THE DIRECT APPLICATION OF POWER.
It is evident that one of the greatest, if not the very greatest, of
the requirements of a practical road wheel, or a man-motor carriage,
is that the power of the rider shall be transmitted to the said wheel
in the most direct manner possible; that is, by causing the strain
to come upon the muscles in such a way that these muscles shall be
placed in the best possible position to overcome such strain, and to
take advantage of such conditions as nature has already provided for,
in training our muscles to the work we have had to do under the old
_régime_, without the wheel.
The muscles of man are best adapted to a direct pull or push. If we
push upon a weight with the muscles at an angle to the direction in
which we want the weight to move, the effective power is limited in the
same way that the effect upon a weight is limited if we push at it in a
direction at an angle to that in which we wish to move it; that is to
say, not the total, but only a portion of the power will be effective
in moving the weight.
The above facts apply particularly to our subject when we desire to
transmit motion to a wheel by means of the weight or gravity of our
bodies. Gravity acting downward in a vertical line, if we are not
placed over the resistance, the resultant effect is in proportion to
the cosine of the angle at which we work, as follows:
Let _W_ = the weight of the man and _a_ be the centre of gravity and
also the location of the source of power of said weight, and let _c_
represent the point at which it is desired to apply the power to turn
the wheel.
[Illustration: Power angle.]
Now, it is known that the weight _W_, acting by gravity in the
direction _ab_, may be taken as proportional to the length of the line
_ab_, and the portion of the pressure _P_ in the direction _ac_, which
will be effective to turn the wheel, may be taken as proportional to
_P_ _ac_ _ac_
the length of the line _ac_; that is, ——— = ————, or _P_ = ———— _W_,
_W_ _ab_ _ab_
_ac_
where ———— is evidently always less than unity. Now, if the angle _bac_
_ab_
_ac_
is thirty degrees, and _W_ = 150 pounds, _W_ times ———— is 130 pounds.
_ab_
Or, by trigonometry, the weight _W_, acting in the direction _ab_, by
gravity as in working a cycle, will have a resultant in the direction
_ac_ representing the power acting to turn the wheel equal to _W_ cos
_bac_. If the angle _bac_ is thirty degrees and _W_ = 150 pounds, then
_W_ cos _bac_ = 130 pounds. Now, in order to still get one hundred and
fifty pounds of force on the wheel, a pull on the handle-bars would
have to be given sufficient to make up the lost twenty pounds, which
the rider would get without any pull on the bars if placed directly
over the work. This pull, while not fatiguing to the legs beyond the
necessary requirement of power, is an entire loss of work in the arms,
and must tell on the system. This is all an additional loss to that
which ensues from the fact that nature has fitted us to stand upright
and not to work in an angular position; our every-day experience in
walking gives us practice in a direct vertical strain on the muscles
of the body, and we should make it a point to apply our force as
nature intended, in so far as it is applicable to our wheel method.
These conditions apply more or less to any form of locomotion, and
particularly to the cycle.
From the foregoing remarks we are amply justified in drawing the
conclusion that the resultant force available in the application of
the physical power of man is in proportion to the cosine of the angle
at which he exercises this force. We are well aware that many apparent
variations will occur when so rigid a mathematical fact comes to be
applied to the exercise of man’s energy in driving a bicycle; but
all we care for is to lead the reader well up to the point by means
of reasoning, which we hope will give at least a partial hypothesis
for a conclusion well demonstrated by practical experience. We assert
that when we consider the application of the _gravity_ of the body to
work on either a bicycle, or to other work of similar requirements,
our mathematical demonstration is strictly true. It is justifiable,
therefore, from a purely theoretical stand-point, to say that the rider
of a bicycle wants to get directly over the work; let us see how our
experience demonstrates this conclusion.
