The Effects of Wind and Altitude in the 400m Sprint with Various IAAF Track Geometries

Vanessa Alday and Michael Frantz

Presented by: Crystal Bennett, Adrienne Godette, Shywanda Surgeon, Constance Williams

Objective• Investigate the effects that wind and altitude have on the 400m

sprint when run on various IAAF track geometries.• To validate Quinn’s ordinary differential equations model

using data from the 1999 World Athletics Championships. • Maple is used to solve the model’s equations numerically. • Find performance differences between running lanes,

indicating possible disadvantages of running in certain lanes.

BackgroundThe International Associate of Athletics Federations track

(IAAF)

This track has eight lanes to accommodate a maximum of eight runners.

Each track is 400 meters in length with each lane having different radii:

Although track design is standard, wind and altitude vary

Models have been developed for the 100m, 200m and 4x100m relay races as far back as the late 1920’s. These were relatively simple review.

A model for the 400m was not developed until 2004 and presents unique problems.• Consideration for the runner covering the entire track

during the race.• The path for each runner will vary because of the

range of radii of the track lanes.• Research suggests wind blowing across a closed loop

track has a detrimental effect on a runner’s time.

Early ModelsOne of the earliest recorded models for energy balance of a runner was

provided by Archibald V. Hill and is based on Newton’s Law.

Later a model is presented by J.B. Keller that expands Hill’s:

Details of the equation:

is the runner’s velocity at time

is the runner’s total propulsive force per unit mass

is the damping coefficient

A more modern model known as Quinn’s model that extends Keller’s

is shown:

Details of the equation:

is the propulsive force per unit mass that declines as the athlete’s muscles tire.

where is air density, is the coefficient of drag, and is the frontal area of the athlete.

is the velocity of the wind.

The IAAF Track and its Effect On Runners The IAAF track which is known as the standard running track is

400 meters long with two straights 84.4 meters, and two bends 115.6 meters long. So 57.8% of the 400m race is run around bends.

Runners have the same run along the straights but not along the bends since they vary in radii. So runners will experience a different wind velocity which will effect the velocity the velocity the runner can maintain around the bend.

It is obvious that the velocity around the bend is less than that run along the straights. The runner has to adjust the distribution of their weight to compensate for their run around the bend.

This model further reveals that the runners total velocity in relation to the radius of the bend is where satisfies the cubic equation . where R is the bend radius and g is the gravitational force. is the runner’s peak velocity.

The cubic equations is satisfied by

Where ..

Computation of the Effects of Wind

The geometry of the IAAF standard track and wind direction

Relative wind velocity around the IAAF standard track

Further considerations for the runners is how they are placed on the track. It well understood that the runners are staggered around the track based on their lane. Each runner runs a different length around the bend at different intervals of the race.

The wind velocity which is the wind velocity relative to the ground and tangent to the path of the runner. This value will vary in each four segments of the track and depends on wind velocity and relative wind direction.

The component of the wind blowing in the direction of the runner for a runner traveling in a straight line with a wind velocity of blowing at an angle of is The angle is shown in the figure following.

• 1. J. Alvarez-Ramirez, An improved Peronnet-Thibault mathematical model of human running performance, European Journal of Applied Physiology 86 (2002) 617-525.

• 2. H. Behncke, Small effects in running, Journal of Applied Biomechanics 10 (1994) 270-290. • 3. A. Ferro, A. Rivera, and I. Pagola et al., Biomechanical research project at the 77th World • Championships in Athletics Seville 1999, New Studies in Athletics 16 (2001) 25-60. • 4. P. R. Greene, Running on flat turns: experiments, theory, and applications, Journal of • Biomechanical Engineering: Transactions of the American Society of Mechanical • Engineers 107 (1985) 96-103. • 5. J. B. Keller, A theory of competitive running, Physics Today 26 (1973) 42-47. • 6. W. D. McArdle, F. I. Katch, and V. L. Katch, V.L., Exercise Physiology: Energy, Nutrition and Human

Performance, 6th ed., Lippincott, Williams, and Wilkins, Philadelphia, PA, 2007. • 7. M. D. Quinn, The effects of wind and altitude in the 200-m sprint, Journal of Applied • Biomechanics 19 (2003) 49-59. 17 • 8. M. D. Quinn, The effects of wind and altitude in the 400-m sprint, Journal of Sports • Science 22 (2004) 1073-1081. • 9. M. R. Spencer and P. B. Gastin, Energy system contribution during 200 to 1500 m • running in highly trained athletes, Medicine and Science in Sports and Exercise 33 (2001) • 157-162. • 10. R. A. Walpert and C. R. Kyle, Aerodynamics of the human body in sports, Journal of Biomechanics 22 (1989)

1096. • 11. A. J. Ward-Smith and P.F. Radford, A mathematical analysis of the 4 x 100m relay, • Journal of Sports Sciences 20 (2002) 369-381.

