Factor the weight of suspended air-dome luminaires when motion is pivotal (MAGAZINE)

While the static hanging weight of an Eclipse LED fixture is significantly lighter than the maximum static hanging weight of 25 lb that is typical in an air-supported structure, static weight is not the only concern. The fixtures inherently move and are attached to fabric patches affixed to the inner surface of the dome. A 30° swing motion from vertical as external wind exerts force against an air dome could produce a dynamic realized fixture weight of 26.5 lb. That dynamic weight remains well below the maximum tear strength threshold (from supporting patches) of 36 lb, but specifiers must be able to calculate such stresses to ensure reliability.

Here we will consider why the weight and maximum threshold of hanging light fixtures, as well as the method of installation, is important within any inflatable structure. The discussion validates why the concept should be considered across the inflatable structure community to prevent the occurrence of light fixtures tearing from supporting dome patches and causing potential injury below.

Blooming domes

There are numerous air-dome structures catering to sports and recreational activities, and other functions too, all across the United States and Canada. In fact, the largest air dome in the world, the Sports KingDome, is scheduled to open sometime in the latter half of 2019 in East Fishkill, NY, which includes 160-ft-high ceilings and nearly 350,000 ft² of field space. Fig. 3 shows the exterior of a dome at a golf practice facility in New York. Though they generally vary in design and size, all inflatable structures share the same operational principle of being evenly pressurized, meaning the internal pressure must equal or exceed any external pressure being applied to the structure, notably high winds and heavy snow.

Maintaining the integrity of an air dome means that its level of inflation must be adjusted accordingly. This is typically achieved with computer-controlled mechanical systems that monitor the structure’s degree of inflation, making automatic adjustments accordingly. Of course, the majority of air domes are designed to handle external forces like wind and accumulating snow loads and are structurally stable and safe. They also can be used on a permanent or temporary basis during any season of the year, since the envelope, or skin, is engineered with durable yet pliable synthetic materials like fiberglass and polyester that are coated with polymers to protect from moisture and ultraviolet light.

Nevertheless, all air domes are subject to varying wind speeds and will naturally move up and down and oscillate, despite monitoring systems that adjust for the pressure exerted on them. This means that suspended internal components such as light fixtures will inevitably experience some degree of motion, too. Of course, this is natural and expected. However, issues can arise if light fixtures are too heavy and unable to fully handle the stress exerted on supporting components like patches and D-rings when the fixtures are in motion due to heavy winds. This can result in the fixtures swinging violently, posing the risk of becoming compromised and detaching from their respective patch and potentially falling to the court surface or athletic field.

Lighting the dome

The issue of heavy light fixtures within air domes suspended from dome-mounted fabric patches continues to raise questions with air-dome owners contemplating conversions to LED-based fixtures. In an attempt to eliminate any ambiguity by dome or fixture manufacturers, Green Arc Energy Advisors, based in New York City, commissioned physicist O. Sepper, PhD, a former research fellow at Argonne National Laboratory, to analyze the actual effects of suspended light fixtures when in motion. Since air domes are not static structures, their constant movement in the wind generates motion that is imparted to suspended fixtures — a phenomenon which naturally does not exist in fixed or steel-frame buildings. For larger domes, with apex heights of 60 ft or higher, movement off center by 5 ft or more in any direction is not uncommon. In the event of extreme weather with sustained or gusting wind speeds of more than 20 mph, the motion of the dome is magnified accordingly.

Typically, the majority of existing domes utilize patches that are 8–10 in. in diameter and are chemically bonded or heat fused to the enveloping skin of the dome. For these typical attachment methods, the maximum recommended operating static weight is approximately 25 lb, with tear strengths up to 36 lb. It is at this critical juncture (i.e., 36 lb) that the failure of a patch can occur, with the net result being the fixture falling within the dome.

Guy Albert de Chimay, executive vice president of Green Arc Energy Advisors, explained, “With our commissioned analysis, we were able to demonstrate the maximum weight capacity of 36 lb, which means the maximum suspended weight of a static fixture is 25 lb. This is because when the fixture is in motion, it is similar to the physics of a pendulum. At the bottom of the arc, meaning at its very lowest point, when the fixture moves it has the maximum amount of kinetic energy, which can increase the static weight from 25 lb and make it as much as 150% higher. This means that as the weight transfers up the suspension cable, it increases the pull that the supporting patch experiences, which can be 150% of 25 lb, vastly exceeding the recommended 36-lb threshold.”

Potential liability

The quality of the patch adhesion, the age of the patch, and the age of the dome can also factor significantly on this limit. And considering that many domes have been modified over different times, the age of patches, the quality of the bond, and the age of domes may not be the same. According to de Chimay, “There have actually been several instances in which the installation of induction-based fixtures weighing between 28 and 32 lb resulted in the failure of patches.”

The implications are so severe that members of the dome installation community are often unwilling to install such fixtures. Professional installers contracted to erect and/or remove domes understand that there are serious liabilities associated with such an installation. “Dome installers never want to be anywhere near 30 lb when it comes to effective fixture weight,” said de Chimay.

