Chapter 4

In Chapter 3, it was stated that most natural movements of animals are linear and angular.

In this chapter, we will look at some aspects of the movement of animals.
The basic equations used in this chapter are reviewed in Appendix A.

The simplest motion is one in which the body moves along a curved path at a constant speed.

The problem here is to determine the effect on the motion of the object.

The maximum speed at which an automobile can round a curve without skidding is a common problem solved in basic physics texts.

This problem will be solved because it leads to an analysis of running.

The car needs a centripetal force between the road and the tires to stay on the curved path.

When the force is greater than the force on the curve, the car skids.

Banking the road along the curve may increase the safe speed on a curved path.

Skidding can be prevented if the road is properly banked.
The weight of the car is supported by this force.

A runner on a track is subject to the same type of forces as a car.

The runner leans toward the center of the curve.
An analysis of the forces acting on the runner can be used to understand the reason for this position.

This is a 4-min.

angle for a speed of 6.7 m/sec.

No effort is required to lean into the curve.

The body is balanced at the proper angle.
There are four exercises that look at other aspects of the force.

The swinging motion of animals is basically a straight line because the limbs are pivoted at the joints.

When the swing is through 120* (60* in each direction), the period is only 7% longer than predicted.

There is constant interchange between poten tial and kinetic energy as the pendulum swings.

The pendulum is temporarily stationary at the extreme of the swing.
Potential energy is what it is here.
The force of gravity causes the pendulum to start returning to the center.
When the pendulum begins to return toward the center, the acceleration is at a maximum.

The potential energy is converted to kinetic energy when the pendulum is accelerated toward the center.

When the pendulum moves to the center position, it's at its maximum speed.

The simple motion of a pendulum can be used to analyze some aspects of walking.

The motion of one foot in each step is considered to be a half-cycle of a simple motion.
Assume that a person walks at a rate of 120 steps/min and that each step is 90 cm long.
Each foot rests on the ground for a short time and then swings forward 180 cm and comes to rest 90 cm ahead of the other foot.
The full period of the motion is one second.

This is 3.6 times the force of gravity.

The leg is seen as a physical pendulum with a moment of inertia of a thin rod pivoted at one end.

The period is 1.6 seconds for a 90- cm leg.

The number of steps per second is simply the inverse of the half period because each step in the act of walking can be regarded as a half-swing of a simple motion.

It is tiring to walk faster or slower.

The effect of the walker's size on the speed of walking is now known.

The speed of walking is determined by the number of steps taken and the length of the step.

The size of the step is related to the size of the bibliography.

The square root of a person's legs increases the speed of his/her walk.

The walk of a small animal is slower than that of a large animal.

When a person runs at full speed, the situation is different.

In a fast run the swing Torque is mostly produced by the muscles, whereas in a natural walk it is mostly produced by gravity.
We can show that similar built animals can run at the same maximum speed, even if they have different leg sizes.

If one animal has a leg twice as long as another, the area of its muscle is four times larger and the mass of its leg is eight times larger.

A pendulum swinging under the force of gravity is an example of a pendulum swinging under the expression in the equation.

The maximum speed of running is determined by the leg size, which is in line with observation: A fox can run at about the same speed as a horse.

There is another clearly observed aspect of run ning.

The arms are straight when a person runs at a slow pace.

The elbows assume a bent position as the speed of running increases.

This increases the natural frequencies of the arm and the steps.

In Chapter 3, we calculated the energy needed to accelerate the leg to the speed of the run and then decelerating it to rest.

We will use the physical pendulum as a model for the swinging leg to compute the same quantity.
The legs swing at the hips.
The model is not strictly correct because in running the legs swing at the knees and hips.

The method for calculating the energy spent in swinging the legs will be outlined.

The leg muscles provide the energy in each step of the run.

We use this value for the period to calculate.

The agreement is acceptable considering that both approaches are close to each other.

When calculating the energy requirements of walking and running, we assumed that the leg's motion is stopped within each step cycle and that the energy is dissipated.

