Mechanics of Automobiles

254 Pages·1964·10.005 MB·English

by  H. E. Barnacle (Auth.)

MECHANICS OF
AUTOMOBILES
H. E. BARNACLE
B.Sc.(Eng.) London, A.M.I.Mech.E.
PERGAMON PRESS
OXFORD · LONDON · EDINBURGH · NEW YORK
PARIS · FRANKFURT
1964
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Copyright © 1964
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Library of Congress Card No. 63-18930
Set in 10 on 12 pt. Times and printed in Great Britain by
PITMAN PRESS, BATH
PREFACE
THIS book deals with the application of the basic theory of
mechanics to certain problems arising from the motion of an
automobile.
Whilst many books have been written on the construction,
functioning, maintenance etc., of vehicles and some topics in this
book appear in books on Theory or Mechanics of Machines, few
have been published dealing specifically with dynamics applied to
automobiles. Development of research in vehicle ride and
stability points to the need of such a book for engineering students,
and particularly those attending Technical Colleges. It is hoped
that the present book will help to satisfy this need.
The material and method of presentation, which is based on
teaching the subject to full time National Diploma Courses at
Higher and Advanced level, should be of direct value to students
preparing for the examination of the Institution of Mechanical
Engineers and those at Technical Colleges studying Automobile
Engineering, in H.N.D. or Dip. Tech. Courses. It has been the
custom for examination papers in Theory or Mechanics of
Machines for B.Sc. London External Engineering Degrees to in­
clude questions on vehicle dynamics and vibrations, and students
preparing for parts I, II and III should find the appropriate
chapters adequate for these examinations. The book should also
be of value to many junior research engineers, designers and
draughtsmen employed in the automobile industry.
Throughout, many worked examples are included as experience
shows that students derive most benefit from these. The examples
form an integral and necessary part of the book and they have been
ix
X PREFACE
carefully selected and graded. Almost all are taken from Examina­
tions of the University of London and the Institution of Mechani­
cal Engineers, and the author wishes to thank these bodies for
permission to use the examples. Neither body is, however, com­
mitted to approve the solutions given in this book.
In order to keep the book to a reasonable size consistent with
coverage of topics, some problems have had to be excluded. A
detailed study of vehicle stability is one of these. However, the
basic material for such a study is contained in Chapters 9 and 11.
Knowledge of vehicle stability is increasing at a fast rate and
treatment of it is, in the author's opinion, more suited to research
papers than to a text book at the present time.
H. E. BARNACLE
CHAPTER ONE
VEHICLE PERFORMANCE
Linear Inertia
ONE of the essential preliminaries to automobile design is pre
diction of performance. Essentially, power from the engine is
made available at the wheels and a tractive effort is exerted on the
vehicle due to the interaction between the tyres and the road
surface. Certain "losses" occur within the vehicle and there are
resistances to the motion of the vehicle. Thus knowledge of these
resistances is important if a reasonable estimate of the effective
tractive effort is to be made. In addition, knowledge of the forces
acting between the tyres and the road is required since, no matter
how large the engine output may be, the tyre forces limit the
eventual performance.
1.1. Acceleration and Inertia
The tractive effort (P) between tyres and road give rise to the
vehicle acceleration if) and in the absence of any resistances to
motion, the full tractive effort would be available to accelerate
the vehicle. The acceleration is then given by,
W
r- f 0.1)
T
where, Wjg is the vehicle mass in slugs.
1
2 MECHANICS OF AUTOMOBILES
If the vehicle is accelerated by the forces from the road, the
vehicle itself, due to its inertia, will react with equal and opposite
forces on the road. A state of "dynamic" equilibrium is assumed
to exist when the resultant of the external forces on the vehicle is
equal and opposite to the inertia force.
WORKED EXAMPLE
1.1. A motor car weighs 3000 lb and the engine develops 50
b.h.p. at 4000 r.p.m. The transmission efficiency is 85 % when the
gear ratio of engine to road wheels is 5-4 to 1. The effective
diameter of the road wheels is 26 in. Ignoring resistances to
motion, determine the acceleration of the car on a level road when
the engine speed is 4000 r.p.m.
Solution
Power at wheels (transmission efficiency 100%) = 50
Power at wheels (transmission efficiency 85%) = 50 x 0-85
= 42-5 h.p.
4000
Speed of wheels = —— r.p.m.
42-5 X 33,000
hence total torque at wheels = TT^TTZ-Z = 301 lb ft.
M 2π X 4000/5-4
torque 301
Total tractive effort on car = , /—T = ΤΤΓΓ^ = 277 lb.
wheel rad. 13/12
W 3000
Inertia force of car = / = —— ./lb = total external force.
g 32-2
= 277 lb.
„ 277 X 32-2 _ „ ,
