The accelยญerยญaยญtion theยญory can help you crush your competition.
At times in life, it might seem like everyยญone is ahead.
At such times, you might experยญiยญence stress, self-doubt, and perยญformยญance anxiยญetyโโโespeยญcially if you have a comยญpetยญitยญive personality.
Struggling to stay ahead at all times might be drainยญing menยญtally and physยญicยญally. Just keepยญing up becomes a chore.
Turns out that stayยญing ahead might also be overยญrated. I came to this conยญcluยญsion when researchยญing how to become a betยญter sprinter.
Here we go:
My Sprint Experiment in Greenwich Park
In 2004, I lived in Greenwich, London. My girlยญfriend and I renยญted a runยญdown apartยญment near Cutty Sark above a locยญal post office.
Broke and restยญless, we spent much time exerยญcising in Greenwich Park, home of the GMT date line. The park was an excelยญlent place to play around with a stopยญwatch and some sprints.
Why not? We were both strong sprintยญers in high school and wanted to see if we could still hit some decent times.
I quickly learned I wasยญnโt even close to my high school records. As disยญapยญpointยญing as this was, I added some interยญval trainยญing to my regiยญmen. I pushed myself hard but could not slow down my new, slow times.
Whatever speed I had as a teenยญager now seemed to be gone.
Still, I wasยญnโt ready to give up.
I turned to research.
Inspired by World Champions
I rememยญber watchยญing the 100-meter dash in the Olympics as a kid. I was mesยญmerยญised by how some sprintยญers could come up from behind in the last part of the race and crush their opponents.
But at the same time, I always wondered:
If an รฉlite sprintยญer is leadยญing the 100-meter dash at 80 meters and someone else is comยญing up fast from behind, why isnโt the pack leadยญer putยญting up more of a fight?
I reasoned that someยญthing must be left in the tank with only 20 meters to the finยญish line. But no. I donโt think Iโve ever seen a 100-meter dash sprintยญer pick up the pace that close to the finยญish line.
Naturally, I starยญted searchยญing for how the 100-meter dash works from a mathยญemยญatยญicยญal perspective.
I will use some interยญestยญing data points from Maurice Green and Usain Bolt to illusยญtrate some of my findings:
Data Points from Maurice Green
In his paper, A Mathematical Model of the 100M and What It Means, Kevin Prendergast outยญlines a forยญmula for describยญing what hapยญpens durยญing a 100-meter dash. Prendergast tests his proof on the resยญults from the 1999 World Championships, where data from the eight finalยญists were anaยญlysed. Seven sprintยญers were then grouped and comยญpared to the winยญner, Maurice Greene. 1Prendergast, K. (2018, January 21). A mathยญemยญatยญicยญal modยญel of the 100m and what it means. Silo. https://silo.tips/download/aโmathematical-model-of-the-100m-and-what-it-means
Data points from the sprintยญers (excludยญing Maurice Greene) in that race showed:
And here are the same data points, but for Maurice Greene alone:
The sevยญen finalยญists reached their points of maxยญimยญum speed at an averยญage of 59.79 meters into the race, at which point Maurice Green was still accelยญerยญatยญing, reachยญing his maxยญimยญum speed at 86.84 meters! It shows in the durยญaยญtion of accelยญerยญaยญtion, which for Greene was 8,68 seconds (almost the entire race!) and 6,44 seconds for the rest.
Greeneโs max speed wasยญnโt much highยญer than the othยญers, but the othยญers decelยญerยญated for 3.38 seconds while Greene only slowed down for 0.99 seconds.
