GEOLOGICAL SURVEY CIRCULAR 405

INSTRUMENTAL IMPROVEMENTS 

IN ALTIMETRY
ERRATA

Page 10 5 last paragraph should reads :

wSize, weight and ruggedness For field use an altimeter should be 

convenient to carry over difficult terrain....**

Page IS, top of left-hand column should reads

w .. 0. .connections do not move appreciably^ the stress on the diaphragrams 

changes considerably with extreme variations in atmospheric pressure, as 

can be seen in figure 9. The barostat, previously described^ can be eon« 

sidered an instrument of the null type in which the altitude measurements 

are based on weights rather than spring movement.**
UNITED STATES DEPARTMENT Qf1 THE INTERIOR 

FRED A, SEATON, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

GEOLOGICAL SURVEY CIRCULAR 405

INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

By James L. Buckmaster and Atherton H. Mears

Washington, D. C., 1958

Free on application to the Geological Survey, Washington 25, D. C.

CONTENTS

Page

Abstract............................................... 1

Use of altimetry by the Geological Survey ............................. 1

Accuracy attainable with present instruments and methods .................... 2

Sources of error ......................................... 2

Geological Survey instrumental experience ........................... 3

Characteristics of an ideal surveying altimeter ........................... 7

Considerations in altimeter design. ................................ 11

Pressure-sensitive element. . . ................................ 11

Freedom from constraints. ... ................................ 11

Performance requirements ... ................................ 13

The optical altimeter ........ ................................ 13

Optical magnification ...... ................................ 13

Experimental optical altimeters ................................ 14

Performance of experimental models ............................... 20

Conclusion. ....................................... . . .' . 21

Appendix A. The air density correction factor in altimetry ................... 23

B. Precision altigrams ................................. 31

C. A method for calibrating altimeters. ........................ 32

D. Strain in flexural elements. ............................. 33

ILLUSTRATIONS 

________ Page

Figure 1. Nomogram for obtaining air temperature and relative humidity correction factor . . 2

2. Variations in barometric gradient during a field test ................. 3

3. Schematic diagram of barostat ............................. 4

4. Barostat (right) and test chamber with manifold system (left). ............ 5

5. A. Sensitive unit of barostat; B. Weights for barostat . ............... 6

6. Calibration curves for service altimeter T-25270. .................. 7

7. Temperature correction curve for a service altimeter ................ 7

8. Generalized graph of change in elastic error with time and stress .......... 9

9. Cross-sectional diagram of vacuum box in null-type altimeter ............ 13

10. Schematic diagram of direct-reading optical altimeter. ................ 13

11. Schematic diagram of tilting-mirror optical altimeter. ................ 14

12. Experimental optical altimeter, model X-2 ....... ............... 15

13. Experimental optical altimeter, model X-l ....... ............... 15

14. View of model X-2 with case removed, looking toward objective ........... 16

15. View of model X-2 with case removed, looking toward mirror ............ 17

16. Calibration correction curves for optical altimeter X-l and

	service altimeter T-25270 .............................. 19

17. Cross-sectional diagram of lighting unit for tilting-mirror optical altimeter. .... 19

18. Corrections to air density factors for lower base readings below 5,000 ....... 27

19. Corrections to air density factors for lower base readings above 5,000 ....... 28

20. Electronic altigraph records .............................. 31

21. Strain in curved flexural element. ........................... 33

III

INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

By James L. Buckmaster and Atherton H. Mears

ABSTRACT

The Topographic Division of the Geological Survey has conducted a research program in altimetry since 1954 in an effort to improve the accuracy 

of the method so that it can be used more widely to provide control elevations 

for photogrammetric mapping. Results of this research include the construction of a barostat, to provide an improved calibration standard, and the design 

and construction of experimental altimeters that use optical instead of mechanical magnification in measuring the displacement of the pressure-sensitive 

element.

USE OF ALTIMETRY BY THE 

GEOLOGICAL SURVEY

Altimetry for determining elevations 

above sea level1 has been used in the Geological Survey from the time of its foundation. In 

fact,, the "Second Annual Report of the United 

States Geological Survey, 1880-81, " contains 

an outstanding article on the subject by Dr. 

