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Understanding the Influence of Technology on Athletic Performance
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T
hrough better nutrition and
training, the athletes of today are
becoming faster and stronger. Old
records are constantly being broken, and
new ones set. While the vast majority of
these achievements are likely due to the
athelete themselves, improvements in
sports technology have also played a notable
role (1). New sports gear technologies have
especially been relevant to the sports of
rowing, cycling, swimming and tennis,
giving rise not only to new records, but also
ways in which the sport is played.
!"#$%&'
At top speed, nintey percent of an
elite cyclist’s energy is used to counter airresistance (2). By comparison, 3 to 7 percent
of a runner’s energy is spent overcoming
air-resistance (3). Cycling behind a
competitor or teammate, or drafting, can
reduce drag on a cyclist by up to 38 percent
(3). However, since most cycling teams
already practice this technique, cyclists
today are searching for new ways to reduce
air-resistance and differentiate themselves
!"##$%&'%
from their competitors.
A rough formula used to calculate the
drag of a cyclist is 0.5qCA, q being the
air density, C being the drag coefficient,
and A being the projected cross-sectional
area of the front of the bike and rider. The
cross-sectional area is the variable cycling
teams can best modify and reduce, and
has the been focus of recent technological
improvements. Using wind tunnels and
computer models, engineers have found
that something as simple as attaching a
water bottle on the lower part of the bicycle
frame rather than the upper part, can have
a major impact on reducing drag (2).
Engineers have also improved
handlebars, primarily by smoothing over
the edges. In 1992, the standard racing
handlebars of the time contributed to
10% of the drag created by the bicycle (2).
Over the years, engineers have been able
to dramatically reduce the drag created
by the handlebars. For example, aerobars
(handlebars that are low and forward that a
cyclist rests his elbows on) have been shown
to reduce the time taken to race across 15
kilometers in a time trial by 60 seconds
(2). The handlebars of a bicycle are the
first part of the bicycle to cut through the
air, so minimizing turbulence is essential
(2). Although smoothing over the edges
barely reduces the projected cross-sectional
area, it does prevent recirculating currents
and eddies from forming in front of the
cyclist’s body. This helps the cyclist better
cut through the air (2).
The wheels of a bicycle also have a
large effect on the airflow around a bike (2).
Racing bicycles have thinner tires to reduce
the cross-sectional area of the front of the
bicycle. More significant improvements
have come from changing the spokes in
wheels (13, 14). When a wheel spins at
high speed, the spokes rapidly cut through
the air, and the drag incurred slows down
the wheel (2). Additionally, a large number
of spokes cutting through the air disturbs
the air current flowing around the bike,
creating eddies which reduce the overall
aerodynamics of the bicycle (2).
A simple solution to this problem is to
remove the spokes entirely, and make the
wheel a solid disk (2). While this increases
the weight of the wheel, new lightweight
materials mean that the positive impact
of removing spokes far outweighs the
detriment on performance due to additional
weight (2). Solid disk wheels are used on
all bicycles during indoor racing events.
However, such wheel are not used outdoors
(2). In the presence of a cross wind, solid
wheels act like sails, throwing the rider off
course. As a result, 3-spoked wheels that
allow air to pass through them are favored
for outdoor races (2). These provide
reduction in drag, while still preventing
cross-winds from being a problem.
Bicycles are approaching the limit of
how thin they can be. Over the last decade
engineers have shifted their focus from
reducing the projected cross-sectional area
to ensuring that air flows smoothly around
the cyclist (2). The most advanced helmets
aim to smoothen out the area between
the cyclist’s head and upper back. These
helmets protrude from behind the cyclist’s
head covering the cyclist’s neck, and thus
eliminating the dip between head and
upper back. This ensures that air turbulence
!"
is minimized and eddies and recirculating eliminating wiggle (provided each rower
tract
N even numbers
and N odd
get zero, of
which
currents are not formed behind the is
cyclist’s
is applying
thenumbers
same toamount
force).
(a)
possible only if N is even because only then will the comhead (5).
