NBSIR 75-786

The CPSC Road Test of

Bicycle Braking Performance —

Kinetic and Error Analyses

Leonard Mordfin

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

October 1 975

Final Report

Prepared for Office of Consumer Product Safety

Center for Consumer Product Technology

institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

NBSIR 75-786

THE CPSC ROAD TEST OF

BICYCLE BRAKING PERFORMANCE - KINETIC AND ERROR ANALYSES

Leonard Mordfin

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

October 1 975

Final Report

Prepared for Office of Consumer Product Safety

Center for Consumer Product Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

CONTENTS

page

1. INTRODUCTION 1

2. SCOPE AND TERMINOLOGY 3

2.1 The Typical Bicycle 3

2.2 Brake Characteristics 3

2.3 Braking Performance 4

3. KINETIC ANALYSIS 5

4. ERROR ANALYSIS: PRELIMINARY REMARKS 10

5. MEASURING THE STOPPING DISTANCE 11,

5.1 Defining the Starting Point 12

5.2 Locating the Starting Point 13

5.3 Straightness of the Bicycle Path 14

6. REACTION TIME 15

7. MEASUREMENT AND CONTROL OF INITIAL SPEED 17

7.1 Measurement 17

7.2 Control 19

8. EFFECTS OF PAVEMENT SURFACE 20

9. UNCERTAINTIES IN THE APPLIED LEVER FORCES 22

9.1 Kinetic Analysis 22

9.2 Error Analysis 23

10. MASS (WEIGHT) EFFECTS 24

10.1 Locating the Center of Gravity 24

10.2 Effect of Rider Mass on Maximum Deceleration 26'

10.3 Effect of Rider 'Mass on Stopping Distance 27

10.4 Instrumentation Mass 28

10.5 Pitchover 29
CONTENTS (con't) page

11. EFFECT OF INCLINED ROAbWAY 30

12. WIND EFFECTS 30

13. ERROR ANALYSIS: INTERPRETATIONS AND IMPLICATIONS 33

13.1 Summary of Individual Error Analyses 33

13.2 The Measurement System: An Example 35

13.3 Linear Accumulation of Errors 36

13.4 Significance of Random and Systematic Errors 37

13.5 Test-to-Test Variability 37

13.6 Lab-to-Lab Variability 38

13.7 Reducing the Effects of Test-to-Test Variability 40

14. DISCUSSION 'f. 41

14.1 Brake Sensitivities 41

14.2 Optimum Tire/Pavement Friction Coefficients 42

14.3 Other Kinds of Bicycles 43

14.4 Other Test Parameters 43

14.5 Improved Testing Techniques 43

15. CONCLUSIONS 44

16. REFERENCES 46

APPENDIX - List of Symbols 49

TABLES 53

FIGURES 56

ADDENDUM - Error Analyses of Three Specific Systems 66
THE CPSC ROAD TEST OF BICYCLE BRAKING PERFORMNCE

--KINETIC AND ERROR ANALYSES

Leonard Mordfin

ABSTRACT

The Consumer Product Safety Conmission has

promulgated a safety standard for bicycle braking

systems based on the stopping distances achieved

in road tests under specified conditions. This re- port presents an error analysis of the test method,

for the Commission's use in justifying or modifying

the test criteria. The error analysis is based on experimental data, for the most part, and on theoretical

principles where sufficient data are lacking. The

theory, a kinetic analysis of the bicycle braking

process, is included in the report together with

proposed definitions of terms intended to quantify

important aspects of bicycle braking performance.

The error analysis produced estimates of rather

large lab-to-lab and test-to-test variabilities

to be expected from the test method. These, in turn, were found to be principally dominated by errors resulting from an incorrect overweight-rider allowance

specified by the Commission, and by variations in

rider reaction times, respectively. Suggestions

are made for more accurate methods of accommodating

variations in rider mass, for reducing the effects

of the test-to-test variability, and for reducing

the danger of pitchover in the performance of the

road test.

Key Words: Bicycle brakes; brakes, bicycle; dynamics,

bicycle; error analysis; friction, tire/pavement;

kinetics, bicycle; measurements, bicycle braking;

pitchover; standards, bicycle safety; test method,

bicycle.

INTRODUCTION

In July 1974, the Consumer Product Safety Commission (CPSC) promulgated

a regulation that established safety requirements for bicycles [ij. This

regulation, together with a subsequent amendment [2j (which will hereinafter

be referred to as the Bicycle Safety Regulation) includes a requirement

for braking performance tests to be carried out on bicycles equipped
with handbrakes.* While the test criteria vary somewhat depending upon

a bicycle's gear ratio, the size of the rider, etc., the basic test calls

for the bicycle, with a 68.1-kg (150-lb) rider, to be stopped from a speed of 24 km/h (15 mph) within a distance of 4.57 m (15 ft), with forces

of not more than 178 N (40 Ibf) applied to the handbrake levers.

Several bicycle manufacturers have objected to this requirement

(see, for example, [3, 4]). The manufacturers claim that errors. inherent

in the test procedure lead to a large spread, or variability, in the

test results, even under closely controlled, nominally identical, test

conditions. In order to insure that a bicycle will pass the road test,

they state, its braking system would have to be overdesigned and this,

it is contended, increases the bicycle's susceptibility to accidents

resulting from pitchover. The manfacturers cite a similar test method

which is under development by a working group of the International Organization for Standardization (ISO) which, in view of the observed variability of test results, specifies a less-stringent stopping-distance

requirement (5.5 m, 18 ft).

This report presents the results of a study which was devoted, primarily, to an analysis of the errors that are encountered in conducting

the braking performance test. It is thought that, with definitive information of this kind, certain allowances in the test criteria could be stipulated

which would resolve the differences between the Commission and the manufacturers. In carrying out the error analysis it was found that while the

effects of certain test parameters could be examined through the use

of available experimental data, the effects of others could only be assessed

theoretically. Therefore, a two-dimensional kinetic analysis of the braking

process was developed so that all of the relevant test parameters could

be examined critically. The kinetic analysis also enabled the pitchover

problem to be addressed briefly.

Since, clearly, all bicycles and all braking systems could not be

studied, some generalizations regarding bicycle characteristics and braking

performance are set forth at first. These, together with subsequent results,

effectively delineate the boundaries of applicability of the error analysis.

This study was carried out in the Engineering Mechanics Section

of the National Bureau of Standards (NBS) for the NBS Office of Consumer

Product Safety.

*For bicycles equipped with other types of brakes see Section 14.3.
2. SCOPE AND TERMINOLOGY

The symbols used in this report are defined in the Appendix. In

addition, each symbol is defined where it is first used, either in the

text or by reference to an associated figure.

2.1 The Typical Bicycle

There are a great many different types, styles and sizes of bicycles

on the market today. It would be a virtually impossible task to analyze

each one. Therefore, most of the calculations carried out in this study

were limited to what will hereafter be referred to as "the typical bicycle".

The characteristics of this bicycle, which are given in Table 1, represent

approximate averages of the characteristics of fifty-two different, real

bicycles. (The basis upon which the coordinates of the center of gravity

(eg) were selected is given later in Section 10.1).

The rationale for using the typical bicycle in most calculations

is quite obvious. As mentioned above, the error analysis may be used

to establish allowances in the test criteria. These allowances, if based

on the typical bicycle, will, strictly speaking, be correct only for

bicycles which are similar to the typical bicycle. For other bicycles

they can be too large or too small. For bicycles which have characteristics

which enable them to stop more easily than the typical bicycle (e.g.,

less mass, lower eg) the allowances will be larger than necessary. This

is not a serious problem since these bicycles, being easier to stop, are not the ones which the test method is intended to identify. On the

other hand, the allowances would be too small for bicycles which are more difficult to stop than the typical bicycle. This would, of course,

make it more difficult for these bicycles to pass the performance test

and thereby help to identify them.

2.2 Brake Characteristics

If a force P is applied to a handbrake lever at a specified point

and in a specified direction, the brake pads are thereby caused to exert

a squeezing force Q on the wheel rim. Let

Q = mP

where m is the mechanical advantage, which depends primarily on the lever

ratios of the handbrake lever and the caliper brake assembly. If the

wheel is rotating, the squeezing force Q produces a tangential force

F, on the wheel rim which tends to retard the rotation. Thus,

b

'

F^ = vQ

3
where v is the coefficient of friction between the brake pads and the

wheel rim. From these two expressions it is seen that

F^ = vmP.

In a real brake system vm is not constant because of friction and play

in the brake linkage, accumulation of foreign matter on the brake pads

and wheel rim, and so on. Nevertheless, the quantity

is a meaningful parameter which describes the brake sensitivity . In this

context, a sensitive brake system is one which exerts a strong retarding

force to a rotating wheel when a given force is applied to the handbrake

lever.

Further discussion of brake sensitivity is given in Section 14.1,

2.3 Braking Performance

While brake characteristics and bicycle characteristics can be discussed

separately, as above, the effectiveness of a given brake system depends

upon the characteristics of the bicycle it is intended to serve. In other

words, a given brake system which may be adequate for one bicycle may

be entirely inadequate for another. This leads to the concept of braking

capability , B, which is intended to provide a measure of the effectiveness

of a given brake system on a given bicycle.

In order to quantify braking capability it is helpful to have some standard of braking performance against which it may be compared. Such

a standard is provided by the CPSC braking performance test. Let marginal

braking capability , B = 1, be defined as that level of braking perforroance

which enables a bicycle to satisfy the CPSC braking performance test

with nothing to spare. Stated more precisely,

A bicycle's brake system exhibits marginal braking

capability when an average 68.1-kg (150-lb) test

rider brings it to a stop on a specified pavement,

from a speed of 24 km/h (15 mph), in a distance of

exactly 4.57 m (15.0 ft), by applying 178 N (40 Ibf)

to the handbrake levers.

(The characteristics of an "average" test rider and the "specified" pavement

will be developed later.) If the brake system which exhibits marginal

4
braking capability has a brake sensitivity Z^, then the braking capability

of any other brake system on the same bicycle is, siniply.

B = |- (2) o

where Z is the brake sensitivity of the other brake system.

3. KINETIC ANALYSIS

The equations of motion of a bicycle/rider system can, in principle,

be derived from a consideration of only the external forces acting on

the system. These external forces consist of the reactions at the tire/pavement interfaces and wind resistance. This approach is inadequate for

present purposes, however, since it provides no direct understanding

of the role played by the braking forces themselves, i.e., the retarding

forces applied by the brake pads. Therefore, in order to obtain such

understanding, the system is examined in three parts: the rear wheel,

the front wheel, and the bicycle frame-plus-rider combination. For simplicity,

wind resistance, which has a second-order effect on bicycle braking,

is ignored at first and then analyzed as a perturbation of the principal

system later on (Section 12).

Free-body diagrams of the rear wheel, the front wheel and the frame/rider

combination are given in Figures 1, 2 and 3, respectively. In Figures

1 and 2 the small difference between the outer radius of the tire, and

the radius of the wheel rim at which the brake pads make contact, has

been ignored for simplicity. Rolling friction in the wheel bearings has

been neglected. In Figure 3 the rider is not shown, for convenience in

drawing, but the force of gravity which acts upon him is included in

the total force of gravity acting at the center of gravity of the frame/rider

combination.

Using D'Alembert's principle, the three equations of equilibrium

for the rear wheel, in the vertical, horizontal and rotational directions,

respectively, are

R + F^ sin 6 - F - W = 0, (3)

r br r yr w

W

f + F^ cos e - F - a = 0, ' (4)

r br r xr g

W

f - F, + — a = 0, (5A)

r br g

5
where, in the third equation, it has been assumed that the wheel rolls

without slipping on the pavement and that the mass of the wheel is concentrated

at its outer periphery. That is,

2a

" =5"

and

2 W D

I =

^

4g

•

In general, the wheel may be expected to rotate without slipping on the

pavement if

, f

where y is the coefficient of friction at the tire/pavement interface,

If the wheel is locked, and skids without rotating, then

a = 0

and

so Equation (5A) becomes

f = yR

r r

f = yR = F, . (5B) r r br

(Note that the value of u which determines whether or not a rotating

wheel will lock and skid is the coefficient of static friction, while

the value which detemlines the retarding force on a locked, skidding

wheel is the coefficient of sliding friction. The difference between

these two values has been ignored as representing a refinement in the

analysis which is not warranted for present purposes.)

Following the same procedure, the equations for the front wheel are

R - F, ^ sin 0. - F ^ - W = 0, (6)

r bf f yf w

6
w

f . + F, ^ COS 0 - F ^ - — a = 0, (7)

f bf f xf g

'

W

when the v^eel rolls without slipping. If the wheel is locked, and skids

without rotating, then Equation (8A) becomes = yR^ = F^^. (8B)

Using D'Alembert's principle again, the equations of equilibrium for

the rider-frame combination are

F + F ^ - F, sin e + F, ^ sin 9 . - (W^ + W ) = 0, (9)

yr yf br r bf f f r

F + F ^

- F, cos e + F, ^ cos 9 - ^ a = 0, (10) xr xf br r bf f g

'

yr

(L - q) - Fyfq + (F^r ^xf ^r [f " ^ """^ 3^ - (L - q) sin

gJ

+F^^ [j

- h cos 6

J

- q sin e J= 0. (11)

The eg location of the bicycle/rider system (Jl,H) is slightly different

from that of the frame/rider combination (q,h) because of the mass of

the bicycle wheels. It is easily shown that

h =

W, + W

b - (H - t) (12) + W ' 2 f r

and

(W^ + W )«, - W L

f r

where I is the distance of the eg of the bicycle/rider system aft of

the front wheel axis, H is the height of the eg of the bicycle/rider

system above the pavement, and

W, = + 2W . b f w

Increasing the deceleration causes the vertical reaction force at the rear wheel, R^, to diminish. The condition R^ = 0 represents the thres7
hold of the instability condition which is commonly referred to as "pitchover".

