Computer Modeling Activity

Introduction

Part of the development of this activity was funded by an NSTA's and Toyota's TAPESTRY grant and by the Wright Center for Science Education, at Tufts University.

The Computer Modeling Activity is designed for use with Knowledge Revolution's Interactive Physics II software and a Macintosh computer. Interactive Physics II has a Windows version therefore, this activity will work equally well in the Windows oriented world. You can link to Knowledge Revolution's web site by going to the reference section of Slam Dunk Science.

As the ability of sport scientists and researchers to collect data grows so too does the need to test quickly new hypothesis that are generated from these data. A sport researcher who believes that position on a bicycle can influence energy consumption can test a cyclist in a wind tunnel while monitoring the riders oxygen consumption as a measure of energy use and efficiency. A researcher might believe that plantar pressure distribution is a major contributor to lesion development on the diabetic's foot. They may measure this pressure distribution by using an insole that contains hundreds of individual load cells.

Figure 1 - Pressure Distribution at Various Points on the Foot

Do you think this pressure varies relative to the age of an individual? Does it influence the development of lesions on the feet of diabetics?

Researchers, in their quest to understand and prove theories, collect mounds of data that allows them to accept or reject hypothesis. What happens when the researchers decide that their data supports their hypothesis and they want to test their theory in other ways? For example, the researcher working on plantar pressure distribution might want to see how different insoles might effect this distribution to decide on the best way to reduce the likelihood of lesion development.

In the past the researcher would design a new experiment, enlist further subjects, collect more data, analyze that data, and then modify their world view again. This, as you probably know, is the basis of all good science: the testing and retesting, refining and defining of hypothesis, the integrating of many experiments into a body of knowledge that forms a theory. It is easy to imagine how such a process can become a time and money consuming prospect. Researchers, in sports and other disciplines, have been working on ways to speed up this process by using computers and computer modeling. Once enough data has been collected a computer model can be constructed that is enough like the real world that further experiments can be run on the model itself.

Computer modeling allows researchers to build models of systems, based on real world data collected from many studies, and then test the model under conditions that are not always possible given the time and materials that might be available. Using the idea of alluded to earlier, the building of an insole for diabetics, it is possible to see how a computer model of the foot can be used to facilitate the process of building an insole that meets the specific needs of diabetics.

In a presentation entitled: Measurement of Foot Stiffness Distribution and Computational Simulation of Plantar Pressure Distribution, N. Praxmarer of the Technical University of Vienna, outlines his model of this distribution and how it might be applied to help design insoles for diabetic's shoes.

His goal is to help optimize the design of such insoles by building a computer model based on stiffness characteristics in the heel and forefoot that influence pressure distribution. Dr. Praxmarer is following up on this research and model by developing additional models for the shoe and elastic insole. By integrating all three of these models he hopes to help improve the development of orthopedic footwear.

Figure 2 - Measured Stiffness Characteristics

What does this graph tell you about the displacement of the tissue in the heel of the foot vs the forefoot? (graphic after Praxmarer)

The model constructed from the plantar pressure distribution project showed that the foot could be modeled under well defined conditions. Further research will show how accurate this model is in helping to design and test insoles that will help address the problem of lesions in the diabetic's foot. Early models are never as dynamic as models that are built on their foundation. Basically a researcher starts with a simple model that allows them to test basic assumptions then builds on that model by refining it with new data. As their model grows in complexity, so to does its predictive ability.

As researchers' techniques improve and data grow, so too does the researchers' computer model of the foot. It is not too far out of the realm of possibility to believe that in the future an individual computer model of your feet will be stored in a shoe company's computer and a custom "Super-Dynamo Stabilo-Pak 190-Blazer" could be sent to you after ordering through the World Wide Web. Your custom shoe would reflect changes in your foot morphology based on scientists' understanding of how foot morphology changes with age, or, in the case of the diabetic, with disease. You would always get the most up to the minute model tuned to a computer model derived from data collected from your feet. (Hmmm, get my patent attorney on the line!)

