This month’s 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? Factors to take into consideration: Assume the football is kicked from one of the hash marks (offset from the center of the field) and 7 yards behind the line of scrimmage. The goal post is located at the back of the end zone. The horizontal bar is 10 feet above the ground and extend another 35 feet. For this exercise, the football must pass through the box defined by the goal post. 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 pertaining to the shape of the football 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? Find the Mathcad Community Challenge Guidelines here! 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 a 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.

16-Pearl

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Mathcad Community Challenge November 2022 - American Football Field Goal Geometry

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This month’s 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? 2560px-Acre_over_US_and_Associationl_football_field.png

Factors to take into consideration:

Assume the football is kicked from one of the hash marks (offset from the center of the field) and 7 yards behind the line of scrimmage.
The goal post is located at the back of the end zone. The horizontal bar is 10 feet above the ground and extend another 35 feet. For this exercise, the football must pass through the box defined by the goal post.
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 pertaining to the shape of the football 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?

Find the Mathcad Community Challenge Guidelines here!

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 a 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.

C

ChasePAnswer

1-Visitor

I didn't do the best job of documenting my trigonometry and what my variable names refer to, but I think I hit the two objectives!

P

ppal_255687

18-Opal

So that I dont have to talk to Bill Belichick can the kicks be made from the extreme left and right offset or just the middle offsets?

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DaveMartin

Author

16-Pearl

For this challenge, the kick will be made from either the left or right hash mark in the middle of the field (the ones located 40 feet apart from each other). Not the ones along the sideline that help players judge whether they are in the field of play.

And you spelled Belicheat wrong.

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Fred_Kohlhepp

23-Emerald I

Hmmm! Did I miss it? Or have you not specified the initial velocity or the impulse of the kick? If it's me kicking, the ball won't ever get to the goalposts! 😉

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