COMPARISON OF THE CURVES OF TRANSLATION, IN MACHINES OF WHICH THE
DIAMETERS OR COMBINATION OF WHEELS DIFFER, OF A POINT TAKEN IN
THE SAME RELATIVE POSITION ON THE SEVERAL SADDLES—CONSEQUENT
CONCUSSION AND EFFECT UPON MOMENTUM.
In discussing this matter it has been taken for granted that the proper
point upon which to base calculations is that point in the saddle at
which the motion of the machine may be supposed to be transmitted to
the rider; this happens to be very near the centre of gravity of the
system, and is also quite near the centre of gravity of the man. The
motion is of course partially transmitted to the rider at the pedals,
but we will for the present waive that modification.
Simple as the running of two wheels over an obstruction seems to be,
there are some interesting points to study. It was a surprise to the
writer, and it is his hope that it may be of interest to others, that
the saddle, and of consequence the rider, actually goes backward at
times when the wheels are running forward; as, for instance, when the
machine rolls slowly from a four-inch obstacle, as shown by the curve
of the point in the fifty-two-inch Ordinary given below, and also
particularly in the advance upon the same of the Star rear-driver. This
reversion of momentum sometimes results in a drop of the rear wheel,
but it is always an actual reacting force in the front. We feel the
curves very plainly on a rigid machine, but it is a satisfaction to
know exactly what they are and what the springs must overcome.
MOTION AT THE SADDLE AS WHEELS ROLL OVER AN OBSTRUCTION.
[Illustration: Fig. 1.
Ordinary, 52 F., 18 R.; 4-in. obstruction; saddle twenty degrees
back.]
[Illustration: Fig 2.
Rational Ordinary, 52 F., 18 R.; 4-in. obstruction; saddle thirty
degrees back.]
[Illustration: Fig. 3.
Lever Rear-driver Star, 18 F., 52 R.; 4-in. obstruction; saddle
twenty degrees forward.]
[Illustration: Fig. 4.
Star, 20 F., 52 R.; saddle vertically over axle.]
[Illustration: Fig. 5.
Star, 24 F., 39 R.; saddle over axle.]
[Illustration: Fig. 6.
Kangaroo, 40 F., 18 R.; saddle twenty-five degrees back.]
[Illustration: Fig. 7.
Rear-driver Rover, 30-in. wheels, eleven inches apart; saddle forty
inches high, twelve inches forward.]
[Illustration: Fig. 8.
Rear-driver, 30 F., 24 R.; saddle forty inches high.]
[Illustration: Fig. 9.
Dennis Johnson, 30-in. wheels; saddle thirty inches high, midway
between wheels.]
The diagrams show the paths of the point in the various machines
passing over a four-inch obstruction; _F_ designates the front
and _R_ the rear wheel, and the arrows indicate the direction of
translation,—that is, the way the machine is running. The degrees
designate the angle between lines from the drive-wheel axle, one
extending vertically and the other through the saddle; sometimes
also expressed in inches of horizontal distance between verticals
through the rear axle and saddle. The heights or top points of the
curves from the base line show the amount the machine is raised at
the saddle as each wheel passes over the obstruction; these heights
give inferentially the position of the saddle between the wheels,
or, rather, between the vertical lines through the respective axles
thereof, since the nearer over a wheel the saddle is placed the more
it will be elevated when the wheel passes over the obstruction. Again,
from the location of the saddle with reference to the axles we can
determine the amount of weight carried by each wheel, the weight each
carries being proportional to the respective distances from the saddle
horizontally. The sum of the heights of the two curves from the general
level will be the height of the obstacle.
Theoretically there is no difference in the amount of work required to
pass over an impediment, no matter where the saddle is placed, as the
man must be raised in all to the height of the same, and it does not
matter whether he is lifted up half way twice or all the way once in so
far as the amount of labor is concerned. The man and the machine must
be lifted up to a certain height in some way; as it happens, it is more
comfortable to be lifted twice through half the distance than all at
once; but this should not affect the actual work done nor the energy
expended.
