**Diving terminology:**

**- the approach**-
An approach is the diver's walk down the board where thery press the board
on the last step. The "press" is an exaggerated step which, along

with the walk, create an oscillation and rhythm in the board. An approach typically has four steps.

**Types of dives:**

**- forward **-
forward takeoff with forward rotation

**Position of dives:**

**- straight**-
This position is when a diver's body is as fully extended and rigid as
possible. Because it has the greatest possible radius, the fewest
somersaults are

possible.

**- pike**
- This position is when the body is bent only at the hips, with legs straight
and arms and head by their ankles. This position has a smaller radius
than the

straight position, making somersaulting easier.

**- tuck**
- This position is then the body is bent at the hips and the knees, creating
the smallest radius possible. This position has the largest possible
angular

acceleration and therefore the greatest number of somersaults are possible in the tuck position.

**- free**
- This position is a combination of the three above positions, used only
in twisting dives where multiple positions are required at different parts
of the dive.

While somersaulting, the dive may be tuck or pike; while twisting, the body must be straight.

**Judging:**
Diving competitions can have five to nine judges. Dives are rated
from 0 to 10, 10 being perfect and 0 being incorrect dive. A dive
may considered

incorrect or incomplete if you do the wrong dive (front 1.5 tuck instead
of back 1.5 tuck) or if the wrong part of the diver's body hits the water
first. In

a dive landing on the head, the hands must enter the water first.
In a dive landing on the feet, the feet must enter first. Dives are
scored with digital or

manual score cards in increments of 0.5.

Each dive has its own degree of difficulty based on the position, which
board height it is preformed from, and the number of rotations and twists.
For each dive, the highest and lowest scores of the judges are discarded.
The sum of the other scores are added and multiplied by the degree of difficulty,
which is larger for more difficult dives. Therefore, divers are rewarded
for learning more difficult dives, but not enough that the finesse of the
dive can be discounted.

In international competition, a Maxiflex diving board is used. Created and produced by Duraflex, the board has an aluminum I-beam center. It is 16 feet long, 19 5/8 inches wide and 1 5/8 inches thick. The website for more information on Duraflex is available at www.springboardsandmore.com.

**The Physics of Springboard and Platform Diving**

**Rotation and Inertia**

Before applying physics concepts to diving, a few basic terms must be understood.

**- moment of inertia
( I )** - It is the measure of the distribution of the
object's mass about the axis of rotation. I = mr

**- angular velocity
( w )**- It is the speed of rotation about the axis of
rotation. w = change in angle / change in time

**- angular momentum**
- It is the quantity of rotation a body has about a given axis as a result
of its speed of rotation and the distribution of mass about its

axis. Angular momentum = Iw

** - angular acceleration
( a )** - It is the change in angular velocity over time.
a = w / change in t.

**- torque ( T )**
- It is the tendency of a force to rotate an object about some axis.
T = Fd, where F is the force applied and d is the distance. Also,
T
= Ia.

** Question**: Does
a diver break the law of conservation of angular momentum?

**Answer:** Once
the diver leaves the diving board, his angular speed may increase or decrease.
This does not violate conservation of angular momentum because the moment
of inertia will vary also. The equation for angular momentum conservation
is I_{i}w_{i} = I_{f}w_{f} .
Becuase no torque is applied to the diver once he leaves the diving board,
momentum is conserved. When the angular speed increases due to changing
his body's radius, the moment of inertia subsequently decreases, thus keeping
the equation constant.

** Question**: In
many dives, divers begin twisting after their feet have left the board.
With no object to push off from, how is this possible if the net torque
equals 0?

**Answer:**By
changing the radius, the moment of inertia must change due to the equation
I = mr^{2}. Because we know that the net torque, moment of
inertia, and angular acceleration are related by T = Ia, it is seen that
the angular acceleration must change if no net torque exists. To
increase the speed of the somersaults, a diver curls up into a tight tuck
position, thus drastically reducing his radius. For T = 0, the angular
acceleration must increase. After completing the desired somersaults,
the diver extends his arms and legs, thus increasing his radius and decreasing
the angular acceleration. I increases as the square of the distance
of the mass. Therefore, a small increase in the distance can result
in a relatively large increase in I.

**Spring Constant and its Effect
on Springboard Diving**

** Question**:

Answer:If
the person weighs 150lbs, their crouch height (the amount they bend down
before attempting to jump) is approximately 0.4m; the time it takes for
their body to extend is approximately 0.25s (this is the speed at which
muscle can contract). They are then able to jump about 0.52m (1.7ft)
off the ground. If a 150lb (68kg) person is jumping off a springboard
with a spring constant (k) of 833N/m, then they are able to jump to a height
of 0.92m (3.0ft) off the board. So, using the springboard can almost
double the liftoff height of a diver!!! In addition, a springboard
is constructed with a fulcrum (as seen in picture below). Located
in approximately the middle of the board (closer to the stand then to the
tip of the board), the spring constant is fairly large (more resistance
to force), thereby decreasing the possible distance of board depression.
However, if you move the fulcrum closer to the stand, the distance the
board can be depressed will increase and the spring constant will decrease
(less resistance to force). Therefore, the height the diver can jump
from the board will also increase. In fact, if the distance the board can
be depressed by a 150lb person increases to 1.2m (by moving the fulcrum
closer to the stand) the height will increase from 0.92m to 1.2m.
This is almost a 1 foot increase. Also, a diver uses an approach
before they take off for a dive. In the hurdle, they initially jump
up then land on the tip of the board. This creates a higher force
acting on the board, which will in turn increase the height of the jump.

