BLD-ELEV10-03 · Lesson 3 · 12 clock hours · theory
Sheaves, Roping Configurations, and Counterweighting
Objective. Students will calculate counterweight mass, traction ratio, and rope tension for a given car capacity and roping arrangement using the formulas taught in the course.
⚠ Pending professional review
This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.
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Sheaves, Roping Configurations, and Counterweighting
What Is a Traction Elevator?
A traction elevator moves the car by gripping wire rope between a grooved drive sheave (also called the driving machine sheave) and the ropes themselves. Friction — traction — between the rope and the sheave groove transmits force from the motor to the car and counterweight. Understanding how ropes are arranged and how the counterweight is sized is fundamental to installing, inspecting, and troubleshooting any traction elevator.
Sheaves and Their Roles
The drive sheave is mounted on the motor/gearbox output shaft and is the primary powered sheave. Deflector sheaves redirect the rope path when the drive sheave is not positioned directly above the car or counterweight. Secondary or idler sheaves are unpowered sheaves used in 2:1 roping to create a mechanical advantage. All sheaves must be inspected regularly for groove wear, tread diameter, and alignment. A worn groove can reduce traction and accelerate rope wear — two safety-critical conditions.
Roping Configurations
1:1 Roping is the simplest arrangement. The rope goes from the car, over the drive sheave, and straight down to the counterweight. One sheave revolution moves the car and counterweight by the same distance. The rope pull (tension on each side of the drive sheave) equals the actual load being supported — car weight on one side, counterweight on the other.
2:1 Roping introduces a secondary (idler) sheave on the car or counterweight. The rope's dead end is anchored to the overhead structure; the rope then loops under the car or counterweight sheave, back up over the drive sheave, and down to the opposite side. This halves the rope pull compared to 1:1 but requires the drive sheave to rotate twice as far to move the car the same distance. The mechanical advantage reduces the motor torque requirement, which is why 2:1 roping is used for heavier-duty or higher-capacity installations.
A useful rule of thumb: in 1:1 roping, rope speed equals car speed; in 2:1 roping, rope speed equals twice the car speed.
Counterweight Principles
The counterweight (CWT) balances most of the car's weight so the motor only needs to overcome the net load difference plus friction and acceleration forces. Industry practice and NEIEP references establish that the counterweight is set equal to the empty car weight plus a percentage of the rated load — typically 40 to 50 percent, with 40 percent being the most commonly specified value. Always use the percentage given in the job specification or the manufacturer's data sheet; the worksheet problems in this course use 40 percent unless stated otherwise.
Counterweight formula:
> CWT = Car Weight + (Percentage × Rated Load)
This balance point means the motor lifts or lowers only the unbalanced portion of the load during normal operation, reducing energy consumption and motor size.
Rope Tension and Traction Ratio
Wire rope in a traction system has two critical tensions at the drive sheave:
- T1 — the tight side (heavier side, normally the car side when loaded)
- T2 — the slack side (lighter side, normally the counterweight side when loaded)
For basic calculations in pre-apprentice work, approximate T1 and T2 by dividing the total side load by the number of rope falls supporting that side (important in 2:1 roping).
Traction ratio is T1 ÷ T2. The drive sheave must be capable of sustaining traction without slipping under any operating condition. The Elevator Safety Code (ASME A17.1) sets minimum traction requirements; the machine manufacturer's engineering ensures the groove geometry meets them. As a technician, you must never substitute sheaves or change groove profiles without engineering approval.
Safety factor for wire rope is calculated as:
> SF = Rope Breaking Strength ÷ Maximum Load on One Rope
ASME A17.1 specifies minimum safety factors for suspension ropes; confirm the applicable requirement with your inspector or NEIEP reference tables.
Safety Points
- Lockout/Tagout (LOTO): Before inspecting, measuring, or replacing any sheave or rope component, de-energize the elevator controller, apply your personal lock to the disconnect, and verify zero energy with a test instrument. Sheaves can rotate unexpectedly if the brake releases.
- PPE: Wear safety glasses when near moving rope or when inspecting sheave grooves. Hard hats are required in the hoistway at all times.
- Rope inspection: Never operate an elevator with broken wires, corrosion, or kinking beyond the limits in ASME A17.1 and the manufacturer's data. Tag the equipment out of service immediately.
- Overhead work: Use fall protection when working at heights in the machine room or pit; follow your employer's and the IUEC's fall protection procedures.
- Never bypass the governor or safeties to test traction manually. Any slip test must be performed according to the approved testing procedure with all safety devices active.
Summary
Sheaves direct rope path and create mechanical advantage. Roping configuration (1:1 or 2:1) determines the relationship between motor output and car movement. Counterweight mass is calculated as car weight plus approximately 40 percent of rated load. Rope tension and traction ratio confirm the machine can safely move the car. Every calculation you do in the field has a safety implication — set up your formulas correctly, label your units, and double-check your arithmetic before any equipment is commissioned or returned to service.
