GRAPHIC ILLUSTRATION OF THE APPLICATION OF POWER
TO CYCLES—KINEMATICS.
The manner in which the construction and general arrangement of the
driving mechanism, the road surface, and other conditions control the
application of power is a curious study. In connection with it I have
made an instrument to illustrate the same graphically, which, for the
sake of a name, we will call the “Cyclograph,” an engraving of which
will be found below.
[Illustration: The Cyclograph.]
A frame, _A A_, is provided with means to attach it to the pedal
of any machine. A table, _B_, supported by springs, _E_, _E_, has
a vertical movement through the frame _A A_, and carries a marker,
_C_. The frame carries a drum, _D_, containing within it mechanism
which causes it to revolve regularly upon its axis. The cylindrical
surface of this drum, _D_, is wrapped with a slip of registering paper
removable at will. When we wish to take the total foot-pressure, the
cyclograph is placed upon the pedal and the foot upon the table. The
drum having been wound and supplied with the registering slip, and the
marker _C_ with a pencil bearing against the slip, we are ready to
throw the trigger and start the drum, by means of a string attached
to the trigger, which is held by the rider so that he can start the
apparatus at just such time as he desires a record of the pressure.
The following are a few sample sections cut from registering slips
illustrating some of the points discovered in these experiments. Only
a few strokes of the crank or lever can be shown; it is evident that
great space and expense of reproduction would be required to give the
entire record for even a small part of a mile. It will be understood, I
think, without further explanation, that these curves show the extent
and variation of pressure of the foot upon the pedal in order to drive
the respective machines under circumstances named and described by the
figures and thereafter.
[Illustration: 52-inch Ordinary; race-track; getting up steam.]
[Illustration: 52-inch Ordinary; race-track; speed, eighteen miles per
hour.]
[Illustration: 52-inch Ordinary; race-track; speed, ten miles per hour.]
[Illustration: 52-inch Ordinary; race-track; speed, ten miles per hour.]
[Illustration: 52-inch Ordinary; up hill, grade, one foot in
twenty-five; speed, about eight miles per hour.]
[Illustration: 52-inch Ordinary; starting up hill.]
[Illustration: 52-inch Ordinary; up hill, grade, one foot in ten;
stalled at four miles per hour.]
[Illustration: 52-inch Ordinary; up hill, grade, one foot in
twenty-five; curves of both pedals superposed.]
[Illustration: 52-inch Ordinary; back pedal; down hill, grade, one
foot in twelve.]
[Illustration: Rear-driver Rover type, 54-gear; up hill, grade, one
foot in twenty; speed, nine miles per hour.]
[Illustration: Rear-driver Rover type, 54-gear; up hill, grade, one
foot in twenty; continuation of No. 10.]
[Illustration: Rear-driver Rover type, 54-gear; up hill, grade, one
foot in seven; speed, ten miles per hour.]
[Illustration: Lever rear-driver, 30-inch wheels, gear about 50; up
hill, grade, one foot in twenty; speed, eight miles per hour.]
[Illustration: Lever rear-driver, 30-inch wheels, gear about 50; up
hill, grade, one foot in twenty; speed, twelve miles per hour.]
[Illustration: Lever rear-driver, 30-inch wheels, gear about 50; up
hill, grade, one foot in twenty; continuation of No. 14, over top
of hill.]
A six-inch crank was used upon the machines in these experiments, and
the lever action was such as to be comparable to a fifty-inch gear. The
height of a point on the curve shows the extent of and variation in
power upon the pedal, and the translation from left to right the time.
In consequence of the limit of pressure occurring but once in each
stroke, the number of undulations determines the speed, since it would
show the number of strokes in a given time, and we know the number that
make a mile.
The number of pounds’ pressure at any point on a curve is shown by the
figures upon the perpendicular line, as, for example, in No. 1 the apex
of the curve just to the right of the scale is about even with the
hundred-and-fifty-pound point; this pressure was maintained for a very
short space of time, since the curve travels a very short distance to
the right at this point; in other words, it is quite sharp at the top.
Stronger springs were used on the Cyclograph in testing the safeties,
as I found myself liable to compress them beyond their limit; hence
the scales must be closely observed in making comparisons. Among
the interesting results noticeable in these experiments I find, for
instance, in Nos. 3 and 4, an abnormal deviation in the height of the
curves at the same speed upon the same track at nearly the same time,
though running in opposite directions. Finding this strange difference
of some fifty pounds in pressure, I noticed an almost imperceptible
breeze against me in the one, and in my favor in the other, direction.
