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 0-yard 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(512 + 17.42)

 

= 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.

 

 

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