Of importance from the ownership perspective, aside from the possibility of serious injury, is the risk of invalidating a dome owner’s general liability insurance coverage. Considering the maximum operating weight of the D-ring patch is typically stated within the dome’s operating manual, disregarding the limits could result in the risk of total exposure to the liability. De Chimay stated, “The way that Green Arc suspends fixtures in air domes is by utilizing the strength of the power cable that we traverse through the hole and down the skin. This method generates a tremendous amount of friction that gets imparted from the skin against as much as 100 ft of cable against it, meaning if the patch was to let go, the power cord would become the backup, preventing the fixture from falling. The physics is pivotal and intended to protect people engaged in sports and activities beneath.”

Math analysis

To clarify what actually occurs within an air dome while it moves due to the force of wind, the following analysis by Sepper helps put the concept in greater perspective. Keep in mind that the most important point is that the weight of a static fixture is not what the D-ring patch realizes when the fixture swings. It’s common to see an installation where a fixture is at an approximate 30° swing angle from center directly below the attachment point. According to Sepper, the effective weight of a swinging fixture can be approximated by the following formula:

W = Wo[3 ‒ 2cos(θ)]

Wo represents the actual weight of a fixture (e.g., 19 lb) and θ (theta) is the maximum angle of the swinging motion. This approximation treats the fixture as a point mass located at the center of gravity. The result in this approximation is independent of the length of the cable from the D-ring. However, the angle θ depends on the motion of the dome and the length of the power cable.

For example, Wo = 19 lb and the maximum swing angle of 30° demonstrates effective weight. W = 24 lb at the bottom of the arc.

The next computation involves equating the fixture as a pendulum, for which the exact mass distribution (i.e., precise length measurements and weight of each component that makes up a fixture) is needed. The previous formula denotes the upper bound for the effective weight.

A large uncertainty factor is the angle of swinging motion, which typically depends on the motion of the dome and the mass distribution of the fixture. The additional increase in effective weight due to uncertainties in the angle is approximately:

ΔW = 2Wo sin(θ) Δθ

Assuming that Δθ (delta theta) ranges between 5° to 10° give an extra weight of up to 3 lb, with all parameters kept the same.

To figure out the maximum angle, an assumption is derived regarding how the motion of the dome translates into motion of the fixture. By using an approximation based on immediate response of the fixture to the motion of dome, the result is:

tan(θ) = k x/L

Where x is the distance the dome moves (e.g., 5 or 6 ft) or displacement, L is the length of the cable from the D-ring (e.g., 8 or 10 ft), and k is an experimental factor that depends on many variables, including velocity, resistance, and whether oscillations are synchronous or out of phase. Green Arc tested a few reasonable values. In most situations, k should be in order of 1, though k=0.5 or k=2 is possible as well.

The following summarizes the analysis:

W = Wo[3 ‒ 2cos(θ)]

tan(θ) = k x/L

To facilitate the understanding of what the above analysis means in actual practice, the graphs in Fig. 4 and Fig. 5 demonstrate the findings of effective weight versus displacement, and effective weight versus angle. The blue lines start at 36 lb and the red lines start at 19 lb, both of which demonstrate increases as a function of displacement. For a 19-lb fixture, the maximum effective weight is 25 lb, and for a 36-lb fixture, the maximum effective weight is 48 lb. These results are based on the assumption that the displacement of a fixture is proportional to the displacement of the dome. The dashed lines illustrate the range of other possible scenarios. There is a phenomenon of resonance in which the amplitude of the swinging motion can increase dramatically if the driving force (i.e., the dome) is moving in phase with the pendulum. However, there are damping effects that can counteract this increase. The dashed lines capture some of these effects.

Summarizing the analysis

In short, it is important to emphasize that a fixture weight increase on the order of nearly 50% apparent to the D-ring can easily be achieved based on the normal operation of an air-dome structure. As the dome moves, the fixtures move as well, and with a demonstrable effect. Simply put, any assertion that a 35-lb fixture can be easily supported within a dome defies the physics of the dome itself. A fixture can weigh as much as 48 lb when in motion. And while it provides only empirical data, the demonstrated analysis should help bolster the notion that it is not prudent to suspend a fixture weighing 35 lb or more above a field or court surface, regardless of the addition of larger patches.

Green Arc Energy Advisors has successfully engineered all its LED fixtures with the clear purpose of being safe, practical, and suitable within air domes, not to mention to provide better luminosity, color rendering, and energy efficiency. “With the analysis, we were able to see that a 30° swing of a heavy metal-halide fixture resulted in going above the maximum threshold. Our proprietary LED fixtures, however, puts them way below the maximum threshold. In other words, by multiplying 17.5 lb by 150%, we’re still at 26.4 lb and well below the maximum,” said de Chimay.

Green Arc’s proprietary LED fixtures have never experienced a D-ring failure over the 5-year period since their introduction to the marketplace, which includes installations in more than 12 of the nation’s largest air-supported dome structures.

In conclusion, de Chimay said, “The bottom line is that understanding the weight of suspended light fixtures is pivotal within any type of inflatable structure like an air dome. Utilizing lightweight fixtures and understanding the physics will significantly reduce the risk of compromising fixtures and spare owners and operators from any liability damage that may result if a fixture was to fall when people are engaged in activities below.”

Get to know our expert

MARCUS VAN DER HEYDEN is a creative marketing consultant for Green Arc Energy Advisors. The company began by selling specialized sports lighting and has advanced to provide full lighting conversion services, with photometrics, lighting design, and energy analysis.