Our scale in the study of this question is one-sixteenth of an inch to
the inch; therefore in these diagrams one-eighth of an inch represents
two inches in the full-size bicycle. In this connection also it must
be taken into consideration that the effect upon momentum is not shown
entirely by the contour of these lines; the sudden stoppage or checking
of the system is generally shown by a vertical tendency in the curve,
but a very disagreeable shock to the body may occur and momentum be
lost without any deviation in the curve whatever when, for instance,
in the most pronounced case, the saddle goes straight back upon its
course. This is shown by means of the short vertical or diverging lines
upon the curves. These short lines show the distance forward the point
in the saddle travels in proportion to the advance of the wheels in a
forward direction in space; each short line indicates an advance of two
inches in the wheels. When the lines are below the curve, the saddle
has actually dropped backward,—that is, it has been directly reversed
in its course.
When the short lines upon the curve are close together, it shows that
the saddle and rider are being checked proportionately as these lines
are less than one-eighth of an inch apart. On the other hand, when the
normal pace of the momentum of the heavier parts is slower than that of
the wheels, it is shown by the lines being more than an eighth of an
inch apart. In this case there is a tendency to increase the momentum
instead of decreasing it,—a state of affairs not so much to be deplored
if it were not evident that it is equally checked at some other point.
We know, in practice with the Ordinary, that the loss of momentum by
sudden checking can only happen to the full extent when the pace is
reasonably slow; should the momentum be too great it will simply refuse
to be interfered with in its forward course, and the rear wheel will
leave the ground with a result and in a manner quite well known.
In the safer forms of bicycles,—those from which a header is
improbable,—without proper springs, the rider will simply slide forward
on the saddle, causing considerable loss of momentum besides that due
to vibration, since he must afterwards slide himself back again.
Referring to the diagrams, Fig. 1 shows the Ordinary bicycle with a
fifty-two-inch front and an eighteen-inch rear wheel. The front wheel
mounts the obstacle with some difficulty, the curve upward being rather
sudden in its change of direction from the base line, thus showing that
the momentum is checked very rapidly; see the short vertical lines upon
the curves, which are about one-half the distance apart of those on the
base line between the curves and at the ends. Also notice that _F_ (the
front wheel) carries three-fourths of the weight, one curve being about
three times as high as the other.
Particular attention is called to the easy and gradual curve shown by
the mounting of the small rear wheel _R_; it would seem to show that
the great clamor of theorists for large rear wheels in the Ordinary
is somewhat unwarranted; the drop down and back in rolling off the
obstacle will be seen to be quite sudden, but notice not very much
more so than in Fig. 2, which shows the Rational, so called, with a
fifty-two-inch driver and twenty-four-inch rear wheel. The large rear
wheel affects the drop to some extent, but in all obstacles under four
inches in height there is no perceptible benefit derived, at least not
such as to warrant the extra weight and disarrangement of the steering.
Fig. 3 shows a machine with a fifty-two-inch rear driver, _R_, and an
eighteen-inch front steering wheel, _F_, with the saddle twenty degrees
in front of the vertical line through the driving axle. The curves are
just the reverse of the Ordinary; in the latter the quick drop, down
and back, of the rear wheel in leaving is comparable to the backward
thrust of the front wheel in Fig. 3 running upon the obstruction. No
machine in the market at present makes exactly the curve of Fig. 3;
it is about that which the American Star would make with its saddle a
little farther forward, and that of a recent rear-driving crank machine
called the “Eagle.”
Fig. 4 shows the American Star, as commonly seen, with a fifty-two-inch
rear driver and the saddle directly over the driving axle. This
curve shows no elevation of the saddle as the front wheel mounts the
obstacle, but a radical check to the momentum is shown; observe the
curve (_F_), and note that the saddle is forced back in the order of
the small numerals, advancing to 1, going back to 2, then on to 3 and
4, which shows that the momentum is not deviated up or down, but is
directly reversed in its course.
Fig. 5 shows a new machine of the Star pattern, with twenty-four-inch
front steerer, _F_, and a thirty-nine-inch rear driver, _R_. The check
in the momentum is not so radical as that shown in Fig. 4, as the front
wheel mounts the obstacle. The one short line below the curve shows the
backward thrust.
The sudden check in striking an obstacle, with the machines last
referred to, shows the necessity and enormous advantage of a forward
give to the saddle support adopted in some of those patterns. This
arrangement is not so necessary in the Ordinary, yet it would do no
harm, for it will be seen that the large front wheel of the latter
strikes the obstacle with quite a sudden upward curve and check in the
momentum sufficient to justify its use.
In the Star, Eagle, and such other types the man is raised upon the
obstacle entirely by the large rear wheel, which carries nearly all of
the weight, as shown by the height of the curve; it raises beautifully
upon the obstruction with little or no check in the momentum, the
diverging lines showing about the same distance apart as at the base.
