1. Contact Distance, Contact Time, and Vertical Force

To begin, we examine the relationship between contact distance, contact time, and vertical force requirements. During the ground contact phase, the contact excursion angle is the total angle traveled by the leg. For most runners, this angle varies between 50 and 60 degrees, or approximately one radian. The contact distance is the distance the center of mass travels during this phase, and it is generally equal to the length of the leg, about one meter.

Running speed can be quantified by dividing the contact distance (meters) by the contact time (seconds). Thus, faster speeds are related to shorter contact times. Studies have consistently shown that as speed increases, contact time decreases, requiring greater vertical force applied in a shorter time.

Contact, Angular Excursion, and Contact Distance

To define these terms more clearly, the contact excursion angle is the amplitude of the angular movement of the leg during ground contact. On average, this angle ranges between 50 and 60 degrees for most runners. The contact distance, on the other hand, is the distance the runner’s center of mass travels during this contact phase. Given the geometry of ground contact, this distance is approximately equal to the leg length, which is about one meter for average-height runners.

Relationship Between Speed and Contact Time

An effective way to understand the relationship to speed is through the speed formula:

Speed=Contact Distance / Contact Time

This equation illustrates that for an average runner with a contact distance of approximately one meter, running speed increases as contact time decreases. This principle is empirically validated: faster runners exhibit shorter contact times, thereby exerting heightened vertical forces within a condensed timeframe.

Vertical Force and Contact Time

The application of vertical force is crucial for maintaining running speed. The necessary vertical force increases as contact time decreases. This is because, to maintain balance and speed, the vertical impulse (the product of average vertical force and contact time) must be sufficient to counteract the runner’s body weight. Thus, faster runners not only apply greater vertical forces but do so more quickly, especially in the first part of the contact phase.

2. Angular Movement of the Legs

The next aspect to consider is the angular movement of the legs, which includes angular velocity and acceleration. New research from the Human Performance Laboratory at Westchester University shows that contact angular velocity is calculated by dividing the contact excursion angle by the contact time. Since this angle is usually similar for most runners, shorter contact times require faster leg angular velocity.

Angular Velocity of the Legs

The angular velocity of the legs during ground contact is a critical factor in achieving high speeds. Mathematically, it is expressed as the ratio of the contact excursion angle (in degrees) to the contact time (in seconds). For example, if a runner has a contact excursion angle of 60 degrees and a contact time of 0.12 seconds, their angular velocity will be 500 degrees per second.

Angular Acceleration and Thigh Swing Frequency

Angular acceleration is equally important, as it represents the runner’s ability to quickly change the direction of their leg movement. Faster runners have a greater amplitude and frequency of thigh swing, meaning their thighs move back and forth more rapidly and with a greater amplitude. This oscillatory motion is crucial for generating the necessary force to achieve and maintain high speeds.

Studies on Thigh Oscillation

Various studies have shown that during high-speed running, thighs oscillate in a continuous sinusoidal pattern. This means the thigh movement follows a harmonic pattern, similar to a sine wave, which is efficient for force and speed generation. Compared to slower runners, sprinters have a faster oscillation frequency and greater amplitude, allowing them to apply forces more rapidly during ground contact.

3. Foot Landing Speed and Vertical Force Application

Finally, we examine the relationship between leg angular velocity, foot landing speed, and vertical force application. Recent research shows a strong correlation between leg angular velocity and the tangential speed of the foot upon ground contact. This tangential speed directly affects the vertical force applied during ground contact, being crucial for runners aiming to reach maximum speeds.

Tangential Speed of the Foot

The tangential speed of the foot upon ground contact is crucial for the effective application of vertical force. Runners with higher leg angular velocities tend to have higher tangential foot speeds, resulting in greater force applied in the shortest time possible. This factor is essential for achieving high speeds, as a higher tangential foot speed allows for more efficient contact and better force transmission.

Two-Mass Model

A theoretical model used to better understand this process is the two-mass model. This model suggests that the vertical forces during running consist of two components: a smaller mass related to the impact of the lower limb and a larger mass supporting the body weight. Sprinters apply greater and faster vertical forces compared to other athletes, allowing them to maintain higher speeds.

Rapid Application of Vertical Force

The ability to apply vertical forces quickly is what distinguishes sprinters from other athletes. Studies from the Human Performance Laboratory at Westchester University have shown that sprinters apply most of their vertical force in the first half of ground contact. This is crucial, as the speed at which vertical force is applied greatly determines running speed. Slower runners tend to apply less intense forces over a longer period, resulting in lower speeds.

Training to improve thigh angular speed and the ability to apply rapid vertical forces can be fundamental for sprinters. Additionally, focusing on developing more rigid ground contacts from the foot to the kinetic chain is essential for effective force transmission. Training programs should focus on improving the speed and angular acceleration of the thighs, as well as the athlete’s ability to strike the ground with firm and quick contact.

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