NATIONAL CENTER Series 2

For HEALTH STATISTICS Number 21

VITAL and HEALTH STATISTXCS

DATA EVALUATION AND METHODS RESEARCH

Calibrationof Two Bicycle

ErgometersUsedby the

HealthExaminationSurvey

A description of the calibration of two bicycle ergometers,

including detoils on techniques and on precision of measurement, and the absolute workloads for each bicycle.

Washington, D. C. February 1967

U.S. DEPARTMENT OF

HEALTH, EDUCATION, AND WELFARE Public Health Service

John W. Gardner William H. Stewart

Secretary Surgeon General

NATIONAL CENTER FOR HEALTH STATISTICS

FORREST E. LINDER, PH.D., Di~ectoiTHEODORE D. WOOLSEY, Deputy Direc~o~

OSWALD K. SAGEN, PH.D.,Assist&t Director

WALT R. SIMMONS,M.A.,~tUti.StiCL7~ Advisor

ALICEM.WATERHOUSE,M.D.,Medical ~onsu[tant

JAMES E. KELLY, D.D.S.,Dental Advisor

LOUIS R. STOLCIS,M.A.,Executive O//icer

DONALD GREEN, In/onnczzion O//ice~

OFFICE OF HEALTH STATISTICS ANALYSIS

IWAO M. MORIYAMA, PH.D., Chief

DIVISION OF VITAL STATISTICS

ROBERT D. GROVE, PH.D., Cbie/’

DIVISION OF HEALTH INTERVIEW STATISTICS

PHILIP S. LAWRENCE, SC.D., Cbie/

DIVISION OF HEALTH RECORDS STATISTICS

MONROE G. SIRKEN, PH.D., Chic/

DIVISION OF HEALTH EXAMINATION STATISTICS

ARTHUR J.MCDOWELL, Chic/

DIVISION OF DATA PROCESSING

LEONARD D. MCGANN, Cbie/

Public Health Service Publication No. 1000-Series 2-No. 21

Library of Congress Catalog Card Number 66-62208
FOREWORD

Between 1963 and 1965 the Health Examination Survey (HES) undertook a study of the noninstitutionalized population of the United States

aged 6-11 years. A total of 7,119 children of a sample of 7,417 were examined. This group was so chosen as to represent a population of 23.8

million children.

One part of the examination was a test for exercise tolerance. The

child was seated on a “bicycle, ” which he was instructed to pedal for 2

minutes. The “bicycle” was actually an ergometer. It was set at a predetermined load so that the rate of work that the child performed in

pedaling was indicated by the dial setting. The child’s pulse rate at

the end of a 2-minute ride served to measure his response to exercise.

Two different bicycle ergometers were used.

The question naturally arose as to the accuracy of the workload

settings. This was a matter of concern for two reasons. If other populations were to be compared with the U.S. population using a similar

test it was naturally important that the true work required by the HES

test be accurately known. For example, a comparison of Swedish and

American children which purported to show differences between these

two populations in their “physical fitness” might understate or overstate

the difference if the test instruments they used were calibrated differently. This was of less concern, however, in comparing different

subgroups of U.S. children. For that purpose it was important to know

how the two bicycle ergometers used by HES compared with each other,

since it was entirely possible (if the bicycles were not calibrated at

the same level) thar apparent differences between subgroups of the

population might really be differences between the bicycle ergometers

used in their tests or that real ~pulation differences might be concealed.

The H ES therefore contracted with Stein Industries, Inc., to conduct

a physical calibration of the two ergometers used in the survey of

children 6-11 years old. The results of this calibration are presented in

this report. They are pertinent not only to the Health Examination Survey

but also to other studies which use similar ergometers for population

studies.