Take first the differences between a modern ordinary bicycle and the
old velocipede, or “bone-shaker,” so called. The former is lighter
and better made; but the one great difference is that the rider is
more nearly over his work. It was this one advance which encouraged
the development of other minor differences which had been roughly
thought out before. In fact, the Patent Office shows that many of these
improvements were on record, but there would have been little use for
them if the rider had not worked himself up into a place where he could
do something. Just who raised him up from a midway position between
the two wheels, the saddle seventy-five degrees back of the vertical
through the drive-wheel axle, as in the old bone-shaker, to nearly the
top of the forward wheel, working at an angle of thirty degrees, as in
some ordinaries, we will not attempt to say; but when he got there he
has been willing, for a long time at least, to try to stay there, even
at the expense of frequently going _down_ on the other side, much to
his annoyance, particularly as the general construction of the thing
compelled him to go down the other end up, which end nature did not
intend for terrestrial impact. It may as well be stated just here,
however, that when our rider raised and moved his saddle forward he
would have gone clear up to the vertical had it not been that it was
absolutely impossible for him to stay there at all without hanging a
heavy counter-balance somewhere in the neighborhood of the rear wheel,
a scheme which, by the way, has been really recommended in modern cycle
history.
One excuse for dwelling upon the foregoing dissertation is that many
casual observers and some riders, strange as it may seem, assert that
in the development of the modern rear-driving Rover pattern, we have
been retrograding to the old velocipede, whereas, in fact, we have made
another step forward of a similar nature to that spoken of before in
raising the rider up above the point of application of power. In the
Rover machine we have landed the rider practically where, as before
said, he could not remain at all before; but in this new machine he has
gained the advantage of being able to stay there.
Thus our rider has been gradually getting up and over the work.
Various devices have been used in order to facilitate this operation,
but, unfortunately for our power-development theory, many of the
changes have been coupled with the safety feature so prominently that,
in efforts by makers to place the rider in the best possible position
for work, the safety feature is all that the casual observer has been
able to see; therefore it is that in several machines, such as that
called the “Extraordinary Challenge,” the sales have been made more on
the strength of safety than on their other great point of real merit,
the advantage in power. In such machines, the rider has often been
surprised to find that he had more power than he supposed, but having
bought his mount with a view to safety, and it being still found to
contain almost as great an element of risk as he before incurred,
considerable disfavor has been the result. Had the element of increased
power been thoroughly understood and appreciated, such machines would,
in spite of the great deterioration in appearance, have been regarded
more kindly.
No better illustration in other arts of the desire and tendency of the
operator to get over his work can be had than in that of the ordinary
foot-lathe. No maker of lathes would think of attaching a treadle in
such a manner that the workman could not perch himself directly over
it. In some experiments on foot-lathes, the writer found that he could
run at a given speed and resistance three times as long when over the
work as when standing some twelve inches back and he had to reach out
for it; in fact, it seems quite evident that our theoretical conclusion
is fully established in actual practice.
Granting then that the direct vertical application of power by the
rider is a desirable acquisition, let it be called a fundamental
requirement. It must not, however, be supposed, in this connection,
that the foregoing in any way justifies the swimming position, or
kicking back, which some experimenters have of late been prone to
adopt. We must approach but never get beyond the vertical limit.
Since this manuscript has been ready for the publisher, articles in
the _Bicycling News_ by “Warrior” and “Semi-Racer” have come under my
notice, from which I clip sections, appertaining to this subject, as
follows:
“If, as ‘Crawler’ says, it is a very great improvement to have the
saddle well over the pedals, how comes it that the contrary is now
so universally advised, and as much as four inches recommended
between the line of saddle-peak and the line of crank-axle? There
never was a greater mistake made than when the saddle was generally
placed in advance of the crank-axle. Apart altogether from its
effect on the steering or easy running of the machine, there
are two very strong reasons why the saddle should be kept well
back. In the first place, it is quite impossible to sit upon the
tuberosities designed by nature to carry the weight of the body
unless the legs are flexed at the hip-joints. The parts resting
upon the saddle are, otherwise, soft and delicate structures,
liable to injury from the violence of the saddle. Were it for no
other reason, this is enough to determine the position well to the
rear of the crank-axle. But another reason: it is not a fact that
one has greater power with the saddle, as suggested by ‘Crawler.’