The general solution of Equations (3) through (11) is

f + f.

a r f

(^^^

and

g W, + W

b r

f b r r Specific solutions for the several cases of rolling and/or locked wheels

follow. The substitutions represented by Equations (12) and (13) have

been made so that the solutions are given in terms of the eg location

of the bicycle/rider system.

Case I . With gentle-to-moderate braking on pavements which offer moderate

to-high coefficients of friction, both wheels of the bicycle roll without

slipping. Under this condition

F + F

a _ "^br bf (15)

g W, + W + 2W

b r w

= ^bf - "w t «f ' ^'*£>'

and

R = (w + w )~ - [(W^ + W )7+ W 7]- . (18)

r b rL'-b rL wL-'g

If F^^ = F^ (that is, if the brake sensitivities of the front and rear brakes are the same and if equal forces are applied to both handbrake

levers) then this condition exists as long as A

0<^< ^1 (19)

2^ ^tl"" 2 + W ^ or

Pitchover will not occur while both wheels roll without slipping.

8
Case II . There is a range of decelerations in which the front wheel

rolls without slipping while the rear wheel rolls and slips simultaneously.

If F, = F, - this range is

br br

h < a, L

W e W

1 , ur" I ^ ^ n I 1 I I ^

2 "^t^ 2 irnr + 2 + + w + w v

b r b r

This range is quite narrow and need not be considered further.

Case III . With moderate-to-hard braking on pavements which offer moderateto-high coefficients of friction, the front wheel rolls without slipping

while the rear wheel skids without rolling. Under this condition

I

F, ^ +V<W, + W ) -

a bf b r L , (20)

^ + W + W + y[(W^ + W ) 7^ + ^ W 7] b r w "-b rL2wL-'

(W^ + W ) - UW R

^ bf b r w r /^-^-^n

ff =

+ W +W (f. <VR„), (21)

b r w

and

R = .(W, + W ) ^ - [(W, + W ) 7 + ~ W ^] . (22)

r b rL '-b rL 2wL-'g

This condition exists as long as

a ^ 1-1 y (23) W e

2 W, + W

b r

and

- < h • ^24)

^ H 1^ w D

L 2 W^. + W L

b r

If the deceleration exceeds the latter condition (24) pitchover will occur.

9
Case IV . On pavements offering low coefficients of friction, or with

hard braking on pavements which offer moderate coefficients of friction,

both wheels of the bicycle skid without rolling. Under this condition

(25)

and

H a L g

(26)

This condition exists as long as

a

g

< IH* (27)

If the deceleration exceeds the latter condition pitchover will occur.

With sufficient braking capability, Equation (25) represents the

maximum possible deceleration which bicycle/rider systems can attain

on a given pavement, and Equation (27) represents the maximum possible

deceleration which a given bicycle/rider system can attain on any pavement.

There are many parameters which influence the results of the CPSC

brake performance test. Some of these parameters such as, for example,

the rider's reaction time*, are relatively uncontrollable and the stopping

distances, in any series of tests, will reflect this. Other parameters,

such as the tire/pavement friction coefficient, are reasonably controllable

but, since different test courses offer different coefficients, different

stopping distances will be obtained even with the same bicycle/rider

system. Thus, all of the pertinent parameters are seen to contribute

to a variability of test results. But, without further information, no single test result can be described as being more correct than any other

and, therefore, it is meaningless to speak of the error in any given

test result.

However, if a predetermined set of parametric values were postulated

as being the "correct" values, then the stopping distance obtained with

these parametric values and a given bicycle could be denoted as the true

"Reaction time is defined later as the interval between the instant

at which the rider first begins actuating the handbrake levers and the

instant at which the prescribed force levels are reached.

4. ERROR ANALYSIS: PRELIMINARY REMARKS

10
or correct stopping distance for this bicycle. In this vein, the variations

in stopping distance, which arise from variations of the pertinent parameters,

can properly be termed "errors" if they are expressed as deviations from

the correct stopping distance.

These errors, like those encountered in most measurement processes,

fall into two categories. A systematic (or bias) error is one that is

characteristic of the measurement system which, in this case, includes

the instrumentation, the test course and the wind as well as the bicycle/rider

system. If a series of tests were conducted with a given system the systematic

errors would not change from test to test and, in principle at least,

the magnitudes of these errors can be determined.

A random error, on the other hand, is typified by a test-to-test

variability and cannot be estimated, except within broad limits, prior

to any given test. The average random error experienced in a number of

tests, however, tends toward zero as the number of tests increases.

In the absence of adequate data from a well-planned test program

it is often difficult to determine whether a given error is systematic

or random, or whether it contains components of both. In such cases this

determination, if it is to be made at all, must sometimes be based on little more than an educated guess. 'I'ithin this context, the various

errors involved in the performance of the road test are analyzed in the

following eight sections of this report.

Each section is devoted to the errors which arise from the variability

of a single parameter or a set of related parameters. T'Thile the order

in which the parameters are treated may appear to be haphazard, this

is not entirely the case. The effects of several of the parameters were

found to be dependent on others, and so the order is that which enabled

each analysis to build upon the findings of prior ones. As it turned

out, the first few error analyses are based primarily on available ex- perimental data while the later ones rely chiefly on the kinetic analysis

presented in the previous section.

5. 1-EASURING THE STOPPING DISTANCE

"A bicycle equipped with only handbrakes shall...

have a stopping distance of no greater than 4,57

m (15 ft)...

"The bicycle shall be ridden over a ...test course

and, after attaining the specified ground speed,

shall be stopped by the rider... The stopping distance shall be measured" [Bicycle Safety Regulation].

The state-of-the-art in length measurements is more than adequate

for the needs of the braking performance test. The uncertainties involved

11
in measuring the length of a straight line segment between two points

are very small and need not be considered further. However, problems

arise because the starting point is not rigorously defined and because

the path over which the bicycle travels, in coming to a stop, may not

be straight.

5.1 Defining the Starting Point

The brakes are applied, by the rider, through the use of the handbrake levers. What instant in the process of brake application corresponds

to the starting point for the measurement of stopping distance? Is

it the instant at which the actuation of the brake lever begins? Is

it the instant at which the brake pads contact the wheel rim? Or is

it the instant at which the force applied to the brake lever reaches

its maximum or prescribed magnitude?

If the starting point is defined as the instant at which the force

applied to the lever reaches its maximum or prescribed magnitude then

some braking will be achieved before this instant and a gradual application of force could result in the measurement of very short stopping

distances, even with inefficient braking systems. This would defeat

the purpose of the test.

If the starting point is defined as the instant at which the brake

pads contact the rim then the distance traveled by the bicycle while

the slack in the brake system is being overcome is not included in

the stopping distance. Yet this is an important consideration in the

safety of the braking system in the sense that a large amount of slack

degrades a rider's ability to stop quickly in an emergency situation.

On the basis of this reasoning it is postulated that the starting

point, for the measurement of stopping distance, is the point corresponding

to the instant of brake lever actuation. But which brake, the front or the rear? In a hard stop, with both brakes actuated, there is a substantial dynamic mass transfer of the center of gravity of the bicycle/rider system toward the front of the bicycle. This generally

results in skidding of the rear wheel and most of the braking action

is achieved through the front wheel brake. Recognizing this, the ISO

has taken the position that the road test should be declared invalid

if the front brake is not applied first [5,6j. However, this approach

appears to compromise the usefulness of the test; in an emergency situation in which a rider is seeking maximum braking he can hardly be expected

to exercise that degree of mental control which would be required to

consciously apply the front brake first. This analysis is, therefore,

based on the postulate that the starting point for the measurement

(pf stopping distance is that point corresponding to the location of

the bicycle at the instant that the first brake lever actuation begins .

12
This is consistent with the method used for evaluating the braking

performance of motorcycles [7].

5.2 Locating the Starting Point

Having defined the starting point, it remains to locate it. Two

methods have been used rather widely. In the first method a starting

line is painted on the pavement and the rider is required to actuate

the brakes as the front wheel of the bicycle crosses the line. Tests

conducted by one manufacturer at a nominal bicycle speed of 24 km/h

(15 mph) have shown that, in general, the rider is able to commence brake

actuation within +0.3 m (+1 ft) of the line. The average of six "good" runs fell only 0.02 m (0.07 ft) before the line [Sj. Tests by a second

manufacturer at the same nominal speed showed a spread of +0.6 m (+2 ft)

with the average of twenty runs falling 0.05 m (0.2 ft) oast the line

[9J.

These data suggest that the stopping distance measured by this

method in any given test may be in error by up to +0.6 m (+2 ft), while

the average stopping distance measured in a large number of tests may

be in error by only +0.05 m (+0.2 ft). These errors are principally

random, although they may contain a systematic component reflecting

a subconscious bias on the part of the rider.

In the second method, which is more widely used at the present

time, actuation of the brake lever operates a device which propels

a marker to the pavement. A variety of techniques of this kind have

been used, including:

(a) a spring-loaded metal rod treated with a marking substance is

released by a spring-loaded trigger pin upon actuation of the brake

lever [lOj;

(b) a chalk pellet is propelled by a fuze that is electrically energized

through a switch which operates upon actuation of the brake lever [llj;

(c) a chalk cartridge is propelled by an explosively fired gun upon

actuation of the brake lever [l2j;

(d) an electromagnetically activated paint gun is disengaged by a trip switch upon actuation of the brake lever [8,13 J;

(e) a charge of colored paste is fired with a pneumatic marker gun

upon actuation of the brake lever, which opens a pneumatic valve to

a reservoir of compressed air [9j.

Clearly, some error is involved in the use of this method because (1)

there is some delay, due to electrical or mechanical causes, between

the instant of actuation of the brake lever and the instant of firing

13
and (2) the bicycle -- and the marker -- travel forward at the test

speed during the interval between firing of the marker and its impact

on the pavement. The latter part of the error may be rendered negligible

by assuring that the marker is propelled vertically, at high velocity,

from a point close to the pavement. The delay between lever actuation

and actual firing may not be negligible. For the chalk gun (item (c)

above), limited data [14] indicate that the delay is approximately

0.025 seconds which, at a bicycle speed of 24 km/h (15 mph), is equivalent to a forward distance of approximately 0.17 m (0.6 ft). Data for

the paint gun (item (d) above) suggest that the forward distance could

be reduced to approximately 0.1 m (0.3 ft) with suitably powered electro

magnets [8j.

It would appear that the error involved in all of these techniques

is a systematic one which, with good equipment, should be very repeatabl

From the above data it is estimated that, in general, this error may

be up to -0.2 m (-0.7 ft). (The minus sign indicates that the measured

stopping distance is less than the correct stopping distance.

)

When the marker strikes the pavement it leaves a spot, rather

than a point. This introduces a further uncertainty in the measurement

of stopping distance, which is estimated to be approximately +0.02

m (+0.07 ft). This uncertainty comprises a random error.

5.3 Straightness of the Bicycle Path

When the bicycle brakes are applied in the road test, the rear wheels generally lock and commence to skid on the pavement. In this

situation the rear wheels lose stability and, if the bicycle is not

moving on a straight path, a certain amount of lateral breakaway, or side skid, may occur [l5j. In correcting for this, either consciously

or subconsciously, the rider causes the bicycle to track a crooked

path in coming to a stop. The energy dissipated in the brakes and at

the tire/pavement interfaces depends upon the actual distance traveled,

yet the stopping distance is invariably measured over a straight line

between the starting line or starting point and the end point. Thus,

insofar as the bicycle does not track a straight path, the measurement

of the stopping distance is in error. This problem has resulted in

recommendations that road tests be invalidated when excessive side

skid or loss of control occurs [5,12j. But how much is excessive?

A few exploratory tests were carried out at NBS in which a pressurized container of liquid was used to mark the trail of a bicycle

as it was brought to a stop under the prescribed test conditions. It was found that the path is similar to a sinusoid having between two

and three cycles. In some cases the double anplitude of the sinusoid

was nearly 0.3 m (1 ft) although, in general, it was less than half

of this. Considering a net (straight-line) stopping distance of 4.57

m (15.0 ft), it may be calculated that in the worst case (3 cycles,

0.3-m double amplitude) the measured stopping distance is in error

14
by -0.37 m (-1.2 ft). In the more general case (2 cycles, 0.15-m double

amplitude) the error is only a tenth of this. It would seem appropriate,

therefore, to require that the bicycle be moving in a straight line

when the brakes are applied in the road test, in order to minimize

the side skid. This could be accomplished by painting straight lines,

say 0.3 m (1 ft) apart, along the length of the test pavement, as guides

for the rider.

These errors are primarily of a random nature.

6. REACTION TIME

Most laboratories which have carried out the road test under controlled

conditions have used preset lever stops to assure that the maximxom force

applied to the handbrake lever, by the rider, does not exceed the prescribed

value. A finite interval of time passes between the instant that the

rider first begins to actuate the lever and the instant that the applied

force reaches the maximum or prescribed value. Measurements of this

interval have been made by at least three investigators. NBS data, obtained with a variety of bicycles and riders, indicate that the interval

is approximately 0.11 (+0.22, -0.08) seconds [13]. Measurements by a manufacturer suggest that the interval is much shorter than this [S].

However, examination of the test method used by this manufacturer reveals

that, in reality, only a portion of the interval was measured, namely,

that portion during which the brake pads were moved into contact with

the wheel rim. Data obtained by another manufacturer suggest that the

interval is considerably longer than that indicated by the NBS results

[9]. These data must also be considered suspect because they in5)ly that, on the average, the applied force does not reach the maximum value until

the bicycle has traveled at least 3.7 m (12 ft).