Interestingly,
two
of
the
configurations
bination of the N odd numbers be even like the combination
of the N evenfound
numbersby
and only
then can John
the sumBarrow
of both be were
Professor
zero. The simplest case of all: That of a pair !N = 1" also
experimented
with
in
the
1950s
(11). While
!"#$%&
always has a nonzero moment equal to 1 − 2 = −1. Hence, we
(b)
configurations
“a”
and
“d”
were
completely
can now confine our attention to crews of 4, 8, 12, etc.
Elite rowers face a similar dilemma
We can streamline
the formulation“b”
further
noting that
new, configuration
wasbyalready
known
the with
requirement !6" for a zero moment is equivalent to the
as cyclists. They have to contend
as
a
“bucket”
rig
and
was
used
in
Germany
(c)
drag from water, which creates 12requirement
times that the sum of all the numbers from 1 to 2N be
Configuration
was
equal to twiceinthethe
sum1950s.
of all those
entering with +“c”
signs
!or used
the resistance of air (6). Manufacturers
of
minus all those
minusOlympic
signs",
byentering
the with
Italian
team, which
2N
top-end racing hulls, or shells, claim that
subsequently won gold at the Melbourne
r + 2!# negative entries"
the difference between shells can be #the
(d)
Olympic Games in 1956 (11). However, one
r=1
difference between first and second place 2N
of the reasons that these rigs are unlikely
(7).
=0=#
− 2!used
entries
!7"
Fig. 5. The four possible rigs for Eights, which have zero transverse mo" , only manage
# positive
to r be
is that
they
to
ment: !a" The rig uudddduu; !b" the German rig ududdudu; !c" the Italian rig
Shell manufacturers are constantly r=1
eliminate wiggle if each rower is applying
Figure
(%))*+,-# '%.*/0# 1%/2*0&'34*%/)#
and !d"2:#
the $%&'#
rig udduduud.
looking for the perfect combination
of second sum is only over the N entries with nega- udduuddu;
where the
.5*15#536-#7-'%#4'3/)6-')-#8%8-/49
an
equal
amount
of
power
on
each
stroke—
tive !or
high rigidity, balance, low surface area,
andpositive" signs, respectively. This requirement means
scenario (11).
for a crew ofan
2Nunlikely
rowers that
swimmers to wear swimsuits that go from
smoothness. Unfortunately, not all of these
ududdudu:2 + 4 + 5 + 7 = 18,
N!2N + 1" + 2!# negative entries"
waist to knee, they are a clear example!11b"
of
attributes can be achieved simultaneously.
'#$(($%&
a
technology
that
is
revolutionizing
a
sport
For example, the surface of the shell that
= 0 = N!2N + 1" − 2!# positive entries" .
!8"
udduuddu:2 + 3 + 6 + 7 = 18,
!11c"
comes into contact with the water, Thus,
known
Another sport that struggles with (14).
we need to find the cases where the sum of the N
!11d"
as the wetted area, causes 80 percentnegative
of the!or positive"
water resistance
entries add upistoswimming. After the udduduud:2 + 3 + 5 + 8 = 18.
drag (8). However, reducing the wetted
2008
Beijing
Olympics,
official
competition
These)*%%$+
!together with their four mirrors" give the four posN!2N + 1"
.
sible zero-moment rigs for an Eight shown in Fig. 5.
area leads to a trade-off in stability, and a2 rules
were changed to reduce the!9"effect
Reducing
drag
Two of these
are known.
The is
rig not
in Eq.the
!11c"only
is the way
Italian
smoother material may be less rigidFor(8).
tech
on race
times.
N =A
2 we high
need the
sumswimsuits
of the N = 2had
negative
entries
to be This
or “triple
tandem”
rig thatfrom
was used
by the Italian
Eights in
sports
benefit
scientific
advances.
rigid hull is important, because the equal
moretoa!5, change
came
in response
to the astounding
which was
the case
for the zero-moment
Four
the 1950s as an extension of Carcano’s insight about the
racquets
have undergone
twotogether
majorin
configuration42
in Eq.
!4".
