Few would dispute that the bicycle is the most efficient
means of converting human power into vehicular motion. It satisfies numerous
functions while being extremely simple and light weight, in part, due to the
fact that most of its components do multiple roles. With a bicycle, a runner can double his speed
for the same level of effort.
The modern bicycle is a result of multiple contributors to
numerous to mention. Most bicycle historians list at least four significant
steps in bicycle evolution. Those being:
1.
The Draisienne seated scooter
2.
The velocipede or boneshaker
3.
The ordinary of high-wheel bicycle
4.
The safety bicycle
Since the ordinary is
just a velocipede with un-equal-sized wheels, the above vehicles introduce the three
technical innovations I have listed below.
1.
The seated scooter
2.
Leg pedal cranking
3.
Chain and sprocket gearing
It is hard to over emphasize all the factors that fell into
place when Karl von Drais invented what he christened the laufmachine (running machine). Von Drais had studied mathematics and mechanics in Heidelberg but worked as the master of forests for the Duke of Baden. It has been speculated that he was looking for a faster alternative to walking the forest paths when he invented his seated scooter, now known
universally as the Draisienne.
As one would expect it all begins with the wheel and
walking. If, in the early 1800’s, you didn’t have a horse, you walked from place
to place, or ran if you were in a hurry. To explain the popularity of the Draisienne,
it is useful to compare it to walking and running using four factors involved
in a moving human.
Stride length
Cadence
Efficiency
Postural support
Speed is the product of cadence and stride length. (Stride
length is analogous to gearing in machinery).
Now, runners go faster than walkers because their cadence is higher and
their stride length is longer. A walker’s stride length is just the maximum
spacing between the feet at the end of a step cycle, because, by definition, a
walker always has one foot on the ground. A runner, on the other hand can have
both feet off the ground simultaneously. As a result, during the period of time
that the runner is flying through the air, the effective stride length is increased over the
maximum foot spacing.
The great Cuban middle-distance runner Alberto Juantorena airborne.
With walkers, rearward leg motion is accompanied by the
entire body moving forward. With
runners, the period of the leg accelerating the body is shorter and when
airborne the motion of the leg is only moving the mass of the leg. So, on the
average, the runner’s leg motion is associated with significantly less mass
than is the walkers. For a given force, the acceleration can be greater when moving
a lesser mass, so a runner’s cadence is higher than a walker’s.
A wheel rolling on a horizontal surface provides vertical
support but allows horizontal motion with low resistance. Von Drais realized
that if you supported a rider on a wheeled vehicle whose seat height required
that the leg be almost completely extended to touch the ground, the
airborne phase of running could be extended into a gliding phase where the backward
leg stroke resulted in an enormous stride length. Even though the forward speed
of his running machine could not exceed the maximum speed the leg could be
moved rearward, the time that the vehicle stayed at that speed was longer and
therefore running speed could be maintained with less effort.
Von Drais may not have appreciated that, as a result of the
short-duration kick and long-duration glide associated with the running
machine, the aerobic efficiency of moving the vehicle was improved over walking
and running.
For a given level of aerobic power generation, the oxygen
consumption is lower if the power is produced in short-high-amplitude pulses
with longer rest intervals as compared with longer-lower-amplitude pulses with
shorter rest periods. As a graduate
student, I was able to demonstrate this effect using a pedal drive with an adjustable,
cyclically-variable-gear-ratio. I measuring instantaneous mechanical power,
average mechanical power and oxygen consumption. My speculation as to the cause
of this effect is that the longer rest periods between the power pulses are
more conducive to replacement of chemical stores in the muscles than during
activities with shorter rest periods.
And, since the rider was seated and could additionally support
his body with his arms, the running machine reduced the energy necessary for
postural support when compared to walking or running.
