How to Run the Most Efficient Soccer Field Lap

We all know P.E. as being a fun, competitive class. Every day, you get to compete with your classmates in a variety of different sports. Whenever there is competition, there is a need to be the best. This is the whole reason there are records on the wall of the gym: to promote our competitive spirit. Therefore, in this article, I am going to be answering how to run, theoretically, the most efficient soccer field lap.

First, we have to start with our definitions. We define the soccer field as being 280 ft long and 172 feet wide, measured from Google Earth. We define the starting location and ending location to be halfway along the long side of the field, by the side with the stairs and the basketball court.

The biggest issue we face is how to run around the corners. While multiple different ways could be faster, I am going to be using the most intuitive route, being that you run parallel to the field until you are close to the corner, where you trace out a quarter circle until you are around the corner and parallel to the next side of the field. There should be a path where you don’t have to decelerate, meaning you stay at your top speed for longer.

Now, I am going to provide how to optimally apply this path when running the soccer field lap during PE. First, you are going to start not on the edge of the field, but around 2 feet out (this value was found through some trial and error). Now, once you approach the corner, start to lean into the corner before you pass it, such that you perfectly run around the corner, taking the tightest path possible without cutting the corner. This step is pretty hard, and you may need to practice it. Make sure your corner is cut tight enough that you are not running too far while also making sure that your feet don’t slip from beneath you, or you slow down. Once you master this step, perform it four times at each corner and then sprint the last section. Be sure to maintain your momentum until you cross the finish line to keep as much speed as possible. This process will be harder to perform with other people competing to take the optimal line around the corner, so be careful not to run into anyone.

Now, how fast could you possibly go? Since the field is 172 by 280 feet, and we are starting 2 feet away from the side of the field, we now must find the distance you follow. As shown in the diagram below, there is an image of the corner of the soccer field. Let point A be where we switch from running in a straight line to our quarter-circle path. Let point B be where this circle touches the corner of the field (we know this will happen since we are running the most optimal distance). Let point O be the center of the circle whose path we are running on. Let point I be the intersection of segment AO with the edge of the soccer field. 

We know that the measure of angle BOA is 45° because if we reflect A about the line BO, we get A’. Since the measure of angle A’OA is 90° and we know that BO bisects angle A’OA, the measure of angle BOA is 45°. Now, since the measure of angle BIO is 90°, this is a 45-45-90 triangle. Therefore, since the hypotenuse of the triangle has a length of r, we know that BI = IO = r/sqrt(2) by the properties of 45-45-90 triangles. Since AO is the radius of circle O, we know that AO-IO=2 can be written as r-r/sqrt(2)=2. Now we can solve this equation for r to find that the radius of this circle is 4+2sqrt(2) which is about 6.83 feet. Therefore, the distance run on these corners is 4(2pi*r/4)=pi(8+4sqrt(2)) which is about 42.9 feet. Now, the distance you cover in the straight sections is 172+172+280+280-8(4+sqrt(2))/sqrt(2), since we must subtract the segment BI 8 times, otherwise we would be overcounting that distance. Thus, the total distance on the straight sections is approximately 865.37 feet. Therefore, the total distance is 908.28 feet (276.84 meters) to go through the entire length of this path.

Now that we have the total distance, we can calculate the theoretical minimum time we could achieve on the soccer field lap. 

First, we are going to look at the world record for fastest speed, then the world record on the 200-meter sprint, since the distance is relatively close. Finally, we will calculate this for the fastest animal possible and the fastest man-made machine to consider how fast we could possibly go. 

During his 100-meter world record sprint, Usain Bolt reached a top speed of 43.99 km/h. At this speed, he can travel 12.22 meters per second. To cover the 276.84-meter distance, it would take him 22.66 seconds, almost half the time of the current record. Note that this number is inaccurate for a variety of reasons, such as the fact that the distance is longer than a sprint and that it might be hard to cut corners at that speed. Still, it is fun to see how low the times can get.

During his 200-meter world record dash, Usain Bolt ran the distance in a time of 19.19 seconds. Therefore, his average speed was 10.42 meters per second. At this rate, it would take around 26.56 seconds to run the lap, which is much slower but still very fast.

The fastest animal on earth is the peregrine falcon, being able to reach speeds of up to 300 km/h. This is around 83.33 meters per second. If a peregrine falcon were to fly this path at its max speed, it would take around 3.32 seconds. This value is almost impossible to achieve since the forces at the corners would be very extreme. 

The fastest speed a human has ever gone was in the Apollo 10 command module, achieving a speed of 39,937.7 km/h. This speed is an insanely fast 11093.8 meters per second. If a human were to fly this track at that speed, it would take 0.025 seconds to complete! This amount of time is so small, you might miss it with just one blink.

Overall, the soccer field lap is a hyper-competitive activity that can be made very efficient using some quick math! I hope this article can help you along your running journey!