An additional delay in achieving full braking action results from

the fact that, in general, the two handbrake levers are not applied

simultaneously. NBS measurements, made with a variety of bicycles, indicate that the departure from perfect synchronization is approximately

0.04 (+0.05, -0.04) seconds, taking no heed of whether the front brake

or the rear brake is applied first [13]. Measurements by a manufacturer,

using a variety of riders, essentially confirm this approximation [9].

Data from another manufacturer imply that the departure from synchronization

is only about half this long [l2j.

If the NBS results given in the two preceding paragraphs are combined

it is seen that there is a total delay of 0,15 (+0.27, -0.12) seconds

between the instant that the rider begins actuation of the first brake

lever and the instant at which full braking action is achieved. For

want of a better name this total delay will be called the "reaction

time".

15
These results indicate that if a variety of riders test a variety

of bicycles their average reaction time is 0.15 seconds. But if two

randomly selected riders test randomly selected bicycles their reaction

times may differ by as much as 0.39 seconds. The question that must

be answered is, "What is the error introduced due to the reaction time

of a given rider on a given bicycle?". This question cannot be answered

because the "correct" reaction time is undefined. However, the question

can be posed in a different way, i.e., "What reaction time properly

characterizes the capabilities of a bicycle's braking system?" Considering

the purpose of the road test it appears reasonable to use the average

reaction time. Therefore, it is postulated that the correct measure

of a bicycle's braking capabilities is achieved with a reaction time

of 0.15 seconds .

During the interval represented by the reaction time the deceleration

of the bicycle rises from zero to its maximum value. For the purpose

of this analysis it will be approximated that the deceleration rises

linearly with time. It is further assumed that the level of deceleration

achieved at the end of the interval is thereafter maintained constant

until the bicycle comes to a stop. With these assumptions it may be

shown that the stopping distance is given by

(28)

where s is the stopping distance, v is the initial speed, a is the

maximum deceleration, and t^ is the reaction time. In order for the

bicycle to stop in 4.57 m (15.0 ft) from an initial speed of 24 km/h

(15 mph), with a reaction time of 0.15 seconds, the maximum deceleration

must be not less than 5.52 m/s^ (18.1 ft/s^ ) or 0.563 g. (This, of course,

exceeds the average deceleration rate of 0.5 g which ignores the existence

of a reaction time.)

Consider, now, a bicycle with marginal braking capability (B = 1)

.

This is one which stops in exactly 4.57 m (15.0 ft) with a reaction

time of 0.15 seconds. In other words, it has braking capability that

provides a maximum deceleration of exactly 0.563 g under the specified

test conditions. In a given test of this bicycle the rider's reaction

time, as stated above, will be 0.15 (+0.27, -0.12) seconds, or anywhere

from 0.03 seconds to 0.42 seconds. Using the above equation it may be

shown that this range of reaction times corresponds to stopping distances

ranging from 4.18 m (13.7 ft) to 5.46 m (17.9 ft). Thus, the error band

in the observed stopping distance is -0.39, +0.89 m (-1.3, +2.9 ft),

where the minus and plus signs indicate that the observed stopping distance is less or more, respectively, than the stopping distance which

characterizes the bicycle's true braking capabilities. The total variation

of stopping distances due to reaction time is 1.28 m (4,2 ft), which

is less than that estimated by ISO (1.65 m, 5.5 ft) [5j.

16
7. MEASUREMENT AND CONTROL OF INITIAL SPEED

"Bicycles with an equivalent ground speed in excess

of 24 km/hr (15 mph) (in its highest gear ratio

at a pedal crank rate of 60 revolutions per minute)

shall stop from an actual test speed of 24 km/hr

(15 mph) or greater within a distance of 4,57 m

(15 ft)..." [Bicycle Safety Regulation].

7 . 1 Mea surement

The accuracy with which the ground speed of the bicycle can be

measured, at the start of the road test, has a significant influence

on the results of the test since, as shown in Equation (28), the stopping distance is very nearly proportional to the square of the initial

speed. In effect, the percentage error in the measured stopping distance

is twice the percentage error in the measured speed.

Two basic techniques, with several variations, have been used for

measuring the initial speed. Perhaps the most straightforward approach

involves the use of a speedometer on the test bicycle. Most commercially

available bicycle speedometers are relatively inaccurate, however, and

laboratories which use them generally calibrate them beforehand [lO,15j.

While it has been claimed that calibrated speedometers have an accuracy

of only +5 percent [5], there does not appear to be any reason why a proper calibration perforaed at the desired speed (24 km/h, 15 mph)

should not be capable of providing +1 percent accuracy.

A similar approach involves the use of a laboratory tachometer.

Precision tachometers are available with rated accuracies substantially

better than +1 percent [l6j, and these have been used to assemble accurate

speedometers for bicycle-testing purposes [Sj.

The difficulty with the speedometer technique is that calibration

must be repeated for each size of bicycle wheel [9j. Furthermore, the

rider is so preoccupied with other matters that he cannot be expected

to read the speed carefully an instant before he applies the brakes.

This factor is estimated to degrade the accuracy of this speed-measuring

technique to no better than about +3 percent [3 J.

In order to reduce the reading errors, and to avoid the need for

recal ibration with each size of bicycle wheel, several manufacturers

have experimented with pacer bicycles [9, 12, 17 J. In this approach, which

was at one time specified by ISO [l8], the rider of the test bicycle

follows a second (pacer) bicycle which is equipped with a calibrated

speedometer. The rider of the pacer bicycle, being unconcerned with

braking, can concentrate on reading the speedometer carefully. The rider

of the test bicycle need only keep pace with the pacer bicycle until

he applies the brakes. However, inasmuch as the speed of the test bicycle

17
may differ from that of the pacer bicycle, it is unlikely that speed

measurements with accuracies better than +3 percent can thereby be attained consistently [9].

An error of +3 percent in speed measurement produces an error of

approximately +6 percent in the measured stopping distance, or +0,27

m (+0.9 ft) over a 4.57-m (15.0-ft) course. This error will be considered

random since it consists, primarily, of inaccuracies in reading the

speedometer rather than inaccuracies in calibrating it.

In an effort to achieve better accuracy several testing groups

have used electronic timing traps. In the common version of this technique two tape switches are set out on the pavement, perpendicular to

the bicycle path and at a known distance apart [9,11,12,19], The bicycle

wheels operate the switches as the bicycle passes over them and the

interval between switch operations is measured electronically. The speed

is calculated from the time interval and the distance between the switches,

A variation of this technique uses a single tape switch which is operated,

in succession, by the two bicycle wheels as they pass over it [l3j.

In this case the required length measurement is of the bicycle wheel

base rather than the distance between tape switches. The advantage of

this approach is that it does not require that the tape switch be perfectly normal to the bicycle path.

Regardless of whether one tape switch or two are used, the accuracy

of the speed measurement depends on the accuracies of the length and

time measurements. On this basis it has been asserted that the error

in speed measurement is less than +1 percent [3,9,121 and this assettion

appears to be justifiable, ISO claims of +2 percent [5,6] notwithstanding.

This +1 percent error in speed measurement corresponds to a random error

of +0.09 m (+0.3 ft) in stopping distance.

While the electronic timing trap does provide an accurate measurement of the average bicycle speed while it traverses the trap it does

not, in fact, measure the speed at the instant of brake actuation. Usually,

the rider allows the bicycle to travel a short distance beyond the trap

before actuating the brakes in order to avoid the possibility of braking

before emerging from the trap. In traveling this short distance the

bicycle experiences a reduction in speed due to wind resistance and

to rolling friction in the wheel bearings and at the tire/pavement interfaces. To reduce the effects of this speed reduction ISO has recommended

that a test be declared invalid if the distance between the last timing

strip and the center of the rear wheel at the commencement of braking

exceeds 2 m (6.6 ft) [5,6],

This appears to be a reasonable requirement since NBS riders have

typically actuated the brakes within 1,5 to 2m (4,9 to 6,6 ft) after

passing the trap. One manufacturer, however, reports distances of 1,9

to 2.5 m (6.1 to 8.3 ft) [9].

18
In an effort to evaluate the speed reduction that occurs over this

distance, the deceleration of a freewheeling (coasting) bicycle was measured with the aid of a special dynamometer. The results showed a fairly constant deceleration of 0.37 m/s^ (1.2 ft/s^) [9]. This value

seems high, however, since it implies a freewheeling stopping distance

of only 60 m (200 ft) from an initial speed of 24 km/h (15 mph). It

is speculated that the dynamometer itself may have been responsible

for part of the observed braking action.

NBS calculations of wind resistance and rolling friction show that

for a typical bicycle and rider the freewheeling deceleration is approximately

0.24 m/s^ (0.80 ft/s^) at a speed of 24 km/h (15 mph), and that the

average deceleration, in coming to a stop from this speed, is approximately 0.13 ml (0.42 ft/s ). This implies a freewheeling stopping

distance of approximately 170 m (560 ft). These calculations were roughly

confirmed by two tests with a single bicycle and rider which showed an average freewheeling stopping distance of 129 m (422 ft).

Assume that the distance traveled, between the timing trap and

brake actuation, is 1.75 + 0.25 m (5.7 + 0.8 ft) for a valid test. Then,

with an initial speed of 24 km/h (15 mph) and a freewheeling deceleration

of, say, 0.3 m/ s^ (1 ft/s^), the speed reduction over this distance

is 0.08 + 0.01 m/ s (0.3 + 0.03 ft/s). For a nominal stopping distance

of 4.57 m (15.0 ft) this speed reduction produces an error of approximately

-0.11 + 0.01 m (-0.4 + 0.03 ft), where the minus sign indicates that

the measured stopping distance is less than the true stopping distance

corresponding to the measured speed. This error is primarily of a systematic nature although it contains random components as well.

The Bicycle Safety Regulation calls for the bicycle to be traveling

at a specific speed at the initiation of braking in the road test. This

imposes an almost impossible burden on the rider aside from the aforementioned

difficulties in measuring this speed. It appears more reasonable, therefore,

to permit the initial speed to fall" within a range of values. However,

if the range were set at, say, +5 percent of the specified speed, this

would introduce variations of +10 percent in the stopping distance - an undesirable situation. 'A more acceptable approach would be to permit

the initial speed to fall within a range of values and to correct the

observed stopping distance to that which would probably have been observed

had the initial speed equaled the specified value.

The correction formula is, simply.

7.2 Control

19
where s is the corrected stopping distance, s is the measured stopping

distance, v is the specified initial speed and v is the measured OS om initial speed. While this correction is quite accurate for small deviations

in speed, it is not exact since it ignores the effects of the rider's

reaction time (see Equation (28)). Therefore, it should not be used

to correct for initial speeds which deviate substantially from the

specified initial speed. On this basis it has been proposed [l2j that

tests be declared invalid if the measured initial speed deviates from

the specified value by more than 1.5 km/h (0.9 mph), and ISO has adopted

this proposal [5,6].

8. EFFECTS OF PAVEMENT SURFACE

"The bicycle shall be ridden over a dry, clean,

... paved test course..." [Bicycle Safety Regula

tionj.

If one or both wheels of the bicycle skid during the road test

the stopping distance is affected by the coefficient of friction between

the tires and the pavement. The Bicycle Safety Regulation requires

that the pavement be dry and clean but this description is not adequate

to define y. One manufacturer reports that typical values of y range

from 0.54 to 0.95 [9j but there is evidence that values outside this

range are not uncommon. Handbook values for dry macadam and dry asphalt

range from 0.67 to 0.71 [20,21

as 1.22 have been reported [l3_

but individual measurements as high

, Typical values of y for smooth concrete

surfaces and cement floors range from 0.50 to 0.55 [l, 10,13] but a value

of 0.42 has also been reported [3], Painting concrete and asphalt often

lowers the coefficient of friction but special coatings can double it

to as high as 1.2 [22].

If a single bicycle is tested on two different pavements, under

otherwise identical conditions, different stopping distances will probably be observed. But which one is correct? This question cannot be

answered until a specific pavement surface or a specific coefficient

of friction is established as the test requirement. In the absence of

such a specification the requirement for motorcycle braking tests [7]

will be used as a guide and, on this basis, it is postulated that the

correct measure of a bicycle's braking capability is achieved on a pave- ment offering a coefficient of friction of 0.75 . Marginal braking capability

(B = 1), therefore, corresponds to a stopping distance of exactly 4.57

m (15.0 ft) under the specified test conditions with y = 0.75. With a rider reaction time of 0.15 seconds, as established above, this braking

capability requires a maximum deceleration of 0,563 g.

The effect of y on the maximum deceleration of the typical bicycle

(Table 1) is shown in'Figure 4 for braking capabilities of 0.50 (poor),

1.00 (marginal), 1.25 (good) and 1.50 (excessive). The relationships

20
plotted in the figure were calculated from Equations (1), (2), (15),

(20), (24), (25) and (27). (It is, perhaps, worth noting here that comprehensive

experimental data showing the effects of y on braking performance are

not available simply because no laboratory has a number of suitable test courses with different pavement surfaces offering a wide range of friction

coefficients. Comparing results from different laboratories in order

to ascertain the effects of y is unrewarding since the effects are obscured

by other differences in their respective measurement systems.)

At low values of y both wheels of the bicycle lock and skid and

the relation between maximum deceleration and friction coefficient is

given by line OABCD regardless of the braking capability. At higher values

of y and poor-to-good braking capability the front wheel rolls while

the rear wheel skids (curves AE , BG and CH). With excessive braking capability

pitchover occurs (point D) with both wheels locked and skidding. At very

high values of y and poor braking capability both wheels of the bicycle

roll (line EF).

