What Distance Would Yield the Fastest MPH Speed?

cant you use calculus to figure this stuff out?

I guess you could...

but would calculus factor in fatigue?

Basically just looking for opinions here...

About 165 meters.

Luigi Vercotti wrote:

About 165 meters.

About 60m. Split analysis has shown that 100m sprinters reach their fastest speeds between 50 and 70m, then they decelerate. 200m runners reach their top speeds anywhere between 50 and 150m but their max is lower than the 100m boys.

check out the link

Are you talking about speed (and instantaneous concept, or average speed. If you are talking about runnig speed, are you talking about the time spent before they begin running (reaction time). Highest average speed is the anchor leg on the 4x100 relay, where times under 9.0 have been recorded. The anchor leg might also have the highest speed (peak), although the 100m somewhere around 60m is usually mesured to be the fastest.

A complication with your question has to do with the curve on the track: the 100m and 110mh are both on the straight, however, ignoring that issue I made a simple model of the incremental speed of the next 10m increment under the assumption that this was the terminal increment. Thgis is a little flawed but not too badly. I got about 155m as being the highest average speed, including the start lag. If we take out just the reaction time, it moves to 145m, while if we take out the first 20 meters, which takes close to 3 seconds (I am guessing from memory here from eldrick), then we get 90m; that is even the last 10 meters of the 100 is slowing.

here is a little table (difficult to line up properly:

meters DeltaTime Time m/s =m/s-react =m/s-T20m

0.000 0.1200 0.120 not/app not/app not/app

10.00 1.5500 1.670 5.988 6.4516 not/app

20.00 1.1500 2.820 7.092 7.4074 not/app

30.00 0.9000 3.720 8.065 8.3333 11.1111

40.00 0.8800 4.600 8.696 8.9286 11.2360

50.00 0.8600 5.460 9.158 9.3633 11.3636

60.00 0.8500 6.310 9.509 9.6931 11.4613

70.00 0.8500 7.160 9.777 9.9432 11.5207

80.00 0.8600 8.020 9.975 10.127 11.5385

90.00 0.8650 8.885 10.129 10.268 11.5416

100 0.8750 9.760 10.246 10.373 11.5274

110 0.8861 10.646 10.332 10.450 11.5000

120 0.8984 11.545 10.395 10.504 11.4620

130 0.9119 12.456 10.436 10.538 11.4151

140 0.9266 13.383 10.461 10.556 11.3604

150 0.9425 14.326 10.471 10.559 11.2989

160 0.9596 15.285 10.468 10.551 11.2314

170 0.9779 16.263 10.453 10.531 11.1582

180 0.9974 17.260 10.428 10.502 11.0800

190 1.0181 18.279 10.395 10.463 10.9972

200 1.0400 19.319 10.353 10.417 10.9101

That's a terrible analysis.

Michael Johnson was 10.12 at the 100 in his 19.32

10.12

11.10

12.09

13.06

13.97

14.83

15.61

16.40

17.26

18.23

19.32

http://hypertextbook.com/facts/2000/KatarzynaJanuszkiewicz.shtml

http://72.14.207.104/search?q=cache:II294AXncuEJ:www-stat.stanford.edu/~tibs/ftp/fastest.ps+michael+johnson+19.32+10+meter+split+times&hl=en&gl=us&ct=clnk&cd=2&client=firefox-a

Based on those splits, 180m. Johnson had remarkable speed endurance for a 200m runner (or is that just because he runs the 200m so much faster than anyone else?) though, so for most sprinters I would think it is closer to 160m.

what i got wrote:

Based on those splits, 180m. Johnson had remarkable speed endurance for a 200m runner (or is that just because he runs the 200m so much faster than anyone else?) though, so for most sprinters I would think it is closer to 160m.

That's why no one can touch him at 200.

runmad wrote:

For all you math/physiology wonks out there...

9.76 for 100m is (VERY ROUGHLY) 23.1 mph.

19.32 for 200m is (again, VERY ROUGHLY) 23.3 mph.

Obviously (to me) the max would be somewhere in between.

Without getting too nutty (no 163.2534m, please), to the nearest 10 meters, what distance do you think would give the highest mph value?

I'm thinking 170m... any takers?

You are talking AVERAGE SPEED. In that case, I say 170m.

But for fastest instantaneous speed, it is in the 100m, somewhere around 70m.

malmo wrote:

That's a terrible analysis.

Michael Johnson was 10.12 at the 100 in his 19.32

10.12

11.10

12.09

13.06

13.97

14.83

15.61

16.40

17.26

18.23

19.32

Are you indicating that Johnson ran 9.2 for the last 100 meters? If so, that is incredible.

yeah, you see, he was already running when he hit that 100m mark.

well, i'm thinking if you ever were trying to actually stage a race like this, donovan bailey (tried to) race Michael Johnson over that 150m race thing for a million bucks, so maybe 150 might be the way to go. i'm not saying physically 150m would be optimal, but in light of the media circus surrounding and organizing that event, i think 150m would be very appealing to the public and still yield some fast speeds.

