Calculating the Optimal Pace for Uneven Splits

  • Context: Graduate 
  • Thread starter Thread starter eldrick
  • Start date Start date
  • Tags Tags
    Running
Click For Summary

Discussion Overview

The discussion revolves around calculating the optimal pace for running a 10km race with uneven splits, specifically analyzing the performance of Keninisa Bekele, who achieved notable splits of 14:00 and 13:00 for each 5km segment. Participants explore theoretical methods to determine what these splits imply for a race run at a perfectly even pace, incorporating aspects of physics, physiology, and energy expenditure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to theoretically determine the even pace equivalent of Bekele's uneven splits, expressing difficulty in using kinetic energy approaches.
  • Another participant emphasizes the importance of physiology, suggesting that the ability to run faster in the second half is contingent on the slower pace in the first half.
  • A different perspective proposes analyzing the problem using a point mass model to derive a hypothetical even pace.
  • One participant notes that understanding energy consumption related to speed could help calculate an average speed that matches the energy used in Bekele's race.
  • Another participant reiterates the focus on a physics/mathematics perspective rather than a physiological one.
  • Discussion includes a claim about the relationship between air drag and energy expenditure, with calculations suggesting that running at uneven splits requires more energy than even splits.
  • One participant mentions the strategic use of reserves in uneven pacing, highlighting a potential advantage in race strategy.
  • A later reply indicates an attempt to refine methods for calculating energy equivalence across different distances, acknowledging some mathematical limitations in their approach.

Areas of Agreement / Disagreement

Participants generally agree that both physiological and physical factors play a role in understanding running performance, but multiple competing views remain on how to approach the calculations and the implications of uneven pacing. The discussion does not reach a consensus on a definitive method or conclusion.

Contextual Notes

Some limitations include unresolved assumptions about energy consumption models, the dependence on definitions of speed and energy, and the mathematical validity of proposed methods. The discussion remains exploratory without definitive resolutions.

eldrick
Messages
52
Reaction score
0
I hope someone can help me out with a question I've been trying to answer for quite some time with no success

A few years ago, Keninisa Bekele, the double Olympic Champ at 5 & 10km, won a World Championship 10km with incredible splits of 14:00 & 13:00 for each 5k for a final clocking of 27:00. The World Record at the time was 26:20 for 10km. Many observers felt this performance was superior to the World Record ( obviously run at even pace )

The question is :

Does anyone have a good method of working out theoretically what consecutive splits of 14:00 & 13:00 would imply for a race run at perfectly even pace from start to finish ?

I have tried various approaches using Kinetic Energies, but not really got anywhere.

Any help would be gratefully appreciated
 
Physics news on Phys.org
Not sure what you can really say in terms of physics, tt's more a question of physiology. Yes the second half was run at a pace which would have given a 26:00 record time - but he/she was presumably only able to run the second half at a 13:00 because they took the first half slowly, if they had run the first half at 13:00 they might only have been able to manage 15:00 for the second half.
 
I agree physiology is a huge factor

However, consider the same problem by replacing the human with a point mass. Is there a way of working out the overall hypothetical even pace
 
If you knew how energy consumption (ie power output) varied with speed for a human then you could work out what 'average' speed would use the same amount of energy.
 
I am trying to get a physics/mathematics perspective rather than a physiology one
 
mgb_phys said:
Not sure what you can really say in terms of physics, tt's more a question of physiology.

Exactly. The only "physics answer" (which is really a mathematics answer) is he can run a 10K in 27:00 or faster, and a 5K in 13:00 or faster.
 
If air drag for a runner were similar to automobiles, the power expended goes as speed cubed. (Stokes drag power goes as speed squared). A runner has a much higher drag coefficient than an automobile, but a smaller cross section. So Berkele ran a 10k at an average speed of 0.370k per minute. Let's use this as a reference power level

So running at two splits of 13.5 minutes the relative energy expended (REE) would be

REE = 13.5m x (.370/.370)3 + 13.5m x (.370/.370)3 = 27.00

and running splits of 14m (at .357 kpm) and 13m (at .385 kpm) would be

REE = 14m x (.357/.370)3 + 13m x (.385/.370)3 = 27.22

So more energy is expended if Berkele had run two splits at different speeds. This would imply that Berkele expended about 27.22/27 = 0.81% more energy (not power) than if he had run 2 even splits.
 
One of the reasons for uneven pace running is that the runner can use up "reserves" towards the end of a race, since there's no need for any "reserves" once the race is completed.
 
Bob S said:
If air drag for a runner...

I'd like to post some updates :

1) I think I have an answer for original question based on a very similar method to Bob's, from :

http://www.atm.ox.ac.uk/rowing/physics/basics.html#section5

I tried to move on from there here (as ventolin^2 ) :

http://www.letsrun.com/forum/flat_read.php?thread=3415815&page=6

I would very much appreciate a critique of the various methods


2) I have tried to move on further to actually see if it's possible to use relative "energy equivalence" to find what a time over 1 distance implies for another :

http://www.letsrun.com/forum/flat_read.php?thread=3461310

The problem is, I've used sleight-of-hand with using exponent 3/4 for inverse of s^4/t^3 ( applicable to (s/t)^(4/3) but not s^4/t^3 )

Empirically, it's giving very good answers (?) but like I said, not strictly legit

It's a very important question & can be considered the Holy Grail of Athletics as there are numerous calculators based on physiology or statistical analysis of annual performance lists, all of which are very poor

Any help with getting to a correct physics based solution will answer the biggest question in the main Olympic Sport - there's a challenge !

( post replies either here &/or that athletics forum thread ( no registration required, so you can "freewheel" it there ) )
 

Similar threads

MHB The World Chess Championship 2012 ....
  • · Replies 10 ·
Replies
10
Views
4K
I invented a card game based on the 'wheel'
  • · Replies 4 ·
Replies
4
Views
5K
MHB In memory of Svetozar Gligoric....
  • · Replies 4 ·
Replies
4
Views
2K
A very complicated puzzle: the planet of lies
  • · Replies 2 ·
Replies
2
Views
4K
Swedish programming olympics finals 2005
  • · Replies 13 ·
Replies
13
Views
3K
News Bush Administration: My Indictment
  • · Replies 3 ·
Replies
3
Views
4K
At a crossroads (drop out? chase a dream? time out?)
  • · Replies 13 ·
Replies
13
Views
5K
Mathematica This Week's Finds in Mathematical Physics (Week 266)
  • · Replies 1 ·
Replies
1
Views
4K