The maximum deceleration values can be converted to stopping distances

through the use of Equation (28). This is shown in Figure 5 for the typical

bicycle with marginal braking capability. It is seen that with a friction

coefficient of 0.75 the stopping distance is exactly 4,57 m (15.0 ft);

higher coefficients produce shorter stopping distances and lower coefficients

produce longer stopping distances. The sharp break in the curve, which

occurs at y = 0.547, represents the changeover from both wheels locked

and skidding (on the left) to rear wheel locked and front wheel rolling

(on the right).

Clearly, without specifying y, the stopping distances measured on various pavements would vary widely, even for a single bicycle. In Figure

5 it is seen that, for the typical bicycle with marginal braking capability,

the measured stopping distance could range from 4.39 to 5.96 m (14.4

to 19.6 ft) over the span of observed friction coefficients (0.42 to

1.22). This represents an error band of +1.39, -0.18 m (+4.6, -0.6 ft)

where the plus sign indicates that the observed stopping distance exceeds

the correct one. This is a rather large error band.

Several approaches to reducing this error band might be considered.

The obvious approach would be to specify a particular value of y which

the test pavement should offer. This approach presents difficulties,

however. The friction coefficient is not an easy property to measure

reproducibly . ASTM Method E274 [23] is the method used for characterizing

pavements for motorcycle testing [7], and it is probably the most reproducible

method available, but it requires complex and expensive equipment.

A second approach, following an ISO recommendation [5,6], would

be to simply require that the friction coefficient be high enough to

prevent the front wheel from locking. In the example shown in Figure

5, this would limit y to values between 0.547 and 1.22, which corresponds

21
to stopping distances from 4.39 to 4.69 m (14.4 to 15.4 ft). This represents

an error band of +0.12, -0.18 m (+0.4, -0.6 ft) which is a substantial

improvement over the error band cited above. The problem with this approach

is that it might encourage the use of test pavements with unusually high

friction coefficients, which might introduce a pitchover hazard for bicycles

with powerful braking capabilities.

This problem could probably be overcome by requiring that the pavement,

in addition to being dry and clean, also be flat and free from coarse

or protruding aggregate. This would probably limit the maximum value

of y to no higher than about 1.0. Thus, for y ranging from 0.547 to 1.0,

Figure 5 shows stopping distances ranging from 4.46 to 4.69 m (14.6 to

15.4 ft). This represents an error band of +0.12 m (+0.4 ft), which is

reasonable.

The errors in stopping distance, due to pavements which offer friction coefficients other than 0.75, are systematic errors.

Further discussion of the tire/pavement friction coefficient is

given in Section 14.2.

9. UNCERTAINTIES IN THE APPLIED LEVER FORCES

"A spring scale or other suitable device [shall be

usedj for measuring the specified forces on the handbrake levers...

"The stopping force applied to the hand lever at

a point no closer than 25 mm (1.0 in) from the open

end shall not exceed 178 N (40 Ibf)" [Bicycle Safety

Regulation].

It is clear that the application of a force to the handbrake lever,

which is less than the prescribed maximum, would reduce the braking performance of the bicycle provided that one or both wheels are rolling.

Therefore, except when operating near the pitchover condition, it is

axiomatic that the maximum prescribed force is also the correct force

to be applied.

9.1 Kinetic Analysis

The effect of the applied lever forces, on the maximum deceleration

of the typical bicycle (Table 1) is shown in Figures 6 and 7 for several

braking capabilities. Figure 6 is for a tire/pavement friction coefficient

of 0,75 and Figure 7 is for a coefficient of 0.50. The curves were calculated from Equations (1), (2), (15), (20), (24), (25) and (27).

With low values of applied lever force, both wheels of the bicycle

roll. This condition applies to lines OA, OC and OE in Figure 6, and

22
to lines OA, OD and OF in Figure 7. With higher values of applied lever

force the rear wheel locks and skids while the front wheel continues

to roll. With \i = 0,50, still higher values of applied lever force cause both wheels of the bicycle to lock and skid, resulting in saturation

braking, as shown by line BEGG in Figure 7. Note that, in this case,

the maximum deceleration ratio, a/g, is numerically equal to the friction

coefficient (cf Equation (25)). With y = 0.75 (Figure 6), pitchover occurs

(points B and D) before the saturation condition is reached.

9.2 Error Analysis

Errors in the applied force can result from three principal sources. The measurement of the force may be inaccurate, the force may be applied

at the wrong point, or it may be applied in the wrong direction.

Most testing groups have used preset lever stops to assure that

the applied forces do not exceed the prescribed limit [8,9,10,12,13].

In this technique the stops are adjusted to prevent further travel of

the levers when the prescribed force levels are reached. The prescribed

forces are measured with spring dynamometers of one kind or another.

In principle, at least, spring dynamometers can be calibrated to

better than one-percent accuracy using dead weights. In practice, however,

most of these devices lack a high degree of repeatability. Some degree

of error is also introduced by the fact that the thickness of a wheel

rim is not uniform around the periphery of the wheel. Thus, if the lever

stop is preset with the wheel in one position, the lever force may differ

at other wheel positions [9j. Also, erratic friction between the cable

and the casing of the brake system results in variations of the applied

force using a preset lever stop [lO]. As a consequence of the above factor

it has been estimated that the magnitudes of the applied lever forces

may vary from the prescribed force level by up to +5 percent [9,12 J. This appears to be a fair estimate. Such variations lead to random errors

in stopping distance.

While it is important that the magnitude of the force applied to

the handbrake lever be correct, it is more important that the caliper

brake pads apply the proper forces to the wheel rims. Thus, if the lever

force is applied at the wrong point on the lever or in the wrong direction

the effect will be the same as if the wrong lever force were applied.

When setting the lever stops the spring dynamometer should be attached

to the lever at precisely 25 mm (1,0 in) from the tip. For most bicycles

the lever arm from this point to the lever pivot point is approximately

100 mm (4 in). Since levers are curved it is difficult to attach the

spring dynamometer at the precise point and errors of +2 mm (+0.08 in)

appear to be reasonable. This represents an error of +2 percent in the

lever arm and, in effect, a systematic error of +2 percent in the applied

force. One manufacturer has attributed much larger errors to the difficult

in applying the force at the specified point on the lever [9j.

23
The Bicycle Safety Regulation does not specify the direction in

which the force should be applied. For maximum braking, of course, the

force vector should lie in the plane in which the lever moves and should

be perpendicular to a line from the pivot point to the application point

when the lever is against the preset stop. This is a difficult requirement and it is estimated that deviations of up to +15° in the direction

of the applied force could be encountered. The effective applied force

is proportional to the cosine of the deviation angle so systematic errors

up to -3 percent could result.

Summing up, the total error in the force applied to the handbrake

lever is +7, -10 percent. Stated differently, when pulling the handbrake

lever against its preset lever stop the actual force applied may range

from 160 to 190 N (36 to 43 Ibf). The effect of this variability on the

maximum deceleration of the typical bicycle with marginal braking capability is given by line CD in Figure 6. These deceleration values may

be converted to stopping distances through the use of Equation (28) with

a rider reaction time of 0.15 seconds. The following results are obtained:

Applied lever force Stopping distance

N (Ibf) m (ft)

160 (36) 4.79 (15.7)

178 (40) 4.57 (15.0)

190 (43) 4.43 • (14.5)

These data show that the variability of the applied lever force results

in an error band on the stopping distance of +0.22, -0.14 m (+0.7, -0.5

ft), where the plus sign indicates that the observed stopping distance

exceeds the correct one. The systematic part of this error band is approximately +0.11, -0.03 m (+0.4, -0.1 ft) and the random part is approximately +0.11 m (+0.4 ft).

10. MASS (WEIGHT) EFFECTS

10.1 Locating the Center of Gravity

"The bicycle shall be ... stopped by the rider while

remaining in a normal riding position throughout

the stop..." [Bicycle Safety Regulation].

Since the force of gravity which acts on the rider, W , is the product

of the rider's mass, M , and the local acceleration of gravity, g. Equations

(15) and (20) can be used to show the effect of the rider's mass on the

24
maximum deceleration which is obtained under the specified test conditions."

However, when the rear wheel of the bicycle locks and skids while the

front wheel rolls, the calculation (Equation (20)) is not straightforward

a priori since changing the rider's mass also changes the location of

the center of gravity ,U.) of the bicycle/rider system.

Very little data are available on the manner in which the horizontal

location, I, of the eg changes vjith rider mass, and even less on the

manner in which the vertical location, H, is affected. Intuitively, it

would seem that increasing the mass of the rider would move the eg of

the system both upward and rearward, and that the relative effect would

be greater on lightweight bicycles than on heavy ones. Yet, the following

NBS measurements, made with two bicycles, fail to confirm these trends.

kg

6.8

21

mass Rider mass JJIl

(lb) kg (lb)

(15) 0 (0) 0.57

77 (170) .50

93 (204) .55

98 (215) .54

(46) 0 (0) .42

62 (136) .56

77 (170) .53

91 (200) .51

It is concluded that the differences in the mass distributions of the

riders, due to differences in height, physique, attitude, seat height,

etc., serve to mask the anticipated trends due to changes of rider mass

alone. On the other hand, these data show that the variations of l/L are not large. Since some test results are available [lOj which show

that changing the seat height, with a given rider, affects stopping distance only minimally, the possibility suggests itself that the variations

of the eg location with rider mass may not be an important consideration.

In order to check this hypothesis the data in Tables 2 and 3 were

used. These represent the only data which were found showing the effects

of rider mass on both l/L and H/L for specific bicycles [l5j. The maximum

decelerations for these two bicycles were calculated with Equations (1),

(2) and (20), normalizing the braking capabilities to the marginal con- dition (0.563 g with a 68.1-kg rider). In one set of calculations the

eg location was allowed to vary with rider mass as specified in Tables

*When both wheels of the bicycle lock and skid the deceleration

is independent of the rider's mass (cf Equation (25)).

25
2 and 3; in a second set of calculations the eg location was assumed

to remain fixed regardless of rider mass. The results are as follows:

Bicycle Rider mass,

Maximum deceleration, a/g

varying eg fixed eg

High rise 45.4

68.1

86.2

(100)

(150)

(190)

0.653

.563

.519

0.645

.563

.523

Conventional 45.4

68.1

86.2

(100)

(150)

(190)

.649

.563

.525

.653

.563

.519

These results show that the effect of the changes in the eg location

on maximum deceleration are small indeed, amounting to less than 2 percent

in the most extreme ease. Therefore, it appears that for the purpose

of calculating the effects of rider mass on stopping distance, the use

of a fixed eg will yield reasonably accurate results. It remains only

to select typical values of l/h and H/L for these calculations.

One manufacturer [9] has suggested that for most bicycles

Comparison of these values with the NBS data cited earlier, and with

the data in Tables 2 and 3, suggest that lower values would be more typical,

however. On this basis the values

were selected for the typical bicycle characteristics which were set

forth in Table 1

.

10.2 Effect of Rider Mass on Maximum Deceleration

"A bicycle equipped with only handbrakes shall be

tested for stopping distance by a rider of at least

68.1 kg (150 lb) weight ..." [Bicycle Safety Regulation].

The effect of rider mass on the maximum deceleration of the typical

bicycle (Table 1), with several braking capabilities, is shown in Figures

8 and 9. Figure 8 is for a tire/pavement friction coefficient of 0.75

and Figure 9 is for a coefficient of 0.50. Equations (1), (2), (15),

(20), (24), (25) and (27) were used for these calculations.

Jl/L % 2/3 and H/L * 1.

l/L = 0.60 and H/L = 0.85

26
For a friction coefficient of 0.75, Figure 8 shows that with marginal

or excessive braking capability (curves AB and CD) changing the rider's

mass does not change the mode of braking; the rear wheel skids while

the front wheel rolls, over the entire range of rider masses considered.

These two curves culminate in pitchover (points C and A) for underweight

(i.e., less than 68.1-kg) riders. With poor braking capability the braking

changes to both wheels rolling for heavy riders (curve FG).

For a friction coefficient of 0.50, Figure 9 shows that front-wheel

locking and saturation braking (line ACB) is reached before pitchover

can occur, and the bicycle with excessive braking capability operates

in this mode over the entire range of rider masses considered.

10.3 Effect of Rider Mass on Stopping Distance

"A bicycle. .. shall have a stopping distance of no greater than 4.57 m (15 ft) from the actual test

speed . .

.

"The stopping distances specified are based on a rider weight of 68.1 kg (150 lb) and gre^itrr stopping distances are allowable for heavier riders at

the rate of 0.30 m per 4.5 kg (1.0 ft per 10 lb)"

[Bicycle Safety Regulation].

The maximum deceleration data shown in Figure 8 can be converted

to stopping distances through the use of Equation (28) and a rider re- action time of 0.15 seconds. The effect of rider mass on stopping distance is shown by curve OA in Figure 10 for the typical bicycle with

marginal braking capability. Point 0 in the figure represents the marginal

condition, a stopping distance of 4.57 m (15.0 ft) with a 68.1-kg (150

-lb) rider. Line OC represents the allowable stopping distance permitted

by the Bicycle Safety Regulation for overweight riders, at the rate of

0.30 m per 4.5 kg (1.0 ft per 10 lb).

The allowance for overweight riders clearly exceeds the effect of

overweight riders. The error--the difference between the allowable stopping distance and the actual stopping distance —favors the overweight

rider. The greater the mass of the rider, the greater is his advantage

over the 68.1-kg (150-lb) rider. A bicycle with inadequate braking capability,

which could not pass the road test with a 68.1-kg (150-lb) rider, could

easily do so with a rider of sufficient mass.