Calculation
for jumping on the ground:

Principle of Conservation of Energy: PE_{i}+KE_{i}=PE_{f}+KE_{f}
_{
}PE_{i }= 0 and KE_{f }= 0 so, KE_{i }=
PE_{f}
_{
}KE_{i }= 1/2 mv_{cm}^{2 } and PE_{f
}=
mgH

1/2 mv_{cm}^{2 }= mgH

H = v_{cm}^{2 }/2g

v_{cm }= velocity of the center of mass of the jumper = 2h/t
h=crouch height and t=extension time

v_{cm }= 2(0.40m)/0.25s = 3.2m/s

H = (3.2m/s)^{2}/(2)(9.8m/s^{2})

H = 0.52m (for a 150lb male)

Calculation
for jumping on a springboard:

Principle of Conservation of Energy: PE_{i}+KE_{i }= PE_{f}+KE_{f}
_{
}KE_{f }= 0 but PE_{i }= 1/2 kx^{2} because
there is stored elastic potential energy in the spring, whereas when you
jump off the

ground there is no initial gravitational potential energy because the earth
does not provide any

significant source of potential energy to the jumper.
_{
}So, PE_{i }+ KE_{i }= PE_{f}
_{
}1/2kx^{2 }+ 1/2mv_{cm}^{2
}= mgH
_{
}H = (1/2kx^{2}+1/2mv_{cm}^{2})/mg
_{
}F = kx k=spring constant and x=distance
springboard is depressed with a 150lb person on it
_{
}k = F/x
_{
}k = ((68kg)(9.8m/s^{2}))/0.8m
_{
}k = 833N/m

H = ((1/2(833N/m)(0.8m)^{2}) + (1/2(68kg)(3.2m/s)^{2}))/(68kg)(9.8m/s^{2})

H = 0.92m (for a 150lb male)

The depression of the diving board during a dive is pictured below.
As can be seen from the photo, the board can be depressed quite a

bit by the weight of the diver, especially when compared to the empty board
next to it. More photos and information about the duraflex

diving boards can be found on the Duraflex
International website.

**“Play-time Pool Antics”
~A closer look at projectile motion and velocity**

** Taking a less serious approach at the diving scene,
focusing more on the possibilities of playing around is what most kids
do. Kids like to create their own competitions among each other, seeing
who is the best. One of the things kids do at the pool is see who
can jump the farthest. Applying physics to this can enable one to see what
conditions actually affect this distance. This is a projectile motion problem,
making two equations necessary.**

**Because kids usually don’t have much room around a pool to gain lots
of speed, a velocity estimate of 3 m/s will suffice for the next part.
With this estimate and t, we can now plug into the 1st equation to find
Dx.**
** x = v _{xo}t**

**This is not very far! This approximation isn’t the most accurate,
however, because one usually jumps up and then out, which extends Dx. In
this case, an equation such as Dx = v _{xo}t = (v_{o}cosQ_{o})t
will be used to better approximate. We can, however, explore the
contributions that each parameter makes to this horizontal distance jumped.
For instance, if one were to jump from a height of 5 meters, this would
then affect time considerably, resulting in a 3m horizontal jump.
Similarly, increasing another part, such as velocity, gets different results.
Jumping from the pool’s ledge at 9m/s, as opposed to 3m/s, x will equal
a horizontal 2.2m. Try jumping at 9m/s from 5m, and the horizontal
distance shoots to 9m!**

** Another popular thing to do is see how high one
can climb before jumping. Kids get a rush out of jumping from high
structures. Lots of recreation pools have different platforms, or
a high dive platform, some similar to those found in Olympic dive competition
settings. So how much does height actually affect velocity?**
**To solve this, two equations are again necessary.**
** y = -1/2gt ^{2}
and v_{y} = v_{yo} – gt**

**Now plugging t into the 2nd equation**
** v _{y} = 0 – gt**

** For the not-so-brave kid, 15m is pretty high!
Scaling down to 10m, using the same equations and process to solve, the
velocity reduces from 17m/s to 14m/s. And if you were one of those
kids who couldn’t handle height at all, there was always that platform
just right above the water around 1m. Again, using the same solution process,
one finds the final velocity before entering the water to be 4.41m/s –
not too scary.**
**So it turns out that the higher you climb, the faster you’ll drop!
This method of approximation is also not quite accurate if given varying
conditions. Most pools have springboards, which would increase Dy.
Jumping up, increasing this Dy, contributes to a slightly larger v _{y}.**

** Divers must rotate pretty quickly to do intricate,
multiple flips and sommersaults before entering the water. This is another
enticing game for children. Just how many flips can one do before they
hit the water? For starters, one must consider not only how much
time one has (which we will discuss here), but also how long the average
flip takes. This is one reason belly flops and awkward landings happen
so much. One can only fit so many flips or tricks in safely before
landing.**
**So just how much time does one have before landing? To answer this
question, one needs only know how high he is, and one equation.**
** Dy = v _{yo}t
– 1/2gt^{2}**

**Just looking at these questions, it becomes clear that adjusting
only one thing in the equation can make all the difference in the result.
Physics works ~ playtime is governed by rules after all!**

**Other Useful Links to Learn More About Diving:**
**
**1 ** **USA Diver

2. Hobies

3. US Diving