Rigging Physics Slides Rigging Physics
Vector Mechanics & Load Analysis for the Stage
Scenic Automation Sequence: Lesson 1
The Danger of the Shallow Angle
Consider a 2-leg bridle supporting a 1,000 lbs load. As the interior angle between the legs increases (approaching 180°), the tension on the legs doesn't just increase—it explodes.
T = (W / 2) / sin(θ)
Where θ is the horizontal angle.
Load: 1,000 lbs
What happens to tension as θ → 0°?
Static vs. Dynamic Force
Static Loads
Dead weight of the equipment.
Constant force in a fixed position.
Vector sum of all forces = 0.
Dynamic Loads
Forces generated by acceleration.
Impact loads (Emergency Stops).
Centripetal force in revolving stages.
Rule of Thumb: Dynamic loads can be 2x to 5x the static load during an E-stop!
Safety Factors (Design Factors)
The **Design Factor (DF)** is the ratio of the breaking strength of a component to the maximum intended load.
5:1
Static Rigging
Standard hardware, truss, and fixed hangs.
8:1
Running Rigging
Counterweight sets and manual winch lines.
10:1
Overhead Lifting
Wire rope for scenic automation & people.
Why so high?
We account for material fatigue, shock loads, wear and tear, and the most critical variable: **The lack of precise structural data in touring venues.**
Moving to 3-Dimensions
In 3D space, we decompose forces into X, Y, and Z components.
Load = \(\vec{L} = (L_x, L_y, L_z)\)
Tension = \(\vec{T} = T \cdot \hat{u}\) (unit vector)
Equilibrium: \(\sum \vec{F} = 0\)
"If the math doesn't close the loop, the truss won't hold the hoop."
Complex Point Load Analysis
Rigging Load Challenges Worksheet Rigging Load Challenges
Technical Theater Engineering: Lesson 1 Problem Set
Name:
Date:
Reference Formulas
Bridle Tension (per leg):
\(T = \frac{W}{2 \sin(\theta)}\)
(θ = angle from horizontal)
Design Factor:
\(DF = \frac{BS}{WLL}\)
(Breaking Strength / Working Load Limit)
Resultant Force:
\(R = \sqrt{F_x^2 + F_y^2}\)
(Pythagorean vector addition)
1
The Shallow Bridle
A scenic flat weighing **850 lbs** is hung via a two-leg bridle. The distance between the rigging points is **30 ft**. Each bridle leg is **16 ft** long.
a) Calculate the horizontal angle (\(\theta\)) of the bridle legs.
b) Calculate the tension on each leg.
Sketch Area / Force Vector Diagram
2
Shock Load & Safety Margin
An automated hoist is lifting a **1,200 lbs** scenic piece at a constant velocity. During an emergency stop, the hoist decelerates at **1.5g**. The wire rope being used has a breaking strength of **14,000 lbs**.
a) Calculate the total dynamic load (Peak Force) applied to the wire rope during the E-stop.
b) What is the resulting Design Factor (DF) during this shock event? Does it meet the ETCP 10:1 standard for overhead lifting?
3
Vector Summation: Multi-Point Truss
A section of truss is supported by three motors. Motor A pulls with **600 lbs** at 90° (vertical). Motor B pulls with **400 lbs** at 120°. Motor C pulls with **400 lbs** at 60°.
Determine if the horizontal forces are balanced (\(\sum F_x = 0\)). Show all vector component calculations (\(\cos\) and \(\sin\)).
Rigging Physics Key Answer Key
Rigging Load Challenges | Instructor Copy
Unit: Scenic Automation
Lesson 1: Physics
1
The Shallow Bridle
Part A: Angle Calculation
Span = 30ft; Half-Span (Adjacent) = 15ft
\(\cos(\theta) = 15 / 16 = 0.9375\)
Part B: Tension Calculation
\(T = (W / 2) / \sin(\theta)\)
Note: The tension on each leg is nearly 50% greater than the total weight of the object due to the shallow angle.
2
Shock Load & Safety Margin
Part A: Dynamic Peak Force
\(F_{total} = W + F_{inertial}\) OR \(F_{total} = W(1 + a/g)\)
Part B: Design Factor Compliance
\(DF = \text{Breaking Strength} / \text{Peak Load}\)
Status: FAIL.