Prendergast conยญcludes:
โThe pracยญticยญal lesยญson from this modยญel for sprintยญers and coaches would seem to be the beneยญfit of extendยญing the time of accelยญerยญaยญtion. This, rather than raw power out of the blocks, will resยญult in faster times. It is probยญably a matยญter of conยญtrol. [โฆ] It is posยญsible to derive a mathยญemยญatยญicยญal modยญel that modยญels a 100m perยญformยญance very well. It provides valuยญable informยญaยญtion on the makeup of the perยญformยญance, regardยญing accelยญerยญaยญtion, veloยญcity, and disยญtance at any stage in the race. It enables us to see the vital ingrediยญents of sucยญcess in 100m runยญning, and that the most vital is to accelยญerยญate as long as possible.โ
Data Points from Usain Bolt
Assuming that the fricยญtion between our feet and the ground is conยญstant and that runยญning on two feet is givยญen, a theยญorยญetยญicยญal superยญhuยญman can run 100 meters between 4,5 to 5 seconds.
Going any faster is impossible without alterยญing physยญics.
But hereโs the excitยญing part:
Look at the veloยญcity curve for the worldโs fastยญest sprintยญer, Usain Bolt.
When I looked at breakยญdowns for famยญous 100-meter sprintยญers over the last 40 years, their averยญage top speeds hadยญnโt increased much, but Usain Bolt stands out with his maxยญimยญum speed of 12,2 meters per second.
We can see that Boltโs speed varยญies durยญing a 100-meter dash. So, what can we disยญcern from his data points? I looked closely at sevยญerยญal 100-meter dash finals.
The accelยญerยญaยญtion phase: To accelยญerยญate, you must be at an angle with the ground (leanยญing forยญward, pushยญing with legs) to be able to push hard against gravยญity.
The top speed phase: Once upright (runยญning tall with as little conยญtact with the ground as posยญsible), you can only mainยญtain speed or decelerate.
Turns out Iโve been wrong about sprintยญing. I always tried to reach my top speed as fast as posยญsible in my sprints.
The worldโs best 100-meter dash sprintยญers can only mainยญtain their top speeds for 20โโโ25 meters. Maurice Green accelยญerยญated for an incredยญible 8,69 seconds and kept his top speed for 0,99 seconds.
And what was I doing? I cruised easยญily at my โtop speedโ for 75โโโ80 meters.
Huh.
How fast would I have to run at a top speed that I could only susยญtain for no more than 20โโโ25 meters? I realยญised that I should try to extend my accelยญerยญaยญtion phase.
Time for a new experiment.
Back to Greenwich Park: New Experiment!
My girlยญfriend and I went back to Greenwich Park, marked every 10 meters along a 100-meter track, and I made a few test sprints.
First, I ran as usuยญal. I reached my top speed (runยญning tall with as little conยญtact with the ground as posยญsible) after about 25โโโ30 meters, and I manยญaged to keep my speed reasยญonยญably well for the remainder of the distance.
Now, I wanted to extend my accelยญerยญaยญtion time. But for how long? I decided to go for the 60-meter mark.
I preยญpared myself, and as my girlยญfriend starยญted the stopยญwatch, I got off to a good start. As I kept accelยญerยญatยญing, the strain on my body was immense. At the 30-meter mark, I felt like I was carยญryยญing an eleยญphant. At the 40-meter mark, I could not keep accelยญerยญatยญing for longer.
And as I began closยญing in on the finยญish line, my legs and upper body were spent. At 80โโโ90 meters, I could feel myself decelerating.
Reaching the finยญishยญing line felt like an eternยญity. Also, I felt a lot more drag throughยญout the sprint, almost as if someone had attached a paraยญchute to my waist, slowยญing me down even further.
Discouraged, I asked my girlยญfriend about my time.
โWell, Jerry, that was your fastยญest 100-meter dash ever,โ she said while starยญing at the stopยญwatch like she couldยญnโt believe it. โBy a wide margin.โ
The Acceleration Theory
โDo today what othยญers wonโt, so tomorยญrow you can do what othยญers canโt.โ
According to Prendergastโs mathยญemยญatยญicยญal modยญel for รฉlite sprintยญers, getยญting an early lead can harm your finยญishยญing time. 2Prendergast, K. (2018, January 21). A mathยญemยญatยญicยญal modยญel of the 100m and what it means. Silo. https://silo.tips/download/aโmathematical-model-of-the-100m-and-what-it-means
Can you apply an โaccelยญerยญaยญtion theยญoryโ outยญside sprinting?