I think that you need to read my post more closely before you make your comments. I said that those times are for races where the distance listed is the terminal time. They are NOT the split times that you would have for a longer distance. Do you understand that distinction? You do not use the same strategy, nor do you even train exactly the same for the different hypothesized distances (go read the question at the beginning of the thread). Also, I meant the "data" to be representative of the idea about successive terminal times (as opposed to split times, but I guess that I did not get the point across).

26mi235 wrote:

I think that you need to read my post more closely before you make your comments. I said that those times are for races where the distance listed is the terminal time. They are NOT the split times that you would have for a longer distance. Do you understand that distinction?

Of course I understand the distinction and you're still wrong. Only the 100m time and 200m times you listed are "terminal times", all the intermediate times represent some sort of interpolation, an interpolation which, in my opinion is meaningless.

iloverunning wrote:

Are you indicating that Johnson ran 9.2 for the last 100 meters? If so, that is incredible.

What do you suppose Justin Gatlin ran from 10m to 10m past the finish line? I'd bet he ran 8.8 (or better). Now THAT'S incredible!

What if Gatlin ran a 120m race and was clocked from the 20m mark to the finish. If you take out the first 20m of Gatlins WR race, he would have run 80m in 6.90s. Now add 20 meters in 1.8s - you get 8.7s - not out of the question by any means!

From an old yarn:

------------------------------------------

These are the best incremental splits ever recorded for 100m, which add up to 9.46 for 100m (assuming perfect reaction time of zero) Add .10 (allowable reaction time), and you get 9.56 for the "perfect race."

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 1.69+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, (2.69)

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, (3.58)

Maurice Greene (9.87s Stockholm GP 1999, w+1.3m/s)

30-40m: 0.86s, (4.44)

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, (5.28)

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, (6.10)

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, (6.93)

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, (7.76)

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, (8.61)

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, (9.46)

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)

"Biomechanics of Sport and Exercise" by Peter McGinnis, has splits for Ben Johnson and Carl Lewis during the 1988 Olympic 100m final.

Ben Johnson

position.....elapsed time......interval time

10m..........1.83...............1.83

20m..........2.87...............1.04

30m..........3.80...............0.93

40m..........4.66...............0.86

50m..........5.50...............0.84

60m..........6.33...............0.83

70m..........7.17...............0.84

80m..........8.02...............0.85

90m..........8.89...............0.87

100m.........9.79...............0.90

Carl Lewis

position.....elapsed time......interval time

10m..........1.89...............1.89

20m..........2.96...............1.07

30m..........3.90...............0.94

40m..........4.79...............0.89

50m..........5.65...............0.86

60m..........6.48...............0.83

70m..........7.33...............0.85

80m..........8.18...............0.85

90m..........9.04...............0.86

100m.........9.92...............0.88

Rome '87 wind +1.0

Ben Johnson 1.84 2.86 3.80 4.67 5.53 6.38 7.23 8.10 8.96 9.83

1.71 1.02 0.94 0.87 0.86 0.85 0.85 0.87 0.86 0.87

Reaction Time: 0.129

Carl Lewis 1.94 2.96 3.91 4.78 5.64 6.50 7.36 8.22 9.07 9.93

1.75 1.02 0.95 0.87 0.86 0.86 0.86 0.86 0.85 0.86

Reaction Time: 0.193

Seoul '88 wind +1.1

Ben Johnson 1.83 2.87 3.80 4.66 5.50 6.33 7.17 8.02 8.89 9.79

1.70 1.04 0.93 0.86 0.84 0.83 0.84 0.85 0.87 0.90

Reaction Time: 0.132

Carl Lewis 1.89 2.96 3.90 4.79 5.65 6.48 7.33 8.18 9.04 9.92

1.75 1.07 0.94 0.89 0.86 0.83 0.85 0.85 0.86 0.88

Reaction Time: 0.136

Linf. Christie 1.92 2.97 3.92 4.81 5.66 6.50 7.36 8.22 9.09 9.97

1.05 0.95 0.89 0.85 0.84 0.86 0.86 0.87 0.88

Reaction Time: ?

Tokyo '91 wind +1.2

Carl Lewis 1.88 2.96 3.88 4.77 5.61 6.46 7.30 8.13 9.00 9.86

1.74 1.08 0.92 0.89 0.84 0.85 0.84 0.83 0.87 0.86

Reaction Time: 0.140

Leroy Burrell 1.83 2.89 3.79 4.68 5.55 6.41 7.26 8.12 9.01 9.88

1.71 1.06 0.90 0.89 0.87 0.86 0.87 0.84 0.89 0.87

Reaction Time: 0.120

Dennis Mitchell 1.80 2.87 3.80 4.68 5.55 6.42 7.28 8.14 9.01 9.91

1.71 1.07 0.93 0.88 0.87 0.87 0.86 0.86 0.87 0.90

Reaction Time: 0.090

Raymond Stewart 5.54 9.96

Reaction Time: 0.114

Atlanta '96 (hand-time?)

