## Sunday, August 17, 2008

### Beijing 2008: Men 100m race analysis

Bolt's 9.69s. Analysis of speed during the world record. How fast did Bolt run?

Welcome to The Science of Sport! Be sure to visit our main page for daily comment and analysis on cycling, athletics, and more.

Well, yesterday evening we posted on the incredible performance of Usain Bolt, who took the Olympic 100m title in 9.69 seconds, breaking his own world record by 0.03 seconds, despite the fact that he started celebrating about 20m from the finish!

The splits and speeds

However, for today, we have been sent the split times for each 10m interval from Bolt's race (thank you to Seb and an anonymous poster!), which we've used to calculate average speed for each 10m interval. The graph is shown below. Then below that, you'll find a table showing the times at each 10m marker.

According to these data, his peak speed was hit at 50m, and he then maintained this all the way to 80m, running at about 44 km/hour.

Note that this is the AVERAGE speed - there are reports (which I don't fully believe) that he hit 48km/hour. I can't see where this would have happened, because that would mean that either side of it, he must have run much slower, and the graph above gives no indication that he ran anything but a consistently fast pace. So I think it's far more likely that this figure of about 44km/hour is the speed he hit. The "instantaneous" peak is subject to too much error, unless the data are specifically gathered, which I don't think is the case here.

How does this compare to past values? Well, when Donovan Bailey of Canada ran 9.84 secs to win the 1996 Gold, he was clocked at 43.6 km/hour using a radar gun. A later statistical calculation suggested that Bailey hit 47.6 km/hour, but again, I think this is a little misleading, because the "error" in timing means that 0.5 seconds here or there can swing the "peak speed" by a great deal.

Therefore, I think the better measure is average speed over 10m intervals. I'm quite sure that people have run as fast as Bolt did before. The magic of this performance, however, is not so much in the spectacular top speed between 50m and 80m, but rather that Bolt could maintain his speed for so long.

Remember, a sprinter typically hits peak somewhere between 50 and 60m, but then slows progressively. Bolt's huge victory was created thanks to his incredible 50m stint between 40m and 90m, where he never dropped below 42km/hour.

How much faster can he run?

That is the question flying around today. What if Bolt had not celebrated from 20m out? Could he have run 9.50 seconds? Thompson, who took silver, said he'd run 9.54 seconds. The data above suggest that this is probably a little too optimistic. Even if he had maintained his speed for the final 20m (which is unlikely - he'd probably have dropped off slightly), he would have run 0.09 seconds faster. This would give him a 9.60 second time, which is incredible. More likely, he'd have slowed anyway (as all sprinters do), so I'd guess that his celebrations probably denied him about 0.05s and a time of 9.64s.

However, unless he can find the time somewhere else - in the start perhaps (he was second slowest in reaction time) - he won't run 9.50 seconds. Then again, Bolt is a young man, and he's already shown incredible ability. Who knows what the next two years will bring?

Ross

Seb said...

Any chance of a graph comparison with your previous study?
(I discovered your blog with this one :-) )

Andrew said...

I second Seb's request, and would also like to see that first plot compared with others in the race, especially Thompson and his amazingly fast start.

SempreNaRoda said...

I listen some explanations about why jaimaicans are dominating the 100m.

Some said that a important factor is that the genetic elite is there. Jaimaican was a colonial where the slaves were sended from Africa. They chose the healthy and the stronger...

Ross Tucker and Jonathan Dugas said...

Hi again guys

Would love to do that. I'm not 100% confident in the data, either from that other study or these numbers, however.

You'll recall from that previous study that the times were obtained from the TV coverage, which is always a little dodgy - there was some very obviously wrong data in among the times for Johnson and Bailey, which I mentioend in the post.

Then as for this data, I'm not 100% sure where it comes from...? It seems legit, and so I will try to get it on the same graph as the previous study's, but direct comparisons will be dodgy...

As for comparing Bolt to other guys, if you have the data, I'll gladly plot it, because that really would make for interesting reading. I've got data somewhere from the 1999 World Champs (Maurice Greene won that race), where the scientists actually set up light sensors every 10m to get the data. So their data is most reliable of all.

