Home > My Fiction, Science > Green Blaze powers addendum: The high jump

Green Blaze powers addendum: The high jump

I’ve added a new paragraph to my earlier post “ONLY SUPERHUMAN reader question: Measuring the Green Blaze’s powers,” since I realized there was one aspect of Emerald Blair’s superstrength that I forgot to address, one that occurred to me as a result of watching The Six Million Dollar Man on DVD. Here’s what I added:

It’s occurred to me to wonder: How high could Emry jump? Of course, that depends on the gravity, so let’s assume a 1g baseline. According to my physics textbook, the maximum height of a projectile is proportional to the square of its initial velocity (specifically, the velocity squared times the square of the sine of the launch angle, divided by twice the gravity). So if we use my earlier, very rough assumption that Emry’s speed relative to an unenhanced athlete goes as the square root of her relative strength, that would cancel out the square, and thus jumping height (for the same gravity and angle) would increase linearly with strength. If she’s four times stronger than the strongest human athlete today, then, it follows she could jump roughly four times the world record for the high jump. Except it’s more complicated than that, since we’re dealing with the trajectory of her center of mass. The current world record is 2.45 meters by Javier Sotomayor. But that’s the height of the bar he cleared, not the height of his center of mass. He used a technique called the Fosbury flop, in which the body arcs over the bar in a way that keeps the center of mass below it. So his CoM was probably no more than about 2.15 meters off the ground, give or take. And he was pretty much fully upright when he made the jump. since he’s 1.95 meters tall to start with, and the average man’s CoM height is 0.56 of his total height (or about 1.09 m in this case), that would mean the world-record high jump entailed an increase in center-of-mass altitude of slightly over one meter. So if we assume that Emry is doing more of a “bionic”-style jump, keeping her body vertical and landing on her feet on whatever she’s jumping up to, then she might possibly be able to raise her center of mass up to four meters in Earthlike gravity. Which means she could jump to the roof of a one-story building or clear a typical security fence — comparable to the jumping ability of Steve Austin or Jaime Sommers.

And just a reminder: I’m open to more reader questions about Only Superhuman or my other writing.

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  1. Physics
    February 5, 2014 at 5:47 pm

    Highest vertical leap measured by NBA: DJ Stephens – 46 in. Kenny Gregory, Lebron James, and Michael Jordan were around 44 inches; with a host of also rans at the 40 inch range. Go with the low estimate at 40 and multiply that by 4. You get 160 inches or 13’4″. Even if you figured at 36 inches as an average you would get 12′ even. Remember, this is a static vertical crouch exploding straight upward.

    With horizontal motion and a launch angle, those heights can be eclipsed by converting that horizontal force into a vertical force.

    If standing still she can likely jump 12′ – 14′. If running, she might be able to clear 15′ – 20′.

    • February 5, 2014 at 6:42 pm

      The question is how NBA vertical leaps are measured. I checked, and apparently it’s computed by comparing the highest point a person’s hand can reach from a standing position to the highest point their hand can reach while jumping. I suppose that more or less cancels out body movement around the center of mass, since it’s trying for an analogous body position in both cases.

      The first figure works out to about what I calculated for a running jump, four meters give or take. The second estimate you give is about 4.6 to 6 meters, but I don’t think it works the way you suggest. After all, 40 inches is a shade over 1 meter, and as I said, my estimate is that Sotomayor’s world-record high jump, which was from a running start followed by a mostly vertical jump, didn’t really raise his center of mass much more than a meter. He used the force he built from running instead of launching from a crouch, rather than in addition to it. So it seems to me the two methods, static and running, have similar maximum results. It stands to reason there might be some limit on performance that can only be asymptotically approached by any method short of transhuman enhancement.

      • Physics
        February 5, 2014 at 9:26 pm

        I am now 44 yrs old but back in the day I could “get up.” Static vertical of 30″ as tested on my college basketball team. This equated to a rim grab from straight under the basketball rim. However, when running and using the horizontal momentum could nearly get my elbow above the rim. That would be more to the tune of 40″. I am sure the static verticals of pro athletes would differ from their fluid movement leaps.

        Another thing to consider is that if there is no difference between static vertical leap and Fosbury flop then there would be equal splits of athletes using each technique. Not to mention the old front leg over belly style or even the scissor method. However, only one method is taught and used as it employs the most efficient combination of a horizontal (specifically centripetal) and a vertical force to reach the pinnacle of achievable height.

        By the way, I wasn’t questioning your calculations or figuring, just trying to simplify.

      • February 5, 2014 at 9:54 pm

        I’m not saying there’s no difference between the techniques — just that their curves probably tend toward the same maximum. At a more normal level there may be a substantial difference, but there may be some upper limit on performance that neither can surpass. The fact that the world records in both techniques are so comparable seems to suggest that.

  2. Physics
    February 5, 2014 at 10:16 pm

    “I checked, and apparently it’s computed by comparing the highest point a person’s hand can reach from a standing position to the highest point their hand can reach while jumping.”

    Absolutely correct. They move a stack of horizontal rods up a pole to the height of the athlete’s maximum standing reach (zero point measure). The athlete then crouches, accelerates upward, and strikes the “pile” of horizontal rods. The horizontal rods can be rotated about the vertical pole and in fact the measurement taken is to the top of the highest rod that was rotated, or to the bottom of the rod pile that was not touched or moved.

    “He used the force he built from running instead of launching from a crouch, rather than in addition to it. So it seems to me the two methods, static and running, have similar maximum results.”

    I’ll disagree. If that were the case, we would see similar numbers of athletes using static vertical, Fosbury Flop, front leg over – belly roll, or the old scissor kick to equal success in the high jump. However, the only method used is the Fosbury Flop in the current competitions as it combines the horizontal momentum (specifically centripetal) and vertical momentum to attain the most efficient blend of forces for the highest leap possible.

    Personally, I had a differential of ten inches between my vertical static vs. moving leap as tested for college basketball. That is quite significant.

    Finally, think of it as an energy problem in a closed system. I will agree that no more energy is used by either, but it is a question as to how well human muscle performs. In a crouch explosion you must accelerate your body upward from a static position with limited vertical motion to overcome 9.8 m/s/s. I estimate that one may lower their hipbone 12″-14″ to crouch. This leaves little space and time for the acceleration to occur and puts great stress on human muscle. If you jogged up to the point of launch and jumped the energy expended is spread out over a further distance to accelerate and more time to build momentum. What is beneficial is the apparent (perceived) reduction of stress to the muscle that allows for ease of completion of the jump.

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