3
Vector Summation: Multi-Point Truss
Horizontal Component Summation (\(\sum F_x\))
Motor A (90°)
\(F_x = 600 \cdot \cos(90^\circ)\)
Motor B (120°)
\(F_x = 400 \cdot \cos(120^\circ)\)
Motor C (60°)
\(F_x = 400 \cdot \cos(60^\circ)\)
\(0 + (-200) + 200 = 0 \text{ lbs}\)
Horizontal forces are perfectly balanced.
Mechanical Design Slides Mechanical Design
Power, Torque, and Transmission for Scenic Motion
Scenic Automation Sequence: Lesson 2
The Automation "Holy Trinity"
Speed
(Velocity)
How fast does the piece need to travel?
Torque
(Moment of Force)
How much turning force is required to start/stop the load?
Power
(Work / Time)
The total energy required from the motor.
Power = Torque × Angular Velocity (\(P = \tau \omega\))
Choosing Your "Engine"
3-Phase AC Induction
The theater workhorse. Robust, reliable, and easily controlled by Variable Frequency Drives (VFDs).
Servo Motors
High precision, closed-loop feedback. Best for "path following" and synchronization where position is critical.
Stepper Motors
Excellent for indexing and small, consistent steps. High holding torque but prone to "missing steps" under heavy load.
DC Motors
Legacy systems or battery-operated mobile scenic units. Simple speed control but brush wear is a factor.
Torque Multiplication
A motor's native speed is usually too high and its torque too low for theater applications.
Transmission Components:
**Worm Gear**: Self-locking, high ratio, quiet.
**Planetary**: Compact, high efficiency, durable.
**Helical**: Smooth, very quiet, high efficiency.
Gear Ratio Math
Output Speed \(RPM_{in} / Ratio\)
Output Torque \(\tau_{in} \cdot Ratio \cdot Eff\)
Don't forget efficiency! Friction eats 5% to 40% of your power.
The Suitcase Winch Challenge
Design a winch capable of lifting **1,500 lbs** at **2 ft/sec**. Every component—motor, gearbox, drum, and frame—must fit inside a volume of **24" × 18" × 10"**.
Constraint Driven
Torque Calculation
Component Sourcing
Suitcase Winch Project Brief Project: The Suitcase Winch
Engineering Design Challenge: Lesson 2
Project Code SW-1500-A
1. Mission Objective
Your firm has been contracted to design a compact, high-capacity scenic winch for a touring production. The winch must be capable of being concealed within standard set pieces and transported easily. You are tasked with selecting the motor, gearbox, and drum sizing to meet the specified performance metrics while adhering to strict volumetric constraints.
Performance Requirements
Vertical Lift Capacity: 1,500 lbs
Line Speed: 2.0 ft / second
Travel Distance: 40 ft
Acceleration Time: 1.0 second
Wire Rope Type: 1/4" 7x19 GAC
Volumetric Constraints
Maximum Length: 24.0 inches
Maximum Width: 18.0 inches
Maximum Height: 10.0 inches
Max Unit Weight: 180 lbs (including frame)
2. Design Phase: Calculations
Use the "Mechanical Technical Reference" sheet for efficiency constants and formulas.
Stage A: Drum Selection & Torque
Select a drum diameter (D/d ratio for 1/4" wire rope should be at least 15:1 for theater).
Calculate the required Torque (\(\tau\)) at the drum shaft based on your chosen radius.
Stage B: Horsepower & Gear Ratio
Determine the required Horsepower (HP) at the output shaft, accounting for 80% total system efficiency.
Based on a 1750 RPM AC Motor, what gear ratio is required to achieve the 2.0 fps line speed?
3. Final Deliverables
Bill of Materials
Specific motor (frame size), gearbox type, and drum manufacturer/specs.
Layout Sketch
A top-down plan view (1/4" = 1' scale) showing how components fit within the 24"x18" footprint.
Safety Summary
Calculation of the static safety factor and the chosen braking method.