I'll see if I can pull that off and get Bolt's numbers on the same axis.

Finally, to Semprenaroda, you're quite correct. That's the theory. It's also why the African Americans are so dominant. Just as people talk about the distance running gene in East Africans, there really does seem to be a genetic disposition to sprinting. In fact, in my opinion, it's even more convincing than the East African gene, because these guys seem "born fast", whereas work ethic and training introduce a lot more complexity into long distance running!

It doesn't explain why they have suddenly now produced the two fastest men in history, plus gold, silver and bronze in the women's race...or am I just being unnecessarily suspicious?

I mean, Bolt is a guy who before this year showed little sign of this speed, and the woman who won today's 100m title has improved from 11.28 to 10.78 seconds in 8 months. Remarkable. I hope it's legit...

Ross

Anonymous said...

Ross, what does a dip give you on a torso the size of Bolts?

8 inches?

so that is about .03 of a second to be rough.

Lets take that 8 inches to assume it is a neutralisation of the slow down from .82 to whatever it may have been. So adding two .82 sectors, gives you the 9.60.

Quentin said...

It doesn't explain why they have suddenly now produced the two fastest men in history, plus gold, silver and bronze in the women's race...or am I just being unnecessarily suspicious?

To be fair, do not forget that both Ben Johnson and Donovan Bailey (and maybe others?) were both born in Jamaica.

Ross Tucker and Jonathan Dugas said...

Hi Anonymous

Fair point. I'm not sure how much the dip contributes. I'd guess that 0.03s is probably a little optimistic - I'd put it at about 3 inches or 1/100th, maybe 2. The guy is already running at 40km/hour, and so throwing the chest forward might add a tiny amount, though I don't know the exact amount.

If I had to guess, he lost about 0.02 on the dip, and another 0.05 on the premature celebration. So maybe 9.62s, but I still think he'd have run 9.64s...At most...but it's fun to guess anyway!

One thing that will be interesting to see the 200m race, but if it's anything like this, he'll be celebrating from about 40m out!

Ross

Pedro said...

I have the 300 frames of the run in HDTV. In fact Bolt took 291 frames at 29.97 fps to complete the race.

Is it possible to use this data to a more accurate graphic modeling of the run?

My measurements stats that Bolt ran in 9.686

Luke said...

His 60m time of 6.32sec–is that a WR also? I see The current WR is 6.39 by Maurice (G.O.A.T) in Madrid in '98.

Since these times are just splits you can't count the right? Even if the wind was +0.0?

Anonymous said...

[quote]Remember, a sprinter typically hits peak somewhere between 50 and 60m, but then slows progressively.[/quote]

realy? in 1991 World Championships (where Carl Lewis did his 9.84 WR) 5 from 6 runner had there peak at 80m:

Carl Lewis:

50: 0,84
60: 0,85
70: 0,84
80: 0,83

Leroy Burrell:

50: 0,87
60: 0,86
70: 0,87
80: 0,84

Denis Mitchell:

50: 0,87
60: 0,87
70: 0,86
80: 0,86

Linford Christie:

50: 0,85
60: 0,86
70: 0,86
80: 0,85

Frank Fredericks:

50: 0,87
60: 0,87
70: 0,86
80: 0,85

Ray Stewart:

50: 0,86
60: 0,87
70: 0,88
80: 0,87

Anonymous said...

ups, it was Carl Lewis 9.86 WR, all other times seams to be correct retyped..

Anonymous said...

Nice Article .
We wish Usain Bolt all the Very Best from Sri Lanka

Anonymous said...

Hello from Germany !

Why you don't wait the 200 meter Finals. As the Ahtlets have to run in the same manner they do in 100 meter, you can watch how long Usain Bolt can maintain TOP SPEED. If he can pass the first 100 meter with 9,65 sec. the WR of Michael Johnson (19,32sec 1996 in Atlanta) could be crushed.
But what about ATP resources, the can only last for 8 seconds. So about 80 meter Usain Bolt must have no ATP reserves.
If he can maintain TOP Speed more than at meter 80, this would be an evident sign for Doping.
There a new biologics, that prevent the soon exhaustion of the skelett muscle. Some kind of ATP Booster ?

