david and goliath: strength and power in sport

David and Goliath:David and Goliath:Strength and Power Strength and Power

in Sportin SportJohn D BarrowJohn D Barrow

Mass and WeightMass and Weight Mass = Force/Acceleration m= F/AMass = Force/Acceleration m= F/A Weight is a force W = MgWeight is a force W = Mg A= M/m A= M/m g g Expt: (M-m)/(M+m) < 10Expt: (M-m)/(M+m) < 10-12-12

Implies m = M exactly (Einstein)Implies m = M exactly (Einstein)

accelerate

M M’M

M’If m m’

gravity

Latitude and GravityLatitude and Gravity

Weight of mass M is least at Equator and most at PolesMgMgEquatorEquator < Mg < MgPolesPoles

100 Kg weighs 0.5% more at the Poles = 500 gm

Mr2 r

Throwing and JumpingThrowing and Jumping

Maximum Horizontal Range: VV22/2g/2g

Maximum vertical height: V V22/g /g

The Best Place to Be a The Best Place to Be a WeightlifterWeightlifter

High altitude High altitude greater distance from Earth’s centre greater distance from Earth’s centre lower g lower g

Some of worst venues areSome of worst venues areOslo or Helsinki, where 9.819 m/s² and Oslo or Helsinki, where 9.819 m/s² and

100 kg weighs 981.9 N 100 kg weighs 981.9 N

Mexico City is the best venue to combine height and latitude gainsMexico City is the best venue to combine height and latitude gainsg = 9.779 m/s² so 100kg weighs 977.9 Ng = 9.779 m/s² so 100kg weighs 977.9 N

A good place to lose weightA good place to lose weight

Mg = GMME/R2

LeverageLeverage

Class 1 Class 2 Class 3

press ups Barbell curlsrowing

Wrestling holds: Wrestling holds: class 2 > class 3 > class 1class 2 > class 3 > class 1

Cael Sanderson2004 Olympic

champion

4.5-5m

2m 2.45mHJ

6.14mPV

KarateKarate

Need 3100 N3100 N to split 20x30x1cm pine block3200 N for same area brick 4cm thick

Black belt strikes at V = 7m/s Arm mass is about m = 3.4 kg Momentum of arm is mV = 7 × 3.4 = 24 kg m/s

contact time with the target is less than T = 5 millisec Force m x V/T = 24 ÷ 0.005 = 4800 N4800 N[A 70kg person weighs 70 × 9.8 = 686 N]

Easy !Easy !

The Giant SwingThe Giant Swing

Bangkok 1784-1935 Wat Suthat Temple, 30m high !

1910

Ceremonies stopped in 1932 due to fatal accidentsCeremonies stopped in 1932 due to fatal accidents

To thank the god Shiva for the annual rice harvest

How big a force do you feel?How big a force do you feel?

2.5m

Angular velocity at top = w

Angular velocityat bottom = W

Centre of gravity

Rotation energy at bottom = Rotation energy at top + Potential Energy lost

½ IW½ IW22 = ½ Iw = ½ Iw22 + 2Mgh + 2Mgh

Max force on gymnast is at the bottom

Maximum force felt by the gymnast = Mg + MhWMaximum force felt by the gymnast = Mg + MhW22 = Mg + 4M = Mg + 4M22ghgh22/I/I

I = Mk2 Mh2

Total force felt by the gymnast = Mg(1 + 4hTotal force felt by the gymnast = Mg(1 + 4h22/k/k2 2 +hw+hw22/g)/g)

With a typical angular velocity at the top of 2-3 per sand g = 9.8 m/s2 and a typical body size with h = 1.3m,

Total force felt by the gymnast Total force felt by the gymnast Mg(1 + 4 + 1.2) Mg(1 + 4 + 1.2) 6Mg 6Mg

Start from handstand only reduces it by 1g

Head spins in circle h approx 1.3m only

ww

WW

AngAngVelyVely ss-1-1

Naim Suleymanoglu (b.1967) lifts 3 times his body weightNaim Suleymanoglu (b.1967) lifts 3 times his body weight

Strength versus SizeStrength versus SizeStrength is proportional to area Strength is proportional to area R R22

Weight is proportional to volume Weight is proportional to volume R R33

Strength and WeightStrength and Weight

strength strength (weight) (weight)2/32/3

Giants eventually break!Giants eventually break!

World Weightlifting RecordsWorld Weightlifting Records(strength)(strength)33 (weight) (weight)22

Putting The Shot – Two Putting The Shot – Two SurprisesSurprises

World record 23.12 metres

Max range isn’t achieved withMax range isn’t achieved with45 degree launch angle45 degree launch angle

Launching from above Launching from above ground levelground level

h 2 m

The Second SurpriseThe Second Surprise

Top class shot putters use a launch angle Top class shot putters use a launch angle of about 37 deg – not 42-43 degof about 37 deg – not 42-43 deg

Because…Because…

They can’t achieve the same launch speedThey can’t achieve the same launch speed at all launch anglesat all launch angles

A Constrained OptimisationA Constrained Optimisation

Typically 34-38 degrees is bestTypically 34-38 degrees is bestBut is athlete dependentBut is athlete dependent

Launch speed falls as Launch speed falls as angle increasesangle increases

Rmax = h tan(2max)

21.3 metres (= 70 ft) optimal angle is 42 deg15.24 metres (=50 ft) ------------------- 41 deg10.7 metres (= 35 ft) -------------------- 39 deg

Rowing in NumbersRowing in NumbersHow does the speed of the boat depend on the number of rowers?How does the speed of the boat depend on the number of rowers?

Drag on boat Drag on boat V V22 wetted surface area of boat wetted surface area of boat V V22 L L2 2

Volume of boat Volume of boat L L33 N – the number of crew N – the number of crew

Drag Drag V V22 N N2/32/3

Crew Power overcoming drag = N P = V Drag V3 N2/3 P is the constant power exerted by each (identical rower)

V V N N1/91/9

With a cox With a cox V V N N1/31/3/[N + 1/3 ]/[N + 1/3 ]2/9 2/9 if cox is third the weight of a rower if cox is third the weight of a rower

Results of 1980 Olympic Results of 1980 Olympic coxless races (N = 1, 2, 4) + coxed N = 8coxless races (N = 1, 2, 4) + coxed N = 8

Distance is 2000 metresDistance is 2000 metres

NN Time, TTime, T

(sec)(sec)

11 429.6429.6

22 408.0408.0

44 368.2368.2

88 349.1349.1

T = (2000) / V T = (2000) / V N N-0.11-0.11

V V N N0.11 0.11 N N1/91/9

Compare with a coxCompare with a cox N = 2, T = 422.5 s N = 2, T = 422.5 s N = 4 ,T = 374.5 s N = 4 ,T = 374.5 s (predicted if cox = 1/3 of a rower mass)(predicted if cox = 1/3 of a rower mass)

Better without one!Better without one!

Weight ClassesWeight Classes

Why do we have them in Why do we have them in boxing, wrestling, judo and weightlifting?boxing, wrestling, judo and weightlifting?

But not inBut not inShot put, hammer, rowing, …..?

Why not height classes in high jump and basketball?Why not height classes in high jump and basketball?