Some Thoughts On Weight: By Scott Bridgman (The MUniac)

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If your riding style includes maneuvers that require rapid
acceleration and/or moves against gravity, choosing lighter
equipment will help you accomplish them. Subtle reductions in MUni
weight will help ease stress on the pulling arm joints from the
fingers to the shoulder. To explore how force, mass and acceleration
relate to a MUni maneuvers we'll need some basic physics. Although
experience suggests that relations exist between the forces supplied
to sports equipment, the properties of that equipment and the change
in motion of that equipment, it required the work of many eminent
men (sorry ladies) and a period of several centuries before definite
and complete fundamental relations between these three factors were
finally established. Sir Isaac Newton (1642-1727) was the first to
develop three such relationships which we know as Newton's
Fundamental Laws of Motion. I doubt Newton did any mountain
unicycling but his second law of motion will help us to understand
the relationship between force, mass and acceleration during a ride.
In his second law, Newton discovered simply that when an outside
force acts on a mass, that mass is accelerated (a change in speed).
He also discovered that the magnitude of the acceleration is in
direct proportion to the applied force and inversely proportional to
mass of the body. For physics buffs and the scientifically minded,
Newton's second law may be written as F=ma. In layman's language
this means that heavier masses require greater amounts of force to
accelerate them. Stated another way, heavier masses tend to resist
being accelerated. To mathematically evaluate Newton's second law
would require delving into constants and measurement units that are
beyond the scope of this article so we won't do it here. Instead,
let's explore the concepts of force, mass and acceleration without
the number crunching.
Mass is the universal property of a body (object) independent of the
pull of gravity. An object has the same mass regardless of its
location in the universe. This is not true of weight, since in the
absence of gravity objects have no weight. When an object comes
under the influence of gravity it is pulled with a force equal to
its weight. Precisely stated, an object's weight "W" is equal to its
mass "m" times the acceleration of gravity "g". Since MUni would be
impossible in zero gravity let's figure in earth's gravitational
pull. As previously mentioned, objects (masses) under the influence
of earth's gravity take on weight. For the purists amongst us, it's
true that gravity varies slightly over the earth's surface causing
an object's weight to vary slightly depending on its location on
earth. For example, a MUni will weigh a little less on the summit of
Mt. Everest than on the beach. These variations are so slight they
may be neglected for our analysis. It's also true that a MUni
travelling at the speed of light won't behave according to Newton's
laws. We'll neglect this situation too. Coming down from Mt. Everest
and travelling at sublight speeds, a person holding a static (not
moving) ten pound MUni will be pulling on that MUni with a force of
tens pounds in a direction opposite to that of gravity. The
important word is static which means without velocity or
acceleration. The instant that person changes their pull (magnitude
or direction), the MUni will move. Simply stated, lightening the
pull will cause the MUni to move towards earth's center and a
heavier pull will cause the MUni to move away from earth's center.
Now that we know weight and the force required to hold it still,
let's explore velocity and acceleration.
Velocity (speed as it were) is the displacement (distance
travelled) of an object from some starting point over time. Greater
amounts of velocity mean an object is covering more distance per
unit of time (going faster). Acceleration refers to how fast an
object's velocity (speed) is changing. It's the acceleration of an
object that involves the force Newton included in his second law.
Stated more precisely, to accelerate an object (ie. change its
speed) an unbalanced force must be supplied. The faster those speed
changes need to occur, the more unbalanced force that is required.
That's why our 10 pound MUni didn't move when it's holder balanced
out gravity's pull with 10 pounds of holding force. Once the 10
pound pull is unbalanced to 9 pounds or 11 pounds then that MUni
will begin to move. The unbalanced force creates an acceleration
which implies a speed change from stationary to moving. Here's a
simple example of Newton's second law. A person weighing 100 pounds
stands on a bathroom scale in an elevator on the first floor. When
the elevator car begins to accelerate towards higher floors the
scale reading will increase according to Newton's law. The scale
reading may peak at 110 or 115 while the elevator car accelerates
to its final speed. Once the elevator car finishes accelerating to
its design speed the scale will come back to 100 pounds. If the
elevator motor was capable of accelerating the car more rapidly say
to two "g"s, the scale would read 200 pounds. The passenger would
feel these forces mostly in the legs. These effects exist in many
places and are common in our everyday lives. An automobile under a
rapid acceleration will push its passengers back in their seats. As
the automobile reaches its cruising speed the acceleration falls to
zero and those pressing forces disappear. Newton's relationship
between weight, force and acceleration, as illustrated above, also
apply to MUni.
The motions involved in MUni are indeed complex ones. Given the very
nature of the sport, one can imagine that many motions and forces
occur simultaneously as riders happen upon the usual collection of