Tavia Gordon

Division of Health Examination Statistics
CONTENTS

Page

Foreword ------------------------------------------------------------

Introduction ----------------------------------------------------------

Physical Description and Operation of Ergometer -------------------------

Calibration Techniques and Equipment -----------------------------------

Measurements and Procedures ------------------------------------------

Results --------------------------------------------------------------

Discussion of Restits and Sources of Error ------------------------------

Text Tables

Table 1. Tachometer calibration: measured pedaling speed on specified

ergometer units at indicated loads and pedaling speeds ---------

2. Calibration averages: average load measurements unspecified

ergometer units at indicated loads and pedaling speeds ---------

3. Calibration detail: loadmeasurements onspecifiedergometer

units at indicated loads and pedaling speeds ------------------

4. Calibration error: standard error and relative error of load

measurements on specified ergometer units at indicated loads

and pedaling speeds ----------------------------------------

Appendix I. CaIlbration Formulas --------------------------------------

Appendix II. Calibrator t_or Ergometer Model Ak13&3--------------------

i

1

1

2

3

4

6

3

4

5

7

9

10
IN THIS REPOR T the calibration of two bicycle ergometers is descvibed. These evgometeys weve used for measuying exevcise tolerance

in Cycle II of the Health Examination SuYvey, which consisted of examinations of a nationwide probability sample of the noninstitutionalized

population of the United States aged 6-11 yeavs.

The technique used in calibration is descyibed, and the pyecision of

mea.swement is indicated. At the pyescvibed pedaling speeds the true

wovkloads weve less than the indicated wovkloads. The amount of difference uayied from one bicycie to the othey. The bicycles diffeyed in

othev @eYfoYmance chayacteyistics as well. Both evgometeys appeayed

to be stable duying the peyiod of testing; that is, while they weye not in

pyecise calibration they weye apparently reliable.

SYMBOLS

Data notavailable ----------------------- ---

Category nonapplicable ------------------ . . .

Quantity zero -------------------------- -

Quantity more than O but less than 0.05---- 0.0

Figure does not meet standards of

reliability or precision -----------------

*
CALIBRATION OF

TWO BICYCLE ERGOMETERS USED BY THE

HEALTH EXAMINATION SURVEY

Edward S. Stein and Mark S. Rothstein, Stein ln,dustYies, Inc.

C. Joseph C lernents, Jr., Prototyfles, Inc.

INTRODUCTION

This report describes the calibration of two

ergometers—Model AM 368—manufactured by

Elema-Schonander of Sweden. The work was performed by Stein Industries, Inc., of Kensington,

Md.

The report explains the methods used, describes the special device constructed for the

calibration, and tabulates the results. Also included are a brief summary of the results, a

discussion of the sources of error, and the formulas to estimate the accuracy of the calibration

technique.

The calibration described here was made for

the purpose of determining differences in energy

loading between two ergometers used in the

Health Examination Survey (HES). The aim of the

calibration was to obtain true measures of

power, and consequently energy, expended by a

subject as a function of the various load settings

on the two machines.

It was found that in addition to a discrepancy

between the two machines tested, each unit displayed inaccuracies in both pedaling speed (&Lchometer indications) and electrical workload

selected by the operator.

PHYSICAL DESCRIPTION AND

OPERATION OF ERGOMETER

The ergometer is a device for making controlled work and energy measurements based on

the principle of presenting a constant powerload

to the subject. This power expended over a bown

period of time can be converted to a known

amount of work. Work is the integral of the

power multiplied by the time during which that

power is developed.

The ergometer consists of a bicycle seat and

a pedal crank coupled to an electrical generator

(see fig. 1). The output of the generator is con-

@olled by an electrical servo system designed

to keep the output voltage constant over a wide

range of pedal shaft speeds. This voltage is impressed upon a series of load resistors which

are, in turn, connected to the output circuit by

individual switches. Thus, the operator may select the amount or size of the load applied against

the subject.

Additional circuitry is incorporated in the

ergometer to compensate for any drift in the

load resistors due to temperature change inside

the unit. The result is an essentially constant

powerload during the testing period, provided

1
Figure I. Illustration of the ergometer. 

the pedal shaft speed is maintained within prescribed limits. 

The subject supplies power to the ergometer 

by turning the pedals at nearly constant speeds, 

developing torque which results from the force 

exerted by his foot on the pedal. This torque can 

be measured by obtaining the product of the subject’s force on the pedal times the distance from 

the center of the pedal to the center of the pedal 

shaft. The product of this torque (which is proportional to the force applied) and the number of 

revolutions per minute yield a figure representing the rate of work, or power. 