Design Challenge Checklist
Motor HP >= (Calculated Load HP / Efficiency)
Gearbox Output Torque >= Required Load Torque
Drum Width accommodates 40ft of 1/4" rope + 2 dead wraps
Components fit inside 24" × 18" × 10" envelope
Mechanical Reference Sheet Mechanical Reference Sheet
REF-MECH-G-2026
Fundamental Formulas
Torque-to-Horsepower
\(HP = \frac{\tau \cdot RPM}{5252}\)
(\(\tau\) in lb-ft)
Linear Velocity (v)
\(v = \frac{RPM \cdot \pi \cdot D}{60 \cdot 12}\)
(\(v\) in ft/sec, \(D\) in inches)
Required Input Torque
\(\tau_{in} = \frac{\tau_{out}}{Ratio \cdot \eta}\)
(\(\eta\) = decimal efficiency)
Transmission Efficiency (\(\eta\))
Gearbox Type Est. \(\eta\) Planetary (Single Stage) 0.95 - 0.98 Planetary (Two Stage) 0.92 - 0.95 In-Line Helical 0.94 - 0.97 Worm (Low Ratio < 10:1) 0.85 - 0.90 Worm (High Ratio > 40:1) 0.50 - 0.70 Chain Drive 0.95 - 0.98
PRO TIP: High-ratio worm gears generate significant heat due to low efficiency. Ensure adequate cooling if used for high-duty cycles.
Drum & Rope Specs
Theater D/d Ratios (Minimum)
• Standard: 15:1 (15" drum for 1" rope)
• Running Lines: 20:1
• High Speed / High Duty: 30:1
Rope Dia. Min Drum Dia. Breaking Strength 1/8" (GAC) 1.875" 2,000 lbs 3/16" (GAC) 2.812" 4,200 lbs 1/4" (GAC) 3.750" 7,000 lbs 3/8" (GAC) 5.625" 14,400 lbs
NEMA Frame Dimensions (Approx)
Frame HP Range Shaft Dia. Length (C) 56 0.25 - 1.5 0.625" ~11" 143T 1.0 - 1.5 0.875" ~13" 145T 2.0 - 3.0 0.875" ~14" 182T 3.0 - 5.0 1.125"
Control Systems Slides Control Systems
Logic, Electronics, and Safety Architecture
Scenic Automation Sequence: Lesson 3
The Brain: The PLC
A **Programmable Logic Controller (PLC)** is a ruggedized industrial computer designed for real-time automation.
Why PLCs?
Reliability: Designed for 24/7 operation in harsh environments.
Deterministic: Executes code in a predictable "scan cycle" (milliseconds).
I/O: Directly interfaces with sensors and actuators.
Input -> Process -> Output
Unlike a standard PC, a PLC won't crash because of a Windows update mid-show.
The Muscle: The VFD
The **Variable Frequency Drive (VFD)** controls the speed of an AC motor by varying the frequency and voltage of the power supply.
Key Functions:
• Ramp Up / Ramp Down (Soft Start/Stop)
• Torque Control (Current limiting)
• Dynamic Braking (Dissipating energy)
Signal Chain
PLC
VFD
MOTOR
60Hz = 100% Speed
Safety Interlocks
E-Stop
Hard-wired circuit that cuts power to the motor drives instantly. **Must be physical, not just software.**
Dead Man
A "Hold-to-Run" switch. Motion stops the moment the operator releases the button.
Limit Switches
Physical sensors that prevent a winch from over-traveling and causing structural damage.
Wiring the Logic
"If the gate is closed AND the dead man is held AND the E-stop is healthy AND the limit is not hit... THEN you may move."
LADDER LOGIC PREVIEW
Input 1
Input 2
M
Output
Ladder Logic Workshop Worksheet Ladder Logic Workshop
Control Systems: Programming & Safety Interlocks
Engineer:
Station:
1. Symbol Identification
Identify the following standard ladder logic symbols and their function.
--| |--
--|/|--
--( )--
--[TON]--
2. The Stage Lift Logic
Design the logic for a hydraulic stage lift. The lift has two buttons (UP and DOWN), two limit switches (TOP and BOTTOM), an Emergency Stop (ESTOP), and a Pressure Sensor (READY).