One may certainly throw his _weight_ alternately upon either pedal
readier, because he is nearer a standing position; but, on the
other hand, with the saddle well back and the handles well forward,
the purchase so obtained gives far greater power from muscular
contraction than the mere weight of the body gives, and, indeed,
many more muscles are called into action when the saddle is kept
back.—+Warrior.+”
“With regard to gearing, I consider that the position of the rider
has much to do with this also. A rider sitting well back can use
his ankles much more effectively than one right over the pedals,
and can consequently exert a driving force through a considerably
greater part of the stroke, whereas the vertical rider depends
chiefly upon the weight of his body during a comparatively short
portion of the down stroke for propulsion, and upon the momentum of
the machine to carry him over the dead centre. It will be found,
therefore, that the rider using his ankles properly will be able to
drive at least three inches higher with the same amount of force,
and, at the same time, there is much more equable strain on the
machine.—+Semi-Racer.+”
The quotations show one great trouble in writing a book: such a long
time elapses between writing and publishing, that new facts and
opinions come up in the mean time which demand attention and suggest
alteration, as, for instance, my former paragraph in regard to the
swimming attitude should have been expanded.
“Warrior” carries his theory to extremes. He is all right in cautiously
avoiding an unduly-forward saddle, but when he places the front tip
back of the vertical through the crank-axle, he goes too far and is
utterly wrong.
The cause for such diversity of opinion in this matter is that it
is tested under different circumstances. In riding over an easy,
slightly rolling country, the tendency to get back on the saddle is
indisputable, for reasons noted by “Warrior” and fully treated of in my
chapter on “Saddles and Springs in Relation to Health;” but notice how
we slip forward, almost off the saddle, when we have any work to do, as
in mounting a difficult hill; and also notice that the farther forward
we get, and the less the angle at the pedals between the saddle and the
vertical, the less will be the pull on the handle-bar. (See early part
of this chapter.)
In this connection the very long saddles, largely adopted in America,
are of great advantage, since, when not working hard, the rider can
sit well back and then slide forward when occasion demands. What
“Warrior” means by “greater power from muscular contraction” is rather
ambiguous. I may admit that more power can be consumed when the saddle
is back, but I deny that more effective power to turn the wheel can be
maintained. The rider may get more exercise from “muscular contraction”
than from the effect of his weight, but he will cover less distance
with equal fatigue.
As to “Semi-Racer,” his statement, that more ankle-motion is available
when sitting back, is absurd. Will he not lose in “clawing” force below
what he gains above?
In my chapter on “Ankle-Motion” I would say that the wonderful power
therein asserted as possible was attained by having the saddle well
over the work. Before disposing finally of this digression, let me
express my pleasure that these subjects are meeting with general and
enlightened discussion. However much opinions may differ, I regret,
as a loyal Yankee, that we in America have to depend so largely upon
cross-water importations for the initiative; but it is hoped that such
importations may always be on the free list, maugre the high-tariff
proclivities of the writer and many others like him on this side.
The next point of importance is the mechanical means whereby the
rider transmits a revolving motion to the drive-wheel, and to lead
up to this let us discuss the evolution from walking to riding. The
actual development has been of a legitimate character; first, walking;
second, walking with the trunk supported on rolling mechanism; third,
propulsion by means of mechanical things like legs, the entire body
supported upon rolling mechanism; fourth, propulsion and support all by
means of, and upon, rolling mechanism.
[Illustration: The Dennis Johnson wheel.]
