Re: Why is a longer field goal kick (football), kicked at a lower angle?

The ballistics or kinematics of general physics class are overly simple. In reality, drag and lift factors play a major role in how far most objects will travel. Lift is the force that counteracts the downward pull of gravity and drag is the frictional force generated by motion through a fluid with viscosity (like air).

Some previous answers on ballistics and aerodynamic forces are available.
http://www.madsci.org/p osts/archives/jun99/927732521.Ph.r.html
http://www.madsci.org/p osts/archives/dec98/913922171.Ph.r.html
http://www.madsci.org/p osts/archives/jun99/928944018.Ph.r.html
http://www.madsci.org/p osts/archives/dec96/850019176.Ph.r.html

Two addition fun sites on the aerodynamics of sports are:
http://wings.ucdavis.edu/Bo ok/Sports/instructor/index.html
http://aci.m ta.ca/TheUmbrella/Physics/P3401/Concepts/AerodynamicsJCM.html

A field goal kick will travel end-over-end. This presents a unique challenge to solving the effects of drag and lift on the flight of the ball because the ball is not presenting a constant face into the air. It turns out that for many objects travelling in the air (or any fluid with viscosity effects), will travel farther at angles of attack greater than 45 or less than 45 degrees depending entirely on the relative strength of lift to drag. The flight path of the ball will not be a symmetric parabola. For example a golf ball with backspin will have lift created from the imbalance on the separation of the air which the spin creates. Therefore a driver will hit the ball farther at a lower attack angle (about 20 to 30 degrees) because the lift will cause the ball to travel farther than if the ball where hit at a 45 degree angle because it would stall out and drop back to earth at a shorter distance.
Similarly a batted baseball drop to earth short of the predicted no-drag path but the effects of lift are not as great as with a golf ball. Here as a sketch (not accurate except in concept) of the the effects of lift and drag on the flight of a ball. In general a projectile with enough lift to drag ratio can be launched at a lower angle to maximize range travelled. A projectile with severe drag will fall to earth short of the no-drag parabola forany angle of incidence. In fact the projectile (ball), can actually fall almost straight down.

No-drag          = +
severe drag      = -
drag & lift      = ?


                             +
                         +       +
                              
                     +               +
                          -   
                      -      -     &
                 +           & -        & +
                  -      &                 &
                                -            & 
                    &                         & 
                                -               
             +-&                -            + &
             & 


same lift/drag ratio and same initial speed but different angle of
incidence.

about 20 degrees = *
about 45 degrees = #





                     #
               #          #           *
                           * #             *
           #          *        #             *
          #      *              #             *
         #   *                  #              *
        #*                      #              *

There are game driven restrictions on the angle. The ball has to be higher than the raised arms of the onrushing defenders and the ball has to be high enough at the cross bar to get over so this significantly reduces the variability in the angle at which the ball can leave the kicker's foot. In addition, one must try to generate as much force through the center of the ball as possible. Otherwise the ball will spin end-over-end significantly but not go far enough. This is the balance between transverse and rotational kinetic energy. On the other extreme if the ball does not turn end-over-end the trajectory of the ball becomes less predictable making putting the ball through the uprights difficult.

I kick field goals all the time just for fun. My best distance with a regulation NCAA football is 38 yards for a made field goal. I work on my technique to make sure my foot strikes the ball in a manner balance the output of end-over-end versus distance and still clear the crossbar. In general to pop the ball up for short kicks (25 yards or less), the ball is struck low with the trajectory of the foot being almost parallel to the ground. To hit the long field goals, I strike the ball with a more upward trajectory which gives more translational energy and less end-over-end spin. This part of why it is easier to kick a ball off a kickoff tee versus the ground.

Sincerely, Tom "Soccer Toe" Cull