Key terms9
Drive SheaveThe grooved wheel mounted on the motor output shaft that grips the suspension ropes and moves the elevator car through friction (traction).
Deflector SheaveAn unpowered sheave used to change the direction of the rope path when the drive sheave is not positioned directly above the car or counterweight.
1:1 RopingA roping arrangement in which the rope runs directly from the car, over the drive sheave, and down to the counterweight; car speed equals rope speed.
2:1 RopingA roping arrangement using an idler sheave on the car or counterweight so that the rope speed is twice the car speed, halving the rope pull and reducing the required motor torque.
Counterweight (CWT)A weighted assembly that balances the car and a portion of the rated load, typically calculated as car weight plus 40 percent of rated load, reducing the net load the motor must move.
Traction RatioThe ratio of T1 (tight-side rope tension) to T2 (slack-side rope tension) at the drive sheave; must remain within limits to prevent rope slip.
Rope Safety FactorThe ratio of a rope's catalog breaking strength to the maximum load carried by a single rope; ASME A17.1 sets minimum values that must be met for the elevator to be placed in service.
Rated LoadThe maximum load in pounds (or kilograms) that an elevator is designed and certified to carry, as specified on the data plate and in the job specification.
T1 / T2The two rope tensions on either side of the drive sheave: T1 is the heavier (tight) side and T2 is the lighter (slack) side; their ratio determines whether adequate traction exists.
Worked examples4
1. A geared traction elevator has a rated load of 2,500 lb and an empty car weight of 3,000 lb. The counterweight percentage is 40%. Calculate the counterweight mass.
- Identify the formula: CWT = Car Weight + (Percentage × Rated Load)
- Substitute values: CWT = 3,000 lb + (0.40 × 2,500 lb)
- Calculate the percentage portion: 0.40 × 2,500 = 1,000 lb
- Add to car weight: CWT = 3,000 + 1,000 = 4,000 lb
Answer: The counterweight mass is 4,000 lb.
2. Using the elevator above (CWT = 4,000 lb, car weight = 3,000 lb, rated load = 2,500 lb) in a 1:1 roping arrangement, calculate T1 and T2 when the car is fully loaded, and find the traction ratio. (Ignore friction and acceleration for this basic calculation.)
- In 1:1 roping, each side of the drive sheave supports the full weight of that side — no mechanical advantage adjustment is needed.
- T1 (car side, fully loaded) = Car Weight + Rated Load = 3,000 + 2,500 = 5,500 lb
- T2 (counterweight side) = CWT = 4,000 lb
- Traction ratio = T1 ÷ T2 = 5,500 ÷ 4,000 = 1.375
Answer: T1 = 5,500 lb, T2 = 4,000 lb, Traction ratio = 1.375.
3. The same elevator is re-rigged with 2:1 roping (idler sheave on the car; rope anchored overhead on the car side). The car is fully loaded. Calculate the rope pull (tension in the rope) on the car side.
- In 2:1 roping, two rope falls support the car side, so each fall carries half the total car-side load.
- Total car-side load = Car Weight + Rated Load = 3,000 + 2,500 = 5,500 lb
- Rope pull on car side = Total car-side load ÷ 2 = 5,500 ÷ 2 = 2,750 lb
Answer: The rope pull on the car side is 2,750 lb per rope fall.
4. A suspension rope has a catalog breaking strength of 22,000 lb. In the 1:1 installation above, the elevator uses 6 ropes. The maximum load per rope is calculated from T1 divided by the number of ropes. Calculate the safety factor.
- Maximum load on one rope = T1 ÷ Number of ropes = 5,500 ÷ 6 = 916.67 lb
- Safety Factor = Breaking Strength ÷ Maximum Load per Rope = 22,000 ÷ 916.67
- Calculate: 22,000 ÷ 916.67 ≈ 24.0
Answer: The rope safety factor is approximately 24.0, which exceeds the minimum required by ASME A17.1 for traction elevators.
The math in this lesson2
Learners compute counterweight as car weight plus 40% of rated load.
7.RP.3A-SSE.1
In class: Lecture on 1:1 and 2:1 roping configurations with force diagrams; students trace rope paths on hoistway drawings and label all sheaves. · Math workshop: students complete a six-problem worksheet calculating counterweight (car weight plus a percentage of rated load per industry practice), rope pull, and safety factor; instructor reviews each calculation step. · Partner activity: given a spec sheet for a hypothetical installation, each pair determines the correct roping arrangement, counterweight specification, and machine capacity, then presents a one-page summary.
Materials: Hoistway layout drawings, roping configuration diagrams, scientific calculators, counterweight calculation worksheets, NEIEP Traction module reference tables
Check: Six-problem math quiz on counterweighting and rope tension; pass mark 80 percent with all formulas set up correctly and units labeled.
Practice check8
Answer each question, then check it. Nothing is recorded; this is your own practice.
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