You can see that the ability to model a system, like the model of the diabetic foot above, based on the power of the computer is extremely valuable to the researcher. It is another tool that you, as a scientist, should be aware of. Computer modeling allows the sport researcher to speculate infinitely on the what ifs inherent in trying to build a total understanding of a system.

Objectives

This activity will focus on constructing a simple model of one system, in particular the shock absorbing capability of the leg, and testing this model under varied conditions. These conditions will include loading the leg with greater mass, and seeing how this simple model might react. Students will use Knowledge Revolution's Interactive Physics software to build and test the model. At the end of this activity students will understand:

1. How and why a sport researcher or shoe designer would use computer modeling,
2. How to set up a simple model using Interactive Physics software,
3. How to test a simple model under varied conditions,
4. How computer modeling might apply to other fields besides sport research,
5. Where to go for more information on computer modeling.

The field of computer modeling is one of the most dynamic and fastest growing fields in science. In fact, modeling is a field unto itself that is applicable to virtually every aspect of life from environmental studies to business. For example, systems dynamics, a specific type of computer modeling, is actually being used in schools as a central theme, or philosophy, for understanding all aspects of the world around us.

• Knowledge Revolution Interactive Physics II software
• Macintosh or Intel-compatible Computer

This procedure uses Interactive Physics II software. This software, running on a Macintosh computer, provides a good balance between ease of use, features, and cost. An alternate procedure using Knowledge Revolution's Working Model software would allow your students to build more robust models. In fact, many researchers in biomechanics labs at major universities are using Working Model for their computer modeling.

It is suggested that you familiarize yourself with the Interactive Physics II software before you start this procedure. This activity is based on the assumption that you have done so before you start to experiment with computer modeling.

It is important to realize that the model built here is relatively simple. You will most likely see how it can be modified to more accurately depict the real world data that you are attempting to represent. We have deliberately focused on a very simple model, an attempt to replicate the ground reaction force (figure 3) generated when an athlete runs across a force plate, to encourage students and schools to develop their own models, to share them with (via the Internet) and, in turn, to share them with other schools.

Figure 3 - Ground Reaction Force

When an athlete runs across a force plate the impact can be recorded and looks similar to this. This is a representation of a runner who hits the force plate first with the heel (like many marathon runners) and then rolls on to the forefoot. What do you think the impact record would look like for an athlete who hits the force plate only with the forefoot first (like a sprinter) and then pushed off?

The model you are going to build uses work done by R. McNeill Alexander as a starting point. He describes the leg and foot muscles and tendons as springs. His view is based on his research studying the elastic properties of muscles and tendons in a dynamic testing machine along with force plate and motion analysis data collection of runners.

Assumptions of the model:

1. A 70kg man running at a six minute per mile pace who exhibits a change in his center of gravity of 6.0 cm.
2. The force record for this runner, a heel striker, is similar to figure 3.
3. That the peak force for this runner is about 1900 N, or 2.7 times body weight, and this relationship holds true for any mass runner.
4. That the components of the body (feet, legs, torso, tendons, ligaments, muscles, etc.) act as a solid mass during one phase of the stride cycle.
5. That we are looking at one aspect of the stride cycle, the impact of the foot with the ground and push off.
6. The data used to build the equations that allow Interactive Physics to model the real world are accurate.
7. Most of the default settings in Interactive Physics are acceptable for our initial model.

(Note: This model uses a very simplified view of Dr. Alexander's work, a model based on his actual data would be much more complicated and beyond the scope of this activity.)

Setting up Interactive Physics

Start Interactive Physics on your computer and open a new document. Follow the directions below to set up an initial model. After you set up and test this model you will critique it and attempt to modify it to bring it closer to the assumptions listed above. The model you will build will look like figure 4.

Figure 4 - Impact Model built with Interactive Physics

Set up Workspace - To help facilitate setting up the impact model you should turn on rulers, gridlines, and coordinates. This will help you align objects. Also, change the units of measurement for distance from meters to centimeters.

