Calculated fitness. Big ideas are engineered. in the gym. Big ideas are engineered: a resource for schools. Case Study 01: Simple sums

Transcription

1 Calculated fitness Case Study 01: Simple sums in the gym The modern gym is full of complex equipment used by those who want to keep fit by checking on what they are doing while they are doing it. Software that does sums makes this possible. This is a short case study that introduces you to some ideas about the simple calculations that software can perform. You will find these ideas useful when you read about the work of systems engineers in the more advanced case studies. The case study is in three parts. Each part deals with a different piece of equipment used in a modern gymnasium and describes the systems it contains and how they help the user get the best from the equipment. Big ideas are engineered A resource for schools page 34

2 Part One>The treadmill When you use a treadmill you have to input information into the machine so that it knows what you want it to do. There is usually a screen which asks you questions through single words: Time which means How long do you want your exercise session to last Weight which means How heavy are you? Incline which means At what slope do you want the running surface Speed which means How fast do you want to run? You put the answers to these questions into the machine by pressing a keypad with numbers and an enter key. If you put in incorrect information there is a clear button to enable you to start again. Some treadmills have pre-set work outs which will change the elevation of the running surface at particular times during the work out. There are usually arrow keys which enable you to increase or decrease the speed or elevation. Once you have put in all the necessary information the treadmill starts and behaves according to your instructions. You can change the behaviour of the treadmill by using the up and down keys. You can stop the treadmill by pushing the emergency stop button. As you run the computer inside the treadmill uses the information to display your progress. The most basic machines will show the following in number form: How fast you are currently running The elevation of the running surface How does the machine know this? It uses a speed sensor and when the information from the speed sensor matches the information you have put in as your desired running speed it knows to keep going at this speed until it gets further speed change instructions or the work out time is up. In which case it slows down to zero speed. activity: discussion point: What are the advantages of using a treadmill as opposed to running outside? What are the disadvantages of using a treadmill as opposed to running outside? Visit this website to find out more about a large fitness club organisation page 35

3 The best way to have a good idea is to have a lot of ideas. Linus Pauling Big idea 02: Successful design More complex machines have several displays giving the following information in number form: How far you have run How long you have been running How much time you have left to run How many calories you have burned Your work rate in calories per hour How does the software in the machine work all this out? The mathematics is very simple. The software has an inbuilt clock so it can measure how long you are on the machine. So it s simple to show how much time you have left to run. It simply subtracts how long you ve been running from the total time you wanted to run. You have told the machine how fast you want to run, say six miles per hour. And the machine sets the running surface to travel at that speed. If you run at this speed for ten minutes you will run a distance of one mile, if you run for only one minute at this speed you will run a distance of one tenth of a mile. The displays usually show distance to a tenth or 0.1 of a mile. To work out the number of calories you have burned the software simply takes your weight (which you told the machine) and multiplies it by the distance you have run (which it has been able to work out from your speed and how long you ve been running). To calculate your work rate the software takes how many calories you have burned and divides this by the time you have been running. There is usually a display giving you information graphically. Some times this is shown as a bar chart with each bar representing a particular time slot (say 40 seconds) with the height of the bar showing how steep the slope of the running surface. It is the inbuilt clock that allows the software to move the display on to the next bar as you complete each time slot. research: Visit your local gym or leisure centre and find out about the different workouts available on the treadmills and the information the display provides to the user. activity: page 36