• UP (I:0/1): NO Pushbutton
• DOWN (I:0/2): NO Pushbutton
• ESTOP (I:0/0): NC Contact
• READY (I:0/3): NO Sensor
• TOP_LIM (I:0/4): NC Switch
• BOT_LIM (I:0/5): NC Switch
Rung 1: Lift Up Control
Conditions: The UP coil (O:0/1) should activate only if UP is pressed, ESTOP is NOT active, READY is TRUE, and TOP_LIM is NOT hit.
Rung 2: Lift Down Control
Conditions: The DOWN coil (O:0/2) should activate only if DOWN is pressed, ESTOP is NOT active, and BOT_LIM is NOT hit.
3. Fault Detection Logic
An automation system should detect "Stall" conditions. If a motor is commanded to move (OUTPUT_ACTIVE) but the encoder does not report motion (MOTION_DETECTED) for 3 seconds, a FAULT (O:0/3) should trigger.
Sketch Ladder Logic Here
Automation Facilitation Guide Automation Facilitation Guide
Instructor Resource | Lesson 3 & 5
Technical Theater Engineering
Graduate Level
1. Ladder Logic Solutions
Stage Lift Up Control (I:0/1 -> O:0/1)
--[ UP_PB ]--[ ESTOP_OK ]--[ READY_SEN ]--[ TOP_LIMIT ]--( UP_COIL )--
Note: Use Normally Closed (NC) contacts for ESTOP and LIMITS in the physical world to ensure "Fail-Safe" operation. If the wire breaks, the system stops.
2. Motion Profiling Pedagogy
The "Jerk" Factor
Explain to students that **Jerk** is the derivative of acceleration. While trapezoidal profiles have infinite jerk at the corners, S-curves ramp acceleration, making them essential for delicate scenic transitions or performers on moving platforms.
Sync Strategies
When synchronizing multiple axes, the best strategy is to define the "Master" axis (usually the slowest) and scale all other "Slave" axes to match the Master's duration.
3. Safety Benchmarks (ETCP)
Redundancy: Any software limit must be backed by a physical hard limit that breaks the safety loop.E-Stop Recovery: A system should never "Resume" motion after an E-stop is cleared. It must require a manual "Reset" followed by a fresh "Play" command.Watchdogs: Teach students about PLC watchdogs—heartbeat signals that verify the software is actually running and hasn't hung while a motor is moving. Fluid Power Slides Fluid Power
Hydraulics & Pneumatics in the Theater
Scenic Automation Sequence: Lesson 4
Pascal's Law
"Pressure applied to a confined fluid is transmitted undiminished in every direction."
P = F / A
Pressure = Force / Area
This is how a small cylinder can lift a massive stage: by trading distance for force.
A1
A2
Hydraulic Mechanical Advantage
Comparing the Mediums
Pneumatics (Air)
Fast and snappy motion.
Clean; no oil spills on costumes.
Components are inexpensive.
"Spongy" motion (air is compressible).
Loud (exhaust noise).
Hydraulics (Oil)
Immense force capacity.
Extremely smooth & precise.
Rigid (oil is incompressible).
Dirty; potential for leaks.
Heavy and expensive components.
The Fluid Circuit
Reservoir / Tank
Stores the fluid/air medium.
Pump / Compressor
Generates flow and pressure.
Control Valve
Directs fluid to extend/retract.
Actuator / Cylinder
The end-effector doing work.
The Hook: Power Density
A 2-inch hydraulic cylinder can lift **9 tons** at 6000 PSI. The same-sized pneumatic cylinder at 100 PSI can lift **314 lbs**. That is a **60x difference** in power density!
Pressurized Danger
Fluid systems are stored energy systems. They do not need electricity to be dangerous.
LOTO
Lock-Out Tag-Out: Zero Energy State is required for maintenance.
Pinholes
Hydraulic injection is a surgical emergency. **Never use your hand to check for leaks.**
Fluid Circuit Lab Guide Fluid Circuit Design Lab
Lesson 4: Hydraulics & Pneumatics
Lab ID FLUID-402
Scenario: The Vampire Trap
A touring production of *Dracula* requires a "Vampire Trap" that must snap shut in less than **0.5 seconds**. The trap door weighs **45 lbs** and must be operated by a pneumatic cylinder. You need to design the circuit and specify the components to ensure rapid, reliable, and safe operation.