Ross Tucker and Jonathan Dugas said...

Hi Anonymous

Absolutely, I am sitting here right now waiting for that 200m race, because I plan to do exactly what you've suggested.

If you know where I can find the 10m splits for the 200m race, please let me know, so that I can do a graph of both races and we can compare how he runs it!

Thanks
Ross

Anonymous said...

Well, he did it! This man is awesome! And to all those people who cry "doping" (especially from Germany) I say "Shut up!"

Anonymous said...

what was his reaction time?

Anonymous said...

The Fastest Ever Recorded 10m Split Times (The Split Times below come from careful Video-Tape analysis footage. the Splits are taken by X King)

Men
Reaction Time (RT) Limit: 0.100s

0-10m: 1.69s (Minus RT), Raymond Stewart (9.96s Tokyo WCH 1991, w+1.2m/s), Frankie Fredericks (9.86s Lausanne GP 1996, w-0.4m/s), Maurice Greene (9.79WR Athens GP 1999, w+0.1m/s & 9.82s Edmonton WCH 2001, w-0.2m/s) & Tim Montgomery (9.85s Edmonton WCH 2001, w-0.2m/s) (Note: 1.69s, also by Ben Johnson Seoul OG 1988 DQ*, 9.79s w+1.1m/s)
10-20m: 1.00s, Bruny Surin (9.84s Sevilla WCH 1999, w+0.2m/s) & Maurice Greene (9.82s Edmonton WCH 2001, w-0.2m/s) (Note: 1.00s, also by Ben Johnson Roma WCH sf. 1987 DQ*)
20-30m: 0.89s, Maurice Greene (9.87s Stockholm GP 1999, w+1.3m/s)
30-40m: 0.86s, Maurice Greene (9.97s Crystal Palace BGP 1999) & Tim Montogmery (9.84s Olso GL 2001, w+2.0m/s) (Note: 0.86s, also by Ben Johnson Seoul OG 1988 DQ*, 9.79s w+1.1m/s)
40-50m: 0.84s, Carl Lewis (9.86WR Tokyo WCH 1991, w+1.2m/s), Frankie Fredericks (9.86s Lausanne GP 1996, w-0.4m/s), Maurice Greene (9.93s Lausanne GP 1999) & Tim Montgomery (9.78WR Paris GP Final 2002, w+2.0m/s), (Note: 0.84s, aslo by Ben Johnson Seoul OG 1988 DQ*, 9.79s)
50-60m: 0.82s, Maurice Greene (9.85s Roma GP 1999, w+0.8m/s, 9.86s Berlin GL 2000, w-0.2m/s & 9.87s Sydney OG 2000, w-0.3m/s)
60-70m: 0.83s, Donovan Bailey (9.93s Lausanne GP 1996) & Maurice Greene (9.86s Berlin GL 2000, w-0.2m/s 9.87s Sydney OG 2000, w-0.3m/s & 9.82s Edmonton WCH 2001, w-0.2m/s)
70-80m: 0.83s, Carl Lewis (9.86WR Tokyo WCH 1991, w+1.2m/s) & Maurice Greene (9.86s Berlin GL 2000, w-0.2m/s & 9.87s Sydney OG 2000, w-0.3m/s)
80-90m: 0.85s, Carl Lewis (10.03s Roma WCH sf. 1987,w-1.4m/s, 9.93WR Roma WCH 1987, w+1.0m/s, 9.97s Seoul OG sf. 1988,w+0.6m/s, & 10.02s Stuttgart WCH 1993, w+0.3m/s) & Maurice Greene (9.79WR Athens GP 1999, w+0.1m/s, 9.80s Sevilla WCH 1999, w+0.2m/s & Sydney OG 2000,w-0.3m/s)
90-100m: 0.85s, Carl Lewis (9.99s Los Angeles OG 1984,w+0.2m/s & 10.02s Stuttgart WCH 1993, w+0.3m/s) & Maurice Greene (9.79WR Athens GP 1999, w+0.1m/s)
Fastest ever recorded 'legal' Reaction Time: 0.100s, Jon Drummond(Monaco GP 1993)
Total (without Jon Drummond's Perfect 0.100s reaction time from the Monaco GP in 1993): 9.46s
Total (with Jon Drummonds Perfect 0.100s reaction time from the Monaco GP in 1993): 9.56s

http://run-down.com/statistics/100m_top_splits.php

Nick said...

