Mechanical Design for the Stage

Alan Hendrickson

• Publisher: Routledge
• Year: 2012
• ISBN:
  9781136036019
• Edition: 1
• Topic: Langues et linguistique
• Subtopic: Études sur la communication

Scenic effects involving rotating turntables, tracking stage wagons, and the vertical movement of curtains and painted drops have become common in both Broadway and Regional theatre productions. The machines that drive these effects range from small pneumatic cylinders pushing loads of a few pounds an inch or two, to 40 horsepower winches running multi-ton scenery at speeds 6 feet per second or more. Usually this machinery is designed by theatre technicians specifically for a particular show's effect. Compared to general industry, this design process is short, often only a few days long, it is done by one person, design teams are rare, and it is done in the absence of reference material specifically addressing the issues involved. The main goal of this book is to remedy this last situation.Mechanical Design for the Stage will be a reference for you that will:
* provide the basic engineering formulas needed to predict the forces, torques, speeds, and power required by a given move
* give a technician a design process to follow which will direct their work from general concepts to specific detail as a design evolves, and
* show many examples of traditional stage machinery designs.The book's emphasis will be on following standard engineering design and construction practices, and developing machines that are functional, efficient to build, easily maintained, and safe to use.

Part I: The Physics of Stage Machinery

Mechanical design in the broadest sense involves the process of developing a machine to meet an identified set of goals. Mechanical design, as it relates to a production to be developed for theatre, involves the conversion of a director’s and set designer’s vision for the production into the reality of a machine that will move scenery as they imagine. An essential and early part of this process is quantifying the relevant aspects of the scenery and its move. Numerous questions need to be asked and answered. For instance, what is the top speed of the fastest move? How much does the scenery weigh? What exactly is the move: a wagon traveling 25 feet straight down a raked deck, a turntable spinning half a turn, a lift rising 2.2 meters? Does it roll on casters riding on a smooth stage floor, or does it just slide? From the answers to these and other questions, estimates of the power, force, and speed needed to perform a given move can be determined. These values become the loading conditions for the machine that can then be designed.

In Part I of this book, comprising Chapters 1 through 12, each of the component terms of a formula describing the maximum power needed by scenery for a given move will be methodically defined and described. This occurs twice, once for scenic effects that move in straight lines, such as wagons, lifts, or flown units, and once for those things that rotate, mainly turntables. To provide an overview of what is to come, a brief qualitative description of the terms in these two formulas will prove useful.

During linear motion, the maximum power required by the scenic unit being moved is:

P_max = (F_acceleration + F_friction + F_lifting) v_max

In words this says that the maximum power equals the sum of three forces times the top speed. The three forces are:

• the force needed to accelerate, or speed up, the mass of the scenery,

• the force needed to overcome the resistance to movement imposed by friction,

• and any force needed to lift the piece if its motion has any vertical component.

The underlying logic of this relationship may appear evident from our experiences outside of theatre, driving around in cars.

• A sports car, with a relatively powerful engine in a light weight body, is capable of much greater acceleration than either a heavier or less powerful vehicle.

• Roads are paved, and tires pressurized correctly to reduce frictional resistance. Driving on sand or in deep mud involves much more force to overcome the friction involved, and so these surfaces make poor roads.

• It is obvious from the sound of the engine that driving up a steep mountain road involves more effort than coasting downhill on that same road.

Not surprisingly, the same basic relationships hold true for simple circular rotation:

P_max = (T_acceleration + T_friction + T_lifting) ω_max

Here the basic formula is the same, but force has been replaced by its rotational equivalent torque, and speed by angular speed (denoted by the Greek letter lowercase omega). The same everyday example of the car given above actually applies here too, because everything providing or transmitting power there, from the engine to the tires, is actually rotating. It is only where the tires contact the road that torque is converted to force.

These formulas, as presented in the following chapters, are not universal. They are in fact case formulas, applicable only to certain very specific situations, but since most scenery moves either in straight lines or rotates, these two find continual use.

1

Basic Concepts & Definitions

Fundamentals

There are concepts, called fundamentals, that form the base of all of physics. Anything that physics describes can be expressed in terms made up only of fundamentals. The fundamentals are not reducible to anything more basic, and are undefinable by definition. The fundamentals therefore are the starting point for our development of a mathematics of motion.

There is a certain element of arbitrary choice in picking what to use for fundamentals. Science seeks simplicity where possible, and fundamentals should be concepts commonly understood as obvious. Also the fundamentals should be as few in number as possible, while still as a group remaining a complete base for the physics built upon them. The fundamentals needed to cover all the material in this book are: time, length, and one of either mass or force. The choice between mass or force as a fundamental is an arbitrary one, and in the past each have had their advocates. Mass and force are related to each other through Newton’s 2nd law, a topic of a later chapter—so discussion is deferred until then.

Time is perhaps the most intangible of the fundamentals, yet everyone has a sense of what time is. Einstein notwithstanding, the rate and direction of the passage of time are invariant. Time moves forward; only its passing may be measured. The units of time are the most universal of any of the fundamentals. Throughout this book the units of seconds, minutes, and hours will be freely mixed. Such mixing is justified by the variety displayed in common usage: feet per second, revolutions per minute, kilometers per hour.

The fundamental length provides a measure of space. With length, the position of a object in space can be specified. A fixed origin is needed, but can be anything that is appropriate to the problem. A judicious choice of an origin can often simplify a problem right from the start. An exaggerated example relating to origin choice involves measuring the width of a flat. A perfectly valid measurement could be obtained by starting with an origin at some prominent location, say the center of town. Surveyor-like measurements and trig calculations in three dimensions could yield the flat’s width, but this would not be quick, accurate, or easy. Reducing the task down to one dimension helps by eliminating all trigonometry from the problem. Careful alignment of the flat’s edges relative to a straight line from the flat to the origin could occur before taking two measurements to the flat; one to each edge. By taking the absolute value of the result of the subtraction of one measurement from another, the answer would be found. Mathematically:

flat width = |x₁ – x₂|

where: x₁ and x₂ are the two length measurements (feet or meters)

If, though, we had assumed one edge of the flat as the origin, just temporarily, then our two measurements of lengths from origin to edges would always include one measurement of zero. This has two benefits. We do not need to measure anything from the center of town, and perform...