Since the ergometer is soconstructed as to 

yield a constant powerload over a fairly wide 

range of r.p.m., an unusual characteristic results in that as the speed of the shaft increases, 

the torque required to turn the pedal shaft decreases. Thus, as the subject tires and is unable 

to sustain a constant speed, the apparent drag 

on a real bicycle. There the torque is set by the 

drag associated with factors such as terrain 

and wind resistance, and it tends to remain constant. The sensation is that the amount of work 

increases with the speed. Thus, on a bicycle, by 

diminishing speed the rider decreases his rate 

ofdoing work and his rate of tiring. The ergometer, on the other hand, tends to tire the subject at a constant rate as he slows down by 

making the drag at the pedals increase. 

CALIBRATION TECHNIQUES AND 

EQUIPMENT 

A calibrating technique was required to 

ascertain whether the two ergometers did in 

fact present similar loads for similar switch 

settings. Besides measuring the uniformity between the two ergometers, it was necessary to 

be able to determine the actual force exerted by 

the subject upon the pedals when working against 

various loads. 

A mechanical power source, consisting of 

a known rotational force, was applied to the 

sprocket shaft in such a way as to drive it at 

the nominal speedof 60 r.p.m., as well as 45 and 

75 r.p.m. This simulated the subject’s operation 

of the ergometer. The transmitted power for 

various settings of the load switches and for 

several different speeds was measured accurately. 

The tests were performed on both ergometers within a few days of each other to avoid 

the possibility of drift or other changes taking 

place in the calibration apparatus between tests. 

The ergometers were in no way adjusted or altered 

prior to or during the calibration runs. 

The calibrating accuracy was to be within 

2 percent of true. In order to achieve such 

accuracy, it was necessary to keep the speed of 

the input shaft constant to within 1 percent while 

taking measurements on the ergometers. 

A calibrating device was constructed consisting of an electric motor coupled to a Vickers 

hydraulic transmission (see Appendix II). The 

motor was rated at H horsepower and operated 

continuously at 1,725 r.p.m. The hydraulic pump 
Uansmission was constructed so that the speed

of its output shaft could be carefully adjusted by

moving an internal valve which regulated the

length of the smoke of the pump piston.

The output of the transmission was connected to a speed reducer consisting of a

sprocket gear and chain drive. The speed reducer was coupled to the output drive shaft which

transmitted the torque through universal bearings

to the pedal shaft of the ergometer being tested.

Both pedal cranks were removed from the ergometer. This reduced the mass of the driven

ergometer but had a negligible effect on the

drag measurement.

The motor, transmission, and speed reducer

made up the drive assembly, which was mounted

on a rigid platform. The platform was suspended

from the output drive shaft by a paiy of pillowblock bearings. The drive shaft was supported

from the floor by a second set of bearings. Thus

the entire assembly was free to rotate about the

drive shaft.

This configuration allowed an accurate measurement of the torque transmitted to the ergometer by simply balancing the moment created

by the reaction of the load upon the suspended

power source at any given shaft speed.

After an initial balancing at no-load, counterweights were added to balance the drive assembly

platform at the discrete loads chosen and at

constant shaft speed.

The torque was then computed from the

product of the counter-weights necessary to

balance the drive assembly and the moment arm

length (distance from the balance pan suspension

point to the center of the drive shaft). The

torque measurement thus derived was independent of the weight of the driving platform as well

as all sources of drag within the drive assembly.

The drive shaft speed was carefully measured and constantly monitored by the method

described in the section ‘‘hleasurements and

Procedures. ”

A final calibration of power delivered to

the ergometer was made by averaging torque

readings and multiplying by the angular frequency

(speed in r.p.m.) of the drive shaft with appropriate conversion factors. These power figures

then were tabulated against ergometer load

switch settings.

MEASUREMENTS AND PROCEDURES

Each of the basic elements used in the calibration was initially checked against standards

traceable to l&borator y primary standards. The

weights were checked on a scale balance to an

accuracy better than %percent.

Primary tachometer measurements (see

table 1) were made by counting revolutions of the

pedal shaft with a stopwatch. The watch was

checked with an electronic timer. After the ergometer tachometer was initially calibrated, a

monitoring system was devised for keeping the

angular frequency (shaft rotational speed) constant during the load calibration runs.