Hence,/ = = 2-97 ft/s ec92 .
VEHICLE PERFORMANCE: LINEAR INERTIA 3
1.2. Resistances to Motion
Resistances to motion, ignoring transmission losses between
the power unit and the wheels, are usually considered to be (a)
air resistance; (b) rolling resistance; (c) gradient effect.
(a) AIR RESISTANCE (R)
a
The air offers a resistance to the movement of a vehicle and can
have an influence on the performance, ride and stability of the
vehicle. So far as performance is concerned, the air force is found
to depend upon several factors including the shape, size and sur
face of the frontal part of the vehicle, and its speed relative to the
air. The air resistance is given in the form
R = C .A.vn (1.2)
a D
where C is a drag coefficient, A the projected frontal area, v the
D
relative velocity through the air, and n some index, n is normally
taken as 2, C can vary over a wide range, but for a given vehicle
D
the air resistance can be expressed in the form,
R = k.v* (1.3)
a
acting in a direction opposing the car relative velocity.
(b) ROLLING RESISTANCE (R)
r
This arises from the interaction of the tyres and the road surface
and in the case of cars operating on hard surfaces, the interaction
manifests itself primarily in the deformation of the tyres. The
deformation and recovery of shape is not completely elastic and as
a result energy is released. In addition, the relative drag between
the tyre and the road causes wear of the tyre tread. The energy
dissipated as heat etc. from these causes, together with other
losses such as bearing friction, can be represented as the work done
against a resistance to rolling.
The value of the rolling resistance depends upon several factors
such as, vehicle speed, tyre inflation pressure, vertical load on the
4 MECHANICS OF AUTOMOBILES
tyre, tyre diameter, road surface, and there are many others par­
ticularly concerned with the tyre construction. Prediction of
rolling resistance is still uncertain, particularly in view of the
experimental difficulties in its measurement, but there seems to be
general acceptance that
R= W(a + b.vn) (1.4)
r
The index, n, is assigned values between 1 and 3 but n = 1 is
common, and the values of a and b, can vary considerably, having,
if v is in m.p.h., mean values of a = 0-015, b = 0-0001.
(c) GRADIENT (R)
g
If a vehicle moving along a level road at constant speed, under
the action of a fixed engine output, starts to climb a gradient,
FIG. 1.1. Resistance due to gradient
energy is required to provide for the change^in potential energy.
The effect is the same as though the vehicle were acted on by a
resistance to its motion. The value of the resistance is given by
R = W .sin(9 (1.5)
g
as shown in Fig. 1.1.
Provided 0 is small, as in most practical gradients, then if the
gradient is specified as 1 in x, then
W
Rg = — (approximately). (1.6)
VEHICLE PERFORMANCE: LINEAR INERTIA 5
WORKED EXAMPLE (A.M.I.Mech.E., 1950)
1.2. For a typical motor car the rolling resistance is given by
the expression 35 + 0-25 V and the air resistance by the expression
0-048 V2, the resistance being in lb and V, the speed in m.p.h. in
each case. If the transmission efficiency is 88%, calculate the
b.h.p. required for a top speed of 90 m.p.h. Assuming that the
engine torque at 30 m.p.h. in top gear is 25% more than at
90 m.p.h. and that the vehicle inertia corresponds to a weight of
4500 lb, calculate the acceleration in ft/sec2 at 30 m.p.h.
Solution
For a speed of 90 m.p.h., the total resistance
= 35 + 0-25 x 90 + 0-048 X 902 lb = 35 + 22-5 + 389 lb
= 446-5 lb.
Rate of working against this resistance = resistance x velocity
44
= 446-5 x 90 x — ft lb/sec.
30 '
Therefore horsepower
90 x 44
= ^6*5 X ™ 77Z = 107 h-P-
30 X 550 v
Hence engine b.h.p. = 107 x —- = 122 h.p.
Tractive effort at 30 m.p.h. = 446-5 x 1-25 = 557 lb.
Resistance at 30 m.p.h. = 35 + 0-25 x 30 + 0-048 x 900
= 85-7 lb.
Resultant force (available for acceleration)
= 557 - 85-7
= 471-3 lb
32-3 -
/= 3-38 ft/sec2
6 MECHANICS OF AUTOMOBILES
WORKED EXAMPLE (U.L.I Ext. 1954)
1.3. A car weighing 3000 lb has when running on the level a
resistance to motion of a + bV^lb, where a is 60 lb, è is a con­
stant and V the speed in m.p.h. It is also found that the car main­
tains a speed of 80 m.p.h. with an effective horsepower of 50
when running on the level. Find
(i) the value of b,
(ii) how far the car will run up a slope o f1 in 10 before the
speed drops to 40 m.p.h. assuming it starts a t80 m.p.h. and that a
constant torque is maintained.
Solution
(i) Resistance at V m.p.h. = 60 + bJ^lb.
Horsepower on level road = rate of work in ft-lb/sec/550
= (60 * . 8 0 ' ) κ ( ^ = 5 0.
+
lb ft/sec
60 + 64006 = 234,
b = -^ = 0-0272
6400
(ii) When the car ascends the slope, its speed drops and so the
motion will not be at constant retardation as the resistances will
vary.
Resistance to motion = (60 + 0-0272 K2) if V is in m.p.h.
= (60 + 0-0272 X (52)',»)
lb if v in ft/sec
= 60 + 0-01265t;2 lb.
The car is slowing down hence the inertia force helps the
tractive effort,
3000 3000
234 + — /= 60 + <M>1265*» + —