No. 12 illustrates how a hundred-and-fifty-pound man gets up a pressure
of two hundred and forty pounds presumably by a ninety-pound pull on
the handle-bar.
In No. 9 we see how one hundred and fifty pounds pressure is applied
in back-pedalling down a grade of one foot in twelve. That the curve
would not be very regular is easily impressed upon the mind of the
average rider.
One part of curve (not shown), of peculiar contour, terminated
experiment No. 9 at a rut a little farther down the hill, with dire
results to the operator and provoking influence upon the running gear
of the ’graph, which has been making some erratic curves of its own,
now and then, ever since.
Comparing Nos. 5, 10, and 13, the curve of the lever machine (13)
indicates that, while pressure is not so great as in the others, it is
held for a longer time, shown by the greater height and sharper tops to
the curves of the crank machines.
The short cross-lines about three-fourths up on the left sides of the
undulations in Nos. 10, 11, and 12 designate the points at which the
crank crosses the perpendicular at the top. There is quite a pressure,
and it is a little odd that it should be found at this point; it can
only be attributed to ankle-action back of the natural dead centre.
In No. 6, and to some extent in all the others, observe the jagged
appearance in the general advance of the curves, which must be due
to vibration: these results were all obtained upon tolerably smooth
roads, mostly in Druid Hill Park, Baltimore. No. 6 was taken upon a
road perhaps a little rougher than the track around the lake, but still
upon an unusually smooth surface, and it was a surprise, not to say
an alarming discovery, that this vibration should occur under such
circumstances.
The lake track, upon which results 2 and 3 were found, was in perfect
condition, smooth as a surface-plate, and without the customary
sprinkling of pebbles so common when dry weather has loosed the
settings of these tiny obstructions and suffered them to roll out upon
the roadway; yet these figures show the saw-teeth, and I have been
unable to find a road smooth enough, or jointed machine frames and
springs good enough, to make unwavering symmetrical lines. These little
deviations in the curves always seem to show themselves to the extent
of several pounds in height in spite of all alleviating conditions,
suggesting that we have much to strive for in the construction of the
ideal wheel free from all concussion. In order to judge accurately
of the total amount of power to turn the wheel, we have to consider
the register of both pedals superposed, as in No. 8, but the curve
made upon one generally answers all purposes. The possibilities in
this study are unlimited, and, with a perfectly-accurate instrument,
it strikes me, the results of much more definite bearing than those
acquired in the silly practice of testing machines by the strength of
men.
I have refrained from giving any tests as to the comparative
power required to drive machines of the same type and of different
manufacture, differences being liable to result from a bad condition
of the machine, such as the want of oil, or from happening to get
hold of an unusually bad sample, making the liability to do injustice
too great. The writer does not feel himself called upon to judge of
or express differences in quality of workmanship in general, if for
no other reason than that by the time the matter goes to press, such
merits or defects as he might have discovered may change. Workmanship
does change, principles never can; and, what is more, the hypotheses
and conclusions in regard to principles, treated of in this or any
other book, are always open to contradiction; if injustice is done
to any maker of wares in a matter of principle, said maker always
has a remedy in defence, and if he can disprove assertions made his
justification is complete, whereas if a mistake of fact is recorded,
such as the operation of a certain machine, and the machine upon which
the alleged fact is based happens to disappear, the party interested
is denied a just remedy. There are of course certain criteria of good
workmanship, and the same should be touched upon in order to teach the
reader how to judge of it; but beyond this no writer should be allowed
to go, unless at least he has been paid for advertising competing wares
at regular rates.
The cyclograph attached to the revolving pedal shows the total amount
of pressure required to do a certain work on a machine; but if it is
desired to ascertain the track resistance or the friction of parts
alone, it is necessary to so place the instrument as to register the
tangential resultant in turning the crank, taking no note of any power
thrown away by indirect application; that is, if we wish to register
the circular or tangential resultant, the cyclograph is attached by
its frame rigidly to the crank or lever of a cycle, and the revolving
pedal, which has been detached, is hung upon the spring platform. This
last arrangement is used in experimenting to ascertain the extra power
available by ankle-motion, as will be shown hereafter.
ANKLE-MOTION AS SHOWN BY THE CYCLOGRAPH.
Throughout this work a slight tendency to urge the element of dead
centre as against the crank-cycle may have been discovered. Makers
and riders who find fault with this apparent praise of lever and
non-dead-centre devices can derive considerable comfort by the study
of ankle-motion. No better introduction to our diagrams, showing the
possibilities arising therefrom, can be given than the following
extract from the _Irish Cyclist_, via _The Bicycling News and
Wheelman’s Gazette_:
“ANKLE-ACTION.
