physics of surfing energy - satellite geodesy at the ...topex.ucsd.edu/ps/energy.pdf · physics of...
TRANSCRIPT
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Physics of Surfing
Energetics of a SurferDavid T. Sandwell
(http://topex.ucsd.edu)
• Four styles of surfing
• Waves– Big swell coming? (storms)
– What makes “sets”? (dispersion)
– Why is Blacks Beach good for surfing?(refraction)
• Riding waves– “catching” the wave (speed)
– “dropping-in” (energy conservation)
– “tube riding” (tapping wave energy)
– “need more speed” (surfboard drag)
1 2 kg 1 kg
Which ball is going faster when it reaches the bottom?
(a) (b)
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Which ball is going faster when it reaches the bottom?
(a) (b) (c)
conservation of energy(assume no friction)
kinetic energy + potential energy = constant
�
mgH =1
2mv
2m
m
v
H
mv
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optimal skateboard ramp(The brachistochrone problem)
What is the best ramp shape for the minimum time down?
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60 ft
35 mph
24 ft
22 mph15 ft
18 mph4.5 ft
10 mph
ocean depth and breaker height - empirical
Hb - height of breaker
db - depth where wave
breaks
�
db
=1.28Hb
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Mavericks video
shallow water waves
�
cs = gd
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breaking waves
db
surfers
empirical relation
Hb - height of breaker
db - depth where wave
breaks�
db
=1.28Hb
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“catching the wave”
db
surfers
paddle speed
Hb - height of breaker
db - depth where wave
breaks�
cb = 1.28gHb
paddle speed <= wave speed
60 ft
35 mph
24 ft
22 mph15 ft
18 mph4.5 ft
10 mph
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“dropping in”
Hb
top of wave
bottom of wave
KEbottom = KEtop + PE
�
1
2mvd
2=1
2mcb
2+ mgHb
vd2
= cb2
+ 2gHb = 3.28gHb
g - acc. Gravity
cb - wave speed
vd - surfer speed after drop
“dropping in”
59.827.217.023tow-in
35.216.010.08tube
27.912.77.95fun
15.26.94.3 1.5longboard
vd
(mph)
vd
(m/s)
cb
(m/s)
Hb
(m)
style
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correction for surfer height
H' Hb
H' = Hb - 1/2 Hs
effective height = breaker height - 1/2 surfer height
- overhead waves are good
- waist high waves are bad
- short surfers and heavy boards have an advantage in small waves
Pipeline video
dropping in
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“dropping in”
Hb
top of wave
bottom of wave
KEbottom = KEtop + PE
�
1
2mvd
2=1
2mcb
2+ mgHb
vd2
= cb2
+ 2gHb = 3.28gHb
g - acc. Gravity
cb - wave speed
vd - surfer speed after drop
“dropping in”
59.827.217.023tow-in
35.216.010.08tube
27.912.77.95fun
15.26.94.3 1.5longboard
vd
(mph)
vd
(m/s)
cb
(m/s)
Hb
(m)
style
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“cutting across”
back of wave
front of wave
vd !
cb
�
cb
2
vd
2=1.28
3.28= cos
2!
! =~ 50˚
top
view
This angle is independent of
wave height or wave speed!
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“riding the wave”
Suppose the surfer remains on the steepest part of the wave having
a slope s. What is the rate of potential energy increase supplied to
the surfer?
cb s
�
P ˙ E = sgcbside view
�
v(t)2
= vd2
+ sgcbo
t
! dt
v(t)2
= 3.28gHb + tsg 1.28gHb
How does speed increase
with time?
speed video
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“the drag”
�
v(t)2 = 3.28gHb + 1.13g
3 / 2 s Hb
1/ 2 t ! drag
total
velocity= paddle
drop in+ -slope of
“the curl”breaker
height
duration
of ride
energy
dissipation
Future Research
– Are the best surf spots in areas of narrow continental margin?
– Are “sets” real? What are the statistical properties of sets? Do “sets”become amplified when they reach shallow water?
– How does the shape of the bottom translate into the “perfect wave”?
– What is the terminal velocity for a given breaker height? (Can we establishthe magnitude of the drag term?)
– Need to instrument surfers with intertial sensors.