Set up Virtual Force Plate - In this activity you will build a "virtual force plate" that will provide an output similar to a real one that might be found in a research lab. To set up the virtual force plate:

1. Select the rectangle tool from Interactive Physics' tool palette. Draw a rectangle similar to that found in figure 4.
2. Draw a rectangle that is 20 centimeters high by 120 centimeters wide.Position the rectangle's center of mass at (0,0) on the x,y axis of Interactive Physics.
3. Use the anchor tool to attach the force plate to the background so that it does not move.
4. You may modify the color and label of your force plate by selecting the appearance and properties windows from the main menu.

Set up the Body - As mentioned, we will simplify the body by representing it as a solid mass. Here is one place that you can start (later) to modify the model by breaking the body into segments with springs and dampers as well as placing objects to act as cushioning systems between the body and the force plate to represent systems that might be found in shoes. To set up the body:

1. Select the rectangle tool from Interactive Physics' tool palette. Draw a rectangle similar to that found in figure 4.
2. Draw a rectangle that is 80 centimeters high by 40 centimeters wide.Position the rectangle's center of mass at (0,60) on the x,y axis of Interactive Physics.
3. Position it above the force plate.
4. You may modify the color and label of your body by selecting the appearance and properties windows from the main menu.

Set up the Slider Controls for the Body - You will set up two controls for the body. The first, "Position of Body", will control the position of the center of mass of the body. The second, "Mass of Body", will control the mass of the body. Each slider will allow you to control a specific variable for the body to simulate different runners and see how the changes affect impact forces. To set up the Slider Control for Adjusting Position of Body:

1. With the rectangle that represents the body selected go to the main menu under "Define" and chose "New Control, Initial Y Position." This will place a control for positioning the center of mass of your body.
2. Select this new control and, by using the Appearance and Property windows modify the following parameters:
   1. under Appearance, change the name to "Position of Body (m)"
   2. under Properties, change Min = 50 and Max = 60 centimeters.
   3. under Properties change the number of snaps to 10.

To set up the Slider Control for Adjusting Mass of Body

1. With the rectangle that represents the body selected go to the main menu under "Define" and chose "New Control, Mass." This will place a control for adjusting the mass of your body.
2. Select this new control and, by using the Appearance and Property windows modify the following parameters:
   1. under Appearance, change the name to "Mass of Body (kg)"
   2. under Properties, change Min = 60 and Max = 150 kilograms.

Set up the Output Meter for Virtual Force Plate - This meter will let you see what the "force record" looks like when the body impacts your force plate. You will use this record to see how close your simulation comes to a real representation of a force plate record. By comparing your virtual record with a real record you will be able to modify your model to try and bring it closer in line with the real world.

1. Select the force plate and body objects. The Output Meter will measure the contact force between these two objects.
2. Under the Measure option in the Main Menu, select "Contact Force." This will create a meter that you will modify.
3. The default option for output from a meter is "Digital". Change the output so that your meter represents the data in a line graph format. At this time we are only interested in measuring the total force so turn off Fx and Fy by clicking on them.
4. Open the appearance window for the meter so that you may modify the ranges recorded by your meter. In the appearance window change x (time) to Min=0 and Max = .5 seconds. Turn auto scaling of time off by clicking in the box under Auto next to x to clear it. Also change y3 (total force) to Min = 0 and Max = 5000 Newtons.
5. Open the properties window for the meter so that you may modify the look of your meter's output so that it is easier to read. In the properties window select Frame, Labels, Axes, Show, Show Name, Units, Grid, and Connect Points options by clicking on their boxes. Change the name of this meter to "Force Plate Record (N)."
6. Resize the size of your meter so that you can see the y-axis from 0 to 5000 N and the x-axis from 0 to .3 seconds.
7. You may want to position the components of your entire Interactive Physics simulation so that everything is lined up and neat. You may also want to adjust background colors, names and other properties of your simulation so that it is attractive to someone viewing your model.

Running the Interactive Physics Model - Now you are ready to test your model to see how accurate it is in representing the "real world" force record shown in figure 3. Make sure you save your model (if you already haven't) before you test it. To test your model:

1. Set the body position, using the Body Position slider, to .7 meters. This will allow the body to drop .2m (20cm) to the force plate.
2. Either click Run on the tool palette or select Run from the World options on the Main Menu. The body should drop onto the force plate and the impact force register on the meter. Your simulation will run until you stop it.
3. Either click Stop on the tool palette or select Stop from the World options on the Main Menu to stop the simulation.

