Physics and Physiology Define the Hammer Throw

hammerthrowThe Hammer Throw is a Track and Field event which involves throwing a 12-16 pound ball secured on the end of a ~ 3.5 ft wire. Angles, trajectories, and even a unique physiological approach make this sport a precise and complex skill.

Learn the basics of how physics and physiology define the hammer throw.

Articles by Dave Kieda

Physics and Physiology Define the Hammer Throw (Basic)

The Hammer Throw is a Track and Field event which involves throwing a 12-16 lb ball secured on the end of a ~ 3.5 ft wire. The other end of the wire is secured to a handle which is used to grip the hammer as it is thrown. The hammer is thrown by gripping the handle and swinging the hammer in a circle, then spinning one’s entire body for 3-4 turns and then the handle is released. A men’s championship collegiate hammer thrower will toss a 16 lb hammer 190 ft or more; the current world record distance (2011) is approximately 285 ft.

A primary concept associated with the hammer (as well as the shot-put) is the ballistic trajectory of the object, used to determine the optimal angle to release the device. The optimal  angle is almost independent of the speed of the steel ball when the hammer is released. In a vacuum, the optimal release angle  (angle between the velocity at release and the horizontal plane) for maximum distance would be 45°, but the presence of air resistance slows the horizontal velocity of the ball down, making the optimal release angle closer to 42-43°.

Achieving the proper release angle requires some thought and planning. When the hammer thrower begins the first turn, the plane of the hammer swing is considerably lower than 45°, closer to 10°. At the start of the throw, the velocity of the hammer in the ‘orbit’, combined with the radial distance from the thrower to the steel ball, defines the angular momentum of the hammer.  As the hammer thrower uses his legs to turn and accelerate the ball, he applies an off-axis torque to the angular momentum, and rapidly turns the orbital plane to steeper and steeper angles, achieving the optimal release angle near 42° in the final turn.

Since most hammer throwers will learn to throw near the optimal release angle fairly easily, the most important factor affecting the final travel distance of the hammer is the speed of the steel ball upon release. Because the hammer thrower uses a circular orbit to throw the hammer, the hammer thrower must exert a centripetal force to keep the steel ball moving on the circular orbit. This force is proportional to the square of the velocity of the hammer divided by the radial distance between the steel ball and the hammer thrower’s body (center of mass), and can easily reach 600lbs or more at release. The ability of the hammer thrower to withstand such huge force is the main limitation in the distance that can be thrown; most hammer thrower perform heavy weight lifting exercises in order to increase their ability to withstand this extraordinary force.

Having developed one’s strength to the maximum feasible, the hammer thrower has additional strategies for increasing the final velocity of the hammer while exerting the same centripetal force.  Since the centripetal force depends upon the square of the hammer velocity divided by the radial distance between the steel ball and the hammer thrower’s center of mass, higher velocities can be accommodated (with the same centripetal force ) by increasing that radial distance. Physiologically, this requires allowing one’s arms to extend as far our as possible, so championship class hammer throwers are generally tall, with exceptionally long arms. A particular individual, with a given arm length, can also increase the radial distance by working to keep the steel wire exactly perpendicular to one’s chest throughout the entire throwing motion. In addition, the hammer thrower will substantially increase the  orbit radius by completely relaxing the upper body and arms, allowing  the arms to dangle completely freely and relaxed as they carry the centripetal force.

At the same time the lower body and legs will drive as explosively as possible in order to accelerate the steel ball as quickly as possible to the final speed. The optimal technique for the maximum hammer throw distance is therefore “schizophrenic”: the upper half of the body is completely relaxed and passive, and the lower half of the body is completely energized with explosive power. This seemingly contradictory combination is what makes the hammer throw one of the most unique and spectacular events in track and field!

By: Dave Kieda, Department of Physics and Astronomy, University of Utah

From Tee to Fairway: How Physics Affects the Drive, the Club, and the Golf Ball

Golf Ball Velocity

Golf Ball Velocity

The average golfer drives the golf ball with an initial velocity of over 100 miles per hour.  If the player uses a club with a flexible shaft, the act of swinging adds an additional measure of torque as the head of the club also propels forward to connect with the ball.  The head of the club has grooves that increase the friction between the club and the ball, allowing the club to more effectively focus the area of contact.

The optimal angle to hit the ball ranges from about 12 to 20 degrees.  Putting a backspin on the ball increases lift and can add significant distance to the drive.  The dimples on the golf ball itself help reduce drag from the air stream by reducing turbulent air pressure around and behind the ball, shifting the wake further behind the ball, thus allowing for smoother, less resistant flight.   Any combination of these variables contributes to how well the ball overcomes the forces of gravity and air resistance.

Learn the basics of how physics affects golf or read the more technical details here.

Articles by Trevor Stoddard