Assignment #6:
Most Advantageous Field Goal
By Amber Krug
The regulation field goal width
in college football is 18.5 feet.
The distance between the hash marks is 53.3 feet. We want to discover at what yardage
does the kicker have the maximum angle from the hash marks.
LH to RH is the field where
LH is the left hash mark, RH is the right hash mark, and the distance between
the two points is 53.3 feet. LG to
RG is the field goal where LG is the left goal post, RG is the right goal post,
and the distance between LG and RG is 18.5 feet. Because the field goal is beyond the end zone, the distance
between these two lines is 10 yards plus the kicker stands 7 yards back from
the line of scrimmage (51 feet).
The red line begins at the 0yard mark.
We can determine this angle
by finding the distance of (RG)(RH) since we know (LG)(RG) is 18.5. We can then use the inverse tangent to
discover the degree of the angle.
We can now use the
Pythagorean Theorem to find the length of (RG)(RH).
(RG)(RH) =
sqrt(51^{2} + 17.4^{2})
= sqrt(2601 + 302.76)
= 53.89 feet
Now, letŐs take the inverse
tangent of opposite over adjacent or
tan^{1}(18.5/53.89)
= 18.95 degrees
So the angle at which a
kicker would have to kick from a hash mark is 18.95 degrees. Using this same process, we can
determine the angle from any yard mark.
Below is a table of some yardages along with all of the figures
necessary to determine the angle.
These were all calculated in Excel.
Yardage

Plus 17 yd Difference 
Converted to Feet 
Distance of (RH)(RG) 
Angle (Degrees) 
0 
17 
51 
53.88655 
18.94806 
5 
22 
66 
68.25511 
15.16521 
10 
27 
81 
82.84781 
12.5877 
15 
32 
96 
97.56413 
10.73689 
20 
37 
111 
112.3555 
9.350192 
25 
42 
126 
127.1958 
8.275363 
30 
47 
141 
142.0696 
7.419189 
35 
52 
156 
156.9674 
6.721807 
40 
57 
171 
171.883 
6.143174 
45 
62 
186 
186.8121 
5.655561 
Apparently some commentators
argue that the place kicker will have a better angle for the field goal if he
takes a penalty. The above table
illustrates that taking a penalty would not be a good idea.