Debugging the Interactive Physics Model - Now that you've run your model compare the output from your virtual force plate to that of the force plate record in figure 3. Most models need some kind of modification to improve their accuracy. In this last part of this procedure you will note how your model's output differs from the real world and list ways in which you might modify it. Use the chart provided to help you organize and record your thoughts. The chart points out a couple of places to start working on modifications, but leaves the follow up to you.

Differences Between Interactive Physics Impact Model and Real World

(Use figure 3 and what you can observe from watching athletes run to make suggestions as to what might be changed in the Interactive Physics Model that you built to make it more like the real world.)

In the computer model many short cuts were taken to simplify a very complex system--the human body. For example, the spring/damper system used was a very simple way to represent a complex of muscles, tendons, ligaments and bones that comprise the leg and upper body of the human machine. Simplification of a system is often necessary in the first stages of building a model. As data grows and computer power increases, more sophisticated models can be built. The model you built was not possible in the early years of sport research without the power of a room size computer. Given the speed that computer technology is progressing, the model that will be possible in another five years will certainly out perform anything we can build today.

As mentioned earlier, the model you built was based on work done by R. McNeill Alexander. The idea that the leg and foot muscles and tendons can be modeled by springs is based on his research studying the elastic properties of muscles and tendons in a dynamic testing machine (see figure 5) along with force plate and motion analysis data collected from subjects in the lab.

Figure 5 - Dynamic Testing Machine

This machine measures the elastic properties of materials. What advantage might this machine have when used by designers searching for materials that might be used for the outsoles of shoes?

Alexander's work showed that the springs in the legs and feet act as energy saving devices. He cites that a 70kg man running at a six minute per mile pace exhibits a change in his center of gravity of 0.06 m. The gain of potential energy between the lowest and highest point he calculated to be 41 joules (70kg * 9.8m/s2 *0.06m). He also found that the forward velocity of a runner varies between 4.4m-1 and 4.6 m-1 giving a change in kinetic energy of 63 joules ((1/2 * 70 (4.62 - 4.42)). Therefore the total energy (potential + kinetic) that is subject to loss at each stride is 100 joules.

Without springs (tendons) this energy would be degraded to heat by the braking effect of muscles. Then the energy would have to be replaced by the work of the muscles. The cost of running would be high without springs. The tendons allow some of the energy to be stored by stretching the elastic tendons and returned to the system when they recoil. This reduces the work that the muscles have to do.

This idea of elastic storage of energy is apparent in many other types of organisms. From the tendons and muscles associated with the spine of a cheetah, the elastic ligaments in the legs of a pronghorn antelope, to the spring like effect of the wishbone in flying birds, nature has found a way to optimize the energy cost of locomotion. Shoe designers try to follow nature's lead by making cushioning systems that utilize properties of elastic materials.

Figure 6 - UC Berkeley Springboard Model

By building a simple model of the human body based on Alexander's idea that the leg and foot act like a spring allows us to test ideas about how shoes might further enhance or detract from this system.

Researchers around the world are building more complex models of how the skeleton, muscles and tendons of the body interact. Their understanding will impact everything from shoe design to the design of artificial limbs for amputees.

Finding other resources of computer modeling

In this exercise students were introduced to a simple computer model based on data collected from the real world. This activity barely scratched the surface of a field of study that applies to virtually any scientific study. To introduce students to some of this diversity have them check out local universities and research institutions and ask how they use computers to build models of the real world.

Another area that to investigate is the World Wide Web. The reference section of the Slam Dunk Science Guide lists several links to computer modeling sites.

Ideas for Computer Modeling

Students most likely have many ideas of how they might apply the techniques learned in this activity. Here are several questions to consider:

1. What modifications could be made to the computer model of the body built in this activity to make it more accurate?
2. What modifications would have to be made to the model to make it more like a Pronghorn Antelope?
3. An insect's wing might be modeled using Interactive Physics. What information would be needed to build such a model?