condensed version of the post above:

Comparison of best 10m splits of all time vs Bolt's 9.69 run

0-10m: 1.69 vs 1.85*
10-20m: 1.00 vs 1.02
20-30m: 0.89 vs 0.91
30-40m: 0.86 vs 0.87
40-50m: 0.84 vs 0.85
50-60m: 0.82 vs 0.82
60-70m: 0.83 vs 0.82
70-80m: 0.83 vs 0.82
80-90m: 0.85 vs 0.83
90-100m: 0.85 vs 0.90

*Bolt's time here includes his reaction time

Hi to all,

Does anyone have Bolt's anthropometric measurements? One of the predictor of sprinting speed may be the ratio lower to leg ratio.

Thank you to all
Biomechanics and Neural Control of Movement
The University of Iowa

Anonymous said...

Just to let you in to where Bolt came from: Carifta Games held annually in the Caribbean for Under 17 and Under 20 athletes:
At age 15 Bolt ran 21.81 for 200m and 48.28 for 400m.
At age 16 he ran 21.12 and 47.33 and at the CAC Juniors (Central America and the Caribbean) he ran 20.61 and 47.12 later in the same year.
He also won the World Junior Championships 200 that year with a 20.61 200m.
In 2003, at 17 years, he ran 20.43 and 46.35 and was the World youth Champion in the 200m 20.40.
In 2004 at 18 he ran 19.93 in the 200m at the Carifta Games.Same year at Pan Am Juniors he ran a World Junior Record 200m 20.13.
So Bolt has always been a performer. I guess the eddoes, yams, potatoes, salt fish and dumplings from Trelawny, Jamaica has worked.

tim said...

i think that the 10m splits comparison shows the most relevant info regarding what Bolt "couldve" ran. What it shows is essentially a profile of a curve for most athletes which can be applied to the Bolt Run to determine the amount of deceleration expected, versus actual. from nick's post, it is a collection of the condensed 10m splits so is not indicative. The splits from previous athletes is a better indicator and using that suggests that there is a drop off over the last 20m. Considering Bolt's unrivalled top speed, it is not unreasonable to suggest that for 80-90m he may have maintained his 0.82s, or perhaps from 60-80 even gone lower to 0.81s.. the last 10m "could" have been as fast as 0.82 also. So speculatively it makes sense to believe that the best Bolt couldve ran- assuming that at 60m he began to "switch off"- or more accurately "not push", his 10m splits could read 60-70, 0.81, 70-80, 0.81, 80-90, 0.82, 90-100, 0.83..taking historical deceleration into acccount. Thereby giving him 9.59s. A conservative assessment may look like this , all splits unchanged except for the last 10m, 0.85. yielding 9.64s.
Whats left is the effect of perfect conditions on the run. Given 2m/s tail wind, and Bolt's frame size, this equates to close to 0.08s faster. (http://condellpark.com/kd/sprintlogistic.htm)

tim said...

start reaction times..i believe that the new official false start is declared at anything better than 0.12 seconds. Am I correct?

Joon said...

this is great. does anybody have similar splits from his 200m?

cosmo said...

hey guys bolt also ran 45.35 at 16 at the Jamaica Boys and Girls Championship in 2003.

zzzz111 said...

http://www.nydailynews.com/sports/2008olympics/2008/08/18/2008-08-18_conte_world_antidoping_agency_needs_to_b.html

Ross Tucker and Jonathan Dugas said...

HI Joon

Thanks. I wish we could analyse the 200m. I've been trying hard to get hold of the times to do just that, but it's not available anywhere. If you have access, please let us know and we'll definitely do a post on it!

And then to Cosmo, yes, I dug up all Bolt's PB's and times, and I did a whole post on it. You will find it in our Archives, on the 21st of August.