The magnitude of the error increases indefinitely with increasing

rider mass, ranging, for example, from zero for a 68.1-kg (150-lb) rider

to -2.50 m (-8.2 ft) for a 120-kg (265-lb) rider. This error is a systematic

one, and the minus sign indicates that the braking performance of the

bicycle, as indicated by the allowable stopping distance, is less than

that required for marginally acceptable performance. One approach toward

reducing the size of this error, which has been proposed by ISO [6j,

27
would limit the combined weight of the rider and instrumentation to

a maximum of 85 kg (187 lb). Ignoring the weight of the instrumentation

for the moment, Figure 10 shows that this limitation reduces the maximum

error to -0.76 m (-2.5 ft). This is still a sizeable error.

A better approach might be to change the allowable correction from

0.3 m/4.5 kg (1 ft/10 lb) to that which would make the line OC, in Figure

10, tangent to the stopping distance curve at point 0. The slope of the

stopping distance curve may be found from Equations (20) and (28) by

differentiation, and it is found, in this manner, that a suitable cor- rection factor would be 0,024 m/kg (0.035 ft/lb)* which is equivalent

to a rate of approximately 0.11 m per 4.5 kg (0.35 ft per 10 lb). With

this allowance the error in stopping distance, with a 120-kg (265-lb)

rider would be only -0,31 m (-1.0 ft),

10,4 Instrumentation Mass

Regarding the mass of the instrumentation which must be carried

by the bicycle in order to perform the road test, it has been suggested

that this mass be treated in the same manner as added rider mass for

the purpose of correcting the measured stopping distance [6], This is a reasonable suggestion provided that the instrumentation is located

such that it does not significantly change the location of the center

of gravity of the bicycle/rider system. This is the practice which has

been advocated by one manufacturer [9], If the instrumentation is located

principally over the front wheel then the eg is moved forward and the

correction factor proposed above would not be sufficient to account for

the effect of the instrumentation mass. For example, adding 10 kg (22

lb) over the front wheel of the typical bicycle would raise the stopping

distance from 4,57 m (15,0 ft) to 5.04 m (16.5 ft), an increase of 0.47

m (1.5 ft), while the correction factor proposed above would only allow

for an additional 0.24 m (0.8 ft). On the other hand, adding the 10 kg

(22 lb) over the rear wheel of this bicycle would reduce the stopping

distance to 4,43 m (14.5 ft) without any correction factor having been

appl ied

!

In order to avoid the variabilities in stopping distance that can result from placement of the instrumentation and from rider mass, the

practice used for thoroughbred racing and for motorcycle testing [7j

could serve as a guide. As applied to bicycle testing, this approach

would specify a fixed payload of, say, 91 kg (200 lb), consisting of

*This appears to be a conservative value. Calculations show that

the corresponding factor for the high rise bicycle (Table 2) is 0.019

m/kg (0.028 ft/lb), and for the conventional bicycle (Table 3) it is

0,021 m/kg (0,031 ft/lb).

28
the rider, the instrumentation and added mass, with the instrumentation

and the added mass distributed fore and aft so as not to cause a major

dislocation of the center of gravity of the bicycle/rider system. With

this approach, all bicycles would be tested with the same total payload

and a correction for overweight riders would be obviated.

10.5 Pitchover

The final topic to be discussed under the subject of mass effects

is pitchover. This topic has generated considerable controversy. One

manufacturer has stated that the 4.57-m (15.0-ft) stopping distance requirement

of the performance test presents a serious pitchover hazard [24j. A second

manufacturer has claimed that its test riders would refuse to test if

the full 178 N (40 Ibf) were required to be applied to the hand brake

levers [25J. An independent laboratory, however, which conducted over

two hundred braking tests in which the applied lever forces were not

limited to 178 N (40 Ibf), reported that no instance of pitchover (or even lifting of the rear wheel) occurred when the rider remained seated

throughout the braking period [15]. Several pitchovers occurred in tests

conducted at NBS ri3j but only on a test course which offerred an excessively

high tire/pavement coefficient of friction (v = 1.22).

The threshold decelerations for pitchover, calculated from Equations

(24) and (27), are tabulated below for the typical bicycle (Table 1),

the high rise bicycle (Table 2) and the conventional bicycle (Table 3).

The latter bicycles are included in this tabulation in order to examine

the effects on pitchover of the change in eg location with rider mass.

a/g at pitchover

Bicycle Rider mass 2 wheels locked front wheel ; kg (lb)

Typical 68.1 (150) 0.706 0.700

High rise 45.4 (100) .875 .866

68.1 (150) .833 .827

86.2 (190) .803 .798

Conventional 45.4 (100) .850 .836

68.1 (150) .847 .837

86.2 (190) .846 .839

The results show that the decelerations which cause pitchover exceed,

by a comfortable margin, the minimum deceleration ••rhich is required to

pass the road test (0.563 g). For the high rise and conventional bicycles

pitchover cannot be attained on a test course offering a tire/pavement

friction coefficient of 0.75.

29
11. EFFECT OF INCLINED ROADWAY

"The bicycle shall be ridden over a ... level paved

test course..." [Bicycle Safety Regulation].

Although the Regulation requires that the test course be level,

it can hardly be expected that many testing groups will build test courses specifically for this purpose. The ISO requires only that the test surface

be "substantially" level [6j. NBS measurements suggest that inclinations

up to about 1/4 degrees may be undetectable to the naked eye without

a comparison reference.

If the test surface is inclined then the deceleration is

f + f

.

a r f , . „ ~ — 7t— TT + Sin 3

g w, + w ° b r

which, of course, reduces to Equation (14) when 3 is zero. The angle

of inclination, 3, is considered positive for an upward incline. This

equation shows that a bicycle which could achieve the minimum required

deceleration rate of 0.563 g on a level surface would attain a deceleration

of 0.570 g on an upward incline of 0.25 degrees, and a deceleration of

0.556 g on a downward incline of 0.25 degrees. Using Equation (28) and

a rider reaction time of 0.15 seconds it is found that these deceleration

values correspond to stopping distances of 4.52 and 4.62 m (14.8 and

15.2 ft), respectively, or an error band of +0.05 m (+0.2 ft).

With a one-percent grade (sin 3 = 0.01, 3 = 0.57 deg) the error band

is +0.08 m (+0.3 ft).

These errors, which are systematic, could be rendered negligible

by conducting the road tests in both directions on the test course and

averaging the results.

12. WIND EFFECTS

The procedure for conducting performance tests on motorcycle braking

systems specifies that the tests be carried out under conditions of zero wind velocity [7j. While the Bicycle Safety Regulation does not address

this problem it is obvious that, in order to minimize the variability

of test results, it is desirable that these tests also be carried out

under conditions of zero wind velocity. Unfortunately, such conditions

are not consistently attainable on outdoor test courses and, recognizing

this, the ISO has specified that the wind speed shall not exceed 3 m/

s

(6.7 mph) [6J.

30
Wind resistance is, in essence, a force which, depending upon its

direction, may aid or retard the deceleration of the test bicycle. If

the effects of wind resistance are included, the deceleration of the

bicycle may be expressed as (cf Equation (14))

f + f^ + F 1= \ ' "

(29)

g W + W

b r

where, following the customary approach,

(v

F = kCp w

V )' w

in which C is the aerodynamic drag coefficient,

p is the mass density of air,

V is the bicycle speed,

is the component of wind velocity in the direction of bicycle

motion,

A is the projected area of the bicycle/rider system normal

to the direction of motion, and

/+1 if v-v > 0, ^ (-1 if v-v^ < 0.

^ w

Since, in the road test, the bicycle speed varies from its initial value

to zero, F also changes continuously. Thus, the deceleration is not

constant and the exact calculation of stopping distance, while entirely

feasible, is exceedingly tedious. As a simplifying approximation, therefore,

it is assumed that F is given with sufficient accuracy by its average

value, F . That is.

f =1 /° F dv, W V / w

o J

o

which leads to

^

2

Fw2= CPA I - vv+v^l, v4 0, (3aA) \3 ow w/' w

'

F = ^[(v - V )^ - V , 0 ^ v < V , (30B) W DV 0 W W J — W - 0

0

F =

W

"2 CPA I—r— - V V + V /, y 3 o w w /

V A V , w ~ o (30C)

31
Since the aerodynamic drag on the bicycle/rider system probably

lies somewhere between the drag on a finite flat plate normal to the

direction of air flow and that on a finite cylinder in this orientation,

a value of unity for G appears reasonable [26j. The mass density of air,

p, under standard conditions is 1.23 kg/m^ (0.077 Ib/ft^) [26]. The projected area of the bicycle/rider system, A, may be taken as approximately

0.6 m^ (6 ft2 ).

With these data, Equations (29) and (30) show that for the typical

bicycle with marginal braking capability (a/g = 0.563) under zero wind

conditions, the braking system furnishes only 0.558 g of deceleration,

with the remaining 0.005 g provided by air resistance. This point is

only academic however, since bicycles are not tested in a vacuum, and

nothing is lost by attributing all of the braking action to the braking

system.

Using Equations (28), (29) and (30), the effect of wind on the stopping distances attained by the typical bicycle with marginal braking

capability may be calculated, with the following results:

Wind speed, v Stopping distance, s Error

m/s (mph) m (ft) m (ft)

4.5 (10.0) 4.63 (15.2) 0.06 (0.2)

3.0 (6.7) 4.61 (15.1) .04 (.1)

2.2 (5.0) 4.61 (15.1) .04 (.1)

0 (0) 4.57 (15.0) 0 (0)

-2.2 (-5.0) 4.51 (14.8) -.06 (-.2)

-3.0 (-6.7) 4.48 (14.7) -.09 (-.3)

-4.5 (-10.0) 4.42 (14.5) -.15 (-.5)

It may be seen that if the maximum permissible wind speed is taken as +2.2 m/s (+5.0 mph) then the maximum error in stopping distance, due

to the wind, is +0.04, -0.06 m (+0.1, -0.2 ft). With this same wind speed

a manufacturer calculated the error as +0.1 m (+0.3 ft) [9]. While the

rationale of the latter calculation is not obvious it is nonetheless

clear that if the road tests were carried out alternately in opposite

directions, and the results averaged, the net error would be very small.

Using this approach, with permissible wind speeds up to +4.5 m/s (10.0

mph), the error band would be only +0, -0.05 m (+0, -0.2 ft) according

to the above table, and zero according to the manufacturer's calculations. Since wind speed can be measured and suitably corrected for, the errors in stopping distance due to wind are systematic errors. However,

recognizing that wind speed may change from one test to the next, it

is probably more appropriate to consider these errors as though they

were random.

32
13. ERROR ANALYSIS: INTERPRETATIONS AND IMPLICATIONS

13. I Summary of Individual Error Analyses

The preceding eight sections of this report have examined the errors

that arise in the performance of the road test as a result of the variabilities of the several test parameters. The principal problem to be

addressed in this section concerns the manner in which these errors ac- cumulate. In order to facilitate discussion of this problem, some of

the more pertinent results of the individual error analyses are summarized

below. Since this summary cannot include all details and variations the

reader is referred back to the appropriate sections of the report for

further explanation and elaboration of the material presented here.

All of the errors cited here are given in units of meters (feet)

and refer to deviations from the true stopping distance which properly

characterizes the braking performance of the typical bicycle with marginal

braking capability. Systematic errors are denoted by the symbol b and

random errors by the symbol r. A positive error is one in which the measured

(or measured and corrected) stopping distance exceeds the true stopping

distance. A negative error is one in which the measured stopping distance

is less than the true stopping distance.

(a) Error due to uncertainty in locating the starting point (Section

5.2):

Using a starting line, b « 0 and -0.6 < r < 0.6 m (-2 < r < 2 ft).

Using propelled markers, -0.2 < b < 0 m (-0.7 < b < 0 ft) and -0.02 < r < 0.02 m (-0.07 < r < 0.07 ft).

(b) Error due to failure to track a straight path (Section 5.3):

Without guidance, b = 0 and -0.37 < r < 0 m (-1.2 < r < 0 ft).

With guidance, b ^ 0 and -0.04 < r < 0 m (-0.1 < r < 0 ft).

(c) Error due to rider's reaction time (Section 6):

b ^ 0 and -0.39 < r < 0.89 m (-1.3 < r < 2.9 ft).

(d) Error due to inaccuracy in measuring initial speed (Section 7.1):

With a speedometer, b «• 0 and -0.27 < r < 0.27 m (-0.9 < r < 0.9

ft).

With a timing trap, -0.12 < b <-0.I0 m (-0.4 < b <-0.3 ft) and -0.09

r < 0.09 m (-0.3 < r < 0.3 ft).

33
(e) Error due to tire /pavement friction coefficient (Section 8):

With no limits on y, -0.18 < b < 1.39 m (-0.6 < b < 4.6 ft) and r = 0.

Without front wheel locking, -0.18 < b < 0.12 m (-0.6 < b < 0.4 ft)

and r = 0.

Without front wheel locking and with \i < 1.0, -0.12 < b < 0.12 m

(.0.4 < b < 0»4 ft) and r = 0.

(f) Error due to inaccuracy in the applied lever force (Section 9.2):

-0.03 < b < 0.11 m (-0.1 < b < 0.4 ft) and -0.11 < r < 0.11 m

(-0.4 < r < 0.4 ft).

(g) Error due to the incorrect overweight-rider (and instrumentation)

allowance (Sections 10.3 and 10,4):

With riders up to 120 kg (265 lb), -2.50 < b < 0 m (-8.2 < b < 0

ft ) and r ~ 0.