References

• Quinn's 2004 model considered winds of constant speed and direction throughout the stadium. The architecture of the stadium is included in the wind off the stadium onto the track.• Measuring modeling and including factors such

as runners performance, physical conditions, clothing, and nervous tension. Which are all almost impossible.• Strategy influences such as whether to beat the

other runners, the fastest time, or their personal time. This is also non-quantifiable.

Future Work

• The biggest disadvantage to the runner in windless conditions are in lane 1, since the tighter bends the runner spends more time on the ground rather then in the air.

• Lane 8 is the fastest lane having shorter distance around the bend the runner stays in the air longer.

• Wind directions parallel to the straights provide the worst conditions.

• It is to the runner advantage to have the wind on its back first earlier and run into the headwind later.

• Wind conditions have such an advantage on a runner that it could change a winner and loser on different days.

• Lane selection, wind speed, wind direction, location , altitude, and even track geometry play an important role on a 400 meter sprint.

Results

Effect of a 2 m/s wind on lanes 1, 4, and 8, with time corrections from windless (Panathenian track)

Time correction factors for a 2 m/s wind on the Panathenian track

Data

Comparison of lane 4 (windless) times; IAAF standard vs. Panathenian track

The two tracks• The ancient Greeks used an panathenaic stadium during their

Olympic games.

• The track geometry is different with the 180 meter straights and the 20 meter curves.

• The panathenaian track permits longer runs at peek speed, but the curves slow the runner down tremendously.

Altitude and Propulsive Force

• Considered the propulsive force,- Propulsive force- propelling force that causes something to move

forward or onward.

• Factor that affects the propulsive force:- Aerobic energy system ( the muscle energy that requires oxygen)

- contributes significantly to the amount of energy supply during a long sprints.

- total contribution for 400m sprint was found to be 43%- Concludes that aerobic energy system is affect by the altitude.

• The faster rates in higher altitudes causes a decline in the propulsive force.• βdepends on the altitude H and the aerobic energy system• Rewrote • - the parameter value at the sea level.

Results of Quinn model• Using previous data from a 400m sprint, where• (maximum force) = 7.91m/s²• ( decay rate) = .006 1/s• (resistive force) = 1.45s for men

• Compared a model written using Maple

Our model times closely approximate Quinn's results, the major difference being 0.04 seconds at 150m. The finishing time is the same for all three models.

Effects of Wind Direction

Runners performance is affected by different wind directions angles .

Effect of a 2 m/s wind on lanes 1, 4, and 8, with time corrections from windless

Effects of Altitude and Air Density • Altitude effects the aerobic

energy system

• Runners favor high altitude because of less air density

• Modify expression , replace , is distance above sea level in meters.

• is air density.

• is the drag coefficient.

• is the frontal area of athlete

• is the mass

• So

• T is air temperature (Celsius)

• Gas Constant R,

Time corrections for lanes 1, 4, and 8 for different altitudes in windless conditions

• In model • T = 25°C• Altitude H, varies.

• Image contains time corrections for lanes 1, 4, and 8 on standard track at various altitudes under windless conditions.

• Time corrections are almost identical across lanes at each altitude.

• Expected, The only effect on race times due to lane geometry comes from physical mechanics of negotiation of tighter bends, which should not be affected by altitude.

• Largest time correction was 0.32 sec.• Big deal for world records.• Why it has been accepted races at altitudes higher than 1000

meters, these performances are marked by an “A” (IAAF)

The Equal Quadrant Track

• IAAF standard track is the norm for track dimensions• IAAF accepts other tracks. Like equal quadrant track • 400m track, 100m bends,100m straightaways, measured along

lane 1. • Our model has only been applied to the IAAF standard track,

but we will now examine how the wind affects a runner's performance on an equal quadrant track.

Equal Quadrant Track .

• The equal quadrant track differs from the standard track only in its dimensions.

• So all the equations will remain the same, except for the wind velocity.

• Changes to the wind velocity functions can be easily determined, and the simulation run with virtually the same code.

• Using the standard track data from Ward-Smith and Radford (2002), but now for an equal quadrant track, we have the lane radii in the following figure.

Turning radii for the lanes on an equal quadrant track .

Analyzing as before, we obtain in Table 7 new expressions on different portions of the track for the relative wind velocity 𝑣𝜔.

Wind Effects on the Equal Quadrant Track Comparison of times for equal quadrant and

standard tracks (windless)

• Final time in the equal quadrant track is 0.06 seconds slower than the IAAF standard track simulation.

• Due to smaller radii on the bends. Causes runners to spend more time on the ground than in the air

• Increases their time.• An equal quadrant track has longer straights than the standard

track,• Gives runners on an equal quadrant track an advantage to be

able to run faster on the straights. • Does not outweigh the disadvantage that they have on the

bends.

Effect of a 2 m/s wind on lanes 1, 4, and 8, with time corrections from windless

Previous data smoothed. Time correction factors for a 2 m/s wind on an equal

quadrant track .

• Results similar to those for standard track.

• Optimal wind direction for lane 4 is still in the 210°-240° range, for lane 8 at 240°.

• Lane 1 remains disadvantaged at all wind angles.

• Best race times are achieved at angles of either around 120° or 240°.