Thanks for the visit!
Ross

tim said...

one thing that i have seen come up with a very definite unsavoury theme has been the drug slur over world record times. The perpetrators of this theme have been, without exception, americans. (I am writing objectively so please dont think i have an alterior motive). The recent comment to this article by zzzz111 further supports this "theme" by citing american journalism as another source of doubt. The article cites comments made back in December 2007, by the now infamous Victor Conte.

I'd like to address this if i may, and propose an alternative speculative viewpoint.

1. Why does the article make strong inferences to records now rather than pre Beijing- considering it was known last December?
2. Anything Victor Conte says must surely be met with some doubt. It was by the entire US nation until it was proven beyond doubt that he is a cheat- so why now how the article used his statement as the only source of legitimate basis?
3. The only athlete that has risen to stardom, and produced feats worthy of any heightened suspicion has been Usain Bolt. The other athletes at the top level are amongst the very same crop of achievers that have been produced from that country since man could run....so, what must be going on in the psychii of a man whom, from age 14, has won everything before him, achieved so much with seemingly little effort (his ore race prep for the 100m final consisted of 2 "sessions" of TV, sleep and chicken nuggets), resort to drugs? I personally am not aware of any athlete that does not have a problem with their performance, using drugs and it seems a ridiculous suggestion given the history and long list of wins.
4. No such article surfaced when Maurice Green, Tim Montogomery, Gatlin, Michael Johnson, Marion Jones, Steve Lewis, Florence Grffith Joyner, Jackie Joyner, Mike Powell (1n 1991), each produced their eras and performances that dominated the competition- many of them exhibiting what is usually a sign of drug use- that being that they had reached a level of performance where they had appeared to plateau, at an age where most athletes begin the gradual slow down in their careers- or show only very minor improvements through hard work. Not a single slur or inference from the US press. Furthermore no spotlight has fallen on other athletes not directly involved in the BALCO scandal but dominated during the time of its (BALCO) operations.
5. Regardless of out of season testing, the behaviours of Powell and Bolt et al are compelling as counter argument to the article. The fact that both compete regularly in the IAAF GP, yet are selective enough to pursue events that line with their training goals as opposed to generating income also exposes them to the usual IAAF testing- which is, relatively speaking, far enough out from big events like the olympics to be considered as "out of season"- arguably. This behaviour is quite the contrast of the now proven "antics" of, for instance, the many Greek athletes who have eluded, dodged, squirmed, wiggled and ran from testing as well as not competed at all except for at the biggest of all stages.
6. The IAAF lists who they tested each year via their website. Viewing this shows that all of the high profile athletes received more than their fair share of testing over the year- US athletes receiving no more testing than any other country and in fact, the top athletes received the most tests.
7. With the exception of Ben Johnson and Flo-Jo, who both fitted into the "also ran never was, never had been" then "incredible adult aged world record breaker and world beater" (Flo-Jo moreso), any of the previously busted drug users have not destroyed the world records and competitors- "merely" been able to win regularly in smart times. If any users were present, it was subtle..hey, maybe they are all using...

the point is that of the 4 most dominant athletes since the mid 1980s, none have tested positive, one foolishly and naively used highly androgenic anabolics pre competition and the other 3 were american. Of the 3 americans, 1 exhibited virtually every telltale sing of hormonal manipulation and the others reigned supreme during the BALCO period.

Due to their extreme dominance during their time, surely they could only do so if they either knew they werent going to get caught, OR were truly special human beings. We now know that the former was certainly in effect, and maybe the latter is in there too.

Extending this suggests that the same thing could be happening here. i.e. Bolt knows he wont get caught, or he's truly a freak of nature. There are glaring exceptions that suggest that the "doping" is less likely than the "freak of nature" angle in that a), he's not from the US. b) he displays a solid pedigree and resume of continual improvement and dominance since a teenager, and c) he has continued to compete throughout.
Finally, given the above, he has still destroyed what we thought were difficult benchmarks in the sport. If he were using wouldnt we see a different pattern- or some level of subtlety applied (as if to avoid suspicion).

