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Issue #4: July 25, 2014
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The Physics of Rigging for a Freestanding Aerial Rig

I received an email last month asking me if I had any opinions on rigging systems for freestanding aerial rigs. Well, of course I do, and said I would try to make some notes on this subject.  This issue of The Flywire is those notes.
 
            Let me begin by saying that you should not be afraid of the word "Physics" in the title. A great deal of physics is common sense, once you start thinking about about what is happening.  And, much of the math you need is simple addition, subtraction, multiplication and division. Sure, there are times when trigonometry is needed to calculate some forces, but knowing some general numbers and get you you around most of these, so just relax.
 
            Before we start taking about the rigging, I want to say that I strongly recommend quad-legged aerial rigs over the tripod style. They are stronger, more stable and more versatile; and in my opinion, they are well worth the extra money. Therefore, this issue will mostly deal with quad rigs.
 
            Quad rigs have a horizontal crane bar (about six feet long) at the top, where the apparatus is attached. Four legs, two on each end of the crane bar, support it. The legs splay-out, rather than being either perpendicular to the crane bar. The more they splay out, the greater the compressive force on the legs, but these forces are internal and not really critical to our discussion, so I will not discuss the angle of the legs (although the rig designer/engineer certainly should be concerned about this angle). The diagram below shows a typical quad rig.
 
In this article, I will discuss ways to hang an apparatus from the crane bar, and the physics/forces related to using each method. Let me also be clear that there is no “perfect” method. Each method will have its “Pros” and “Cons.” Users must evaluate each method based on the properties of each method and his/her own needs/desires, and select the “best” method.
 
In each case, the apparatus will be located in the center of the crane bar, equal distance between the pair of legs on each end of the crane bar. While this is typically where an apparatus would be located, it is also the weakest point on the crane bar. This fact will come up again when I discuss auxiliary (mini) crane bars.
 
There are many forces that occur within a simple aerial rig, and since every pulley adds additional forces, the more pulleys you add to a rig, the greater the number of forces involved. Fortunately, many of these are opposing forces that cancel each other out within the rig, and are not transferred to the ground. It is important to remember that forces have both magnitude and direction, and both are important.
 In each section below, I will show some of the forces on various points on the rig - mostly where apparatus and pulleys attaching to the crane bar, as well as there the legs meet the ground (remember, all vertical loads on the rig must eventually go to the ground). In my descriptions, I will use a 100-pound person/load hanging on the apparatus. While this is not necessarily a realistic number for the load, it is a round number that is both easy to work with mentally (and mathematically) in helping you understand the relationships of the forces. Assuming you do BIG drops on your rig, just can add a zero to the right side of each number so that your shock load is 1,000 pounds (the upper end of shock load force that most people can generate) and adjust the other forces on the rig in proportion.
 
 
Dead-hanging system
            The simplest way to hang and apparatus on a freestanding aerial rig is to hang it directly to the crane bar. This called “dead-hanging” because the apparatus is “fixed” in place – it cannot be easily lowered. Below is a diagram of this rig and the forces.
 
            As you can see, the entire 100-lb load hangs vertically on a single point in the center of the crane bar, the weakest point of the crane bar.  However, this load must eventually be transferred to the ground.  Since the load is centered in the “span,” half of the load (50 pounds of vertical/downward force) is on each end of the crane bar.  That load is then transferred to the legs, half (25 pounds) to each leg/foot, and then to the ground.  
 
            The number of components/forces on this type of rig is minimal and therefore they are easy to understand. If you have a tripod style aerial rig, this is how you should rig your apparatus. The pulley systems described below do not work for a tripod style aerial rig.
 
 
Simple pulley system
            Pulley systems have one big advantage of a dead-hung system – they allow you to lower a “point” which make it is easy to attach and then raise the apparatus. They also have a big disadvantage – they add additional forces to the rig. This will make a lot more sense very soon, but first, below is a view if the overall rig.

            The 100-lb load attaches to a line that goes over the pulley at the center of the crane bar (turning 90 degrees), over to a pulley at one end of the crane bar (turning 60 degrees, and then traveling to a cleat on one of the legs, where it is tied-off.
 
Now, lets break this down so that you can see some of the forces in more detail.

            A pulley not only change the direction of the line, but it also create a “resultant force” that is shown by the RED arrows. It is important to remember that the more the rope bends around the pulley, the greater the resultant force.
 
