This forum is about wrong numbers in science, politics and the media. It respects good science and good English.
Couldn't that same sentence be written as,
The center of mass of the heavier athletes did not increase in height as much as the lighter athlete, resulting in the heavier athletes feet getting to the ground again quicker?
The increased inertia of the heavier athlete allows the athlete to maintain a more consistent center of inertia keeping his locomotive appendages closer to the ground.
I don't think either of those actually make Galileo irrelevant, but sort of say the same thing.
Of course the line of study leaves me choking on my corn flakes. Some idiot my decide and come to me (since I am definitely heavier) and suggest I would make a better athlete... The danger of trying to apply averages to the individual.
So that's why you go faster riding a bicycle? Your centre of mass remains the same; or maybe not?
I thought the silliest part of the 'investigation' was in the way the authors apparently failed to note the most probable explanation for increasing athlete size: larger bodies equate to more musculature, longer legs and so forth, with no need for a warped take on physics. The glaring failure of this research was the fact that they ignored a patently obvious explanation in favour of the convoluted.
As for bikes, the speed they grant is unrelated to the center of mass or inertia of the rider, but rather the mechanical advantage granted by the chain assembly. The pedals are attached to the larger sprocket, which is in turn linked to the smaller by chain. The different circumferences mean that for every one revolution of the large sprocket, the small undergoes *more than one*. This in turn is directly linked to the much greater circumference of the wheel, further increasing distance travelled per pedal revolution.
The newspaper report of this research also claimed that athletes in ancient Greece weighed 70% less than modern athletes. How did they ever manage to beat the Persians if they weighed 25 to 30 kg each?
I think more significantly for bikes there are wheels and bearings. As long as you carry out a few pedal strokes here and there you keep moving. But running is a more complicated movement and you can't just coast like on a bicycle, massive deceleration accompanies any compromise in technique. In a sprint every pedal stroke will go to adding to your speed, at least until air resistance becomes too great.
Er, I'm lost.
Galileo's experiment is supposed to show that a feather and a cannonball would fall to earth in equal times.
The trouble is that a feather and a cannonball have quite different air resistances.
It would have been a much better experiment to drop a solid cannonball and a hollow cannonball each identical in size and surface finish but only differing in mass (I remember thinking this at the time i.e. in school or college when I first encountered this story). Of course, it is a much more memorable thing to compare a feather and a cannon ball so Gallileo obviously had some smart PR agency at the time.
It would be more appropriate therefore to suspect that a heavier athlete might fall slightly faster than a lighter athlete (or the inverse) based on some measure of their surface area to mass ratios. More logically I can't see the difference in size or mass having any significance based of gravity.
I would have to suspect some other influence, if indeed, the differences measured were both measurably and statistically significant.
At any rate, surely, if presented with such data the true approach would be to come up with as many different possible mechanisms as possible and then conduct tests to identify which if any could have significance.
Incidentally, we seem to be in the season of "research" showing us that previously delivered pronouncements are wrong, you know the sort of thing, butter is bad, then it is good. IN recent months we have discovered again that two glasses of wine are good for you and now that two cups of coffee are good for you and may even fend off altzheimers disease.
Of course, the trouble is that if one followed each and every piece of advice, I suspect ones metabolism would be unable to cope with everything al at once and that in reality we might need to be allowed to choose which drink we want and accept the risks of not drinking some other drink.
The bicycle stores inertial energy. At constant speed the cyclist only has to replace resistance losses. The unaided human frame has a more complicated job, but it has the advantage of higher acceleration over the short term.
I seem to remember from my schooldays that the feather and ball experiment has been performed in vacuo, confirming Galileo’s hypothesis. There are various mind experiments that are relevant (e.g. stuff feathers inside the hollow ball, so that it is now heavier and therefore falls faster). However, the main point is that the whole of gravitational theory fails if the hypothesis is untrue. The jocular reference to the old boy dropping things off the tower in Pisa was a misjudgement, as there seems to be no evidence that the experiment was actually performed.
Air resistance seems to be a red herring in all these arguments. For example the vertical velocity of the athlete is probably too small for this to be a significant factor. As one born with the duck syndrome, short legs, I had much occasion to observe that the predominant variable in athletics is leg length, so I turned to football (soccer).
David Scott, the commander of Apollo 15, famously performed the experiment with a falcon feather (the lunar module for the mission was christened 'Falcon') and a geology hammer on the surface of the moon, almost 38 years ago.
The link to the Daily Telegraph article in JEB's piece has now gone dead, and it looks like the article may have been deleted altogether.
I managed to find a free to view copy of the academic paper that I think the news story was based on:
From checking the paper, it doesn't look like the authors are claiming that heavier athletes fall to the ground more quickly than lighter athletes. They actually claim the opposite - that heavier, taller athletes take longer to fall than lighter, shorter ones.
In the appendix to the paper which gives the background maths they take the time to fall as
t ~ (Lb/g)^0.5 where Lb is a body length scale, g is acceleration due to gravity
then they take Lb ~ (M/density)^0.3333 where M is mass of body
So that gives the fall time t as being proportional to M^0.16666. It looks like the longer fall time for a heavier athlete is coming from them being assumed to drop from a slightly greater height.
The paper also clarifies the point Frank has raised about the implausibility of athletes in ancient times having 70% less mass compared with today, they have 70% of today's mass or a 30% reduction compared with today.
The news media nowadays seems to take the view that there is a lot of overlap between environmental journalism and science journalism, so it makes me wonder whether the Daily Telegraph article was written by an environmental journalist standing in as a science journalist.