The speed monitor consisted of a “ProxiProbe” inductive pickup and a Model 410 Carrier

Amplifier System, both manufactured by Stein

Industries, Inc., and a Hewlett-Packard Model

Table 1. Tachometer calibration: measured

pedaling speed on specified ergometer

units at indicated loads and pedaling

speeds

Indicated load

and

indicated r.p. rn.

200 kpm

45--------------------

60--------------------

75--------------------

450 kpm

45--------------------

-------- -------- ----

::--------------------

750 kpm

45--------------------

60--------------------

75--------------------

Average

45--------------------

60---------------------

75--------------------

Measured r.p. m.

#273

56.9

70.6

87.1

56.1

70.4

86.9

55.8

70.4

86.0

56.2

70.5

86.7

#27 1

54.5

74.4

84.5

59.4

71.9

87.7

58.8

75.5

91.7

57.6

73.9

87.9

3
140A oscilloscope. The inductive probe was

brought close to a projecting rod on the drive

shaft (see Appendix II). The output of the probe

was amplified by the carrier amplifier and displayed on the oscilloscope. The time base was set

for 2 seconds sweep time and set for internal

trigger.

Every third revolution triggered the oscilloscope, and the next succeeding pulse was displayed

on the scope face with the sweep magnified 10:1.

By making careful measurements of the point on

the sweep where the second of the two pulses occurred, it was possible to obtain accurate and

instantaneous speed readings.

The speed was continually monitored during

all of the runs and readjusted as necessary.

The actual testing procedure began with the

calibration of the weights to be used in balancing

the drive assembly. Balancing of the assembly

itself was accomplished next, after which the

drive shaft was attached to the ergometer, The

transmission was set to drive the ergometer at

a given rate of speed. The shaft was timed for

approximately 60 seconds to get the truer.p.m.

indications.

At each load point (each setting of the

switches) the pedal shaft speed was checked for

about 10 seconds with the monitoring system,

adjusted if necessary, and monitored again.

As the drive assembly became imbalance

because of the drag exerted against it from the

electrical generator of the ergometer, weights

were placed on the suspension balance pan at

the end of the moment arm until the assembly

regained and held balance for a period of 1 minute.

The amount of weight required to balance the

assembly was logged, the ergometer turned off,

the load switches reset, and the drive assembly

rebalanced without weights. This procedure was

repeated for each of the load setting at intervals

of approximately 3 minutes, with each test run

requiring about 3 minutes.

The data collected (quantity of weights for

each point in each run) were then multiplied by

the length of the moment arm, yielding the applied torque. The torque, multiplied by the

angular frequency (shaft speed) and appropriate

conversion factors, yielded the calculated power

in kpm/M (Kg- M/Min). (See Appendix I.)

RESULTS

Tables 1-3 show, respectively, the results

of the tachometer calibrations, a summ~zwy of

the ergometer load calibrations, and the detailed

calibration data for each test run performed.

It should be noted that the tachometers on

both units drifted considerably. Because of the

Table 2. Calibration averages: average

load measurements on specified ergometer

units at indicated loads and pedaling

speeds

Indicated load

200

250

300

350

400

450

500

550

600

650

700

750

Unit #273

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kDm---------

Indicated load

200

250

300

350

400

450

500

550

600

650

700

750

Unit #271

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

kpm---------

Calculated load

45/56

r.p. m.]

168

212

260

306

354

404

449

497

546

597

644

691

60/71

r.p.m.]

182

228

279

329

377

427

471

522

577

627

676

723

75/87

r.p. m.L

——

230

271

321

375

418

485

535

582

642

697

749

799

.—

Calculated loacl

45/58

r.p.m.:

141

182

225

268

312

356

399

442

486

532

573

615

60/74

r.p. m.l

141

182

229

273

310

353

401

439

482

528

569

609

lIndicated r.p.m, /true r.p.m.