Now all the gains associated with the Drasienne could be
realized as long as the weight of the vehicle was not excessive. This was no
mean feat when wagons and carts were constructed mostly of iron and wood. The obvious
solution to minimizing weight was to limit the number of wheels the vehicle
had, but could one make a controllable vehicle using only two wheels? Despite
the biomechanical improvements associated with a kick-and-glide propulsion
approach, the real quantum leap von Drais made was creating a two-wheeled
vehicle that could be balanced.
The fascinating thing is that there were no precursors to
the Draisienne. Earlier bicycle historians postulated that things began with a
child’s stick horse. A wheel is added to the bottom of the stick, and then
another wheel is added inline with the first. This is then scaled up to adult
size and the antecedent of the Draisienne is created. Not only is there no solid
historical evidence for this scenario, but more importantly, the two wheel
version of the stick horse could not be balanced.
Here is a key point. The
ability to steer is necessary to balance an inline-two-wheeled vehicle.
Why are steering and balancing linked in the function of a dynamically-stable
two-wheeled inline vehicle?
Let me propose a simple model of the bicycle-rider system,
possibly a bit too simplistic for the academic dynamicists out there and it does
leave out things like the precessional effects of the wheels. But it did aid me
in understanding what was going on during ten years of experimenting with
rear-steering recumbent bicycles.
The two mechanisms that allow a bicycle-type device to
balance are castor and lean-steer. Consider the bicycle as a system with two
masses and three-degrees-freedom for motion. The front mass consists of the
wheel, fork and handlebars. The back mass consists of the rider and the rest of
the vehicle. The front mass is attached to the back mass by a pivoting
connection. From a disturbance standpoint, we will ignore one motion DOF, that
being the bicycle moving forward. The disturbance motions are the fork mass
pivoting with respect to the frame mass and the frame mass leaning from side to
side. The two disturbance motions are not independent and the nature of their
coupling is determined by the steering geometry of the vehicle.
Now for castor to occur, the contact point of the front
wheel with the ground must be located behind where the steering axis intersects
the ground, where behind is defined as opposite the direction of motion. For
any angular disturbance of the fork mass, castor results in a moment being
generated that tends to reduce the disturbance until the contact patch is
inline with and behind the steering axis.
Lean-steer occurs along castor as long as the steered wheel
is at the front of the bicycle. As you lean a bicycle to the side you will observe
that the fork mass rotates toward the direction lean. A disturbance that causes
the frame mass to lean results in the fork mass steering the vehicle in the
direction of the lean. The vehicle is now going in a circle and the radial
acceleration associated with the change in direction picks up the frame mass
and corrects for the lean disturbance.
So the amazing thing is that von Drais could not evolve his
design based on non-steered precursors but has to create it in one quantum-leap
of imagination.
Notice for the Draisienne restoration above the steering axis
appears to be located near the front of the triangle supporting the front wheel
and the axis is near vertical. The contact point “trails” the steering axis by
almost half a wheel diameter. Compared to a modern bicycle with several inches
of castor, the Draisienne has a many times that. However, the friction associated
with the largely wood on wood steering pivot is much greater than that associated
with a ball-bearing steering headset. The torque of the castor moment must
overcome this friction to return the fork mass to being aligned with the
direction of motion. So a significantly
greater amount of trail would make sense.
The weight of the Draisienne was about 44lb. With no
cushioning from pneumatic tires or frame compliance, let alone suspension, the
ride must have been bumpy on all but the smoothest of roads. Prior to inventing
the Draisienne, von Drais was a forester. The mountain biker in me would like to
imagine him gliding along smooth single-track trails, but there is no
documentation of this. Since horse’s hooves and rain make for very bumpy roads,
the opportunities for extended gliding might have been less than frequent.
There we numerous variations on the Draisienne, mostly involving
changes made in the materials of construction but probably with little weight
saving. Whether referred to as the Draisienne, the hobby horse or the dandy horse,
the outlines of the modern bicycle are unmistakable. It would take over 40
years for the next step in bicycle evolution to be invented.
Hephaestus