WE RUN WE LEARN Description of the project In the first part of the project, the students study Trail Running at their Physical Education lessons (discover this sport, training plans, practice, etc.). In the second part of the project, the two schools are involved in an international exchange, where the students are hosted in both countries by the local pupils. During these two exchanges, the students participate together in trail running races, and they apply Physics (Kinematics, Dynamics, Energy) to their own data generated during the race (mass, distance, time, altitude, heart rate). They work in international groups and present the results with spreadsheets and word processors. The students are able to experiment the PE contents in real situations plus the Physics laws during the exchange visits
Objectives Students learn PE applied to Trail Running. Students relate Trail Running and Physics, experimenting the laws with real data. Students practice their English. Students learn about other European cultures, especially when are hosted by the partner school families. In the meanwhile students also improve their ICT skills. Students learn to work and cooperate in international groups.
Resources Physical Awareness 13-14 (2013-14 previous eTwinning project). An ebook with Trail Running and Physics cooperative activities was edited: http://issuu.com/florencisalesvilalta/docs/ebook_pa1314
Activities and Answers (next pages) Kinematics and Trail Running Dynamics and Trail Running Energy Consumption in Trail Running Vectors and Trail Running
KINEMATICS AND TRAIL RUNNING (LA SÉNIA) Answer the following questions in a Word file. Filename: WRWL_Kinematics_Gnumber Use the equations editor or the Excel spreadsheet if it is necessary. 1. Search the data: a. GPS track of your race b. Race standings on the race website 2. Paste the plot of speed and altitude versus distance a. Calculate the average speed of the race (km/h, min/km) b. Calculate the average speeds between the control points (race standings) c. Locate approximately the control points in the GPS track and calculate the
average speed between them using only the GPS data. Compare these results with the previous ones 3. Choose two parts of the race where you speed up and slow down respectively. a. Collect 20 data points (position, time, altitude, speed) for each part and type
them in an Excel spreadsheet b. Draw the plots position/time, speed/time and acceleration/time for each part c. Make brief comments about the shape of the data in each plot (types of motion)
and relate it with the race profile d. Insert trend lines and their equations for all the plots. Work out the meaning of
them in each plot. Information about trend lines: https://www.ncsu.edu/labwrite/res/gt/gt-reg-home.html If you need to revise the basics of Kinematics, click on the following link: http://www.schoolphysics.co.uk/age16-19/Mechanics/Kinematics/
ENERGY CONSUMPTION IN TRAIL RUNNING (LA SÉNIA) Can we work out the energy we spend when we run? Initial Google search https://www.google.es/?gws_rd=ssl#q=energy+consumption+trail+running Not an easy question!!!
1. Introduction
General explanation of how our body gets energy to live. Which variables affect. One example: running https://app.box.com/s/z18nzxtaxtm94wpk1wpo4nxzubm1ecea
2. Energy consumption by Léger and Mercier
Variables: distance, time, average speed, runner’s mass and technical efficacy. a. Calculate the speed of the race in meters per minute. b. Search the energy consumption depending on the speed.
https://app.box.com/s/xnzbm4k2flzaqwikm5w1 https://app.box.com/s/nkiuz4xuq3c3it3e456f (Data table Léger and Mercier 1984) c. Multiply this value by the runner’s mass. This is the energy consumed per kilometre. d. Multiply this value by the kilometres of the run to calculate the total energy
consumption.
3. Energy consumption considering the heart rate (De Lucio, Castañeda, 2004)
Variables: runner’s age, mass, maximal oxygen consumption (VO 2max), average heart rate (HR) and time. a. Estimate the HR max.
HR max = 220 – age(years) This is the usual formula for this estimation, but a recent study shows that it underestimates the real maximum heart rate and proposes another equation (Tanaka 2001):
HR max = 208 – 0,7 x age(years) b. Find the equivalence between the average HR and the percentage of VO 2max.
c. Estimate the runner’s VO2max value
López Chicharro, 2007 The VO2max value (mL kg-1 min-1) for boys is quite constant among 6-16 year-olds and it has an average value of 50-53. For girls the pattern is different since a progressive decrease of the values is shown along the growing period. Thus, a 8-year-old girl has an VO 2max value around 50, but she will reach 45 when she will be a 12-year-old and 40 when she will become a 16year-old. Leger et al., 1998 For ages between 6-18, the following formula is proposed, which depends on the final stage speed (V) in kilometers per hour and the age (A) in years. In this case, V must be obtained in anaerobic conditions to estimate a correct value of VO 2max. VO2max = 31,025 – (3,238 V) – (3,248 A) + (0,1536 V A) d. Calculate the percentage of VO2 max in mL/kg/min related with the average HR. e. Calculate the metabolic equivalent task (MET).
