Did you learn about the Pythagorean theorem in geometry class? And have you wondered whether it would be useful to you beyond the right triangles in the math worksheets you completed?
“I use it all the time” says Skeeter, who takes the designs for roads, sidewalks, ramps, bridges, and walls and figures out what measurements and materials make each structure work well for the people using it.
Hopefully when you walk through a park or along a sidewalk or when you bike along a designated bike lane, you enjoy the walk or ride and don’t think much about all of the things that could go wrong if it were poorly designed. You might admire the view, look for a friend, or wonder how long it will take you to get where you’re going. You’re probably not thinking “If it rains, will the water pool on this path?” Or “Will the pressure of the higher ground on one side of this wall cause it to collapse?”
We’re free to enjoy the parks and transportation systems of our cities and towns because civil engineers like Skeeter have put all sorts of careful work into making them as safe and comfortable as possible.
Perfectly flat sidewalks would catch the rain, creating wet, potentially slippery conditions. But sidewalks with too much of an angle would cause other problems, especially for people traveling by wheelchair.
How can Skeeter find the correct angles for these surfaces — angles that will let people walk and roll comfortably while water flows down nearby drains? Regulations set by the Americans with Disability Act (ADA) guide her, as does math. She uses tape measures, levels, and other tools to find the run and the height of each sidewalk, ramp, or stair and then uses the Pythagorean theorem and what she knows about percentages to make sure things will be safe. “Every time I turn around, it’s like ‘let me do that whole a squared plus b squared equals c squared.’”
When Math4Science spoke with Skeeter, she was working on the Union Turnpike exit of the Clearview Expressway, also in New York City. “We placed a lot of sidewalk over there with ADA curbs and ADA ramps. We had to check that all of the slopes met the requirements for ADA standard.”
While working on the Clearview, Skeeter also worked on a bike lane for Route 9A. As she did that, Skeeter was concerned about runoff: what would happen when it rained? Would there be ponding, which happens when water runs into an area and has no place to go? Puddles and larger flooded areas are dangerous for bike riders and also for the structure of the bike lane itself.
Drilling holes into the walls on the side of the bike lane — “weep holes” the rain could run into, instead of running down the wall and into bikers’ paths — solved the problem. “Say you have an area that is experiencing a lot of ponding because there’s no catch basin — no kind of drainage: there’s just walls. You don’t want the water to sit there but there’s no way to put in a massive drainage system.” “We’ll drill holes through the wall” — holes “big enough to allow the water to drain through” to get to drainage systems on the other side.
“When you drill these holes and you put in PVC pipe,” you also think about angles, says Skeeter. Not only do you want to angle the holes in ways that lets the water drain into and out of them but you also need “the pipe to be at a slope so that the water doesn’t just sit inside the pipe as well: it has to be at a certain angle and you have to determine which angle, so again, there’s the Pythagorean Theorem.”
Tamara’s first professional ambitions were to be a lawyer or to start her own business. Her father worked for the Metropolitan Transit Authority, as a super. “He would find different material and bring it home and the next thing I know…I have a coffee table in my living room.” Tamara enjoyed watching her dad build furniture out of things he found on the job.
Nowadays, Skeeter herself does not call “a contractor every time something needs to be done.” Instead, she says “Hey, Dad, I have a project for you: let’s work on it.” Or she finds extra wood and builds her own furniture, such as the television stand in her bedroom.
Tamara loved math as a child. In elementary school, she was tracked into an upper-level math course. “Math, it just came easy to me.” “I had teachers that saw my strengths and helped to push me towards that. I was encouraged to test for a lot of different specialized junior high schools.”
At Isaac Newton Middle School for Math & Science, where she ended up, Tamara joined the math team and found out about the test to get into New York City’s specialized high schools. Her score on that exam landed her at Brooklyn Technical High School, where she met another future civil engineer: Tysheina Washington (then Tysheina Robertson).
The teachers at Brooklyn Tech also encouraged Skeeter to take advantage of her math skills and go into engineering. “I remember being in college after graduating Tech…. [I was] trying to figure out what I wanted to do with my life, so I went back to Tech and I said ‘You guys want me to work in this field, get me a job in this field’ and I remember the teacher said, ‘Here, call this number.” That’s how Skeeter ended up in a training program for the Department of Transportation (DOT).
Skeeter enjoys working for the DOT. She trained with them more than two decades ago and still consults for different DOT projects. “I’ve done highway inspection, bridge inspection, park inspection.” And she has helped build two different skate-boarding parks, including Golconda Skate Park, in Brooklyn, and has plans to work on a third.
The designs for Golconda Skate Park had a couple of problems. For instance, they called for a wall that had a higher ground on one side than on the other. “People don’t understand that if you don’t have the right foundation, a wall is going to come down…. What’s going to stop this wall from falling down?” Skeeter asked, noting that “the pressure from the soil on one side” would “cause the wall to come down.”
In order to protect skaters and other people spending time in the newly renovated park, Skeeter spoke with the designers, explaining the problem. Then “we redesigned the wall,” adding a foundation to make it more stable.
One of Skeeter’s favorite parts of being a civil engineer is “seeing the math form art.” Golconda’s now the home of skate-boarding competitions. And Skeeter’s particularly proud of helping build parts of the West Side Highway. She helped build the median and the walls of that road from Chambers Street down to Battery Park City, in Lower Manhattan.
“A lot of times when we start” to work on a road, bridge or park, it’s literally just math to us: it’s just numbers. We know we have to build a certain way and everything is numbers. And then, when” all the redesigning and construction ends, “you’re left with this beautiful project.”