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The Long Jump: The Science of Projectile Motion

James Herzing
August 10, 2016

Track & field is one of the most popular groups of Summer Olympic events watched around the world.  On its own or as part of the decathlon, the long jump is one of the most technically challenging; initially, the athlete must accelerate to a maximum controllable speed, accurately transition from running to taking off as a projectile and properly landing for maximum distance.  Let’s take a look at the mechanics of these a bit further.

The approach

The object of the runner during this segment of the jump is to gain maximum controllable speed within 40 meters (131 feet).  This typically equates to 4 to 6 steps.  Usain Bolt is currently the fastest human ever recorded during a race and clocked in at 28mph for the men’s 100m dash.  Considering the distance is 60 meters shorter than that of long jumping, faster runners like Bolt may not reach that maximum in time (slower runners hit top speed sooner than faster ones do).

Another consideration is the muscle fibers of the runner.  Most humans have a 1 to 1 ration of “fast-twitch” fibers to “long-twitch” fibers.  Both use the produce the same amounts of energy, but fast-twitch fibers produce it more rapidly (although for shorter periods of time).  Athletes who tend to favor sprinting versus long-distance running have as much as 80% more fast-twitch fibers than their long-twitch counterparts; how this is so may depend upon genetics and/or may be developed through speed training.

Muscles, while aiding in forward propulsion can also act as an internal resistance when tense.  Coaches recommend that the head and neck muscles remain in a “neutral” position (although the head can be slightly lowered at the start).  Jaw muscles should be kept loose.  Hands should be relaxed with fingers in a slight curve Arms should be at an angle less than 90 degrees.  Any body parts that are tight or hyper-extended will produce inefficient motion, strain and affect other muscle groups in the process.

The takeoff

Once maximum controllable speed is achieved, the last two steps before takeoff are crucial.  The penultimate step is the longest stride of the entire approach and the runner’s hips will sink down.  The final step is “planted” on the board along the midline of the runway while the foot is planted flatly down.  This is done to minimize any vertical motion while maximizing horizontal.

Most engineers intuitively know that in basic Physics 101, when studying projectile motion, the optimum takeoff angle to achieve maximum distance is 45 degrees.  This is not the case in long jumping, however, for two major reasons:

The maximum velocity and the takeoff angle are not independent of each other as in projectile theory, and

The landing area is actually as much as 50cm lower than the takeoff area.

With this in mind, most research has shown that the optimum angle for most long jumpers is actually about 22 degrees, but can range from 15 to 27.

As the feet and legs are active in the takeoff, the rest of the body must respond as well.  The center of mass moves in front of the feet and the arms will swing forward.

Once airborne, there is an initial tendency for the body to experience a forward rotation which can result in a shorter jump.  To compensate for this, some runners will kick their feet and move their arms in a cyclical motion to maintain proper orientation.

The landing

While it would seem that most of the “hard work” has been done during the approach (gaining maximum velocity) and takeoff (launching at the optimum angle) there is not much else the athlete can do but hope and pray.  Obviously, this is the farthest thing from the truth.

Not leaving anything to chance, accomplished long jumpers prepare for landing by transitioning the heels of their feet from being behind the body to being in front.  The heels should be in the direct line of trajectory to make first contact with the ground and to prevent the jumper from falling backwards.  As the heels dig in, the hamstrings contract while the hips rise, causing the forward momentum of the jumper to rock the body forward.

Given this abridged and “simplified” version of the mechanics of long jumping, it should be noted that there have been countless motion studies and various theories on proper orientation of body parts throughout the various stages.  High-speed motion capture software analyze the physics of individual runners allowing for ultimate optimization.

So as you watch the long jump events at this year’s Olympics, think of all the time and effort these athletes undergo not just to perfect their bodies to peak physical health, but to undergo countless hours of analysis and positioning as every extra millimeter will separate those athletes who have medals from those who go home with nothing.


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James Herzing

James Herzing is the Product Marketing Manager for the Autodesk Simulation portfolio. He has spent 12 years in the field of Finite Element Analysis, starting his career at Algor, Inc and with the last 7 spent at Autodesk. He graduated from the Pennsylvania State University with a BS in Mechanical Engineering.