Straight Arm vs. Bent Arm Part 2: Newtonian Physics

By Gary Hall Sr. | May 31, 2016, 4:38 p.m. (ET)

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Go back to school! Erase the smelly, crowded hallways of your high school from your mind and imagine yourself under the Islamorada sun in a clear pool ready to absorb knowledge that will enable you to swim faster. Swim School from Gary Hall Sr. of The Race Club is about lifelong enjoyment of the sport. It’s always more fun to swim to your potential.

A swimmer doing freestyle, moving down a pool, partly immersed in water, the remainder in air, has a complex and variable shape, changing with each moment in an effort to maximize the speed in the water. We have spoken a lot about the mechanics of the underwater pull with respect to compromising the positions of maximal propulsive forces and minimal frontal drag forces in an effort to attain the highest possible body speed. Now let’s turn our attention to the freestyle recovery phase of the pulling cycle — those few tenths of a second between the time the hand leaves the water and when it enters the water for the next cycle.

Unlike backstroke, where everyone recovers with straight arms over the water, we see many variations of freestyle recovery motions. We see great freestylers with bent elbows, fingers barely getting over the surface of the water, and we see great freestylers with straight arms, hands as far away from the shoulder as possible. Forget about biomechanics and possible shoulder injury for a moment. From a pure physics stand point (Newtonian mechanics), which swimmers have it right?

When evaluating the motion of the arm in the recovery phase there is an extremely important law of nature that must be considered and that is the law of conservation of energy. What that means is that within an isolated system, the total energy cannot be created nor destroyed, but it can be transferred.

When determining the kinetic energy of a swimmer doing freestyle, one could divide the body into three separate components. Since the legs are moving harmoniously in opposite directions for relatively short distances, one could consider the kinetic energy of the head, body and its legs as one component moving linearly or what is called translational movement. The kinetic energy of the head, body and legs is determined by the following equation:

K(B) = ½ Mv2, where M is the mass of the swimmer’s head, body and legs and v is the body’s velocity.

The second component of kinetic energy is from the rotation of the body/head along its axis. This rotational energy is angular, not linear, and since this energy is primarily used to create a counter force for the underwater pulling motion and continuously reverses its direction, we shall ignore it for now.

The third component of kinetic energy of the swimmers body is contributed by the arms on the recovery but is also not linear. It is angular and centered at its pivotal point, the shoulder. The kinetic energy of the recovering arm is determined by the following equation: K(A) = ½ Iw2, where I is the moment of Inertia of the arm and w is the angular velocity of the hand.

The moment of inertia is determined by the mass of the arm and by its length. By bending the elbow, we don’t change the mass of the arm, but we shorten its length. That means if the kinetic energy of the system is the same for both straight arm and bent arm, then the hand must be moving much faster on the bent arm recovery than the straight arm recovery. This is similar to what one sees with an ice skater twirling first with the arms out then, when he brings the arms in tight to the body, the twirling goes much faster.

The truth is that we don’t see the hand recover much faster with a bent elbow than we do with a straight arm. In fact, some of the fastest stroke rates I have ever seen are with straight-arm freestylers. So this must mean that the kinetic energy of the recovering arm is higher with the straight arm than it is with a bent elbow, and this is precisely what happens. In order to keep the velocity of the hand nearly the same with the straight arm as with the bent arm, more force (effort) must be given by the swimmer to the recovery motion. That is good and bad for the swimmer.

It is bad because the additional effort required to create that force means that there may not be as much recovery with the straight arm after all as we might have thought. Once the hand hits the water, which is a collision of sorts, and the angular velocity and the mass of the arm drop to almost zero, where does all of that kinetic energy of the arm go?

According to the law of conservation of energy, it must go somewhere, and it does. Some of the energy gets transferred to the splash and disruption of the water molecules at entry. Because the arm is attached to the body at the shoulder, the remainder of that angular kinetic energy gets transferred to the body, helping it to get down the pool a little faster. Since there is more kinetic energy available with a fast straight-arm recovery, then more energy gets transferred to the body with this technique as opposed to bending the arm. It just requires more effort to do it.

You can actually see this transfer of energy occur in the pool by keeping your legs still, swinging your arm aggressively over the top and watching the motion of your body move forward against the tiles on the bottom of the pool as your hand strikes the water. You must be sure to not initiate the pull with the other hand until after the hand strikes the water. Admittedly, you won’t move very far, as the force required to move the human body through water is substantial, but every inch in the right direction counts.

Finally, for shoulder-driven (high stroke rate) freestyle, the kinetic energy of the arm swing on the recovery provides a third counter-force (along with the body rotation and the kick) for the opposite arm/hand to pull against. Since the angular momentum of the arm swing has both magnitude and direction, keeping the arm recovery more in the vertical plane moving forward will create a more effective counter force for the other hand pushing backward than swinging the arm to the side, where the energy is directed more in the horizontal plane. This applies only to shoulder-driven freestyle where the recovery phase of one arm and the propulsive phase of the other arm are occurring simultaneously. With hip-driven freestyle, the propulsive phase does not begin until after the other hand has entered the water. With this technique, all of the counter-forces are provided by the body’s rotation and the kick.

In part three of this aquanote, I will summarize the pros and cons of straight-arm recovery vs. bent arm recovery in freestyle.

Yours in swimming,
Gary Hall Sr.

gary hall srGary Hall Sr., M.D. is a three-time Olympic swimmer (‘68, ‘72, ‘76) who earned a medal in each of the three Olympic Games. At one time he held 10 world records in all strokes except breaststroke and was the World Swimmer of the year in 1969 and 1970.

Gary Sr. serves as president and technical director of The Race Club Inc. based in Islamorada, Florida. He is the current president of the United States Olympians and Paralympians Association and co-founder of World Fit, a non-profit organization promoting childhood exercise and sports. He has six children, the oldest of whom, Gary Jr., also swam in three Olympic Games (‘96, ‘00, ‘04) and earned 10 Olympic medals. Two other children, Richard and Amy, and his wife, Mary, work with Gary Sr. at The Race Club. In 2006, Gary Sr. retired from ophthalmology to dedicate his remaining professional career to teaching advanced swimming techniques for competitive swimmers and triathletes. 

The views expressed in this article are the opinion of the author and not necessarily the practices of USA Triathlon. Before starting any new diet or exercise program, you should check with your physician and/or coach.