——

7sI/88

r.p.m.i

173

210

268

307

354

398

445

492

542

595

636

686

4
Table 3. Calibration detail: load measurements on specified ergometer units at indicated loads and pedaling speeds

Indicated load

Unit #273

200 Kim------------------------------

250 kpm -------.------------.---------

300 kpm --.---.------.--------....----

350 Kim------------------------------

400 kpm ---.--------------------.-----

45o kpm -.------.---.------.------..--

500 Kim------------------------------

55o kpm -----------------..--.--------

600 Kim------------------------------

650 kpm -..---.-------.--.-.-.--------

700 kpm -.....-----.--.----.--.-..----

750 Kim------------------------------

Indicated load

Unit #271

200 kpm --------.---..-----.----------

250 kpm ------------------------------

300 kpm ---.--------------------------

35o kpm -.----------------------------

400 kpm -----------.------------------

450 kpm --.-----------------.---------

500 Kim------------------------------

550 Kim------------------------------

600 Kim------------------------------

650 kpm ------------------------------

700 Kim------------------------------

750 Kim------------------------------

Calculated load

45/56 r.p.m.t

174

212

258

306

357

408

454

502

542

605

647

688

168

216

263

307

353

405

449

:::

595

642

692

162

208

257

305

354

402

447

494

546

593

643

691

166

213

261

307

353

402

446

498

548

596

644

691

45/58 r.p.m.l

138

181

221

269

312

356

400

443

489

533

574

617

141

181

224

265

310

357

397

436

480

529

571

612

-—

141

182

229

270

315

356

400

444

491

537

576

623

60/71 r.p.m.l

176

222

272

323

370

421

464

515

568

618

667

719

i80

226

278

329

378

425

472

524

583

632

680

722

Calculated load

145

184

227

268

309

356

398

444

485

529

570

609

181

226

277

327

376

425

468

519

573

624

674

719

;;;

287

337

384

435

481

531

583

633

683

732

60/74 r.p.m.l

153

198

252

296

336

380

434

472

517

566

611

655

142

184

228

274

311

352

400

439

482

524

565

608

127

165

207

249

284

326

369

406

447

494

531

565

75/87

r.p.m.L

230

271

321

375

418

485

535

582

642

697

749

799

75/88 ~

r.p.m.

173

210

268

307

354

398

445

492

542

595

636

686

lhdicated r.p.m. /true r.p.m.

5
wobble inherent in the needle indicator, it was

difficult to determine indicated r.p.m. accurately.

There appeared to be a 10 to 15 r.p.m. difference

between indicated and true r.p.m. at all operating

speeds, with a pronounced long-term downward

drift noticeable in unit no. 273.

Further discussion of the data and their

implication follows.

DISCUSSION OF RESULTS AND

SOURCES OF ERROR

Error for all the calibrating procedures has

been computed at less than 2 percent, as discussed below. Runs were repeated in part in

order to spot check the results. An interval of

several days between runs was allowed for spot

checking. In each of the points so checked, the

observable variance was under 1 percent.

An analysis of points of calibration on unit

no. 271 shows that between the range of 45 and

60 r.p.m. (indicated), the ergometer presented a

constant power load for each switch setting independent of pedal shaft speed. Above 60 r.p.m.

(indicated), however, the powerload increased.

The difference ranged from approximately 20

percent at the low end to 10 percent at the high

end of the observable range. In any case, all

readings indicated that this unit was delivering

less power than that selected by the switches.

The deviation appeared to be about 20 percent

from the true power output as measured at 60

r .p ,m. (indicated) and at the true value of 500

kpm/M (Kg-M/Min).

Unit no. 273 exhibited a constant power difference between 45 and 60 r.p.m. (indicated):

approximately 20 kpm/M (Kg-M/Min) measured

throughout the entire range. At the higher shaft

speeds, the difference was substantially greater—

nearly 50 kpm/M (Kg-M/Min).

Deviation from true power output figures

was substantially less than in unit no. 271; the

values at 60 r p.m. (indicated) were approximately

18 kpm/M (Kg-M/Min) below the values selected

by the switch settings. This was within the 5 percent figure claimed by the manufacturer throughout most of the calibration range.

Short-term drift of the machines was so

small as to be barely measurable. Over the first

10 minutes a ckift of approximately 10 kpm/M

(Kg-M/Min) was observed at most points. This

time was long compared with testing intervals,

and the long-term drift was not considered

significant.

Several sources of error are inherent in the

calibration technique chosen here. Frc~m the

formula used in computing powerload (see Appendix I) these are rotational speed, cc~unter -

weights, and moment arm.