With riders up to 85 kg (187 lb), 0.76 < b < 0 m (-2.5 < b < 0 ft)

and r " 0.

With proposed new overweight allowance and riders up to 120 kg (265

lb), -0.31 < b < 0 m (-1.0 < b < 0 ft) and r < 0.

With fixed total payload, b = 0 and r = 0.

(h) Error due to inclined roadway (Section 11):

With inclines up to +0.25 degrees, -0.05 < b < 0.05 m (-0.2 < b < 0.2 ft) and r = 0.

With inclines up to 1-percent grade, -0.08 < b < 0.08 m (-0.3 < b < 0.3 ft) and r = 0.

Averaging tests in both directions, b = r = 0.

(i) Error due to wind (Section 12):

With winds up to +4.5 m/s (+10 mph), b = 0 and -0.15 < r < 0.06 m

(-0.5 <: r < 0.2 ft).

With winds up to +3.0 m/s (+6.7 mph), b = 0 and -0.09 < r < 0.04

m (-0.3 < r < 0.1 ft).

34
With i;-7inds up to 4.5 m/ s (10 nph), and averaging tests in both directions,

b = 0 and -0.05 < r < 0 m (-0.2 < r < 0 ft).

13.2 The Measurement System: An Example

In order to further facilitate discussion of the manner in which

the indi\'idual errors accumulate, it is helpful to consider an example

involving a specific, although hypothetical, measuring system. Let the

following general characteristics define the measuring system:

(1) The typical bicycle with m^arginal braking capability.

(2) The starting point is located with propelled markers.

(3) The bicycle is steered along a relatively straight path into

the stopping zone.

(4) Bicycle speed is measured with an electronic timJ.ng trap.

(5) The pa\-em-ent of the test course is such that it offers a tire/pavement friction coefficient less than 1.0 and it does not induce

front wheel locking.

(6) The combined mass of the rider and the instrumentation is lim.ited

to less than 120 kg (265 lb) and the instrumentation mass is

distributed such that is does not significantly alter the eg

location of the bicycle/rider system.

(7) The test course is level in the timing trap and the stopping

zone

.

(8) Wind speeds up to +4.5 m/ s (+10.0 mph) are considered acceptable.

Within the current state of the art this measurement system could

be considered both reasonably typical and reasonably good. With these

characteristics and the error summary given above it is found that the

applicable systematic error bands are

-0.2 < b < 0 m (-0.7 < b < 0 ft),

-0.12 < b < -0.10 m (-0.4 < b < -0.3 ft),

-0.12 < b < 0.12 m ( 0.4 < b < 0.4 ft),

-0.03 < b < 0.11 m (-0.1 < b < 0.4 ft),

-2.50 < b < 0 (-8.2 < b < 0 ft),

and the random error bands are

-0.02 < r < 0.02 m (-0.07 < r < 0.07 ft),

-0.04 < r < 0 m (-0.1 < r < 0 ft).

35
-0.39 < r < 0.89 m (-1.3 < r < 2.9 ft),

-0.09 < r < 0.09 m (-0.3 < r < 0.3 ft),

, -0.11 < r < 0.11 m (-0.4 < r < 0.4 ft),

-0.15 < r < 0.06 m (-0.5 < r < 0.2 ft).

13.3 Linear Accumulation of Errors

If the various errors are simply added together algebraically, fol

lowing one manufacturer's approach [27], then the overall error, e, is

simply

e = B + r

where . .

' " '

.

' " b = Xb

and - . , t:-,^, .,r,-./,

.

T = 2r.

This gives, for the example being considered,

-2.97 < b < 0.13 m (-9.7 < b < 0.4 ft),

-0.80 < r < 1.17 m (-2.6 < r < 3.8 ft),

and -3.77 < i < 1.30 m (-12.4 < i < 4.3 ft).

These figures suggest that in any single test of this bicycle, which

has braking capability just adequate to meet the 4.57-m (15.0-ft) stopping distance, the observed (i.e., the measured and corrected) stopping

distance will deviate from 4.57 m (15.0 ft) by an amount between -3.77

and +1.30 m (-12.4 and +4.3 ft). Stated differently, in any single test

the observed stopping distance may fall anywhere between 0.80 and 5.87

m (2.6 and 19.3 ft)." This is a disturbingly broad range which, because

the errors are predominantly negative, tends to favor bicycles with inadequate braking capabilities. If the overall error band is normalized,

i.e., expressed as a band about its midpoint, a value of +2.535 m (+8.3

ft) is obtained, which far exceeds even the +1.07-m (+3.5-ft) error band

claimed by two manufacturers [3,24j,

"A measured stopping distance of only 0.80 m (2.6 ft) is, of course,

unrealistic. However, a measured stopping distance of 4.26 m (14.0 ft) with

a 120-kg (265-lb) rider is quite conceivable and applying the overweight

allowance brings the corrected stopping distance down to 0.80 m (2.6 ft).

36
The significance of this result can be deceptive, however, because

the systematic and random errors were simply added together in order

to ascertain the overall error.

13.4 Significance of Random and Systematic Errors

For any given measuring system there is a single value of the overall

systematic error -- rather than a range of values -- which is characteristic

of the system. Although this value may be unknown, it does not change

from test to test unless and until the measuring system is changed. The

range of systematic errors therefore defines the variability between

different laboratories, or between different measuring systems which

might be employed in a single laboratory.

The random errors, on the other hand, do change from test to test even with an unchanging measuring system. The range of random errors therefore defines the test-to-test variability.

The overall random error band calculated above indicates that, for

the typical bicycle with marginally acceptable braking capability, the

stopping distance observed in any single test with the sample measuring

system will have a variability of +1.17, -0.80 m (+3.8, -2.6 ft). While

this error band is smaller, of course, than the overall error band, it

is still very large. This result may also be deceptive, though, because

it may suggest that it is equally likely for the observed stopping distance in any single test to fall anywhere within this band. However,

this is not the case simply because it is not likely that the individual

random errors r, due to the individual parameter variabilities, will

all fall at their maximum or minimum values in any single test. Rather,

it is highly unlikely that this will happen even once in any reasonable

number of tests. Because of this, it is, perhaps, inappropriate to ex- press the overall random error as the simple algebraic sum of the individual random errors. It is probably more realistic to estimate the

overall random error as the square root of the sum of the squares of

the individual random errors. This computation should utilize the form

rather than, simp ly, r » vir in order to retain the algebraic signs

of the individual errors. For the example being considered, this computation

shows that the probable overall random error band is

13.5 Test-to-Test Variability

r l[r|r|]

/lX[rlr l]|

-0.44 < r < 0.91 m (-1.4 < r < 3.0 ft).

(when the overall random error is computed in this way it becomes immediately obvious that it is dominated by only one of the individual
random errors, namely, that due to the variability in the rider's re- action time.

)

The magnitude of this test-to-test variability raises a serious

question about the capability of a single test result to serve as the

basis for judging the adequacy of a bicycle's braking system. For example,

suppose that the overall systematic error of the system being considered

is -0.50 m (-1.6 ft). Then, because of the test-to-test variability,

the observed stopping distance in any single test could range from 3.63

to 4.98 m (11.9 to 16.3 ft) for the bicycle with marginal braking capability.

Means for reducing the effects of this test-to-test variability

will be presented later.

As pointed out above, the overall random error band depends primarily

upon the error band attributable to variations in the rider's reaction

time. Therefore, in any given laboratory, the test-to-test variability

in observed stopping distance will reflect the ability of the rider to

maintain consistent reaction times. In this connection it may be noted

that it is clearly in a manufacturer's interest to strive for short re- action times in his tests, while the motivation to achieve this may not

be so great in an independent laboratory. Thus, it is conceivable that

the average reaction time of a rider employed by a manufacturer may be

less than the average reaction time of a rider in another laboratory.

The difference between a rider's average reaction time and the "standard"

value of 0.15 seconds actually represents a systematic error, rather

than a random error. This systematic error has not been treated explicitly

in this analysis but it should be kept in mind that it could contribute

to the lab-to-lab variability in observed stopping distance which is

examined below.

13.6 Lab-to-Lab Variability

For laboratories which employ measurement systems that conform to

the general specifications set forth in Section 13.2, the lab-to-lab

variability is defined by the overall systematic error band calculated

above, namely,

-2.97 < b < 0.13 m (-9.7 < b < 0.4 ft).

However, while this represents the maximum possible range of systematic

errors it does not represent the probable range. In other words, it is

highly unlikely that all of the individual systematic errors will fail

at their respective minima or maxima in any single laboratory. Recognizing

this, and following the procedure used above for random errors, it is

38
estimated that the probable range of the overall systematic error is

given by

^ ^ ^[b|b|]

/lz[b|b| ]

I

which yields, for the measuring systems under consideration,

-2.51 < b < 0.13 m (-8.2 < b < 0.4 ft).

The lab-to-lab variability, which this overall systematic error band defines, is so huge that it tends to render meaningless any com- parisons of results between different laboratories. Fortunately, however, this overall systematic error is thoroughly dominated by only one

of the individual systematic errors, namely, that due to the incorrect

overweight rider allowance, and this source of error is amenable to rectification.

Three ways to reduce the systematic error due to the incorrect overweight

rider allowance were discussed in Sections 10.3 and 10.4. If the ISO

approach [6] were adopted, the combined mass of the rider and the instrumentation would be limited to a maximum of 85 kg (187 lb). In this circumstance it can be shown that the probable overall systematic error band

would be reduced to

a tremendous improvement.

If the overweight rider allowance were changed from 0.30 m per 4.5

kg (1.0 ft per 10 lb) to 0.11 m per 4.5 kg (0.35 ft per 10 lb) then, even with riders plus instrumentation up to 120 kg (265 lb), the probable

overall systematic error band would be further reduced to

Finally, if it were required that all tests be carried out with

the same total payload (rider + instrumentation + added mass) then the

systematic error due to the overweight allowance would disappear entirely,

and the probable overall systematic error would be only

-0.80 < b < 0.13 m (-2.6 < b < 0.4 ft),

-0.41 < b < 0.13 m (-1.3 < b < 0.4 ft).

-0.26 < b < 0.13 m (-0.9 < b < 0.4 ft).

The lab-to-lab variability implied by this systematic error band

is quite acceptable in comparison with the larger test-to-test variabilities of the measuring systems.

39
13.7 Reducing the Effects of Test-to-Test Variability

As shown earlier, the probable overall random error band of the

systems under consideration, which defines the test-to-test variability,

is

:. -0.44 < F < 0.91 m (-1.4 < r < 3.0 ft).

With this variability, the question was raised as to whether the

result of a single test is adequate to determine whether a bicycle's

braking capability is or is not acceptable. Actually, the Bicycle Safety

Regulation does not specify that this determination should, in fact,

be based on a single test. With the option of using the results of several

test runs, rather than one, several methods have been proposed for reducing

the uncertainty that stems from the test-to-test variability.

One method is based on using the average results of several test

runs. The random error band for the average of a number of test runs

is smaller than the random error band for a single test run. In principle, the more tests the better, since the random error band for the

average of a large number of test runs would be quite small. Following

this approach, an independent laboratory conducted a test program in

which, whenever tests of a particular bicycle exhibited an especially

large disparity in observed stopping distances, the tests were continued

until a reasonable consistency was developed and the five shortest distances were averaged [lOj.

However, multiple testing of this kind is both difficult and expensive

and, perhaps with this in mind, a manufacturer suggested, simply, that

each bicycle be subjected to five test runs with the average stopping

distance reported as the final result [3,24j.

A variation of the averaging method is used in motorcycle brake

testing [7]. In this approach, four test runs are performed and only

one of the observed stopping distances is required to be within the specified criterion in order for the braking system to be considered acceptable.

This approach makes use of the "randomness" of random errors, so to speak,

contending that in at least one out of four runs the overall random error will not fall on the positive side of its band.

In an entirely different method an allowance is incorporated into

the stopping distance criterion to compensate for the random errors. Thus, one nation's delegation to the ISO proposed that the stopping distance criterion be raised from 4.57 m (15.0 ft) to 5.5 m (18 ft) and

that none of the stopping distances observed in five test runs exceed

this criterion [l8j. This method also has merit, since in five test runs

it may be expected that the overall random error will approach its probable maximum positive value at least once.

40
The U.S. delegation to the ISO proposed a combination of the two

general methods, requiring that the average stopping distance recorded

in five test runs not exceed a value of 5.5 m (18 ft) [l8j, and the ISO

adopted this proposal [28]. However, the rationale behind this approach

is not immediately evident.

In summary, therefore, either of the two general methods discussed

above could be used to counteract the effects of the test-to-test variability. If the first method is used, whereby the average stopping distance

recorded in a number of test runs is used, it remains only to suitably

select the required number of runs using statistical techniques. If the

second method is used, in which an allowance is added to the stopping

distance criterion and it is required that none of the observed stopping

distances in a series of test runs exceed this value, then the number

of test runs used is not as critical. A suitable value for the allowance

should be based upon the maximum probable positive random and systematic

errors. For the systems under consideration,

i =5 + r = 0.13 + 0.91 = 1.04 m (3.4 ft).

max max max

It appears, from this calculation, that an allowable stopping distance

of 5.5 m (18 ft) is, in fact, a reasonably suitable value for use with

this method, which requires that none of the stopping distances exceed

the allowable value.

The simplest approach would follow the practice used with motocycles.

In this approach the 4.57-m (15.0-ft) criterion would be retained but,

recognizing the test-to-test variability, it would only be required that one out of several test runs satisfy the criterion in order for the braking

system to be judged adequate.

