — zero slip, exact ratio, but more expensive and require specific pulleys. Use V-belts for general power transmission, timing belts where precise positioning matters (engines, robotics, 3D printers).
Why does my belt slip?
Common causes: insufficient tension (most common), worn belt or pulleys, oil/grease contamination, pulley misalignment, overload, wrong belt size, glazing from heat. Check tension first (about 1/64" deflection per inch of span). Replace belt if cracked or stretched. Realign pulleys. For chronic problems consider upgrading to a higher-grip belt or timing belt.
Can I use any rope in a block and tackle?
No. Use rope rated for the load with appropriate safety factor (usually 5:1 for static, 10:1 for dynamic). Pulleys have minimum rope diameter — too small causes wear, too large jams. Don't use shock-loaded or knotted rope. For lifting people, use rated rescue rope only. Soft fiber ropes lose strength when wet — synthetic ropes (Dyneema, polyester) are typically better.
What's belt speed and why does it matter?
Belt speed = π × Diameter × RPM (in ft/min for D in feet). It indicates how fast the belt is moving. Flat belts max around 4000 ft/min, V-belts around 6000 ft/min, timing belts up to 10,000+ ft/min. Above limits, belts can stretch, heat excessively, slip, or fail. Belt speed also determines power capacity — higher speed = more power transmitted per unit belt cross-section.
How do I know how many pulleys to use?
For block and tackle, count rope segments supporting the moving block. A single movable pulley = 2 segments = 2:1. A double block (2 sheaves) + single block = 3:1 or 4:1 depending on rope routing. More pulleys = more advantage but more friction loss. For most household lifts, 4:1 is plenty. Climbing rescue: 3:1 (Z-drag) is standard. Sailing: 6:1 for mainsheets.
What's a compound pulley system?
A compound system combines two or more simple pulley systems in series. Example: a 2:1 feeding into another 2:1 gives 4:1 mechanical advantage overall. A 3:1 feeding a 3:1 gives 9:1. Compound systems achieve high MA with fewer pulleys per block — useful when space is limited or maximum advantage is needed. Common in heavy rigging and rescue.
Is this calculator accurate for V-belts?
It uses outside diameter for simplicity, which is fine for flat belts and general planning. V-belts actually use "pitch diameter" — the diameter where the belt sits in the groove, slightly less than outside diameter. For precise V-belt calculations, subtract about 0.5" from each pulley's outer diameter to get pitch diameter, then use that in the formulas. The error is typically under 5% with this calculator.