            As you can see, where the rope bends 90 degrees, the result force is 1.41 time the load, but where it bends 60 degrees, for resultant force is the same as the tension on the line.
 
            These numbers, by themselves are not all that important, however, the resultant force can be divided into horizontal and vertical forces on these points supporting the pulley, and these numbers are important. The GREEN arrows in this diagram shows both the direction and magnitude of the forces on the points where the pulleys attach to the crane bar.
 
Because the angle that the rope bends at the two pulleys is not the same, the resultant forces (and therefore the horizontal and vertical forces) are not equal. In this case, the horizontal force at the center of the crane bar (the right-hand pulley) is 100 pounds, but the opposing horizontal force at the left end of the crane bare is only 50 pounds. This means that the crane bar is being pulled to the left with 50 pounds of force. And if we had a shock load of 1,000 pounds of force on the line, there would be 500 pounds of force pulling the crane bar to the left – that is a LOT of lateral force.  
 
Now, lets look at all of the vertical forces – remember, these are the forces that gets transferred to the ground.

As you can see, the 100 pounds of downward force at the center of the crane bar gets divided and transferred to the end points of the crane bare and it is divided again and transferred to each leg, and then to the ground. So, there is 25 pounds of force on each leg (if we exclude the weight of the rig). You might be wondering about the 86 pounds of vertical force caused the pulley on the end of the crane bar and where that comes in to play. Well, as long as the line is tied to the cleat, the opposing force of the cleat pushing up on the leg with 86 pounds of force, thereby canceling it.  Now, if the end of the line was attach to something that was NOT on the rig, there would be no opposing force and the two legs on that end of the rig would each have an additional 43 pounds of force on them (or 430 pounds during a 1,000 pound shock load). 

Math note: Calculating the resultant forces, and the resulting horizontal and vertical forces, does require trigonometry.  You can use the RigCalc app to calculate the resultant forces, but chances are that most aerial rigs are going to have angles that are pretty close to the ones in this example, so you can use them help you estimate your forces.

Simple pulley system with 2:1 Mechanical Advantage
            The system below is very similar to the system above, with the exception that a 2:1 Mechanical advantage is rigged at the center of the crane bar. This system has two major advantages over the “Simple pulley system.” First, you can lift an apparatus or performer with half the effort of the earlier system.  Second, you have half of horizontal force that you had in the earlier system (this means far less jerk to the left during shock loads). The diagram below shows general setup of the rig.
 
The image below shows the forces on this rig.
 
Like the system above, the upward force on the leg (at the cleat) cancels out the downward force (at the pulley) so there is 25 pounds of downward force on each leg, excluding the weight of the rig.
 
Dual lift system with 2:1 Mechanical Advantage
            The final system we will look at uses three pulleys – two single pulleys and one double pulley. In my diagram of this rig, I will use two single pulleys instead of a double pulley because it is a little easier to illustrate the forces. Although this rig only has one line, just like the others, both ends of the line terminate at a cleat on a leg on opposite ends of the crane bar, so two individuals can lift the apparatus and performer, each holding half of the load.
 
Because this system is symmetrical, every horizontal force has an opposing force of equal magnitude which cancels in out.  Therefore, shock loads do not cause the rig to want to jerk horizontal.  And like the other systems, there is only 25 pounds of downward force on each leg, not counting the weight of the rig.

Conclusion
            Each system has its advantages and disadvantages.  The Dead-hanging system uses the least hardware and puts the least internal forces on the rig, but it is the most difficult system for changing apparatus. The Dual lift system with 2:1 Mechanical Advantage uses the most hardware, but all of the internal horizontal forces are negated, so it is the most stable of the three rigs that make it easy to change-out apparatus.

            As I have said thousands of times, there is no perfect system. Users just need to look at the pros and cons of each system and choose the one that best meets their needs and budget.

 

Upcoming Workshops
September 12 & 13 - USITT-SE Masterclasses in Tallahassee, FL

Previous Issues
Issue #2 http://eepurl.com/U0-sj
Issue #3 http://eepurl.com/XitQH
Need to learn rigging math?  Check out my book Rigging Math Made Simple, 2nd Edition.
 

Delbert L. Hall

President of D2 Flying Effects, LLC
ETCP Certified Rigger - Theatre
ETCP Recognized Trainer

 
Copyright © 2014 Delbert L. Hall, LLC, All rights reserved.


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