G. K. Gilbert, then chief geologist; although 

the instrumental references are now obsolete, 

the theoretical treatment of physical considerations and errors is classical.

As applied to the operations of the 

Topographic Division of the Survey, altimetry 

was an indispensable source of control elevations for reconnaissance mapping before 

1900. However, as more rigid standards of 

accuracy were adopted, spirit leveling, planetable stadia traverse, and precise trigonometric leveling largely supplanted altimetry 

as a means of supplying control elevations.

In the present paper, the term "elevation" 

will be used exclusively for heights referred to 

sea-level datum. "Altitude" will be used in referring to uncorrected readings of the altimeter 

or to vertical changes that are not specifically 

correlated with sea-level datum.

Compliance with the vertical-accuracy 

specifications of the National Map Accuracy 

Standards requires that at least 90 percent of 

the points tested shall be accurate within onehalf of the contour interval. To meet this 

standard with the photogrammetric methods 

and procedures now employed, elevations used 

to control aerial photographs are required to 

be accurate within the following limits:

Contour interval 

(feet)

5

10

20

25

40

50

80

Error limit,

photocontrol elevation

(feet)

0.5 

1.0 

2.0 

2.5

3.0 

4.0 

5.0

Stadia traverse with planetable and 

alidade can supply photocontrol elevations for 

mapping at any of these contour intervals. 

Precise vertical-angle observations may be 

used to control mapping at contour intervals 

of 20 feet or larger. Both of these methods 

include checks on the observations and ties to
INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

higher order control so that the accuracy of 

the results can be evaluated with certainty. 

However, they involve laborious and expensive 

fieldwork, particularly in remote or heavily 

wooded areas.

The speed and ease with which altimeter 

surveys can be carried out offers an attractive 

possibility for lowering the costs of supplemental control, provided that accuracy standards 

can be met. Altimetry has been successfully 

used to control mapping at contour intervals of 

40 feet and larger despite the fact that tests 

have disclosed anomalous errors of 5 and 6 

feet in the results of even the most carefully 

executed altimeter surveys. The effect of 

these overlarge errors has been minimized by 

obtaining a considerable surplus of elevations 

so that the photogrammetrist can eliminate 

obviously incorrect elevations and apply an 

averaging technique in leveling the stereomodels.

The altimetry research program of the 

Topographic Division has been directed toward 

eliminating anomalous errors and increasing 

the absolute accuracy of the instruments. 

Obviously, if elevations reliable within 1 or 2 

feet can be obtained by altimetry, the method 

can be used to control standard-accuracy photogrammetric mapping at contour intervals of 20 

and possibly 10 feet. The results thus far 

obtained from the research program indicate 

that a redesign of the altimeter will be the 

greatest single factor in reducing the magnitude 

of errors in elevations determined by altimeter 

surveys. In addition, more frequent and precise 

calibration will provide better calibration corrections. Also, it is evident that altimeter 

surveys should not be undertaken when weather 

conditions are unstable.

ACCURACY ATTAINABLE WITH PRESENT 

INSTRUMENTS AND METHODS

Sources of error

Before discussing the possible 

improvements in altimeters that have been 

pointed up by the research to date (1958), the 

fundamental causes of errors in altimetry 

should be reviewed.

Instrumental errors. Errors inherent in the altimeter itself will be described 

below, in the sections concerned with altimeter characteristics and design. These 

errors at present contribute an indeterminate 

part of the net error and complicate the 

analysis of other effects. At times, instrumental error exceeds that due to atmospheric 

variations and hence is a limiting factor, 

especially when atmospheric conditions are 

favorable.

Atmospheric and gravitational 

irregularities. Variations in air temperature over the area being surveyed are difficult to determine and may cause large errors 

unless the influence of local conditions (such 

as wind, timber, and clearings) is taken 

into account. Humidity has a much smaller 

effect and therefore does not need to be 

measured with the same precision as temperature. Below 85°F, humidity corrections are 

small, and they become negligible below 40°F. 

The nomogram shown in figure 1 clearly 

illustrates the relative effects of temperature 

and humidity and provides a convenient means 

for determining the correction factor for the 

combined effect of these two conditions. This 

correction factor is the reciprocal of air

-20 -10 10 20 30 40 50 60 70

Figure 1. Nomogram for obtaining air temperature and relative humidity correction factor.