Four Tennis
by adding
two zero-moment
!uddu" Fours
hull bends and torques, the less efficiently
swimming
world records that were
The problem is now recognizable as a special case of the
series.transformations
Equation !11b" represents
thethe
“German,”
“bucket,”
or
over
past
twenty
5
power is transferred from the rowersubset
to the
broken
thea subset
Beijing
Thirtyin in
which
Sk ofOlympics.
a set of positive
sum problem
“Ratzeburg”
rig,
first usedheads
by crews
traininglarger,
at that famous
years.
Racquet
became
and
integers S is selected
the requirement
that the
sum broken
of the by
German Rowing Club in the late 1950s under Karl Adam,8
water (9).
eight ofbythese
new records
were
strings
have
becomeconfiguration.
better at The
helping
members
of
the
subset
be
equal
to
an
integer
k.
The
version
who
was
motivated
by Carcano’s
German
Much of the technology that has
gone swimmers wearing the Speedo LZR (12).
of this problem that we are faced with here is the same sum
and Italian
crews
were successful
with
these
two zeroplayers
generate
spin
on
the
ball
(15).
A
into reducing the friction between
the5 in which The
Speedo
LZR
is made
nylonwe wish
to find all
the subsets
Sk of of
S that
problem
moment Eights and the zero-moment Four at the 1958 Eurolarge
racquet
head
gives
a
player
more
the same
sum, k = N!2N
+ 1" / 2. Shallit pointed
out a
pean Championships and the German crews coached by
shell and the water flowing past ithave
comes
elastane.
Nylon-elastane
is extremely
enlarges
thesuccessful
“sweet spot”
the10
Adamreach,
went onand
to be
supremely
over theon
next
connection between the finite integer sequences generated in
from racing yachts, which often get
their
light
and
helps
compress
the
swimmer’s
years.racquet (16). Contact at a racquet’s sweet
the problem considered in this paper and the structure of the
6
technology from the aerospace industry
into a more hydrodynamic shape The other two zero-moment rigs, Eqs. !11a" and !11d",
Thue–Morse body
sequence.
located
the center
appearspot,
to be which
new and is
have
not beenatdiscussed.
Note of
thatits
Eq.
(10). An example of this is the riblet. Riblets (12). Although compression is not new to
!11d" head,
is a combination
of athe
zero-moment
Italian
Four with a
results
in
greatest
conservation
III. EIGHTS,
AND AFTER
are v-shaped grooves that run along
the racing
suits, the LZR suit has three times
mirrored
zero-moment
Four. The
other new
rig, Eq.
of energy
of theItalian
ball upon
impact,
meaning
!11a", is special because it has a quadruple tandem configuside of the shell parallel to the direction
of
the
compression
power
at halfEight
thehas
weight
As with the Four, the traditional rig
for a rowing
ball moves
more quickly
(16).
rationthat
with the
a same-side
Four positioned
inside two
same-side
a significant
nonzero
moment
!M =
4" and
a counterprowater flow (10). Developed by NASA,
they of
the suit
used
in"the
previous
Olympic
pairs.
Racquet head enlargement has only
ductive
transverse
wiggle
for
the
cox
to
counter.
The
wiggle
are “no deeper than a scratch,” but can cut Games (12). The compression is so strong The zero-moment Eights have a simple construction from
of the standard rig is smaller for the Eight than the Four
occurred
because
a larger
racquet
the three
possiblerecently
Fours. All
zero-moment
Eights
can be
drag by up to 8 percent (10).
it takes inertia
20 minutes
tothe
squeeze
one’s 7body
because the increased
outweighs
extra moment.
head
requires
greater
string
tension.
made
by
adding
Fours
with
moments
−4
+
4
,
−2
+
2,
0More
+ 0, and
This
nonzerointo
moment
a nonzero
sum in not
No matter how rigid the racing
shells
the corresponds
suit (12). toThis
compression
0 − 0, tension
where the minus
sign indicates
u ↔ d. These
four comis needed
to keep
the strings
which the sum of the negative entries is !20 rather than the
are, sweep shells still experience oscillating
only smoothes out the swimmer’s body, but
binations correspond to the solutions Eqs. !11a"–!11d", revalue of !18 required for a nonzero moment because
taught across a longer distance, which in
spectively.
non-zero transverse movement, or wiggle it also helps support the swimmer’s hips,
udududud:1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 = − 4.