4 Part Two>The cross trainer One of the difficulties of using the treadmill is that the user has to run at the speed of the treadmill. If you get tired and want to slow down you have to decrease the speed of the running surface. Similarly if you feel particularly energetic and want to run faster you have to increase the speed of the running surface. On a cross trainer you can work as quickly or slowly as you like. travelled as follows. It knows how much you move for each step. That is fixed by the geometry of the machine. It keeps count of the number of steps you take and simply multiplies the number of steps by the distance of each step giving the total distance. You can do this quickly lots of steps in a short time, or slowly, the same number of steps in a much longer time. As the machine has information about your weight it can use this with your distancetravelled information to calculate and display the total number of calories you have burned so far. It can use your current speed and weight information to calculate and display your current work rate. As with the treadmill the display will ask you questions. How long do you want to use the machine? How much do you weigh? What level of difficulty (between 1 and 10) and if you would like to use a set programme? So you have given the machine a lot of information. As with the treadmill it can easily tell you how much longer you have to work out. It can easily work out how far you have This makes no difference to how the machine calculates the distance you have travelled. To calculate your speed the machine needs to know how far you have gone (this is given by the number of steps) and how long you have taken (this is given by the inbuilt clock). The machine gives a read out of your current speed and you can see that this rises and falls according to how fast you are stepping. discussion point: If you were a gym owner how would you decide on a) which sort of machines to buy and b) the numbers of each? What would be a sensible ration of treadmills to cross trainers for example? research: Visit your local gym or leisure centre and compare the numbers of cross trainers and treadmills. How did your findings compare with your conclusions in the discussion? Visit this website to find out more about cross trainers and other fitness equipment page 37

5 r The modern rowing machine is the machine that gives the user most feedback about the way they are performing. The basic principle is simple, by pushing with your legs and pulling with your arms and back you pull a chain that is linked to a large fan. The harder and faster you pull the faster the fan goes round. Air is dragged into the fan as it goes round. You can set the level of difficulty by adjusting the air intake to the fan. This is called Part Three>The rowing machine adjusting the vent. Like the cross trainer you can work as hard as you would like depending on your energy levels and training needs. Like the cross trainer there is a screen with a menu that allows you to set up the exercise that you want to do. You can decide on the time that you want to row for or the distance that you want to row. Once you have made this decision there are several possible screens to tell you how you are performing. In some screen there are just numbers that tell you the following: Your speed How far you have gone How far you have to go How long you have been rowing How long you have yet to row The rate at which you are working in watts (joules per second) or calories per hour The number of calories you have burned But there RoroR are also screens that present information graphically including one that plots the force of your pull against time during each stroke. You can use this to adjust the way you row to get the largest force for the longest time and so increase the speed you travel and hence the distance you travel each stroke. The sensors in the rowing machine record the speed of rotation of the fan and how many times it turns for each pull. This gives information that can be used to calculate your discussion point: What are the advantages of using a rowing machine as opposed to rowing in a boat on water? What are the disadvantages of using a rowing machine as opposed to rowing in a boat on water? pulling force, the distance travelled each stroke and the speed of travel. And the software can display this as numbers and graphics on a liquid crystal display. This is a very simplified version of the graphic display system used in a modern aircraft and described in the Vehicle Systems Management case study. Please see the next page of this case study for a worked example. research: Visit your local gym or leisure centre about the different workouts available on rowing machines and the information the display provides to the user. RRotor Visit the concept 2 website at and find out about the latest model and how it works page 38

6 Using formulae for the treadmill Treadmill running at a steady speed at zero incline Image your are running on a treadmill at 6 mph and you run for 30 minutes How far have you run? The formula to use is: s = ut Where s = distance, t = time and u = speed It s important for the units of time and distance to be those used for speed In our example u = 6 mph, so the distance unit is miles and the time unit is hours So to find out how far you ve run in miles (s) you need to put in values for time t = half an hour i.e. 0.5 hours and the speed 6 mph So s = 0.5 hours x 6 mph s = 3 miles s = 30 x 6, so it looks like s = 180 miles! No one can run that far in half an hour! Treadmill running at an ever increasing speed at zero incline Imagine that you start running on treadmill at 5 mph and run for an hour and finish running at 7 mph. How far have you run? The formula to use is s = (u + v)t 2 Where s = distance, t = time, u = starting speed, v = final speed Again it s important for the units of time and distance to be thosed used for speed. In our example u = 5 mph, v = 7 mph so the distance unit is miles and the time unit is hours. So to find out how far you ve run in miles (s) you need to put in values for time t = 1 hour and the starting speed (u) = 5 mph and the final speed (v) = 7 mph So s = (5mph + 7mph) x 1 hour 2 s = 12 x 1 miles 2 s = 6 miles page 39