David and Goliath: Strength and Power in Sport

1
David and GoliathStrength and Power in Sport

• John D Barrow

2
Mass and Weight

• Mass Force/Acceleration m F/A
• Weight is a force W Mg
• A M/m ? g
• Expt (M-m)/(Mm) lt 10-12
• Implies m M exactly (Einstein)

accelerate
gravity
M
M
M
M
If m ? m
3
Latitude and Gravity
r
Mr?2
Weight of mass M is least at Equator and most at
Poles MgEquator lt MgPoles

100 Kg weighs 0.5 more at the Poles 500 gm
4
Throwing and Jumping
Maximum Horizontal Range V2/2g Maximum vertical
height V2/g
5
The Best Place to Be a Weightlifter
High altitude ? greater distance from Earths
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
6
Leverage
press ups
Barbell curls
rowing
Class 1
Class 2
Class 3
7
Wrestling holds class 2 gt class 3 gt class 1
Cael Sanderson 2004 Olympic champion
8
6.14m PV
4.5-5m
2m
2.45m HJ
9
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 !
10
The Giant Swing
Bangkok 1784-1935 Wat Suthat Temple, 30m high !
11
1910
To thank the god Shiva for the annual rice harvest
Ceremonies stopped in 1932 due to fatal accidents
12
How big a force do you feel?
13
Angular velocity at top w
Centre of gravity
2.5m
Angular velocity at bottom W
14
w
Rotation energy at bottom Rotation energy at
top
Potential Energy lost ½ IW2 ½ Iw2 2Mgh
Ang Vely s-1
W
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
15
Naim Suleymanoglu (b.1967) lifts 3 times his body
weight
16
Strength versus Size

• Strength is proportional to area ? R2

Weight is proportional to volume ? R3
17
Strength and Weight
strength ? (weight)2/3
Giants eventually break!
18
World Weightlifting Records (strength)3 ?
(weight)2
19
Putting The Shot Two Surprises
World record 23.12 metres
20
Max range isnt achieved with45 degree launch
angle
21
Launching from above ground level
h ? 2 m
22
The Second Surprise
Top class shot putters use a launch angle of
about 37 deg not 42-43 deg Because
They cant achieve the same launch speed at all
launch angles
23
A Constrained Optimisation
Typically 34-38 degrees is best But is athlete
dependent
Launch speed falls as angle increases
24
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)
25
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
26
Results of 1980 Olympic coxless races (N 1, 2,
4) coxed N 8 Distance is 2000 metres
N Time, T (sec)
1 429.6
2 408.0
4 368.2
8 349.1
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) Better without one!
T (2000) / V ? N-0.11 V ? N0.11 ? N1/9
27
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?