Archive for the ‘Science’ Category:

Speed and Kinetic Energy of Sports Pitches, Shots and Kicks

Posted In: Science | Sports
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I’ve been playing (and watching) alot of soccer recently with the kids and it got me thinking about how hard the pros can kick the ball compared to us. This got me thinking about how much energy athletes can impart to a soccer ball and how that compares to balls and projectiles in other sports. This is not a scientific study, as I just googled the fastest pitch, shot, serve, kick, throw etc. from a variety of sports and the weight of the respective balls/projectiles to calculate their kinetic energy and momentum. I added in the stats for a (sort of) human projectile for comparison as well (Usain Bolt).

The graph is color coded so orange refers to projectiles that require no additional equipment, while the blue requires a bat or racket or club to aid in hitting the ball. You can toggle between log and linear scale on the x-axis to better see the differences between different projectiles.

The hammer throw is interesting because it far exceeds the kinetic energy and momentum of the other balls. If you watch a video of olympic hammer throws, you’ll see how much energy these very large, strong athletes are able to put into the throw. I think another aspect is that the top kinetic energy projectiles are all throws where there is significant acceleration of the projectile over a longer period of time rather than an instantaneous kick or hit.

Switching to the speed tab, all of the fastest projectiles are aided by equipment to achieve their very high speeds, but generally these projectiles have lower weights. This is also seen in the momentum tab, where the heavier projectiles are mostly unaided by equipment, probably because of the challenge of imparting enough momentum onto a heavy ball/projectile would require accelerating an even heavier racket/bat.

Equations and stuff

The equation for kinetic energy is \(E = {1\over2} mv^2\),
where E is kinetic energy (expressed in joules or kilojoules), m is mass and v is velocity (or speed).

The equation for momentum is \(P = mv\), where P is momentum.

The difference between momentum and kinetic energy is slightly tricky. The momentum rankings seem to prioritize the mass of the projectile while kinetic energy is a balance between speed (velocity) and mass. In kicking, throwing or hitting a ball/projectile, the player needs to put impart the energy into the ball. In a collision, total momentum of the system (player and ball) is conserved but kinetic energy is not, although total energy is (some energy may be “lost” as heat, sound, etc). In terms of being “hit” by the projectile, I believe that kinetic energy is probably more important than momentum for gauging the overall effect of the impact, but the total energy is not the only concern.The area over which the impact would occur is also important. Honestly, the table tennis (ping-pong) ball is the only one I think I’d be okay getting hit by (at least at these world record speeds).

Data sources and tools:
Mostly google for ball weights and trying to find some mention of the “fastest” throw or kick or whatever. Calculations are made using the equations above and plotted using Plot.ly javascript library.

Solar (Sun) Intensity By Location and Time

Posted In: Energy | Science
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This visualization shows the amount of solar intensity (also called solar insolation and measured in watts per square meter) all across the globe as a function of time of day and day of year. This is an idealized calculation as it does not take into account reductions in solar intensity due to cloud cover or other things that might block the sun from reaching the earth (e.g dust and pollution).

As would be expected, the highest amount of solar intensity occurs on the globe right where the sun is overhead and as the angle of the sun lowers, the solar intensity declines. This is why the area around the equator and up through the tropics is so sunny, the sun is overhead here the most. If you click on the map you should see a popup of the intensity of sunlight at that location.

As the earth rotates over the course of a day, the angle of the sun changes and eventually the angle is so low, the sun is blocked by the horizon (this is sunset).

Instructions
  • The default is to show the sunlight intensity for the current date and time but you can change it by moving the sliders for hour or day.
  • You can also toggle between the orientation of the surface that you measure the sunlight on. The default shows the intensity of sunlight on a horizontal surface. The other option shows the intensity on a surface that is oriented to face the sun (i.e. perpendicular)

Again, the intensity will depend on the angle it makes with the sun and so it depends on your location on earth (i.e. latitude). Latitudes around the equator will receive more sunlight because their angle is closer to perpendicular.

Shifting through the days of the year, you can start to see the cause of the seasons as the amount of sunlight changes and more or less sunlight goes to each of the northern and southern hemispheres.

Calculations and Tools:
The calculations for solar intensity are based on equations from “Renewable and Efficient Electric Power Systems” by Gilbert Masters Chapter 7. Calculations were made using javascript and visualized using the Leaflet.js library with Open Street Map tiles.

This was a fun project for me to learn online mapping tools and programming.