Transcript David and Goliath: Strength and Power in Sport

David and Goliath:
Strength and Power in Sport
John D Barrow
Mass and Weight
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Mass = Force/Acceleration m= F/A
Weight is a force W = Mg
A= M/m  g
Expt: (M-m)/(M+m) < 10-12
Implies m = M exactly (Einstein)
accelerate
gravity
M
M’
M
M’
If m  m’
Latitude and Gravity
Mr2
r
Weight of mass M is least at Equator and most at Poles
MgEquator < MgPoles
100 Kg weighs 0.5% more at the Poles = 500 gm
Throwing and Jumping
Maximum Horizontal Range: V2/2g
Maximum vertical height: V2/g
The Best Place to Be a Weightlifter
High altitude  greater distance from Earth’s centre  lower g
Mg = GMME/R2
Mexico City is the best venue to combine height and latitude gains
g = 9.779 m/s² so 100kg weighs 977.9 N
A good place to lose weight
Some of worst venues are
Oslo or Helsinki, where 9.819 m/s² and
100 kg weighs 981.9 N
Leverage
rowing
Class 1
press ups
Class 2
Barbell curls
Class 3
Wrestling holds:
class 2 > class 3 > class 1
Cael Sanderson
2004 Olympic
champion
6.14m
PV
4.5-5m
2m
2.45m
HJ
Karate
Need 3100 N to split 20x30x1cm pine block
3200 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 N
[A 70kg person weighs 70 × 9.8 = 686 N]
Easy !
The Giant Swing
Bangkok 1784-1935 Wat Suthat Temple, 30m high !
1910
To thank the god Shiva for the annual rice harvest
Ceremonies stopped in 1932 due to fatal accidents
How big a force do you feel?
Angular velocity
at top = w
Centre of gravity
2.5m
Angular velocity
at bottom = W
Rotation energy at bottom = Rotation energy at top
+ Potential Energy lost
½ IW2 = ½ Iw2 + 2Mgh
w
Ang
Vely
s-1
Max force on gymnast is at the bottom
Maximum force felt by the gymnast = Mg + MhW2 = Mg + 4M2gh2/I
I = Mk2  Mh2
Total force felt by the gymnast = Mg(1 + 4h2/k2 +hw2/g)
With a typical angular velocity at the top of 2-3 per s
and g = 9.8 m/s2 and a typical body size with h = 1.3m,
Total force felt by the gymnast  Mg(1 + 4 + 1.2)  6Mg
Start from handstand only reduces it by 1g
Head spins in circle h approx 1.3m only
W
Naim Suleymanoglu (b.1967) lifts 3 times his body weight
Strength versus Size
Strength is proportional to area  R2
Weight is proportional to volume  R3
Strength and Weight
strength  (weight)2/3
Giants eventually break!
World Weightlifting Records
(strength)3  (weight)2
Putting The Shot – Two Surprises
World record 23.12 metres
Max range isn’t achieved with
45 degree launch angle
Launching from above ground level
h2m
The Second Surprise
Top class shot putters use a launch angle
of about 37 deg – not 42-43 deg
Because…
They can’t achieve the same launch speed
at all launch angles
A Constrained Optimisation
Launch speed falls as
angle increases
Typically 34-38 degrees is best
But is athlete dependent
21.3 metres (= 70 ft) optimal angle is 42 deg
15.24 metres (=50 ft) ------------------- 41 deg
10.7 metres (= 35 ft) -------------------- 39 deg
Rmax = h tan(2max)
Rowing in Numbers
How does the speed of the boat depend on the number of rowers?
Drag on boat  V2  wetted surface area of boat  V2  L2
Volume of boat  L3  N – the number of crew
Drag  V2 N2/3
Crew Power overcoming drag = N  P = V  Drag  V3 N2/3
P is the constant power exerted by each (identical rower)
V  N1/9
With a cox V  N1/3/[N + 1/3 ]2/9 if cox is third the weight of a rower
Results of 1980 Olympic
coxless races (N = 1, 2, 4) + coxed N = 8
Distance is 2000 metres
N
Time, T
(sec)
1
2
4
8
429.6
408.0
368.2
349.1
Compare with a cox
N = 2, T = 422.5 s
N = 4 ,T = 374.5 s
(predicted if cox = 1/3 of a rower mass)
T = (2000) / V  N-0.11
V  N0.11  N1/9
Better without one!
Weight Classes
Why do we have them in
boxing, wrestling, judo and weightlifting?
But not in
Shot put, hammer, rowing, …..?
Why not height classes in high jump and basketball?