Assignment 6: Field Goal Problem
By:
Jonathan Sabo
The football rules in college football were changed a few years ago have made the uprights 5 feet narrower than previously. Many game commentators have harped about how much harder it is to kick field goals from the hash marks. Assume the field goal is attempted from the hash marks. At what yard marker does the kicker have maximum angle to the two uprights. Note: You will need to find out the width of the uprights and the width of the hash marks . . . make a sketchpad model. Is there any merit to some commentators argument to take a penalty in order to have a "better angle" on the field goal kick?
The first thing needed for this exploration is the dimentions of a NCAA football field. By doing an internet search I was able to find the appropriate information for this exploration.
- Length: 360 feet or 120 yards
- Width: 160 feet or 53 1/3 yards
- Hash marks: 40 feet wide and 60 feet from the sidelines.
- Goal Posts: 18 feet 6 inches wide.
This
picture is drawn to scale of a NCAA football field. Point F
represents the right side of the goal posts and point G represents the
left side of the goal posts. Point B represents where the ball is
located. If you would like to manipulate the location of the ball
you can use this GSP file. If
you drag point B, the angle to the uprights will change. After
manipulating the points we find that the largest angle to the goal
posts is actually in the end zone. When the ball is 5.82 yards
away from the goal posts the anlge between the ball and the goal posts
is 
.
However it is not realistic to kick a field goal from inside of
the end zone. In college football, field goals are attempted from
seven yards behind the line of scrimmage. Therefore, the largest
realistic angle would be from the seven yard line. At this discance the angle between the ball and the goal posts is approximately 
.
As the ball moves further away from the goal posts the angle gets
smaller and smaller. Based on this information it would make no sense
to take a penalty to get a better angle at the field goal. If the
ball is moved further away from the goal line the angle to the goal
posts will be smaller.
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.
However it is not realistic to kick a field goal from inside of
the end zone. In college football, field goals are attempted from
seven yards behind the line of scrimmage. Therefore, the largest
realistic angle would be from the seven yard line. At this discance the angle between the ball and the goal posts is approximately .
As the ball moves further away from the goal posts the angle gets
smaller and smaller. Based on this information it would make no sense
to take a penalty to get a better angle at the field goal. If the
ball is moved further away from the goal line the angle to the goal
posts will be smaller. Return to Home Page