The rotational speed was measured with an

oscilloscope which was checked against i~ stopwatch. The watch was compared with an electronic

timer and found to be accurate to within 10

seconds in 24 hours, or an error of ~0.01. 1 percent. The error associated with timing the os -

cilloscope was estimated at 2 milliseconds in 1

second, or ~0,20 percent. Thus, the co]mbined

inaccuracies associated with reading and measuring the pedal shaft rotational speed produced

an error of *0.381 percent, or about 1/3 percent.

The counter-weights were checked at the

University of Maryland. Weights of 100 grams

and less were checked on an analytical balance

with an accuracy to four decimal places. The

larger weights were then compared with the

smaller ones on a torsion balance. The ma ximum

error was -0.53 percent, but the sum of all deviations was under -0.04 percent. All readings during

the calibration procedure were corrected by

adding to the logged amount a correction factor

corresponding to the known deviations of the

weights used.

The moment arm was measured with an

accurate metal scale, but due to difficulties of

measurement, accuracy was estimated at 1./8 inch

in 24 inches, or LO.50 percent.

In addition to these errors, an indeterminacy of measurement of the exact lbalance

point due to the dynamic imbalance of the calibrating apparatus introduced another error factor

This indeterminacy was estimated at 10 grams

over most of the range, and at about 15 grams

at the high end. This is equivalent to approximately 1 percent at the low end and 0.7 percent

near the center of the range.

Therefore, summing all inaccuracies to determine worst case error, error factors of approximately 1.6 percent near the center of the

6
Table 4. Calibration error: standard error and relative error of load measurements on

specified ergometer units at indicated loads and pedaling speeds

Indicated load

Unit #273

zoo Kim----------------

250 kpm----------------

300 Kim----------------

35o Kim----------------

400 Kim----------------

450 kpm------------_---

500 kpm----------------

550 kpm----------------

600 lcpm-------------- .-

650 kpm----------------

700 kpm----------------

750 kpm----------------

Indicated load

Unit #271

200 lcprn----------------

250 kpm----------------

300 kpm----------------

350 kpm----------------

400 kpm----------------

450 kpm----------------

500 kpm----------------

550 kpm----------------

600 kpm----------------

650 kpm----------------

700 kpm----------------

750 kpm----------------

EGzIEzz

Standard error in kpm

5.0

3.3

2.8

1.0

;:;

3.6

3.6

2.5

5.3

2.2

1.7

I

45/58 r.p.m.l 60/74 r.p.m.l

Standard error in kpm

2.9

1.4

3.5

2.2

2.6

0.5

1.5

::;

;:;

6.1

13.0

16.6

22.5

23.5

26.o

27.0

32,5

33.0

35.0

36.2

40.1

45.0

45/56 r.p.m.l 60/71 r.p.m.l

Relative error in percent

3.0

H

0.3

0.5

0.7

0.8

0.7

0.5

0.9

0.3

0.3

3.5

:::

1,8

1.3

1.1

45/58 r.p.m.l 60/74 r.p.m.l

Relative error in percent

2.0

0.8

1.0

u

1.0

9.3

8.6

8.4

7.7

8.1

7.5

7.3

6.8

;::

lIndicated r.p.m./ true r.p.m.

7
range and 2 percent at the low end are obtained.

Another way to evaluate the relative error is to

examine the data in table 3 by standard statistical

methods. This is done ti table 4. At each indicated load the standard error ~ (

w

in the usual notation) and the relative error

(100 s / Z) are tabulated for each indicated load

setting. The relative error is greater at lower

loads and at higher r.p.m., but it is generally of

the order of magnitude indicated by the previous

calculations. Some of this r‘error ,“ of course,

represents variation in the ergometers’ performance over the succession of runs, but it is

evident from the previous reckoning that the

ergometer variation must be small indeed and that

almost all of the indicated variation represents

measurement error.