The early bicycle, such as that of Dennis Johnson, patented in
England, No. 4321, 1818, did not support the rider entirely free
from the ground. It consisted in a pair of wheels placed under him,
constituting a sort of third or rolling leg, the feet, though not for
support, still touching the ground. This machine is a fair sample of an
intermediate stage between the era of oscillating devices subjoined to
the trunk by nature—to wit, the legs—and that of the present cycle. In
the Johnson machine the legs are used for projectile force only, and
serve as a motor, the weight of the body being supported on rolling
mechanism as aforesaid; hence it was a more natural and palpable
sequence to walking than other prior contrivances in which the rider
was raised upon a platform such as shown in the machine of Bolton,
patented in the United States, September 29, 1804.
[Illustration: The Bolton machine.]
The Bolton and similar machines really belong to a different class
from that of Johnson, but if we confine ourselves to our bicycle or
balancing-machine, thus throwing out the Bolton class, the development
from the leg to the wheel method proceeded in order, for we have next
the Lallement crank-wheel, United States patent, November 20, 1866,
which represents substantially the present single-track type.
[Illustration: The Lallement machine.]
One illustrious gentleman, Croft by name, patented a machine in the
United States, August 21, 1877.[4]
[Illustration: The Croft machine.]
In the Croft machine a pair of bars held in the hands are used with
which to propel by pushing against the ground, instead of using the
legs as in the Johnson. By supporting the body entirely free from the
roadway, Croft takes a step in advance of Johnson, but he still retains
his propulsive power by means of oscillating devices having contact
with the ground, and in this respect might be said to use a pair of
mechanical legs. He combined a walking method with that of rolling, as
was the case with Johnson and Baron Draise, but he seemed to think a
mechanical extension to the arms a better medium through which to pass
his energy than nature’s own devices for that purpose. Quite a number
of inventors have gone astray on this question of the power of the arms
in these manumotors. No doubt the arms could be made to help, but our
present physical development suggests the legs as better; especially
if one or the other plan is to be used alone. True, the Croft machine
could use the entire body, as in the case of a man shoving a flat-boat
or scow upon the water, but the inventor’s engraving does not show
any such effort as necessary. What a pity that we did not have a
single-track machine, propelled by the Croft process, between the
time of Johnson and Lallement; how nicely it would have helped us out
in our chronological development. We of the wheeling fraternity may,
however, take a crumb of comfort from the fact that the two bicycles,
or balancing machines, did make their appearance in respectful logical
order.
In naming the Bolton, Johnson, Lallement, and Croft machines, I have
not taken the trouble to ascertain whether they all were the very first
machines of the kind in the art, nor would it matter whether they were
or not, unless it could be shown that others were of equal prominence.
We should not recognize mere vagaries as an advance in the art: the
above gentlemen patented their machines, and it is therefore reasonable
to suppose that they were real workers, and not simply chimerical
characters flitting about in the minds of recent explorers. The famous
Draisaine is worthy of mention, but our man Dennis will answer all
purposes of illustration. Galvin Dalzell is now reputed to have been
the first to raise himself from the ground on a single-track machine,
and back as far as 1693 one Ozanam, a Frenchman, is said to have made a
four-wheeled vehicle of the Bolton type, but driven by the legs.
Blanchard, about 1780, did some work in connection with the subject,
and one Nicephore Niepse, we are told, made a machine of the Johnson
type about the year 1815. For further information on this subject, see
“Sewing-Machine and Cycle News,” in _Wheelman’s Gazette_, September,
1888.
In quite a recent edition of _The Wheel_ the editor gives us a little
foretaste of a book to which we look forward with interest. In it he
mentions improvements by Gompertz in 1821, Mareschal, Woirin, and
Leconde as having worked on cranks in 1865, and David Santon as having
brought a wheel to America in 1876.
L. F. A. Reviere, of England, is said to have made the large front
and small rear wheel; C. K. Bradford, of America, the rubber tire; E.
A. Gilman, of England, anti-friction bearings, and A. D. Chandler, of
Boston, is mentioned as an importer and rider of 1877.
[4] This is not a misprint for 1777.