Well, it seems to me that you can someยญtimes ensure a win by stayยญing in a zone that many find uncomยญfortยญable for longer.
My accelยญerยญaยญtion phase philoยญsophy is as folยญlows: At the beginยญning of a new and chalยญlenยญging endeavยญour, you work hard on improvยญing, not mindยญing that othยญers reap more of the iniยญtial benefits.
Acceleration theยญory (menยญtal modยญel). This concept indicยญates that the winยญner mustnโt lead the race from start to finยญish. Mathematically, delayยญing maxยญimยญum โspeedโ by proยญlongยญing the slower accelยญerยญaยญtion phase will get you across the finยญish line faster. 3Silfwer, J. (2012, October 31). The Acceleration Theory: Use Momentum To Finish First. Doctor Spin | The PR Blog. https://โdocโtorโspinโ.net/โaโcโcโeโlโeโrโaโtโiโoโnโ-โtโhโeโoโry/
Instead, you ignore your comยญpetยญiยญtion at first, strivยญing to keep accelยญerยญatยญing well past the halfway point of the endeavยญour. At the 60% mark, you put everything you learnt and built up into playโโโand you go!
The Intriguing 60% Mark
Based on the mathยญemยญatยญicยญal modยญel for sprintยญers, I often conยญtemยญplate the switch from the accelยญerยญaยญtion to the top speed phase. According to the equaยญtion, the switch should hapยญpen at around 60% of the race.4Prendergast, K. (2018, January 21). A mathยญemยญatยญicยญal modยญel of the 100m and what it means. Silo. https://silo.tips/download/aโmathematical-model-of-the-100m-and-what-it-means
If we play around with this idea:
Itโs anecยญdotยญal and not a โtheยญory,โ sure.
However, the approach of proยญlongยญing the accelยญerยญaยญtion phase has served me well.
Example: When workยญing with a PR cliยญent, I typยญicยญally spend 60% of the iniยญtial proยญject scope doing necesยญsary groundยญwork, askยญing uncomยญfortยญable quesยญtions, doing deep research, preยญparยญing, runยญning tests, comยญpilยญing materยญiยญals, etc.
Key Takeaways: What To Know
Please rememยญber: Your comยญpetยญitยญors are not necesยญsarยญily โahead.โ Lots of people are impaยญtient and peak too soon.
Here are the key takeaways from this mindset:
Know what done (100%) looks like. Always know the disยญtance for a parยญticยญuยญlar underยญtakยญing (i.e. the equiยญvalยญent of knowยญing where the finยญish line will be).
Know what accelยญerยญaยญtion (<60%) looks like. Hunker down and accelยญerยญate conยญtinuยญously. Never mind about your comยญpetยญiยญtion; focus on the hard work of gainยญing momentum.
Know what top speed (>60%) looks like. Get up straight and mainยญtain your hard-earned top speed. Be mindยญful of mainยญtainยญing good form, and donโt try to get back into accelยญerยญatยญing again.
Learn more: The Acceleration Theory
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ANNOTATIONS
1, 2, 4 | Prendergast, K. (2018, January 21). A mathยญemยญatยญicยญal modยญel of the 100m and what it means. Silo. https://silo.tips/download/aโmathematical-model-of-the-100m-and-what-it-means |
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3 | Silfwer, J. (2012, October 31). The Acceleration Theory: Use Momentum To Finish First. Doctor Spin | The PR Blog. https://โdocโtorโspinโ.net/โaโcโcโeโlโeโrโaโtโiโoโnโ-โtโhโeโoโry/ |