Long post i know but as a long time track fan, "survivor of Seoul" and loather of cheats, I simply dont see the same pattern- or similar pattern of events to those whove preceded Usain and ultimately been discovered.

Finally, athletes in Beijing have also had their blood taken and stored for the first time for retrospective testing. The one thing about Jamaica that further distances itself from other countries is it's national pride. If ever caught, an athlete and their family look forward to a long road of discomfort socially in that country. There seems to much to lose, and little anonymity to be able to hide.

Paul 14203 said...

Some bloggers have discussed the emergence of Usain Bolt at the Bejing Olympics. As some background information the following may be useful:

Jamaica has a proud tradition of sprinting at the highest level. On the Mens side our Olympic 100 and 200m record is as follows:

100m Silver - 1952 Helsinki - Herb McKinley
100m Silver - 1968 Mexico City - Lennox Miller
100m Bronze - 1972 Munich - Lennox Miller
100m Silver - 1976 Montreal - Don Quarrie
200m Gold - 1976 Montreal - Don Quarrie
200m Bronze - 1980 Moscow - Don Quarrie

Also Jamaican born athletes of note include:
100m Gold - 1992 Linford Christie (Britain)
100m Gold - 1996 Donovan Bailey (Canada)

Ben Johnson (Canada) was born in Jamica too but he was mostly a product of drugs.

Due to space, I have only listed the medals of the men in the 100 and 200 m. However there were several Jamaican finalists, several other events (e.g. 400m, relays) and I have not mentioned the record of the women which is much better than the men.

Also worthy of note is that for many years, notably in the 70's, 80's and 90's there was rampant drug use by several athletes of other countries. This was particularly evident in several countries of the former Eastern Bloc, where state sanctioned, institutionalized drug use was a way of life for many athletes (this came out publicly several years ago).

The point is that Jamaica has a proud record going back over 1/2 a century, dispite sometimes running against drug enhanced athletes.

Traditionally, most of our athletes went to the US College system to develop there talents and train under the best coaches. The effect was that they became world class athletes, however a side effect was often that they were tired or injured by the time the Olympics came around. Sometimes sub-par performances were a result.

Some may say that the US athletes went through the same system. That is true, however the talent pool that Jamaica has is less than 100 times smaller than the US (300 million to 2.8 million). Therefore the loss of even one athlete due to fatigue or injury hits Jamaica much much more that a simular loss would hit the US.

Jamaica's performaces at this Olympics, and a few recent major games, is largely due to a shift in the way that the athletes are developed. Many now stay in Jamaica and go to Jamaican colleges because a number of Jamaican coaches are as good as anyone else in the world.

Sorry about the length, however it is important to put Bolt's and the rest of the Jamaica's teams performance at Bejing into the proper context.

It is a continuation of the development of a natural talent pool, hard work, dedication, guts and pride in holding up a Proud Tradition!

tim said...

for those who have a sense of humour check this out...i laughed my butt off..

http://www.dailymotion.com/video/x6ih8s_usain-bolt-celebrates-earlyvery-ear_fun

Smakdab said...

He didn't even hit top speed boys... The fact that he is HOLDING 0.82 speed for a good distance AFTER shutting down (he stopped running hard long before he started waving around) tells me he would be nailing 0.79-0.80ish at top speed. You must remember that these splits can't be added up to make 100m... There is missing time in each split (thousandths, ten-thousandths of seconds, etc, etc...) that don't figure into your sums. The suggestion of 9.54 is more accurate than 9.60. Just watching the race, it is obvious to the trained eye he left much more than a tenth out there, closer to two tenths if you ask me. I say 9.53.

tim said...

Bolt's top speed. I have to agree that he didnt hit top speed. which is why i included a 10m split of 0.81 for his time projection.
i dont think 0.79 for 10m is possible however...and doubtful about 0.80 also. But 0.81 very possible considering him sitting on 0.82 for some time..hey, id love to be wrong and see a 0.79/10m split..or better!..lol..

tim said...