1 MET = 3,5 mL/kg/min 1 MET = 1 kcal/kg/h f.
Multiply by the runner’s mass to calculate the spent energy in kcal/h.
g. Multiply by the time to work out the total energy consumption.
Link to the article with examples: https://app.box.com/s/3j1aazb2sqqayr1i8wyrlz3vzedcbdfq 4. Energy consumption in outdoor running (Dennis and Noakes, 1999)
Variables: runner’s mass, average speed and time. a. Runner’s power is estimated with his/her mass (m) and the average speed in meters
per second (v) multiplied by a factor of 4 Joules per metre run and kilogram of mass.
Pr = m v 4 b. The energy is calculated multiplying the power by the time of the run.
E=Pr t 4. Energy consumption in outdoor running with wind resistance (Leger Mercier,
1984) Variables: average speed, runner’s mass and time. The wind resistance significantly affects the energy consumption at speeds higher than 15 km/h (4 minutes per kilometre) a. The energy consumption expressed as VO2 (mL/kg/min) is calculated with the following
formula where the average speed (v) is expressed in kilometres per hour. VO2 = 2,209 + (3,1633 v) + (0,000525542 v3) b. The calculation continues like in sections 2e-2g. 5. Energy consumption applying Physics
Total energy consumption (TEC) = Kinetic Energy (KE) + Gravitational Potencial Energy (PE) + Thermal Energy (TE) a. Kinetic Energy
It can be calculated by multiplying the power (energy per unit time) expended in running and the time: KE = Pr t where Pr can be estimated with the mass (m), the gravity acceleration (g) and the average speed (v): Pr = m g v / 4 See the publication: http://sprott.physics.wisc.edu/technote/walkrun.htm
b. Gravitational Potential Energy
If the runner goes uphill: PEup = m g h depends on the mass (m), the gravity acceleration (g) and the altitude climbed (h). When the runner goes downhill consumes energy too. The runner has to balance the X-Weight, therefore:
PEdown = m g sin(θ) h which includes the angle (θ) of the downhill slope.
c. Thermal Energy
This kind of the energy is lost through the skin and it is very difficult to calculate, since it depends on so many factors. However, it can be estimated by difference as follows: TE = TEC – KE – PE The TEC can be obtained by one of the procedures presented in the previous sections of this text.
ACTIVITY 4. Search the data: a. GPS track of your race b. Race standings on the race website 5. Calculate the energy consumed during the race and compare it with the energy
estimated by your GPS device. Use as many methods as you can but, in every case, make comments about the positive and negative aspects of each method. 6. Draw out conclusions comparing all the results.
Filename: WRWL_Energy_Gnumber Use the equations editor or the Excel spreadsheet if it is necessary.
Participants of the race in La SĂŠnia. More pictures:
https://plus.google.com/photos/106248087627971782031/albums/6140517343299063873
DYNAMICS AND TRAIL RUNNING (GENOVA) Answer the following questions in a Word file. Filename: WRWL_Dynamics_Gnumber Use the equations editor or the Excel spreadsheet if it is necessary. Which forces are exerted when we run? First, we need to state some assumptions about the running process. •
Each foot contacts the ground and is pushed by a reaction force (Newton’s Third Law of Motion) which impulses the body along a parabolic trajectory until the opposite foot strikes the ground
•
The vertical component of the impulsive force at the instant the foot leaves the ground is equal to the horizontal force so as to reach maximum range
Second, answer the questions below: 7. Draw a scheme of the forces acting on a runner who runs on a flat surface. Calculate
the forces. You can find additional info in this link: http://www.real-world-physics-problems.com/physics-of-running.html 8. Why both the vertical and the horizontal components of the force are equal? Watch this
simulation which shows the relation between the launch angle and the range: http://www.animations.physics.unsw.edu.au/mechanics/chapter2_projectiles.html 9. Open the GPS track of your race 10. Study the uphill part of the race. Split the ascent in two parts by the control point.
Calculate the grade percent incline and the inclination angle of each part. Learn about grades, slopes and angles: http://www.1728.org/gradient.htm 11. Do activity 1 again but on the inclined surface of activity 4. Calculate the forces. Draw
out some conclusions 12. Study the downhill part of the race. Split the descent in two parts by the control point.