14. DISCUSSION

This section of the report is not a discussion of the results which

were obtained. Rather, it presents a few discrete observations which

are relevant to the subject matter at hand but only peripheral to the

main thrust of the report.

14.1 Brake Sensitivities

In Section 2.3 the observation was made that a given brake system

which may be adequate for one bicycle may be entirely inadequate for

another. To illustrate this point, the following tabulation shows the

41
brake sensitivity Z which is required to provide marginal braking capability

on each of the three kinds of bicycles examined in this report:

Bicycle 2o Typical 2.32 Conventional 1.99 High rise 1.89 This calculation was based on Equation (1) and Equation (20), which assumes

that the front wheel rolls and the rear wheel skids during the stopping

process. This, of course, is the usual situation with most bicycles,

which are designed to have equal brake sensitivities on the front and rear wheel s.

, One manufacturer, however, has pointed out and rightly so that there are advantages to using unequal brake sensitivities on the front and rear wheels. By using a higher brake sensitivity on the front wheel, and a correspondingly lower value on the rear wheel, enhanced

braking capability is achieved with the same combined brake sensitivity,

particularly under hard braking conditions [27j. Bicycles equipped in this way may be expected to attain higher deceleration rates, with both

wheels rolling, than bicycles with conventional braking systems.

The distribution of total brake sensitivity between the front and rear wheels is a variable which was not explicitly treated in this re- port. All calculations of braking performance with both wheels rolling

were based on the assumption of equal brake sensitivities, front and

rear. 14,2 Optimum Tire/Pavement Friction Coefficients

Although a tire/pavement friction coefficient of 0.75 was adopted

in this report for the purpose of defining marginal braking capability,

it should not be inferred that this is, in fact, the best value to use

for road testing. Rather, it was shown that the error due to y is quite

small so long as it is less than 1.0 yet high enough to avoid front wheel locking. The following tabulation shows the minimum value of y which

can be used for the road test without front wheel locking:

Bicycle min

Typical 0.547 Conventional .531 High rise .528

It is thus evident that there is a wide range of acceptable y values

to choose from. Therefore, it is prudent to select a value on the basis

of other advantages. In order to satisfy the specified stopping distance

42
criterion y must be not less than 0.563. In order to avoid pitchover

except, perhaps, with very unusual bicycles, the data in Section 10.5

suggest that y should be less than 0.7. It thus appears that a value

in the range 0.60 to 0.65 would be optimum for the road test in that

it would enable the stopping distance criterion to be satisfied without

an ever-present danger of pitchover while, at the same time, contributing

to good measurement accuracy. The use of higher values of y would increase

the pitchover hazard but would not reduce the stopping distance significant!

14.3 Other Kinds of Bicycles The error analysis described in this report was concerned only with

bicycles equipped with hand-lever operated brakes, front and rear, which

can attain an initial speed of 24 km/h (15 mph) on a level test course. The Bicycle Safety Regulation, however, does not restrict itself to such bicycles. Rather, it provides for road tests on bicycles equipped with

a variety of brake options and for low-speed bicycles as well. While

the braking performances of these other kinds of bicycles were not ad- dressed directly in the analyses, it is believed that the analytical

procedures which were used provide ample guidance for the preparation

of applicable error analyses for virtually all kinds of commercially

available bicycles.

14.4 Other Test Parameters

The multitude of test parameters which influence the results of

the road test were not all included in the error analyses, although it

is felt that all of the important ones were given reasonably thorough

consideration. Some parameters, such as rolling friction in the bicycle

wheel bearings, were not treated thoroughly because their effects on stopping distance are believed to be only minor in comparison with the effects of the important parameters. Other parameters, such as the con- dition of the wheel rims where the brake pads make contact, were ignored because of insufficient data upon which to base an analysis. The effects

of such parameters, however, can generally be rendered negligible through

good testing technique; in the case of the wheel rims, for example, by

cleaning the rims with a quick-drying solvent prior to each test run. 14,5 Improved Testing Techniques

While the error analyses were primarily concerned with establishing

the limits, or bounds, of each source of error, it should not be inferred

that these limits are either rigid or necessarily applicable in all cases. Certainly, the error bands which apply to any given laboratory can be reduced by careful attention to detail and good testing technique. A

few suggestions have been made in this regard. For example, if alternate

test runs on a bicycle are made in opposite directions then the errors

due to an inclined roadway and wind are significantly reduced in the average test result.

43
It has also been demonstrated that automatic systems for applying

the required forces to the handbrake levers are feasible, and that they

effectively eliminate variability in rider reaction times and the errors which result therefrom [9], Still another technique which merits consideration involves the use of a decelerometer to measure peak performance

during the road test. One such device, reportedly, has an accuracy within

+1 percent and, if used properly, eliminates the errors due to rider

reaction time while, at the same time, obviating the need for accurate

measurement of initial speed [5j.

In this connection it may be noted that a road test may not, in

fact, be the best way to evaluate a bicycle's braking capability. It

has been suggested [l3j, for example, that a dynamometer-type laboratory

test of one kind or another, such as is used to measure braking performance on some motorized vehicles (cf [29j), may be preferable. While

it is outside the scope of this report to evaluate different test methods, one aspect of such an evaluation is relevant to the present discussion.

The major sources of error in the road test (overweight riders and rider

reaction times), as well as its principal operational difficulty (avoiding

pitchover), are all absent in a properly conceived laboratory test.

15. CONCLUSIONS

1. Concepts of brake sensitivity and braking capability were defined,

which enable a bicycle's braking performance to be quantified and

discussed in tangible, rational terms. Other concepts, such as typical

bicycle characteristics and marginal braking capability , were developer

to establish a framework against which various braking performances

could be evaluated. . , >, ,

, • u i ,

2. The test parameters which influence the results of the CPSC road

test for braking performance were identified and the errors (or variabilities) in observed stopping distance, which result from variations

in these parameters, were examined. Insofar as possible, these error analyses were based upon critical evaluations of available test data.

However, in some cases the available data are inadequate and the error analyses had to be based upon theoretical considerations.

3. A two-dimensional analysis of the kinetics of bicycle braking was developed. This yielded equations of motion for the various combinations of skidding and rolling wheels and provided the basis for estima

ting the errors attributable to variations in several of the test

parameters. In addition, it enabled formulation of the threshold

conditions for pitchover-type instabilities.

4. The various errors encountered in the performance of the road test were combined, according to whether they are random or systematic

in nature, to arrive at quantitative estimates of the test-to-test

44
variability and the lab-to-Lab variability of observed stopping distance. These variabilities were found to be excessively large, casting

doubt on the validity of the test method as presently promulgated.

5. With reasonably good testing technique -- including only mild restrictions

on the types of pavements which might be used it was found that

the lab-to-lab variability is dominated by errors which result from

the incorrect overweight-rider allowance specified in the Bicycle

Safety Regulation. Three alternative proposals were introduced, for

changes in the specified method of accommodating different rider

masses, any of which would reduce the lab-to-lab variability to more

acceptable levels.

6. The test-to-test variability, with reasonably good testing technique,

was shown to depend primarily on the variability of the test rider's

reaction times. Methods for reducing the effects of this variability

on the validity of the test results are proposed, based primarily

on the use of a multiple-testing approach.

45
16 . REFERENCES

1. Dunn, S. E., Banning of Hazardous Bicycles; Establishment of Safety

Requirements, Federal Register 39 , No. 137, pp 26100 - 26112 (National

Archives of U.S., Washington, July 16, 1974).

2. Dunn, S. E. , Bicycle Banning and Safety Regulations, Federal Register

40, No. 116, pp 25480 - 25494 (National Archives of U.S., Washington,

June 16, 1975).

3. Anon., Proceedings of the February 3, 1975, public meeting of CPSC

staff, bicycle manufacturers and others, official transcript (undated).

4. Anon., Proceedings of the May 8, 1975, public meeting of CPSC staff,

bicycle manufacturers and others, official transcript (undated).

5. Anon., Braking Performance, Report of meeting of WGl-Paris, Feb. 28, 1975.

6. International Organization for Standardization, Braking Performance,

Document No. ISO/TC149/SCl(WGl-2) 41E (revised) (British Standards

Institution, London, undated).

7. U.S. Department of Transportation, Motorcycle Brake System, Federal

Motor Vehicle Safety Standard No. 122 (Washington, April 1972).

8. Anon., Test Methods for Measuring the Braking Performance of Bicycles,

Fichtel & Sachs AG (Oct. 10, 1975 [sic]).

9. Hesketh, G. P., An Investigation into Performance Testing of Bicycle

Brakes, Raleigh Industries Ltd, Report int. 90 (Jan. 22, 1975).

10. McConnell, W. H. , and Parks, J. T., Capability Criteria of Bicycle

Braking Systems, U. of Iowa, Engineering Report on Contract FDA 73-6

(Dec. 7, 1972).

11. Lewis, G. D. , The Manoeuvrability and Braking Performance of SmallWheeled Bicycles when Ridden by Children, Transportation and Road Research Laboratory, Report LR 500 (Crowthorne, Berkshire, U.K., 1973).

I 46
12. Palsedge, J. and Szymski, E. , Test Report No. 497, Schwinn Bicycle

Co. (Feb. 14, 1975).

13. Marlowe, D. E., The CPSC Road Test of Bicycle Braking Performance - Experimental Evaluation, NBSIR 75-755 (Aug. 1975).

14. Palsedge, J., Test Report No. 507, Schwinn Bicycle Co. (Feb. 25, 1975).

15. Rice, R. S. and Roland, R. D. , Jr., An Evaluation of the Performance

and Handling Qualities of Bicycles, Cornell Aeronautical Laboratory,

Technical Report No. VJ-2888-K (April 1970).

16. Anon., Speed Measuring Instruments, James G. Biddle Co., Bulletin 35b

(Plymouth Meeting, Pa., April 1975).

17. Palsedge, J., Test Report No. 332, Schwinn Bicycle Co. (Aug. 30, 1974).

18. International Organization for Standardization, Report of the Meeting

of Working Group 1 - Braking Performance, Held in London, Thursday

24 October 1974, Document No. ISO/TC149/SC1 (London 1974 - 3) 33,

Exhibit 3 (British Standards Institution, London, Nov. 1974).

19. Ibayashi, H. , Opinion from Our Association on the Task of ISO/TC149/SC1

,

Japan Bicycle Industry Association (undated)

.

20. Doughtie, V. L. , Mechanisms and Machine Elements, Section 7 of Kent '

s

Mechanical Engineers' Handbook , Design and Production Volume, C. Carmichael (ed) , 12th edition, p 7-30 (John Wiley & Sons, N.Y., 1961).

21. Fuller, D. D. , Friction, Chapter 3 in Marks ' Standard Handbook for

Mechanical Engineers , T. Baumeister (ed) , 7th edition, p 3-39 (McGrawHill Book Co., N.Y., 1967).

22. Pettersson, R. , Halkfri Faerg till Betong-och Asf altunderlag (Skidproof

Dyes for Concrete and Asphalt) , Research Institute of National Defence

(Stockholm, Feb. 1973).

47
23. American Society for Testing and Materials, Standard Method of Test

for Skid Resistance of Paved Surfaces Using a Full-Scale Tire, 1973

Annual Book of ASTM Standards , Part 11 (1973).

24. McWhirter, B. J. and Luking, W. H. , Comments on Proposed Amendments

to the Bicycle Banning and Safety Regulations, submitted to the Consumer Products Safety Commission on behalf of Raleigh Industries Ltd

and Raleigh Industries of America, Inc., July 14, 1975.

25. Szymski, E. J., Letter to K. Edinger, Feb. 18, 1975.

26. Dwinnell, J. H. , Principles of Aerodynamics , first edition (McGrawHill Book Co., N.Y., 1949).

27. Raleigh Industries Ltd, Supplementary Information to That Put Forward

by J. F. Harriman to the CPSC [at the public meeting] on 10th September

1974, Exhibit A of Reference 24.

28. International Organization for Standardization, Document No. ISO/TC149/SC1

(London - 1974) 33, loc. cit. [18], Exhibit 2.

29. Lavrentev, N. , Method of Checking and Adjusting Brakes of the GAZ-21 on

the Basis of Braking Time, Army Foreign Science and Technology Center,

FSTC-HT-23-1743-73 (Charlottesville, Va., March 5, 1974). Translated

from Avtomobilnyy Transport , No. 1, pp 25-26 (1972) by Leo Kanner Associates (Redwood City, Calif.).

30. Dunn, S. E. , Bicycle Safety Regulations, Federal Register 40 , No. 220,

pp 52815-52825 (National Archives of U.S., Washington, Nov. 13, 1975).

48
APPENDIX

List of Symbols

A projected area of bicycle/rider system normal to the direction

motion

a linear deceleration of bicycle

a maximum deceleration in the road test

B braking capability. Equation (2)

b systematic error

b overall systematic error

b maximum positive overall systematic error max

C aerodynamic drag coefficient

D wheel diameter

e overall error

e maximum positive overall error max

F, tangential retarding force applied to wheel by brake pads

b

F^^ tangential retarding force applied to front wheel by brake pad

F^^ tangential retarding force applied to rear wheel by brake pads

F aerodynamic drag force on bicycle/rider system

w

F approximate aerodynamic drag force on bicycle/rider system

w

F^^ horizontal component of resultant force at front wheel axis

F^^ horizontal component of resultant force at rear wheel axis

F^^ vertical component of resultant force at front wheel axis

F vertical component of resultant force at rear wheel axis

yr

49
V horizontal component of resultant force at front wheel/pavement

interface

f horizontal component of resultant force at rear wheel /pavement

interface

g acceleration of gravity, 9.80665 m/s^ (32.1740 ft/s^)

H height of eg of bicycle/rider system above the pavement

h height of eg of bicycle frame/rider combination above the wheel axes

I mass moment of inertia of bicycle wheel

i+1 if V - V > 0 k = < w

(-1 if V - V < 0 w

L wheel base .

