Mathematical model of the influence of the time of start reaction in 100 m sprint run
Keywords:Model fit, start reaction time, speed-endurance, 100 m sprint
AbstractAbstract The purpose of this study is to explain the influence of the time of start reaction tR to the results of sprinters in a 100 m run, using a new simple mathematical model based on the measured values for s, t and tR . The research is based on IAAF data obtained by measuring the segment length, the time of start reaction, transient times in 100 m run and final times for the top sprinters C. Lewis (1988), M. Green (2011) and U. Bolt (2009) (men) and F. Griffith - Joyner (1988), E. Ashford (1988) and H. Drechsler (1988) (women). The values of the start reaction tR for both male and female top sprinters indicate that there appear no substantial differences in the values of tR based on gender which would directly favour male or female sprinters in achieving the top results in the 100m run. The influence of the time of start reaction tR decays exponentially with the time t during the run (t > tR ) and ends up at about 30 m, influencing the initial velocity v0 although it is not directly related to the final result of the run. Due to its applicative simplicity, the presented mathematical model and related conclusions can represent a solid basis for the future studies concerning the sprint running.
Andreacci, J.L. et al. (2002) The effects of frequency of encouragement on performance
during maximal exercise testing. J Sports Sci 20:345–352.
Coppenolle, H. & Delecluse, C. (1989) Technology and development of speed. Athletics
Čoh, M. Jošt, B. Skof, B. Tomažin, K. & Dolenec, A. (1998) Kinematic and kinetic
parameters of the sprint start and start acceleration model of top. Gymnica 28:33-42.
Dick, FW (1989) Development of maximum sprinting speed. Track Coach 109:3475-3480.
Doder, D. Babiak, J. Janjić, N. & Doder, R. (2012). Isometric force development of some
muscle groups in athletes. J. Str. Cond. Res 26:293-298.
Guissard, N. Duchateau, J. & Hainaut, K. (1992) EMG and mechanical changes during sprint
start at different front block obliquities. Medicine & Science in Sports & Exercise 24:1257-
Harland, M.J. & Steele, J.R. (1997) Biomehanics of the Sprint Start. Sports Med 23:11-20.
IAAF-International Association of Athletics Federations. (2019) Available at 2019,
Janjić, N. Kapor, D. Doder, D. Doder, R. & Savić, B. (2014) Model for the determination of
instantaneous values of the velocity, instantaneous and average acceleration for 100 m
sprinters. J. Str. Cond. Res 28:3432–3439.
Janjić, N. Kapor, D. Doder, D. Petrović, A. & Jarić, S. (2017) Model for assessment of the
velocity and force at the start of sprint race. J Sport Sci 35:302-309.
Janjić, N. Kapor, D. Doder, D, Petrovic, A. & Doder, R. (2017) Model for Determining the
Effect of the Wind Velocity on 100 m Sprinting Performance. J Hum Kinet 57:159‐167.
Janjić, N. Kapor, D. Doder, D. & Savić, I. (2019) Evaluation of the final time and velocity of
a 100 m run under the realistic conditions. J Hum Kinet 66:19-29.
Keller, J.B. (1973) Theory of competitive running. Phys. Today 26:43-47.
Martin, D. & Buonchristiani, J. (1995) Influence of reaction time on athletics performance.
New Studies in Athletics 10:67-69.
McClements, J. Sanders, L. & Gander, B.E. (1996) Kinetic and kinematic factors related to
sprint starting as mesaured by Saskatchewan Sprint Start Team. New Studies in Athletics
Mero, A. Luhtanen, P. & Komi, P. (1983) A biomehanical study of the sprint start. Scand J
Med Sci Sports 5:20-28.
Mero, A. & Komi, P. (1990) Reaction time and electro myographic activity during a sprint
Start. Eur J App Physiol 61:73-80.
Moravec, P. et al (1988) Time analysis of the 100 metres events at the II World
Championships in Athletics. New Studies in Athletics 3:61-96, 1988.
Pain, MTG. & Hibbs, A (2007) Sprint starts and the minimum auditory reakcion time. J Sport
Pavlović, R. Bonacin, D. & Bonacin, D.A. (2014) Differences in time of start reaction in the
disciplines in the finals of the Olympic games (Athens, 2004-London, 2012). Acta
Pavlovic, R. (2015) Differences in time of start reaction and achieved result in the sprint
disciplines in the finals of the Olympic games in London and the world championship in
Moscow. Sport Scientific & Practical Aspects 12:25-36.
Schot, P.K. & Knutzen, K.M. (1992) A Biomechanical Analysis of Four Sprint Start
Positions, Res Q Exercise Sport 63:137–147.
Smajlović, N. & Kozić, V. (2006) Effects of changes in athletic policies at a time starting
reaction in sprint events. HomoSporticus 9:21-27, 2006.
Susanka, P. Miskos, G. Millerova, V. Dostal, E. & Barac, F. (1998) Time analysis of the
sprint hurdle events at the II World Championships in Athletics NSA. IAAF, 11:63-69.
Tellez, T. and Doolittle, D. (1984) Sprinting from Start to Finish. Track Technique 88:2802–