An overestimate of the energy requirements for walking and running is caused by the assumption of full energy dissipation at each step.

The underestimation of energy is balanced by the underestimation of movement of the center of mass up and down during walking and running.

We presented models of walking and running.

There are more detailed and accurate descriptions in technical journals.
The basic approach in the various methods of analysis is similar in that the highly complex interactiveMusculoskeletal system involved in walking and/or running is represented by a simplified structure that is easy to understand.

We only considered the motion of the legs in the treatment of walking and running.

To model the center of mass motion in walking, you have to consider the motion of the center of mass during a step.

When both feet are on the ground with one foot in front of the other, consider the start of the step.

We decided to be the rear foot.

The step begins when the rear foot leaves the ground and swings forward.

When the swinging foot is in line with the stationary foot, the center of mass is at its highest point.

As the swinging foot passes the stationary foot, it becomes the forward foot and the step is completed with the two feet on the ground with the right foot in the rear.

The center of mass is in front of the point of the single-foot contact with the ground as the free leg swings forward.

The center of mass is behind the supporting right foot when the rear left foot swings forward.
As in the upward swing of a pendulum, the center of mass is swinging toward the stationary right foot and the potential energy is converted to the kinetic energy.
After the left foot passes the stationary right foot, the center of mass moves forward as the potential energy is converted to kinetic energy.

This is an upper limit because it is assumed that the legs stay straight throughout the step in this simplified treatment.

The body in the process of walking is not a perfect pendulum and only part of it is converted back into energy.

To reduce the energy expenditure, the body seeks adjustments to minimize the up-and-down movement of the center of mass.

There is a distinction between walking and running.

Both feet are in contact with the ground at a point in the step cycle.
When both feet are off the ground, there is an interval in running.

The center of mass trajectory is similar to that of a swinging pendulum with a point at which the two feet pass one another.

Running can be compared to a person on a pogo stick bouncing from one leg to another.

The swinging-leg pendulum model we used to calculate the most effortless walking speed of 1.13 m/s is only 8% higher than this.

The amount of energy required per meter of distance is determined by speed.

At both lower and higher walking speeds, the energy consumed per distance traveled increases.

Walking is more efficient than running when the speed is less than 2 m/s.
Most people break into a run past this speed.

450 joules per meter is the amount of energy required to run at 3 m/s for 9 minutes.

The agreement between the two numbers is remarkably good considering the approximate nature of the calculations and the difference in methods.

It takes energy to carry a load.

Most humans, as well as animals such as dogs, horses and rats, have shown that the amount of energy they use when walking increases with the weight of the load being carried.
Carrying a load that is 50% of the body weight increases energy consumption.
The added energy expenditure is the same for most people if they carry the load on their heads or on their backs.

Women in certain areas of East Africa can walk with relative ease carrying large loads balanced on their heads, which has been the focus of recent studies.

Women from the Luo and Kikuyu tribes can carry loads up to 20% of their body weight without using more energy.
The energy consumption increases in proportion to the weight carried.
Carrying 50% of the body weight increases their energy consumption by 30%.
They were the experimenters of Heglund.
The high load-carrying efficiency of these women is due to the fact that the center of mass is moving in a pendulum-like fashion.
Their walking is similar to a swinging pendulum.
It's not known what part of the movement or training that brings about the enhanced load carrying abilities.

Some of the problems in this chapter are related to the weight of limbs.

Table 4.1 can be used to calculate these weights.

1.10 From Cooper and Glassow.

The arms swing back and forth in the act of walking.

The average force on the shoulder is calculated by using the following data and the data in Table 4.1.

The person has a mass of 70 kilograms and a length of 90 cm.

The total mass of the arms should be located at the center of the arm.

There is a carnival ride in which riders stand against a wall.

As the cylinder rotates, the floor of the cylinder drops and the passengers are pressed against the wall.

The arms will rise toward a horizontal position if a person stands on a rotating pedestal with his arms loose.

The physical pendulum model can be used to derive an expression for the amount of work done during each step.