!10"
If we
increase
the number
of rowers,
combinatorical
turn
requires
that frames
be the
stronger
(17).
(11). In sweeping, each rower has only one which hang lower and increase drag as complexity
a
grows quickly. There are 29 distinct zeroBigger,
stronger
frames,
formerly
meant
For N = 4 the same sum problem for a zero-moment rig is the
oar. Although rowers are traditionally
swimmer
tires
(12). of the four negative moment rigs for 12-person crews, 263 zero-moment for 16caselined
where the
sum of the
magnitudes
thicker
racquets. Heavy
racquets
personheavier,
crews, and
2724 zero-moment
for 20-person
crews.
up so that they row on alternate sides,
this
Instead
sewn
which
disrupt
entries
in the alternating
sum of
must
equalseams,
!18. There
are four
For example,
all the
12-rower
crewsfrom
correspond
to all the
with thick
frames
suffer
an increase
distinct
solutions
to
this
problem,
does not achieve the symmetry in power water flow and increase drag, the swimsuit
solutions of the same sum problem, Eq. !10", for which six
air resistance
thetoswing
and are
uudddduu:3
+ 4 + 5together
+ 6 = 18, using ultrasonic !11a"
of thein
numbers
in $1 , 2 , 3 , .during
. . , 12% sum
39. Equations
!12"
application that is required to remove wiggle
is held
welding,
detrimental to players who are looking to
(11). In 2009, Cambridge University730asked Am.which
according
to
Speedo
reduces
drag
by
J. Phys., Vol. 78, No. 7, July 2010
John D. Barrow
730
make fast serves and swings.
a member of its mathematics department, 6 percent (12). The suit is also composed of
The shift in frame material first
John Barrow, to solve the problem of wiggle polyurethane panels that are placed at high
!"#$%"&'(')*+),-.)/+0/).")0/1203+2/0/20442)5('67.869:.6"$)7:9;(-.).")<<=>)%6-($7()"8)-"[email protected])7(()B..?DEE&;?2&&?.2"8AE&:.B"87E-"[email protected]?(8G6776"$
from steel to aluminum, and then from
in an eight-man sweeping boat. The issue friction points on the suit. This further
aluminum to graphite and foam, resulted in
occurs because despite alternating rowers, reduces drag by a stunning 24 percent (12).
frames that are stronger and stiffer without
the forces on the shell are unbalanced. This
Tests have shown that swimmers
being thicker (17). However, despite being
is because the four rowers on one side are wearing the LZR consume 5 percent less
strong enough to withstand increased
on average closer to the bow than the four oxygen to achieve the same performance—a
string tension, graphite racquets were
rowers on the other side (11).
clear indication of the reduction in effort
heavy. The relatively recent incorporation
Figure 2 shows four possible rowing required by the swimmer (13). Although
of titanium in modern racquet frames,
configurations where the transverse waves the suits were banned in 2009 under the
truly allowed frames to become larger,
created by the rowers cancel each other out, new restrictions that only allow male
lighter, and thinner (17).
Image courtesy of John D. Barrow
!"
!"#$%&'$()'*!+#,#"!'"$+)-&'#*".)&/)012+*1+
Image courtesy of Guzmán Lozano. Retrieved from http://www.flickr.com/photos/15650492@N08/4623704120 (accessed 25 October 2012)
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Although racquets have become
lighter and bigger, the biggest improvement
in tennis racquets has come from improved
strings (17). A player who can generate
high amounts of spin is able to hit shots
that drop down onto the court (much like
a curveball in baseball). Hitting a shot that
curves down allows players to hit harder
shots without the fear that the ball will
land outside the court. Studies have shown
that adding 100 rotations per minute to
the rate at which the ball spins reduces
flight distance by 6 to 12 inches (17). Copolyester strings have been shown to create
20% more topspin than nylon strings
(17). Counterintuitively, they create more
topspin despite reducing friction between
racquet and the ball. Co-polyester strings
slide with, rather than grip the ball along
the racquet face (17). The strings then snap
back and add spin to the ball after the ball
has changed direction (17). The use of copolyester has had an astounding effect. In
the words of Andre Agassi, “the advent of
a new elastic co-polyester string, which
creates vicious topspin, has turned average
players into greats, and greats into legends”
(15).