“Among the many thousands of riders in this country, says the
_Irish Cyclist_, very few have any desire to improve their style or
realize for a moment the vast importance of correct ankle-motion.
You meet a rider plodding along, working his legs like pistons,
with a heavy, lifeless motion. Remonstrate with him, and see what
he will say: ‘Oh, he can go well enough; he does not believe
ankle-action makes such a difference, and he does not want to
“scorch” in any case.’ Now, we want our readers to grasp these
facts. Any rider can acquire a tolerable ankle-action by careful
practice, and the acquisition of such will increase his power by
nearly one-fourth, and will enable him to ride hills never before
attempted, and to keep up a better pace at the expense of the same
amount of energy. This being so, the acquisition of such art should
be a _sine quâ non_ to every rider. That it is so can very easily
be proved. In following the pedal the foot describes a complete
circle. Suppose the circle to be divided into eight segments, taken
in order from the highest point.[5] With a rider who does not use
his ankles, force is applicable only through segments 1, 2, 3,
4, and in segments 1 and 4, the force not being applied at right
angles to the end of the crank, a large proportion is wasted, and
consequently it is only thoroughly effective through segments 2
and 3, or during one-fourth of the revolution. The rider who has
mastered the mysteries of ankle-action will drop his heel as the
pedal approaches the highest point, and he can apply a certain
amount of force through segment 8. After passing the so-called dead
point, his heel being still dropped, the force is applied at right
angles to the crank, or nearly so, and consequently he can utilize
his full power through segment 1. By rapidly straightening the
ankle when entering segment 2 an additional impetus is imparted,
and, as before, full power can be applied through segments 2 and 3.
Entering segment 4, the heel should be raised and the pedal clawed
backward, and this clawing action will enable the rider to work
past the dead point and well through segment 5. Consequently, the
man who rides with his ankles stiff can only work through segments
1, 2, 3, 4, or half the whole circumference, and his work is
thoroughly effective only through segments 2 and 3, or one-fourth
the circumference, whereas the man who utilizes his ankles can
work through segments 8, 1, 2, 3, 4, and 5, or two-thirds the
whole circumference, and his work is thoroughly effective through
segments 1, 2, 3, and 4, or one-half the whole circumference.
The advantage gained in the latter case is self-evident. The
acquisition of the art is often tedious and troublesome, but if
cyclists only knew the enormous increase of power which results
they would not be content until they had mastered it. From the
cycling volume of the Badminton Series, written by Lord Bury and G.
Lacy Hillier, we take the following instructions:
“‘Seated either on a bicycle slung so that the wheel may revolve,
or upon a home-trainer, the beginner should raise the pedal to
its highest point, and then, steadying the wheel with the brake,
place his foot upon the pedal, carefully fitting the slots in his
shoes into their places, and seeing in any case that the foot is
straight. Then, using the thigh muscle for the most part, let him
thrust the foot (and pedal) forward in a horizontal direction;
in fact, a sort of sharp forward kick, having the heel dropped
as low as possible, the toes well up, and the foot firmly set on
the pedal, which will be at an angle. This should be practised
carefully with the brake slightly on, and for this purpose, though
a bicycle may be used, a tricycle will be found much handier. If
no home-trainer is available, the brake can be put slightly on
by means of a piece of string or strap to the lever, tied to any
convenient point, and the novice can spend a few minutes daily
practising this exercise; in carrying out which programme the
left foot should at first be used more than the right. As soon
as the usual awkwardness of the ankle-joint has been worked off
this action will be found remarkably effective in starting the
machine; after a time the ankle muscles, and those of the calf,
will become stronger, and a sharp straightening of the ankle, as
the pedal passes through segments 1 and 2, will materially aid the
propulsion of the machine. This straightening of the ankle will be
continued until the foot is brought into a position at right angles
to the leg, the muscular effort of which should now have by equal
gradations become directly downward. The pedal will now assume a
horizontal position, and the power of the leg with the weight of
the body and the pull of the arms will all be exerted to force it
downward; at this point the crank throw is in the most effective
position, and the hardest work is put in. When the pedal begins to
follow a backward course, the ankle-action becomes of the greatest
value. The toe is gradually dropped, and the heel raised as the
pedal gets nearer and nearer to the lowest point, the action having
at length reached the backward or “clawing” stage. To secure the
full advantage of ankle-work, this “_clawing_” action must be
very carefully practised; the toes should be sharply pressed upon
the sole of the shoe as if they were trying to grasp something,
whilst the ankle should be straightened as much as possible, the
foot being almost in a line with the leg, the calf muscles being
strongly retracted, and the backward pull (which of course requires
fitted shoes) can be made practically effective through segment 5,
and also of service well into segment 6. The ineffective portion
which exists on either side is soon reduced to a very small part
of the circle, for as soon as segment 7 is entered upon the heel
should be sharply dropped, and an upward and forward kick or
thrust, as described in the directions for the first position,
will lift the pedal forward and upward through segment 8, when, of
course, the whole series of actions will be repeated.’—_Bicycling
News._”
Using the arrangement of cyclograph spoken of, by which ankle-motion
may be shown, I find that I can begin to get a tangential resultant
force on each crank at an angle of eighteen degrees back of the
vertical line through the axle of the drive-wheel, beginning at _d_ and
ending at _e_, Fig. 1,—in all, thirty-six degrees over a half-circle on
each crank.