Given Specifications
• Supply Pressure: **80 PSI**
• Required Stroke: **10 inches**
• Load: **45 lbs** (Direct vertical lift)
• Safety Margin: **2x minimum**
Deliverables
• Specified Cylinder Bore Size
• Schematic Diagram (ISO Symbols)
• Speed Control Strategy
Task 1: Sizing the Actuator
A) Required Force (\(F_{req}\))
Apply a 2x safety margin to the 45 lbs load.
B) Minimum Bore Diameter
Use \(A = F / P\). Then solve for \(D = \sqrt{4A / \pi}\).
Task 2: ISO Schematic Diagram
Draw a complete schematic for a double-acting cylinder controlled by a 5/2 solenoid valve with speed control (meter-out flow control). Include the air source and regulator.
ISO Standard Fluid Power Symbols Only
Task 3: Engineering Decisions
Speed Control Selection
Explain why **Meter-Out** flow control is superior to **Meter-In** for pneumatic snap-trap applications.
Safety Feature: The "Dump" Valve
Where should the emergency exhaust (dump) valve be placed in your circuit to ensure the trap door fails in a safe position (OPEN)?
Automation Software Slides Cueing & Motion
Software Profiles, Acceleration, and Choreography
Scenic Automation Sequence: Lesson 5
The Motion Profile
A motion profile is the graph of **Velocity vs. Time**.
Trapezoidal Profile
Linear acceleration and deceleration. Efficient but can cause "jerky" motion at the transitions.
S-Curve Profile
Smooth transitions into and out of motion. Essential for fragile scenery or "lifelike" movement.
Time (s) Velocity (v)
Stopping is Harder than Starting
The **Deceleration Curve** is the most critical part of an automation cue for safety.
Over-travel can destroy scenery.
Hard stops cause high shock loads.
Brake engagement delay must be calculated.
Stopping Distance
\(d = \frac{v^2}{2a}\)
d = distance, v = velocity, a = deceleration
Rule of Thumb
If you double the speed, you quadruple the required stopping distance.
Integrated Performance
Timecode
Synchronizing motion with audio and lighting down to the millisecond (LTC/MTC).
OSC
Open Sound Control: Send commands from a sound console to trigger automation cues.
Grouping
Master/Slave relationships for complex movements involving multiple motors.
The Scenic Waltz
Your final challenge: Program a **3-axis motion sequence** (a revolve and two wagons) to move in harmony with a 30-second music clip.
Safety Requirements
• No collisions (proximity check).
• Soft limits enforced.
• Decel curves < 0.5g.
Artistic Requirements
• Fluid S-curve transitions.
• Precise sync with beat 1.
• Synchronized arrival.
Scenic Waltz Programming Sheet The Scenic Waltz
Lesson 5: Cueing & Motion Profiling
Project Code WALTZ-30SEC
1. Programming Objective
You must program a 30-second synchronized motion sequence for three scenic elements: **Revolve A**, **Wagon B**, and **Wagon C**. The sequence must align with the provided musical score, featuring soft starts, fluid transitions, and a synchronized final arrival.
2. Master Cue List
Cue # Trigger (Sec) Element Target Pos Speed (%) Accel (s) Profile 1.0 0.0s Revolve A 360° 25% 2.0s S-Curve Wagon B 12' 0" 40% 1.5s Trapezoid Wagon C -12' 0" 40% 1.5s Trapezoid 2.0 15.5s ALL Home Calc. Required 3.0s S-Curve
3. Sync Calculations
Wagon Synchronization
Calculate the speed for Wagon B so that it arrives at its "Home" position (0' 0") at exactly T = 30.0s.
Deceleration Profile
Determine the deceleration time (s) required to stop Wagon B from its top speed to 0 within 18 inches of travel.
4. Pre-Flight Safety Check
Before running the cue list, verify the following parameters to prevent equipment failure or injury.
Soft Limits Engaged
Are the software-defined travel limits set inside the physical hard-limits?
Max Acceleration Check
Is any axis accelerating faster than 0.5g (16.1 ft/s²)?
E-Stop Health
Is the physical E-Stop loop healthy and verified within the last 2 hours?
Path Clearance
Is the clear zone between Wagon B and C greater than 24" at all times?
