Sunday, December 8, 2013

Physics of Fly systems

So I was working in a theater over the past week setting up lighting equipment for a show, and I needed to raise what is called a batten up using what is called a loft block. A batten is a 80 gauge steel pipe that weighs around 111.97 kg and a loft block is a winch that has a radius of 150mm or .150m. In addition to the wight of the pipe itself, there were 10 lighting instruments on the batten. There were four "source 4"s three 4" fresnels and 3 8" fresnels which weigh 6.4kg, 3.3kg, and 6.5kg respectively. This brings the weight of the batten to 166.97kg in total which represents a force of 1636.306 N pulling on an aircraft cable that suspends the pipe. So I wanted to find out what torque was required to lift the batten:

166.97kg* 9.8 m/s^2 = 1636.306 N

Fg = Ft which means that the force due to gravity is the same as the force of the torque required to move the batten

This means that the torque required to move the batten is:
T= rF (because the sin() is going to equal 1)
T = .150 m * (1636.306 N) = 245.4 N/m

In addition, I wanted to know how much energy would be required to move the batten using the loft block. Assuming that only one cable was attached to batten, I found that the kinetic energy equaled:

I = 1/3 ( 166.97kg) (9.144m)^2 = 4653.6 kgm^2
KE = 1/2 (I) (w^2)
w = v/r assuming that the batten was raised at a speed of 1 m/s
w = 1.0 m/s / .150m = 6.67 rads/s
KE = .5 * 4653.6 kgm^2 * (6.67)^2
KE = 207033.8 J = 207.033 kJ

Though this may seem like a large amount of energy needed to raise a batten, there are multiple lift lines on the pipe which would lessen the amount of energy needed by lessening the moment of inertia. But even without multiple lift lines, it is possible to lift a batten using a hand crank. However, most theaters use a mechanic crank that pulls much more effectively with little to no effort from a stage hand.

Sources:
http://www.etcconnect.com/DOCS/DOCS_DOWNLOADS/DATASHTS/7060L1009_SOURCE_FOUR_36_SPEC_SHT_VG.PDF
http://www.altmanltg.com/altman-lighting-fresnels/75Q%20&%20175Q/fresnel-75Q.PDF
http://www.bhphotovideo.com/c/product/173850-REG/Arri_531602_650W_Fresnel_120_240V_AC.html
http://en.wikipedia.org/wiki/Fly_system
http://www.engineeringtoolbox.com/steel-pipes-weights-d_774.html

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