[Illustration: Fig. 1.
Ankle-power.]
The diagram shows the sections 1 to 8, and also gives an idea of
the extra power. To see the direct circular resultant force to turn
the wheel, imagine the length of a crank from _m_ to _n_ without
ankle-motion and then _m n_ plus _n o_ for the length of the crank
with ankle-motion added. I have been able at each of the points _a_
and _i_ to get thirty pounds when the crank crosses the vertical line
at the top and bottom. Thus it is discovered that by means of this
ankle-motion on both cranks simultaneously, I can get a force of sixty
pounds in the direction to turn the wheel, at a time when absolute dead
centre would otherwise occur, amounting to two-fifths of the maximum
pressure resulting from my entire weight on one crank at the best
possible point, directly out in front, going down.
I have more than verified the results shown by the cyclograph by
suspending a fifty-four-inch bicycle, with six-inch cranks, above the
floor, placing myself in the saddle, and having an attendant attach
a twenty-pound weight at a point on the rim, ninety degrees from the
bottom. This weight I was able to raise at the dead-centre point of
both cranks,—that is, vertically up and down,—which shows a real power
at the pedals of ninety pounds, or forty-five pounds on each, and I do
not suppose that I am by any means an expert in ankle-motion. The above
ninety pounds is a much greater showing than I made on the cyclograph
in actual running, but it is reasonably certain that, by practice, even
such an amount could be obtained.
In the case of no ankle-motion,—that is, with a direct downward
pressure on the crank,—a tangential force in the direction available
in turning the wheel begins as the crank crosses the vertical at the
top, and then increases as the sine of the angle the crank makes with
the vertical, until such angle reaches ninety degrees or extends out
horizontally, after which the power decreases as the sine of the angle
the crank makes with the vertical below the centre until the crank
crosses at the bottom, at which point the power ceases.
To represent this variation of power by actual length of
lines, appended will be found a diagram, Fig. 2, showing the
tangential resultant or force to turn the wheel, imparted by
a one-hundred-and-fifty-pound man with and without the use of
ankle-motion.
_A A_ is a line showing the divisions of the angles through which the
crank passes in its revolution around the axle. The line _a f i_ is a
sine curve.
Using the middle section and beginning at the point _a_, which is
that at which the crank crosses the vertical above the axle, making a
zero angle therewith, we have a direct downward pressure and, without
ankle-motion, zero power. Now, by means of ankle-motion on one crank
at this point we get thirty pounds of power, represented by the length
of the line from _a_ to _b_; and by ankle-motion on both cranks we
have sixty pounds, represented by the total length of the line from
_a_ to _c_. After the crank has advanced forward fifteen degrees, we
have thirty-nine pounds of direct power (_m n_), and then adding the
ankle-power of twenty-three pounds (_n o_), we have a total resultant
of sixty-two pounds, represented by the length of the next line (_m
o_), and so on up, the direct power increasing and the ankle-power
diminishing till we come to the top of the curve _f_, when we have one
hundred and fifty pounds of direct power. Passing through the angle of
ninety degrees, and now counting from the vertical below the axle, we
decrease in power inversely as we increased before.
Fig. 1 will show a little more graphically to the eyes of some casual
readers how the power expands. Take _d a f i e_ as the regular swing
of the crank with no power at _a_, then _d b f h e_ as the increase
of power on one and the dotted lines _c_ and _g_ as the auxiliary
ankle-power on the other crank added.
[Illustration: Fig. 2.
Ankle-power sine curve.]
[5] Observe Fig. 1, p. 58.