Some Thoughts On Weight

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

  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.

Conclusions:

  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!

“The Muniac” (Scott Bridgman)

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

Mountain UNIcycling ACtion

Nice article Scott. Your estimate of a factor of 10 sounds about right to
me. If you are only concerned with how high you can jump up, then you get
a nice light unicycle and it feels great. But then you have to jump
down, and larger and larger drops require stronger and stronger
materials which is directly opposed to ‘light is right’. There is also
the constant pounding the equipment takes on a harsh trail ride (such
as Mr Toads).

My unicycle is finally strong enough, but weighs 16 pounds. If my frame,
seatpost clamp and bearing blocks were weightless, the complete cycle
would still weigh 13.7 pounds. I haven’t broken it down and weighed each
component, but the wheel, cranks, pedals and bearings are 10.6 pounds
together. This is up from 9.9 pounds before I switched to the Profile
splined setup. So I understand the problem, but we need a STRONG and light
solution. Between myself and my friends around here, we have broken
everything, including a frame. And there is no way I will give up using a
3" tire either. I haven’t tried it yet (Chris…help please!) but I think
that Chris Reeder’s ergonomic handle design will make the weight seem not
so bad, although the cycle will probably then weigh in at 16.5 pounds.
Kris Holm has been using a much lighter 24x3 tire for trials which saves
over a pound - I think it’s called the Fireball(?), but this wouldn’t do
for me. I need the Gazz.

The goal of a 10 pound unicycle, strong enough for me and my riding with a
3" Gazz seems unachievable without switching to titanium
frame/hub/cranks/pedals/seat hardware. (For that I would pay thousands!)

—Nathan

“Scott Bridgman” <scott@muniac.com> wrote in message
news:4.2.2.20010620082935.00aa36f0@pop.mindspring.com
> Some Thoughts On Weight: By Scott Bridgman (The MUniac)
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