------------------------

Donovan Bailey 1.9 3.1 4.1 4.9 5.6 6.5 7.2 8.1 9.0 9.84

Reaction time: 0.174

Athens '97

----------

MG 1.71 1.04 0.92 0.88 0.87 0.85 0.85 0.86 0.87 0.88

0.13 1.71 2.75 3.67 4.55 5.42 6.27 7.12 7.98 8.85 9.73

DB 1.78 1.03 0.91 0.87 0.85 0.85 0.85 0.86 0.87 0.90

0.14 1.78 2.81 3.72 4.59 5.44 6.29 7.14 8.00 8.87 9.77

TM 1.73 1.03 0.93 0.88 0.86 0.86 0.86 0.87 0.88 0.90

0.13 1.73 2.76 3.69 4.57 5.43 6.29 7.15 8.02 8.90 9.80

FF 1.73 1.04 0.93 0.89 0.87 0.86 0.86 0.87 0.88 0.89

0.12 1.73 2.77 3.70 4.59 5.46 6.32 7.18 8.05 8.93 9.82

AB 1.72 1.05 0.93 0.89 0.87 0.87 0.87 0.88 0.90 0.92

0.12 1.72 2.77 3.70 4.59 5.46 6.33 7.20 8.08 8.98 9.90

Best 10m Segments

0-10m 1.71 M. Greene '97, B. Johnson '87*, L. Burrell '91

D. Mitchell '91 (1.70 B. Johnson '88*)

10-20m 1.02 C. Lewis '87, B. Johnson '87*

20-30m 0.90 L. Burrell '91 (D. Bailey 0.91 '97)

30-40m 0.87 C. Lewis '87, D. Bailey '97, B. Johnson '87*,

(B. Johnson 0.86 '88)

40-50m 0.84 C. Lewis '91, (B. Johnson '88)

50-60m 0.83 C. Lewis '88 (B. Johnson '88)

60-70m 0.84 C. Lewis '91 (B. Johnson '88)

70-80m 0.83 C. Lewis '91

80-90m 0.85 C. Lewis '87

90-100m0.86 C. Lewis '87, '91

- Carl Lewis' best splits & reaction time add up to 9.74, while his PB was 9.86. A 0.12 difference. Notice Lewis has the fastest times in every split except 0-10m and 20-30m.

- Ben Johnson's best splits & reaction time add up to 9.73, while his PB was 9.79. A 0.06 difference, and considering that he let up in '88, he probably would have run 0.04s faster in the last 20m and matched his '87 splits. That adds up to a time of 9.75, only 0.02 off of his best splits added up. This leads me to believe that Ben simply learned to open his energy envelope larger than Lewis did. It's interesting to note that Ben really wasn't that much better than anyone in the actual acceleration, he just had the ability to accelerate fast without feeling the effects on his nervous system.

Malmo, go read the first post in this thread. The times listed are all interpolations in a way because we do not have top level events at these distance. However, the question was about the fastest average speed (including starting lag), and so I gave an example of the nature of the answer. I also gave some times adjusted for the reaction time and the early speed-up time so that more people could get the distinction, since there have been a couple of threads with the same underlying misconception that the 200 race is "faster". It is good to have the detailed second post. But go read the thread question before saying that talking about it is meaningless. Also, what would be your guess for the WR times if each of those 10m increments were the primary distance raced (since that really is the question here)?

malmo wrote:

26mi235 wrote:

I think that you need to read my post more closely before you make your comments. I said that those times are for races where the distance listed is the terminal time. They are NOT the split times that you would have for a longer distance. Do you understand that distinction?

Of course I understand the distinction and you're still wrong. Only the 100m time and 200m times you listed are "terminal times", all the intermediate times represent some sort of interpolation, an interpolation which, in my opinion is meaningless.

26mi235 wrote:

However, the question was about the fastest average speed (including starting lag), and so I gave an example of the nature of the answer.

Yes, you are much more in line with the original intent of the thread.

Based on Malmo's splits, 180-190m.

The distance that produces the highest overall speed will be the distance where the split for the last 10m is equal to the average 10m split.

MJ's 200m run averaged 0.97 seconds for each 10m.

His splits for the last 100m:

0.98

0.99

0.97

0.91

0.86

0.78

0.81

0.86

0.97

1.09

You see, even though he slowed down after 160m, the 0.81, 0.86, and 0.97 were equal or faster than his average pace, meaning that his overall speed was still increasing. However, I'll go with 180m because MJ doubled in the 400m, and thus might have better endurance than the hypothetical 180m specialist. However, it is conceivable that a race longer than 200m would produce a faster overall speed, assuming the athlete didn't slow down to a point where he ran slower than his average speed.

If I remember correctly back in 96 when bailey set the 100 world record his top speed was clocked at right about 27 mph. But if you look at johnson's 200 you have to bring in the fact he was already running at top end by 100 in and was 10 flat or so.