Technology has helped athletes
hit better shots and race faster. Still,
competition has not fundamentally
!"##$%&'%
changed: it remains the man, not the tool,
that must win.
#/.4!#4ž359!3(ž"5,#(!.!$)ž!4ž359!3(
"5,#(!.$!.) $!24-/54(%$5
References
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Aerodynamics & Drafting.” Available at http://www.
exploratorium.edu/cycling/aerodynamics1.html (15
October 2012).
2. R. A. Lukes, S. B. Chin, S. J. Haake, “The
Understanding and Development of Cycling
Aerodynamics,” Sports Engineering, 8(2), 59-74
(2005).
3. W. D. McArdle, F. I. Katch, V. L. Katch, Essentials of
Exercise Physiology (Lippincott Williams & Wilkins,
Philadelphia, PA, Vol. 1, 2000), pp. 282.
4. Hyperphysics, “Air Friction.” Available at http://
hyperphysics.phy-astr.gsu.edu/hbase/airfri.html (15
October 2012).
5. R. Cahill, “Resistance in Swimming” (21 June
2011). Available at http://www.livestrong.com/
article/475663-resistance-in-swimming (15 October
2012).
6. Vespoli USA, “Vespoli: History” (2008). Available
at http://www.vespoli.com/history (15 October 2012).
7. Vespoli USA, “Boat Science: How Do Hulls from
Different Makers Compare?” (2008). Available
at http://www.vespoli.com/innovation/67boatsciencehulls (15 October 2012).
8. Pocock Racing Shells, “Rowing Shell Glossary:
Performance & Boat Feel” (05 March 2012). Available
at http://www.pocock.com/rowing-boat-information/
rowing-shell-glossary3 (15 October 2012).
9. “NASA riblets for Stars & Stripes.” Available at
http://www.nasa.gov/centers/langley/news/factsheets/
Riblets.html (15 October 2012).
10. MIT Technology Review, “Mathematician Solves
Rowing Boat ‘Wiggle’ Problem” (20 November 2009).
Available at http://www.technologyreview.com/
view/416386/mathematician-solves-rowing-boatwiggle-problem (15 October 2012).
11. ThomasNet, “Polyurethane and Sports:
An Unrivaled Advantage.” Available at http://
www.thomasnet.com/articles/plastics-rubber/
polyurethane-sport-technology (15 October 2012).
12. M. Luebbers, “Speedo Fastskin LZR Racer - The
Fastest Swim Suit in the World for 2008!” (2008).
Available at http://swimming.about.com/od/
swimsuits/qt/speedo_lzr_race.html (15 October
2012).
13. BBC Sport, “Hi-tech suits banned from January”
(31 July 2009). Available at http://news.bbc.co.uk/
sport2/hi/other_sports/swimming/8161867.stm (15
October 2012).
14. A. Agassi, Open: An Autobiography (Knopf, New
York, NY, 2009), pp. 178
15. C. Bowers, “Spin Doctor’s Cure For Tension.”
(29 December 1996). Available at http://www.
independent.co.uk/sport/spin-doctors-cure-fortension-1316396.html (15 October 2012).
16. B. Strauss, “Building a Better Racket: Into the
Laboratory for the Secrets of Spin” (26 August 2012).
Available at http://www.nytimes.com/2012/08/27/
sports/tennis/latest-advances-to-tennis-racket-putnew-spin-on-the-game.html?_r=1 (15 October 2012).
17. A. Agassi, Open: An Autobiography (Knopf, New
York, NY, 2009), pp. 179
!"