% distance of eg of bicycle/rider system aft of the front wheel axis

Mj^ mass of bicycle

= Mj^ - 2M^, mass of bicycle frame

M mass of rider . :\ r . ,

, v: '

• . i M mass of wheel

w

m mechanical advantage of caliper handbrake assembly

P force applied to handbrake lever by rider

Q squeezing force applied to wheel rim by brake pads

q distance of eg of bicycle frame/rider combination aft of the front

wheel axis

vertical component of resultant force at front wheel /pavement interface

vertical component of resultant force at rear wheel/pavement interface

:1 air':-" J: ; v:, 'VV.J

b

r random error

r overall random error

r maximum positive overall random error

max

50
8

S

C

sm

V

V

o

V

om

V

OS

V

w

W

r

W

w

Z

Zo

a

3

e r

u

stopping distance in road test

stopping distance in road test, corrected for Initial speed

measured stopping distance in road test

rider reaction time

bicycle speed

initial bicycle speed

measured initial bicycle speed

specified initial bicycle speed

component of wind speed in direction of bicycle motion

brake sensitivity. Equation (1)

brake sensitivity for marginal braking capability (B=l)

angular deceleration of bicycle wheel

angle of incline of test course

included angle, at the front wheel axis, of the brake pads from the

vertical. Figure 2

included angle, at the rear wheel axis, of the brake pads from the

vertical. Figure 1

coefficient of friction at the tire/pavement interface

51
y . minimum coefficient of friction at the tire/pavement interface for

^'^^ avoiding front wheel locking in the road test

V coefficient of friction between brake pads and wheel rim

p mass density of air

" 5

52
Table 1 - Characteristics of the Typical Bicycle

Mass of bicycle, li^ Mass of bicycle frame, M^

Mass of bicycle wheel, M

Wheel diameter, D

Wheel base, L

w

18 kg

14 kg

2 kg

660 mm

1000 mm

(39.7 lb)

(30.9 lb)

(4.4 lb)

(26.0 in)

(39.4 in)

Nondimenslonal coordinates of the center of gravity of the bicycle

with a 68.1-kg (150 lb) rider:

Distance aft of the front wheel axis, l/L 0.60

Distance above the pavement, H/L 0.85

53
Table 2 - High Rise Bicycle [15]

Characteristics

Mass of bicycle, M^^ 17.7 kg (39 lb)

Mass of bicycle frame, M^ 14.1 kg (31 lb)

Mass of bicycle wheel, M 1.8 kg (4 lb)

Wheel diameter, D ^ 533 mm (21 in)

Wheel base, L . :/ 889 mm (35 in)

Effect of Rider Mass on CG Location

M^ A/L H/L

kg (lb)

0 (0) 0.528

45.4 (100) 0.700

68.1 (150) 0.732

86.2 (190) 0.757

0.528

0.800

0.879(^)

0.943

(a) Interpolated.

54
Table 3 - Conventional Bicycle [15]

Characteristics

Mass of bicycle, M^^ Mass of bicycle frame,

Mass of bicycle wheel, M

Wheel diameter, D

Wheel base, L

17.7 kg

13.1 kg

2.3 kg

673 mm

1092 mm

(39 lb)

(29 lb)

(5 lb)

(26.5 in)

(43 in)

Effect of Rider Mass on CO Location

M

r i/L H/L

kg (lb)

0

45.4

68.1

86.2

(0)

(100)

(150)

(190)

0.512

0.593

0.635(^)

0.669

0.459

0.698

0.750(^)

0. 791

Interpolated.

55

Figure 2. Free-body diagram of bicycle front wheel.

57
Figure 3. Free-body diagram of bicycle frame-rider combination

(rider not shown)

.

58

wo

Friction coefficient

Figure 5. Effect of tire/pavement friction coefficient on the stopping distance of the typical bicycle with

marginal braking capability under the specified

test conditions.

60
9>

«>

a>

43

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61

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62

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63

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64

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ino

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4J

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60

'H
Rider mass, lb

Rider mass, kg

Figure 10. Effect of rider mass on the stopping distance of the

typical bicycle with marginal braking capability under

the specified test conditions, including a tire/pavement

friction coefficient of 0.75.

65
ADDENDUM

ERROR ANALYSES OF THREE SPECIFIC SYSTEMS

December 1975

Following the completion of the main text of this report, the author

was requested to prepare error analyses for three specific systems:

A. The system used by NBS in the series of tests described

in a companion report [13].

B. The system required by a recent revision [30] of the

Bicycle Safety Regulation.

C. The "ideal" system, which is interpreted to mean a road

testing system which would incorporate all of the best

recommendations proposed in the main text of this report.

The characteristics of System A were as follows:

(1) The starting point was located with a paint gun activated by powerful

electromagnets. ,

(2) The bicycle was steered along a relatively straight path into the

stopping zone. >

(3) Bicycle speed was measured with an electronic timing trap.

(A) The pavement of the test course offered a tire/pavement friction co- efficient of 1.22.

(5) The combined mass of the rider and instrumentation varied between

74.4 and 99.8 kg (164 and 220 lb).

(6) Alternate test runs were made in opposite directions and the results

averaged to minimize errors due to wind and grade.

The characteristics of System B are:

(1) A transverse line marker on the pavement may be used to designate

the starting point.

(2) The bicycle must be moving in a straight line at the start of brake

application.

(3) Bicycle speed may be measured with a speedometer.

(4) The pavement of the test course must be such that it offers a tire/pave

ment friction coefficient of less than 1.0, but more than the threshold

value for front-wheel lockup.

66
(5) The combined mass of the rider and

91 kg (200 lb).

the instrumentation may not exceed

(6) The slope of the test course shall not exceed 1 percent.

(7) The wind velocity shall not exceed 3.0 m/s (7 mph)

.

The characteristics of System C are:

(1) The starting point is located with propelled markers.

(2) The bicycle is steered along a straight path into the stopping zone.

(3) Bicycle speed is measured with an electronic timing trap.

(4) The pavement of the test course offers a tire/pavement friction co- efficient which is less than 1.0 but more than the threshold value for

front-wheel lockup.

(5) The combined mass of the rider, the instrumentation and added mass

(if needed) is fixed at 91 kg (200 lb) . (This changes the required stopping distance for the typical bicycle with marginal braking capability

from 4.57 to 5.05 m (15.0 to 16.6 ft) and eliminates the overweight rider

allowance)

.

(6) Alternate test runs are made in opposite directions and the results

averaged to minimize errors due to wind and grade.

The random and systematic error bands corresponding to these charactersitics are given in Table A together with those for the example system

(System X) discussed in Section 13.2, for comparison. Also given in the

table are the probable overall error bands for each system, calculated

as the square root of the sum of the squares of the individual errors,

as described in the main text.

It may be seen that the probable overall random error bands for

Systems A and C are not significantly different from that for System X

since the principal source of random error, namely, the variability in

rider reaction times, is the same in all three systems. The probable overall random error band for System B is considerably larger than this, however, because this system allows additional major sources of random error

by permitting a starting line rather than propelled markers to be used

for indicating the starting point, and by permitting speedometers rather

than timing traps to be used for speed measurement.

The probable overall systematic error band for System A is narrower

than that for System X since the combined masses of rider and instrumentation were limited to the range of 74.4 to 99.8 kg (164 to 220 lb) in System

A. The probable overall systematic error band for System B is better yet,

since this system limits the combined mass of the rider and the instrumentation to maximum of 91 kg (200 lb) . However, the probable overall systematic

67
error band for System C is by far the best of all since in this system

all bicycles are tested with the same pay load, consisting of the combined

masses of the rider, the instrumentation, and added mass as needed, to

attain the specified total.

?. C. .1 I",

'if .

i'. v'

USCOMM-NBS-DC 68

Table A - Error Analyses of Specific Systems as Applied to a Typical Bicycle with

System A System B

Source of systematic random systematic random

error error error error error

m m m m

(ft) (ft) (ft) (ft)

btart location -U.i <D<U -u . uz<r<u . u/ 0 -0.6 <r<0. 6

(-0.3 <b<0) ( -0.07<r<0.07) (0) (-2 <r<2 )

Steering u -K) , U4<r<u u -0.04<r<0

(0) ( -0.1 <r<0 ) (0) (-0.1 <r<0 )

Reaction time U -u . jy<r<u . oy u -0.39<r<0. 89

(0) ( -1.3 <r<2.9 ) (0) (-1.3 <r<2. 9)

Speed measurement u -0.27<r<0. 27

(-0.4 <b<-0.3) ( -0.3 <r<0.3 ) (0) (-0.9 <r<0.9)

Pavement friction — U . lo u 0

(-0.6) (0) (-0.4 <b<0.4) (0)

nanaiever lorces _o 1

—U.Uj*^D<^U.±i —u .±±<-r<u.xi —U . UJ<D<U . ii -0.11<r<0. 11

(-0.1 <b<0.4) ( -0.4 <r<0.4 ) (-0.1 <b<0.4) (-0.4 <r<0. 4)

Mass effects -1.66<b<-0.35 0 -1.05<b<0 0

(-5.4 <b<-l.l) (0) (-3.4 <b<0 ) (0)

Inclined roadway 0 0 -0.08<b<0.08 0

(0) (0) (-0.3 <b<0.3) (0)

Wind effects 0 -0.10<r<0 0 -0.09<r<0. 04

(0) ( -0.3 <r<0 ) (0) (-0.3 <r<0. 1)

Probable overall -1.68<b<-0.39 -0.43<r<0.90 -1.06<b<0.18 -0.78<r<l. 11

(-5.5 <b<-1.3) ( -1.4 <r<3.0 ) (-3.5 <b<0.6) (-2.6 <r<3. 6)

70
Marginal Braking Capability

System C

systematic

error m

(ft)

-0.2 <b<0

(-0.7 <b<0 )

0

(0)

0

(0)

-0.12<b<-0.10

(-0.4 <b<-0.3)

-0.12<b<0.12

(-0.4 <b<0.4)

-0.03<b<0.11

(-0.1 <b<0.4)

0

(0)

0

(0)

0

(0)

random

error m

(ft)

-0.02<r<0.02

(-0.07<r<0.07)

-0.04<r<0

(-0.1 <r<0 )

-0.39<r<0.89

(-1.3 <r<2.9 )

-0.09<r<0.09

(-0.3 <r<0.3 )

0

(0)

-0.11<r<0.11

(-0.4 <r<0.4 )

0

(0)

0

(0)

-0.10<r<0

(-0.3 <r<0 )

systematic

error

System X

m

(ft)

-0.2 <b<0

(-0.7 <b<0 )

0

(0)

0

(0)

random

error m

(ft)

-0.02<r<0.02

(-0.07<r<0.07)

-0.04<r<0

(-0.1 <r<0 )

-0.39<r<0.89

(-1.3 <r<2.9 )

-0.12<b<-0.10

(-0.4 <b<-0.3) (-

-0.12<b<0.12

(-0.4 <b<0.4 )

-0.03<b<0.11

(-0.1 <b<0.4 ) (-

-2.50<b<0

(-8.2 <b<0 ):

0

(0)

0.09<r<0.09

0.3 <r<0.3 )

0

(0)

0.11<r<0.11

0.4 <r<0.4 )

0

(0)

0

(0)

0

(0)

-0.15<r<0.06

(-0.5 <r<0.2)

-0.26<b<0.13

(-0.9 <b<0.4)

-0.43<r<0.90

(-1.4 <r<3.0 ) -2.51<b<0.13

(-8.2 <b<0.4 ) -0.44<r<0.91

(-1.4 <r<3.0 )

71

USCOMM-NBS-OC

NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 75-786

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLH AND SUBTITLE

THE CPSC ROAD TEST OF BICYCLE BRAKING PERFORMANCE —

KINETIC AND ERROR ANALYSES

5. Publication Date October 1975

6. Performing Organization Code

7. AUTHOR(S) 8. Performing Organ. Report No. NBSIR 75-786

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2130540

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as #9

13. Type of Report & Period

Covered

Final

14. sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual sumaiBry of most significant information. If document includes a significant

bibliograptiy or literature survey, mention it here.)

The Consumer Product Safety Commission has promulgated a safety standard for

bicycle braking systems based on the stopping distances achieved in road tests under

specified conditions. This report presents an error analysis of the test method, for

the Commission's use in justifying or modifying the test criteria. The error analysis

is based on experimental data, for the most part, and on theoretical principles where

sufficient data are lacking. The theory, a kinetic analysis of the bicycle braking

process, is Included in the report together with proposed definitions of terms intended to quantify important aspects of bicycle braking performance.

The error analysis produced estimates of rather large lab-to-lab and test-totest variabilities to be expected from the test method. These, in turn, were found

to be principally dominated by errors resulting from an incorrect overweight-rider

allowance specified by the Commission, and by variations in rider reaction times,

respectively. Suggestions are made for more accurate methods of accommodating variations in rider mass, for reducing the effects of the test-to-test variability, and for

reducing the danger of pitchover in the performance of the road test.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of tfje first key word unless a proper name; separated by semicolons)

I Bicycle brakes; brakes, bicycle; dynamics, bicycle; error analysis; friction, tire/pavej ment; kinetics, bicycle; measurements, bicycle braking; pitchover; standards, bicycle

! safety:1 I test —— ——method, ~— r-»'"rT 1—bicycle. tr^xj tt^tt 1 . . 18. AVAILABILITY Unlimited 19. SECURITY CLASS

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21. NO. OF PAGES

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