BTW the "trained eye" knows that just over 1m is around 0.1s at the end of a 100m race..and 1m is a deceivingly large distance in the 100m. The 1987 WC 100m had Lewis and Johnson split by that exact margin..0.1s. and it looked like daylight. So for me, he may have gone 1m or so faster on the night..but not 2, and i dont think 1.5m.. again id love to be wrong.
if you throw in a couple of 0.80 splits then he gains about half a metre.

Terry said...

Usain actually followed good sprint technique which may well have aided him in running as fast as he did. Trying to run fast after hitting your top speed will nly cause you to slow down.

tim said...

did anyone notice that the 10m splits show usain significantly faster than the 50 and 60m indoor world records also?

Anonymous said...

your analysis was very interesting but I'm waiting for the 200m and above al the 4 x 100m same analysis ! I heard somewhere that he ran the relay in 9.10 !!!

tim said...

actually 9.1 isnt that great for a relay leg. sub 8.9s legs have been run by Carl Lewis, maurice green, donovan bailey, asafa powell.
watching the video the 4x100m splits show 10.1, 9.2, 8.9, 8.9 for jamaica.that means usain ran 8.9 around the bend.....!!!

Anonymous said...

I'm definitively a fan of Usain ! he's great !

tim said...

newsflash!
i just watched the athletissima 2008 men's 100m.

i dont think ive ever seen an athlete accelerate and put a distance in between himself and the rest in such a short space of time as Asafa Powell did last night.

would love to see the 10m splits for that..he appears to not have the same top speed as Bolt but darn did he have some zip between 30 and 60m...wouldnt be surprised to see better splits than usain, and powell get the 60m WR this next indoor season.

for those who missed it, he ran 9.72 with 0.2 wind.

un freaking believable.

great time to be a sprint fan.

Tim

Anonymous said...

Hello Ross and Tucker,

I appreciate your efforts to bring science and mathematics to sports, especially, running.

Unfortunately, there is a major error in the analysis of the position versus time curve. The error lies in the assumption that the velocity at the end of each timing interval equals the change in position over the interval divided by the length of the time interval. That is the “average” velocity near the middle of the preceding interval, not at the end of the interval. That might be close the instantaneous velocity at the end of the intervel.

There are many mathematical techniques for estimating the instantaneous velocity at the ends of the intervals. The velocity you need is the slope of the position versus time curve. You should look at the paragraph beginning with “A simple three-point estimation . . .” at:

http://en.wikipedia.org/wiki/Numerical_differentiation

The second formula is the one to use in this application.

Good luck with your efforts. Thank you for all your hard work.

Ted

FYI:
http://members.aol.com/MathPhysicsModel/SM/SM.html

tim said...

Ted, I believe the guys did actually point that out in their article.

So, diagrammatically they have displayed the curve at point estimates, for simplicity and comparison to other similarly conducted measurements of other races.

The converse could also be argued that between the points there may also be periods where the speed was not as high as the mean. For analytics, and discussion, IMO, this graphing method is fine. Too much stats and you lose the audience too...fitting curves and obtaining goodness of fit R values and so on is, dare i say it, bordering on ridiculous. Both these guys have PhDs ...you dont get them without having a sound understanding of the math.

Anonymous said...

There was a link to a draft submission on the Bolt measurements on BIOMCH-L, today.

It's pretty interesting. I like the Conclusions on page 4. It is at:

http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.0209v2.pdf

They used a single spline to fit the distance curve in the section on (4.) on estimationg the motion profile. That's a better way to approach the problem.

Ted

tim said...

hi Ted, thanks for the link. im going to check it out. (i cant see how they could do this though as, as you point out, each interval would consist of acceleration and deceleration periods coinciding with his ground contact- not altogeher unlike the acceleration of a piston in a cylinder for each revolution)...but my mind's open..
Tim

Anonymous said...

i think if the reaction time of Usain Bolt on starting block was faster he could gain 0.03 second comparing with the other athletes(0.165 for usain bolt but per example 0.133 for walter dix), and he could gain more than 0.07s if he didn't slow down at the end , and he lost also about 0.02s because his shoes werent tied and imagine the wind was 2m/s so he could gain also 0.04s so in total he could run the 100m in a time 0.16 faster witch correspnd to
9.53, he could really do it .