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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)
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
optimal skateboard ramp(The brachistochrone problem)
What is the best ramp shape for the minimum time down?
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
Mavericks video
shallow water waves
�
cs = gd
breaking waves
db
surfers
empirical relation
Hb - height of breaker
db - depth where wave
breaks�
db
=1.28Hb
“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
“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
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
“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
“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!
“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
“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.
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