I while back I asked if there was interest in a few Olympic themed posts - after all, sport is a gateway to many other areas. Charlie replied:
How about the high jump? I was fascinated by Randall Cunningham's 18 year old daughter's comment on getting her head over the bar and her body would follow. Also, her body didn’t look like it had the right muscles for her accomplishments. Anything interesting there?
Vashti Cunningham is a world class high jump athlete. The highest levels of competition in hotly contested sports select ideal body types - while body type is important, it is required. Vashti is currently listed at something over 6-foot-1 and weighs 121 pounds. She probably has an extremely high proportion of fast twitch muscle and other genetic gifts, not to mention determination, and for events like this you don't need huge muscle mass as long as its the right kind of muscle but more on that later.
The high school physics approach to the high jump would be to recognize you can turn kinetic energy into potential energy in much the way a roller coaster works - you trade speed to fight gravity to altitude and visa versa. Her kinetic energy depends on her mass and the square of her velocity: Ekin = 1/2 * mv2.and her potential energy depends on how high she is: Epot = mgh where g is the acceleration due to gravity. Set these equal and mass drops out leaving height = v2/2g. She is probably something over 10 meters per second as she transitions to her jump - 22 to 23 mph. This gives around 5 meters of altitude gain - much higher than any high jump record.
But fundamentally high jump is not an efficient way to turn kinetic into potential energy. You want to stop quickly converting all of the energy of motion into throwing your body skyward. To do that you need a machine - a lever in the form of a pole.
High jumping is a pure sport - no apparatus, just see how high you can jump. And it it has its tricks and surprises. Vashti, like most high jumpers, makes use of the changeable shape of her body and physics. Her motion can be described as the motion of her center of mass - the unique point around which her mass is distributed.1 If she's standing, given her body type, Vashti's center of mass is about 55 percent of her height - a bit over a meter in her case. In the high jump she launches her center of mass in an arc. All work she does goes into raising her center of mass hopefully about the bar.
A body's center of mass is not necessarily inside of it. Throw a horseshoe or boomerang and you see a dramatic illustration as the center of mass follows a smooth path with the body spinning around it. You can bend your body and move your center of mass outside of it. This allows for innovation discovered by Dick Fosbury - the Fosbury Flop. Vashti bends her body around the bar - her center of mass clears the bar, but her body only does when it has to. 2
Now she's using physics properly, but there is more going on. Her center of mass is high in the first place. Her limbs are long and light making it easier to bend her body. Height is generally bad for distance, but a plus for sprints. Sprinters don't need huge muscle mass - just enough to get up to speed and launch. The muscles in her back are probably very well developed. She'd probably be good at yoga.
Now it gets into technique. I talked with a Division-I track coach who didn't want his name used. Much of what she wants to do is in the run-up and takeoff. The run-up develops speed - a lot of speed - and positions the body so the foot hits the right place for takeoff to begin. She plants her foot ahead of her body which is traveling over twenty miles per hour at this point. Her leg is mostly firm but she's fighting its flexion. That builds up enormous forces in her takeoff leg's muscles allowing her to create a large downward force as her forward momentum comes almost to zero in well under two tenths of a second (she's decelerating at well over six gs - peaking much higher).3
This phase is complex. She's also swinging her arms upwards - hard - along with her other leg. This pushes her core body down compressing the muscles in her takeoff leg even more. During the run-up she want to have a low position - that big vertical push needs a build up over the takeoff phase. She's adding more swinging her non-contact limbs up and the low position at plant and high position at take-off usually means a long contact time to get as much of the muscle force to the ground as possible. Jumpers run very fast with their hips in a low position - a few centimeters can make a big difference.
1 A bit more technically the center of mass of a distribution of mass (planet, ball, person, car, ... anything with mass) is the unique point where the weighted relative position of the distributed mass sums to zero or the point where if a force is applied causes it to move in direction of force without rotation. Note that center of gravity is often used in place of center of mass if the acceleration due to gravity does not vary (much) over the body.
2 You see this in ballet when a great dancer pulls off a flawless grand jeté. She raises her legs into a nearly horizontal position and raises her arms above her head dropping the level of her head relative to her center of mass as it rises. She reverses the process as she begins to fall earthward again. I timed one at 0.44 seconds - a very long illusion. I also timed a basketball player in a slam dunk contest at about 0.3 seconds. In theory he could probably do it longer with his longer limbs, but he lacked her technique and 0.3s still looks startling and even beautiful to the audience. In volleyball it is more on the order of basketball - I've timed some centers at over 0.3 seconds. I'm sure it must feel wonderful when probably executed.
3 For simplicity I'm avoiding talking about tendons. They act as springs - mechanical batteries that store energy and able to release it very quickly. Their size and stiffness make enormous differences and have a large genetic component.
It is high Summer and we're getting a wide variety of everything including great tomatoes! Nothing specific, but there has been some discussion about less than perfect looking produce - the so-called ugly fruits and vegetables.
Consumers demand cosmetically perfect examples - we seem to equate quality with visual appearance (as we do with too many things we don't understand well). Large amounts are discarded by markets and even larger amounts are simply not harvested by farmers as they don’t believe there is a market. Wastage is about 40% - driving up prices and making healthy eating more difficult as a result.
Generally ugly produce is just fine. In fact - it may even be better for you. (the link is to NPR's The Salt)