714 WHEEL 
planes a 6, « &, equally inclined to the horizontal or 
level line as AB to BX, Fig. 6. Also let the 
points marking the centres of gravity of these car- 
riages be respectively R, 7, 2, of which R is the 
highest above the road, from the smaller breadth of 
the body of the cart NP QO, which, from the shape 
of the wheels, cannot be wider at NO than at PQ. 
It is clear, from Fig. 6, that when the carriage is at 
rest, or moving straight forward, it is just stable, 
though very little more inclination would overset it, 
either by the wheel DI moving over any slightly 
higher obstacle, or by the wheel EM falling into a 
hollow. On account of the greater breadth at the 
top of the cart n p qo, Fig. 7, than that of NPQO, 
Fig. 6, the centre of gravity falls lower than R, and 
consequently the vertical line rt, passing through 
the centre of gravity 7, falls nearer the middle be- 
tween the wheels than RE. By reason of the bend 
in the axle of the cart, Fig. 8, which is, in this in- 
stance, too great, the soles of the wheels approach 
each other much more closely than either of the 
other two; and the vertical line ¢:, passing through 
the centre of gravity ¢, falls nearly upon the bottom 
of the wheel, though, on account of the shape of the 
body of the cart, it is lower than either of the other 
two. Upon the whole, then, the construction of 
the cart or waggon, vg. 7, with properly dished 
wheels on the plan formerly proposed, has still the 
advantage.—In addition to these, other means have 
been resorted to for the purpose of keeping the cen- 
tre of gravity down. One of them consists in hav- 
ing the luggage placed as low as possible in travel- 
ling coaches, by carrying it in a box slung under the 
carriage, so as just to clear the road sufficiently. 
Such are the plans of some of our best coachmakers 
and agricultural implement makers. 
It has as yet been supposed that the carriages 
were either at rest or moving forward in a straight 
line. It frequently happens, however, that, in the 
old roads in particular, a rapid turn, or quick bend, 
is met with in the road, where the carriage must 
turn smartly, producing what is called a centrifugal 
force, which has a tendency to throw the carriage 
over in the opposite direction, or towards the con- 
vex side of the turn. The amount of this force de- 
pends upon the radius of the curve in the road, 
combined with the velocity, which, in the case of 
the mail coaches, and travelling carriages, may 
sometimes be considerable. If this concur to aug- 
ment the danger from the inclination of the road and 
a badly constructed carriage, on entering a bridge, 
or approaching a precipice in particular, the conse- 
quences may be fatal. Indeed, it is generally under 
these circumstances that the greatest accidents hap- 
pen; whence a due attention to the proper formation 
of our roads is as indispensable for the safety of tra- 
vellers, as an eligible construction of our carriages. 
To illustrate this to persons not very conversant 
with mathematical and philosophical inquiries, a few 
results, stated in a table, with conclusions drawn 
from them, will, it is hoped, be sufficient. The 
formule for obtaining the amount of centrifugal force 
are, 
1 ese AH GUMBO (1) 
re 
which gives the effects in feet, supposing the force 
of gravity, generally denoted by g, to be 32 feet; v 
the velocity of the moving body, or the number of 
feet which it passes over in one second of time; r 
the radius of the circle in which the body is moving, 
which, in this case, is the radius of the curve in the 
road; and F the centrifugal force. If the centrifu- 
gal force be required in terms of the weight of the 
moving body, then 
ea Ce (2) 
gr 
f being the value of the force, v the velocity, and r 
327 
CARRIAGE. 
the radius of curvature, as before. Suppose the 
radius, or r, to be 100 feet, which is not an uncom- 
mon case, then will the following table, drawn up 
for the purpose, give the effects to different veloci- 
ties :— 
Velocity in wy 
English miles A na ae an EN | in ee of the 
per hour. ; : | weight. 
5 Us 0°54 0:017 
10 14°6 2°15 0:070 
15 22°0 4°84 0-151 
20 29°3 8:60 0:270 
40 58'6 54:42 1:080 
60 88-0 77-44 2-420 
100 146°6 215-11 6°722 
— 
From an examination of the formule, it is evident 
that the centrifugal forces vary inversely as the ra- 
dius of curvature, the velocity being the same: that 
is, as the radius of the curvature or bend in the road 
increases, the centrifugal force decreases; and, on the 
contrary, when the radius of the turn decreases, the 
centrifugal force increases. Therefore, as any other 
assumed radius is to 100 feet, that adopted in com- 
puting the foregoing table, so is the centrifugal force 
stated in the table to that for the radius required. 
Hence the effects of centrifugal foree may, by this 
means, be estimated for any other curvature wanted. 
Thus, let the radius be 50 feet, one-half of 100, and 
F and f will be doubled, &c. From the principles 
of centrifugal forces, the centre of gravity is virtually 
thrown aside from R, Fig. 6, where it would be if 
the carriage were at rest, or moving forward in a 
straight line to R’; so that when the velocity is 
about ten English miles an hour, and the radius of eur- 
vature 100 feet, if the vertical line RE, passing through 
the centre of gravity R, were 32 feet in length, then 
RR’ would be by the table 2 feet nearly; that is, RR’ 
is ~th of RE, or of the height of the centre of gra- 
vity above the road nearer the wheel EM, if the car- 
riage turn rapidly at the rate of ten miles an hour, or 
143 feet in a second of time round A as a centre, at 
the distance AE of 100 feet. It would be twice 
jth, or 3th, if AE were 50 feet, which is not an un- 
common case. In ordinary circumstances, the centre 
of gravity is less than 4 feet above the road, and 
therefore it might generally be about 3th of 4 feet, 
or 3 foot thrown aside from E to F, which would 
render the carriage, on such an inclined plane, just 
ready to overset. At twenty miles an hour, the cen- 
trifugal force, compared with gravity, is, from column | 
3d, 9 feet nearly, or .2 of the height of the centre of 
gravity, or say, for the sake of simplicity, one-third 
of that height; so that, if the centre of gravity be 4 
feet above the plane of the road, as formerly suppos- 
ed, it would in effect be thrown aside by this means, 
nearly 3 of 4, or $ foot, equal to 13 foot, or 1 foot 4 
inches. Supposing the distance between the bottoms 
of the wheels to be 5 feet, then this effect of centri- 
fugal force would be the same as if the carriage were 
moving on an inclined plane having a rise of | foot 4 
inches in 5 feet, or at an angle of 15°. In like man- 
ner, the investigation might be carried to higher ve- 
locities; but enough, it appears, has been said to 
prove the danger of high velocities at rapid turns or 
curves ina road. On account of the good shape of 
the wheels, axle, and body of the carriage in Ig. 7, 
it is clear it would be just stable, since rr’ would be. 
less than RR’, on account of the centre of gravity 
being lower than that of Fig. 6, which is just ready 
to overset. Consequently 7’ e, the vertical passing 
through the centre of gravity, would be just within 
the wheels, and the carriage would possess some de- 
gree of stability; while ¢«, (fg. 8,) the vertical 
passing through its centre of gravity, just meets the 