The exceptions to this rule of high reliability are the measurements of bicycle no.271

made at a nominal speed of 60 r .p.m. Relative

error of the three runs at this speed ranged

roughly between 7 and 10 percent. These high

values may represent some technical lapse, but

in all likelihood they are largely a measure of

machine instability at that speed. The three

runs were actually done at true speeds of 72,

77, and 84 r.p.m., respectively. The variation

in speed arose from the great instability of the

tachometer. In trying to reproduce a normal

operating situation the machine was being used

in a range outside of the recommended 45-75

r p.m. and across a range of speeds. This may

well be an accurate representation of the usual

operating experience, but if it is, the operating

experience with this machine includes a substantial measurement variability.

000

8
APPENDIX 1

CALIBRATION FORMULAS

The powerload presented by the ergometer can be

computed from the following formula:

where

PC = the calculated powerload

Cl = the angular frequency

7 = the torque transmitted into the ergometer

f = the rotational speed

W = the counter-weights

d = the moment arm

Since the readings on the ergometer load selector

are in kpm/M (Kg-M/Min) the proper conversion

factors were used. The weight measurements were

directly in kilograms, and the moment arm was

measured in inches. By converting to meters, the

torque was computed in Kg-M. If the rotational speed

is now ascertained in revolutions per minute and

multiplied by 211, a multiplying factor is obtained.

This factor times the torque yields the power in

Kg-hl/Min(kpm/M).

000

9
APPENDIX II

CALIBRATOR FOR ERGOMETER MODEL AM 368

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3“ ‘

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OUTPUT DR;VE

SHAFT ~ ‘/’

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TRAN.SM[ SS1 ON

U. S. GOVES.NMENT PRINTING OFFICE :1967 0-243-662
Series 1. Programs and collection procedures .-Reports which describe the general programs of the National 

Center for Health Statistics and its offices and divisions, data collection methods used, definitions, 

and other material necessary for understanding the data. 

Series 2. Data evaluation and methods yesearch .-Studies 

mental tests of new survey methods, 

of new statistical methodology including: experistudies of vital statistics collection methods, new analytical 

techniques, objective evaluations of reliability of collected data, contributions to statistical theory. 

Series 3. Analytical studies.- Reports presenting analytical or interpretive studies based on vital and health 

statistics, carrying the analysis further than the expository types of reports in the other series. 

Series 4. Documents and committee reports .-Final reports of major committees concerned with vital and 

health statistics, and documents such as recommended model vital registration laws and revised birth 

and death certificates. 

Series 10. Data from the Health Interview Survey .-Statistics on illness, accidental injuries, disability, use of 

hospital, medical, dental, and other services, and. other health-related topics, based on data collected 

in a continuing national household interview survey. 

Series 11. Data from the Health Examination Survejl _ .-Data from direct examination, testing, and measurement of national samples of the population prov+de the basis for two types of reports: (1) estimates 

of the medically defined prevalence of specific diseases in the United States and the distributions of 

the population with respect to physical, physiological, and psychological characteristics; and (2) 

analysis of relationships among the various measurelnents without reference to an explicit finite 

universe of persons. 

Series 12. Data from the Znstitutional Population Surveys . .-Statistics relating to the health characteristics of 

persons in institutions, and on medical, nursing, an? personal care received, based on national 

samples of establishments providing these services and samples of the residents or patients. 

Series 13. Data from. the Hospital Discharge Survey _ .-Statistics relating to discharged patients in short-stay 

hospitals, based on a sample of patient records in a national sample of hospitals. 

Series 20. Data on mortality .-Various statistics on mortality other than as included in annual or monthly 

reports- special analyses by cause of death, age, andot5er demographic variables, also geographic 

and time series analyses. 

Series 21. Data on natality, marriage, anddivorce . -Various statistics onnatality, marriage, and divorce other 

than as included in annual or monthly reports -special analyses by demographic variables, also 

geographic and time series analyses, studies of fertility. 

OUTLtNE OF REPORT SERIES FOR VITAL AND HEALTH STATISTICS 

Public Health Service Publication No. 1000 

Series 22. Data from the National Natality and Mortality S?rrveys . -Statistics on characteristics of births and 

deaths not available from the vital records, based on sample surveys stemming from these records, 

including such topics as mortality by socioeconomic class, medical experience in the last year of 

life, characteristics of pregnancy, etc. 

For a list of titles of renorts published in these series, write to: Office of Information and Publications 

National Center for IIealth Statistics 

U.S. Public Health Service 

washingron, D.C. 20201