obstacles found on a trail ride. In order to stay balanced, riders
need to constantly apply corrective forces through the MUni in
response to terrain changes. Since the ride is carried out in 3
dimensions, corrective forces may occur with all orientations to
gravity. For example, a MUni rider free mounting and riding away on
smooth level terrain would do so under slow acceleration
perpendicular to gravity. In contrast, a MUni rider hopping or
jumping up on a 16" log would do so with rapid acceleration against
gravity. From the point of view of a rider, horizontal trajectories
will be somewhat less influenced by gravity, vertical trajectories
will be somewhat more influenced by gravity and all accelerated
motions (except subatomic particles and masses travelling at the
speed of light) are subject to Newton's second law gravity or not.
MUni designs that increase weight will require greater forces to
accelerate them. Heavy rims, tires and tubes at greater radii add
rotational inertia in addition to weight. Rotational inertia, unlike
linear accelerated weight, varies as the square of the radius which
means when the radius is doubled the inertia increases by four
times. Excepting the special case of rotating weight the force
required to accelerate an object of a given weight varies directly
with the magnitude of the acceleration. This means a MUni weighing
12 Lbs will require 20% more force to accelerate it for a given
maneuver than a MUni weighing 10 Lbs. If that accelerated motion is
directly against gravity the entire weight of the MUni must be
overcome first then add to that the pull required to generate the
desired acceleration to satisfy the planned maneuver. For a rider
free mounting and riding away slowly it's doubtful the 2 Lbs would
matter much (slow acceleration perpendicular to gravity). When that
same rider needs to hop up on a 16" object the 2 Lbs will be felt
more (rapid acceleration against gravity). The exact increase could
be calculated if the weight and acceleration were known. Perhaps
someone with the equipment to measure these parameters would
undertake this investigation and make the results available. Even in
the presence of exact figures, the actual feeling or sensation of
that increase will always be a judgement call. From personal
experience, when I dropped 5 Lbs out of my MUni the difference on
vertical style was amazing and puzzling at the same time. The 5 Lbs
was only a very small fraction of the 200 Lbs rider/MUni
combination. After thinking about it I offer the following
explanation for the 5 Lbs making so much difference.
From a muscle and joint perspective the forces required to lift an
object with your arm are much greater than the object's weight. The
function of the human arm is based on the principles embodied in
levels (bones). With a fulcrum (joint) and force (muscle) the level
(bone) can be moved and hence do work. Since the range of swing of
your arm is far greater than the distance its muscle contracts, the
fulcrum (joint) and point of attachment of the muscle (force) have
evolved so as to gear up or amplify the muscle contraction within a
small cross section. All of this occurs at the expense of increased
force and joint pressure. In absolute terms the 10 Lb weight you
pick up with your arm creates far more force than that in the
contracting muscle and joint given the leverage effect of the bone,
muscle and joint system. The exact ratio of increase would require a
detailed study of the arm. Perhaps someone has done this. I'd guess
it to be a factor of at least 10. Add to that a quick snap and lots
of repetitions during practice and it all adds up to significant
stress and strain. Individuals that have or are currently
experiencing joint pain from MUni hops/jumps know this first hand.
The 1 or 2 Lbs shaved off the MUni (in my case 5 Lbs) may translate
into 10 or 20 Lbs off the arm's joints and muscles and that's
significant in my opinion. The 5 Lb reduction above is then a 50 Lbs
reduction inside your arm. From this point of view lighter reduces
wear and tear on the body which is better. It also explains, in my
opinion, why the MUni weighing 5 Lbs less seems so much lighter and
hence was easier to lift quickly.
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Conclusions:

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The issue of MUni weight is not black or white and no quicky rules
exist for determining exactly what the ideal weight should be.
Rider preference and feel also come into play making weights a
matter of personal preference. Some riders may prefer a heavier
MUni given its inertia. My suggestion is to experiment by riding
different MUni designs and styles to see first hand the pros and
cons of specific weights in specific maneuvers. If that's not
practical try to talk with someone you trust that has been on both
extremes and ask for an honest opinion. For riders with a more
horizontal or down style, overall weight is less of a factor and
you probably won't see big advantages in lighter MUnis. For riders
with a more vertical or up style, weight becomes more important and
will be noticed in quick moves against gravity. I would imagine
that more physically fit and skilled riders can overcome the
addition of some weight and still perform well. All things being
equal though the rider with the lightest MUni will jump higher on
it than that same rider on a heavier setup. If you are hopping and
jumping up a lot and are concerned about chronic joint injury, I
would try to ride the lightest MUni you can get your hands on.
That's it for now and as usual, remember to ride like hell and walk
out what you doubt. Happy trails!
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“The Muniac” (Scott Bridgman)

e-mail: scott@muniac.com web visit: http://www.muniac.com

Mountain UNIcycling ACtion