It has been thought to be an advantage to reduce the weight upon the
front wheel, but the importance is very much exaggerated; it will
reduce the impact in dropping down from an obstruction, and will thus
cause less annoyance in rough-road riding; still this does not alter
the fact that the momentum in the man and part of the machine is not
only stopped, but reversed backward, as shown in the diagrams. If
the wheel were lifted entirely free from the ground before advancing
upon the obstruction, it is obvious, then, that no harmful result
would ensue, not so much because the jolt and impact in dropping off
is obviated, but for the reason that the momentum forward is not
interfered with. If the rider should run full force against a wall with
his forward wheel, it would be of little consequence to him whether
there was any weight upon it or not; it is not always a question of
vertical disturbance or of the action of gravity that is of annoyance
to the bicycle rider; it is sometimes better to have a heavy weight
upon a wheel if it can be kept in contact with the obstruction, as, for
instance, upon the front wheel of the Ordinary when it rolls off, as it
will be seen that the curve shows a splendid contour by which to give a
good pull on the machine.
Fig. 6 shows the Kangaroo type, with a forty-inch front driver and an
eighteen-inch rear wheel; this curve presents very little change from
that of the Ordinary.
Fig. 7 illustrates the Rover type, having two thirty-inch wheels with
their centres forty-one inches apart, the saddle forty inches high and
twelve inches in front of the vertical through the rear axle. The mere
contour of the curve in the last figure mentioned would be somewhat
misleading did the diverging lines not show that in the rolling off
of the rear wheel the momentum is considerably checked,—that is, the
saddle moves more slowly forward than the normal forward pace of the
wheels, though there is no direct reversion of the momentum, as occurs
in the Ordinary and some others.
In this connection let me call particular attention to a cardinal
distinction with reference to the action in rolling upon and from an
obstruction. If the wheels in descending hold the man back in order
to remain in contact and thus roll off, it will, of course, result
in a check of momentum exactly equal to that which would occur in
such advance upon an obstacle, as would be shown by a similar curve
in the opposite direction; but, as a matter of fact, the momentum
being a certain amount, the effect is to cause the wheel to leave the
obstruction entirely and not roll, but jump off, which result causes
a great loss of energy and is sure to occur in rapid running. In this
case the forward momentum gets no benefit from the potential energy
acquired in mounting the obstacle, which shows the great necessity of
proper springs such as will enable a man to swing forward slightly
without rigidly drawing the machine after him. The object of the
springs in this connection should be to hold the wheel in contact and
permit it to roll instead of forcing it to jump off; if it rolls and is
not carried off by the force of momentum, the energy will be given out
in driving the machine forward instead of being lost in the vibration
caused by impact when the machine strikes the common level. That is
to say, the machine should roll off, but not hold the man back in
order to do so; by proper springs the wheels remain in contact, while
the man goes on at the regular pace of momentum. The liability of the
rear wheel to jump off is a serious difficulty in the present Rover
type of rear-driver; there is no reversion of the momentum, nor such a
tendency to drop perpendicularly, as in the Ordinary, yet it drops a
greater distance and is charged with more weight. This objection cannot
be entirely remedied by any springs we now have in use; it requires
a lively vertical as well as a horizontal amplitude in the motion of
the springs, and they should be placed at the hub of the rear wheel in
a manner similar to those used of late in connection with the front
wheel. It will be seen from the diagrams that the curves shown by the
front wheels leaving the obstructions are never such as would show any
liability to jump off; advancing _upon_ the obstruction must, in them,
be mostly provided for.
In Fig. 8 we have a machine provided with a thirty-inch front and
twenty-four-inch rear driving-wheel. This is a modification of the
Rover type recently favored by some English makers. The drop of the
rear wheel is more radical than that of a full thirty-inch.
In Fig. 9 appears a Dennis Johnson machine, with two wheels of the
same size, having the seat low down and exactly midway between them.
This is perhaps the easiest riding contrivance in so far as vibration,
jolt, and shock are concerned. Observe the equable motion it displays.
This machine was patented in England, as spoken of in an early chapter,
seventy years ago.
It will be seen, from a general observation and study of all of the
diagrams, that the best and most gradual curves are made by the front
wheel in descending from, and by the rear wheel in advancing upon, the
obstacle; hence it follows that the front wheel works against momentum
more in ascending and the rear wheel more in descending.