Using Physics to Fix & Rebuild

Golden Gate Bridge Dilemma

Using waves and sound in physics to solve an architectural dilemma.

 

I've lived in San Francisco my entire life and remain in awe of one of the greatest architectural feats in history: the Golden Gate Bridge. It is not only a hub for tourism but represents a daily commute for many in the Bay Area. 

During the pandemic, the infrastructure of the Golden Gate Bridge in San Francisco, California was modified in order to strengthen and prepare the bridge for increasingly fast winds as a result of climate change. One of the modifications was the size of the railings, though from the government blueprints and plans on the bridge, it is unclear if the railings were reduced in size or increased in size. Regardless, the effects of this new implementation are felt throughout the Bay Area: a loud humming sound can be heard from miles away as high velocity winds pass through the railings of the Golden Gate Bridge. The physical phenomena behind this sound is vortex shedding, in which an oscillating flow occurs when a fluid (e.g. air or water) flows past a bluff body at certain velocities. This depends on the size and shape of the body. 

                                               (picture shown below)

 

Experiment Design and Overview

When the vortex shedding frequency matches the resonance frequency (natural frequency) the structure can begin to resonate and vibrate with harmonic oscillations that cause the phenomenon of ‘wind humming’.

    Vortex shedding is modeled by this governing equation: St = f*D/v where f is the vortex shedding frequency (s-1), V is the flow velocity (ms-1), D is the diameter of the body (m), and St is the Strouhal Number, a dimensionless number and a constant for which 0.22 is commonly used that describes certain oscillating flow mechanisms. By rearranging the equation, we obtain  f = St*v/D. During this experiment, the wavelength will be measured and in order to find the frequency of the wave, the equation c = λ* f where the speed of the wave will be calculated beforehand. According to the governing equation, the relationship between frequency and diameter should be inversely proportional. To eventually create a linear relationship between diameter and frequency, the equation must be inverted: 1f = D/St * v.

Because wind velocity and frequency can be difficult to measure, I decided to convert this experiment into a water form in order to better visualize the waves being produced and more easily calculate the speed of the water/wind passing the ‘railing’. This works out perfectly as the behavior of wind and water in terms of vortex shedding is very similar. I will model the relationship between the diameter of the railing (what will be used as a substitute for the railing) and the frequency of the vortex shedding to determine the nature of this relationship. I will equally explore the effects of different shapes on the relationship described above in order to propose a new modification to the current model of the bridge that will minimize the sound and vortex shedding that occurs.

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Variable Analysis

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Apparatus and Materials:

  • Water tank (1)

  • Water pump (1)

  • Ruler (2) used as supporting devices and for scales during photo analysis

  • Camera or phone (1)

  • Ping pong ball (1)

  • Timer (1)

  • Strip of water-resistant cardboard that fits the dimensions of the water tank (1)

  • Tape (as needed)

  • 5 cylindrical rods of 2.8, 3.8, 4.8, 5.9, and 7.9 mm in diameter

  • 5 rectangular rods of 6.35, 12.70, 19.05, 25.40, and 31.75 mm in length

 

Safety Precautions:

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Procedure:

  1. Set up the barrier in the tank so the tank is separated into two parts and insert the water pumps

  2. Fill the tank with water but do not submerge the barrier

  3. Insert the pump at the bottom of the tank with the tube emitting water resting over the barrier 

  4. Calculate the speed of the water using a ping pong ball flowing across the tank of water on the barrier and measuring the amount of time it takes to traverse a certain distance; the velocity of the flowing water should be frequently re-tested over the course of the experiment to ensure it remains constant 

  5. Prepare the holding device using the two rulers that will suspend (but keep steady) the different sizes and shapes of the object and place it across the width of the tank 

  6. Place a camera over the holding device (or hold it in an off-hand) that will serve to record the vortex shedding for later analysis

  7. Place the first cylinder of steel on the holding device so that ⅓ of the cylinder is submerged in the flowing water and wait for it to produce vortex shedding

  8.  Have the camera record a 30-60 second clip of the vortex shedding in order to have a substantial amount of data to analyze (the trials will consist of taking the different frequencies at different time stamps during the recording)

  9. Repeat step 6 and 7 but increase the diameter of the cylinder of steel

  10. Repeat steps 6-8 but change the shape of the material to rectangular, following the same procedure as the cylinder of steel 

  11. Turn off the water pump, drain the tank, and process the data 

 

Experiment Setup

 
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Data Overview:

To collect data, I filmed the vortex shedding in water taking place and then analyzed the video footage to measure the time it takes for a complete wave to pass a certain point. The different trials consisted of taking different time segments and measuring the time for different clips of the video. By taking screenshots of various time stamps, I could print out different snapshots and draw out circles where vortex shedding could be observed. From there I can calculate the wavelength of the vortex shedding using proportions. By using the velocity and the wavelength, the frequency can be calculated. This process will be repeated for objects of increasing diameter and varying shapes.

Here is an example of a trial where I took a specific shot within the video:

 
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This photograph can be printed and by using a pen or pencil, the different waves of vortex shedding can be outlined and measured using a digital caliper. The two green marks represent 3 cm which can be a length used to carry out proportions.

 
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