Calculate the grade percent decline and the declination angle of each part 13. Do activity 1 again but on the inclined surface of activity 6. Calculate the forces. Draw
out some conclusions If you need to revise the basics of Dynamics, click on the following link: http://www.schoolphysics.co.uk/age16-19/Mechanics/Dynamics/
VECTORS AND TRAIL RUNNING (GENOVA) Answer the following questions in a Word file. Filename: WRWL_Vectors_Gnumber Use the equations editor or the Excel spreadsheet if it is necessary. How can we use vectors when we run? First, if necessary, have a look to this presentation about vectors: http://prezi.com/dmuz25ztsgnp/?utm_campaign=share&utm_medium=copy Second, after you open the GPS track of your race with the map of the trail your run, answer the questions below: 1. Draw the vectors corresponding to the horizontal displacements from the start to the
control points and calculate the total horizontal displacement. 2. Draw the displacement vector to the max high point, and its horizontal and vertical
components. Calculate the slope of the ascent. 3. Draw the vectors corresponding to the vertical displacements from the start to the
control points. Calculate the sum of these vectors and verify it is the same than the total vertical displacement. 4. After calculating the displacement from the start to the point of max high, calculate the
horizontal component of the force you used to get there (suppose you didn't dissipate any energy because of friction). It is the same than the work you did when you run back downhill? Justify your answer. 5. The plantar flexion of the foot with extended lower limbs is an example of a second-
class lever. Resistance (weight) and strength (muscle) are located on the same side with respect to the hub, the driving force is the most distant and therefore the lever is beneficial. The insertion of very backward triceps therefore facilitates the movement. Take a picture to your running action and analyze the lever point (pivot point, resistance, load). Calculate the momentum of the involved force.
WORGROUPS IN LA SÉNIA https://app.box.com/s/2pf4wvid8rpvur619l16xb6243mf84rp
GPS TRACKS http://connect.garmin.com/activity/183567060 http://connect.garmin.com/activity/293829007 http://connect.garmin.com/activity/464601974 http://connect.garmin.com/page/activity/activity.faces? activityId=464429215&actionMethod=page%2Factivity%2Factivity.xhtml %3AuserSwitcher.switchSystem&cid=26478504 http://www.movescount.com/moves/move28107395
ANSWERS IN LA SÉNIA (KINEMATICS AND ENERGY) https://app.box.com/s/5wul85r1lvyfs3ql8eqqpz6xq5rpnkmx
Students working in the activities in La Sénia. More pictures:
https://plus.google.com/photos/106248087627971782031/albums/6138459144585689489 https://plus.google.com/photos/106248087627971782031/albums/6138461232831472593
WORKGROUPS IN GENOVA https://app.box.com/s/jfttorx7alxxvzesutki2xzphsuktoi1
Participants of the race in Genova. More pictures:
https://photos.google.com/share/AF1QipN56cBEuhvJ8-7EBfaYj2V8R1pBwkvap__kFNGfkb29NGfhJKBbg-5yi9vFCpt5w? key=OWhaTUNGd05aVm44ajNIYVpXLXlVNHNQdjZLRVFR https://photos.google.com/share/AF1QipOIDwmgKCriNIJ6OBIxpaOc6JQSbT8iDUmZZwZBh7 aiuH5kncppa9DPFTCN4SBcTA?key=R2gyLVVZa2pzenRiX19PR2lTYVpVSnYwSUNyN1BR
GPS TRACKS http://app.endomondo.com/workouts/512033715/21911750 https://app.box.com/s/j5g5u7tyhrsjma4bt289gqg05r9p4o79
ANSWERS IN GENOVA (DYNAMICS AND VECTORS) Dynamics F4 https://app.box.com/s/pcqq2uuda6lpbk64axvtsey85oh7wq94 F6 https://app.box.com/s/woxdfz8a0kk8c4rc5givv6p4tugl2lug F8 https://app.box.com/s/g725puz0bugw7fhjaxnw7nuouczje2fk Vectors F1 https://app.box.com/s/mqxaeuwk6asw8x7buhb5qfqe4ter9inj F5 https://app.box.com/s/7d2uuz30vqtser6ikiaildyrz2z0jo5z F7 https://app.box.com/s/5ymh0uvfoksxg4ogx167mipknevond1f Greek and Running (extra cross-curricular activity) https://app.box.com/s/mo4m6wh1of44ufws5jem2erl64n1fw5o
Students working in the activities in Genova