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Mathcad Community Challenge – American Football Field Goal Geometry

    Mathcad Community Challenge

    This time the Mathcad community challenge is around field goals in American football.

    Create a Mathcad worksheet where you calculate the following angles from a given line of scrimmage for making a field goal:

    • The horizontal angle between the left and right field goal posts (18.5 feet apart).
    • The vertical angle between the horizontal bar of the goal post and the upper height of the goal post arms.

    How can you show how those angles change as a function of the line of scrimmage?

    Mathcad Community Challenge - American Football Field Goal Geometry

    Factors to take into consideration:

    • Assume the football is kicked from one of the hash marks (offset from the centre of the field) and 7 yards behind the line of scrimmage.
    • The goalpost is located at the back of the end zone. The horizontal bar is 10 feet above the ground and extends another 35 feet. For this exercise, the football must pass through the box defined by the goalpost.
    • American football uses yards, feet, and even inches, so you might want to take advantage of units in Mathcad.
    • Bonus: Can your worksheet handle entering yards from “your” side of the field (beyond the 50-yard line)? If not, feel free to use lines of scrimmage in excess of 50 yards.
    • You can ignore air resistance for trajectory calculations. You can also ignore anything about the football’s shape or its motion through the air (treat it like a point; no need to turn this into a doctoral thesis).

    We’re dealing with Euclidean geometry, so the math shouldn’t be that complicated. What matters is your execution. What tools (like plots and charts) can help you communicate the results?

    By the way, the longest field goal in NFL history was kicked by Justin Tucker of the Baltimore Ravens in September 2021. It was 66 yards, meaning the line of scrimmage was the Detroit 49-yard line, and it was kicked from the Baltimore 44-yard line. Next time you’re on an American football field, check out how far that is and how narrow the window looks. Field goal range is considered to be within the opposing team’s 35-yard line, which means the kick is 52 yards.

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    Source: PTC

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