Courtesy Wallace&'Tiernan, Inc.
ACCURACY ATTAINABLE WITH PRESENT INSTRUMENTS AND METHODS

density. In the two-base method of altimetry, 

air density and the correction factor are determined through the use of high- and low-base 

altimeter readings, eliminating the need for 

field measurements of temperature and humidity. (See App. A)

Barometric gradients can be accurately 

determined only by using an array of three or 

more base stations.2 As errors caused by atmospheric circulation are difficult, sometimes 

impossible, to estimate, altimeter surveys 

should not be. undertaken in high winds. 

Figure 2 shows by vectors the magnitude and 

variation of the barometric gradient during a 

field test conducted under good weather conditions. Examples of local disturbances can 

be seen in the barograms, figure 20 (App. B).

Corrections for errors due to the variations of gravity are usually negligible but may 

be obtained from the Smithsonian tables if 

desired.

Observational errors and mistakes. 

Mistakes or blunders, such as reading the 

wrong division, can be avoided by using proper 

care in reading the instrument; errors of interpolation, however, are caused by the limitations of perception. The design of the instrument has a definite influence on both mistakes 

and errors. Fewer mistakes will occur if the 

altimeter is well designed in graduations and 

numbering, is well illuminated, and is convenient to use. An optical reading system can 

minimize errors of observation through reduced 

parallax and increased magnification.

Calibration. --When the limit of tolerable error tor an altimeter is set at 1 foot, as 

it must be if the instrument is to be widely 

used for obtaining supplemental photocontrol 

elevations, the methods of calibration now in 

common use are inadequate. To disclose 

instrumental changes that may occur through 

field use, service altimeters should be calibrated before and after each major project.

A°&

Mears, A. H., and Earing, W. F., 1954, 

Multiple-base altimetry: Hiotogramm. Eng., 

v. 20, no. 5, p. 814-22.

X

X

X

X

X

X

J I

0.5 1.0 

i i i i i i

Gradient, in feet per mile

J6;oo

v$? %

-June 30,1954

-July 1, 1954 

Bull Run area, 

Virginia

Figure 2. Variations in barometric gradient 

during a field test.

The method of calibration formerly used by 

the Geological Survey consisted in comparing 

sets of six or more altimeters in a test 

chamber, at successive pressure intervals 

that correspond approximately to even 100- 

foot steps of elevation. (See App. C.) 

Calibration with mercurial standards is 

impractical because it requires mercurials of 

high precision and expert operators and is 

prohibitively expensive. Calibration with a 

precise laboratory aneroid standard is reasonably fast and convenient; but neither this nor 

the other methods previously mentioned will 

provide the accuracy now sought. To provide 

an adequate calibration standard, the Survey 

has constructed a barostat, which will be 

described in detail below.

Geological Survey instrumental experience

It should be possible to determine 

elevations of field stations with an average 

error of less than 2 feet if the following 

conditions are met:
INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Atmospheric conditions are favorable.

The altimeters are highly accurate; that is, 

the sum of instrumental and observational 

error does not exceed 1 foot.

The area of survey is limited to a radius of 

10 miles.

The difference in elevation between any base 

and any field station is less than 2, 000 

feet. This requirement is based on the 

general assumption that error due to atmospheric anomalies is proportional to 

the difference in elevation. With the 

weather favorable and operations limited 

to a 10-mile radius, error due to atmospheric variations is estimated to average 

1/1000 of the difference in elevation.

Results of test survey at Bull Run. -- 

On June 30 and July 1, 1954, a test field survey 

was carried out in the Bull Run Mountains near

Middleburg, Va. The results of this limited 

test demonstrate the accuracy that can be 

obtained in field elevations when the ideal conditions listed above are approximated.

In this test, the difference in elevation 

between the highest and lowest field stations 

was about 450 feet. All -field stations were 

within 250 feet of the average elevation of the 

three base stations. At the base stations, the 

range in altitude readings due to barometric 

changes amounted to less than 50 feet. Two 

altigraphs and four surveying altimeters were 

used. The two altigraphs were used at base 

stations; their charts could be read to 0.1 foot, 

and the indicated altitude changes were accurate to 0. 5 foot. The survey altimeter at the 

third base station had no irregularities in its 

calibration curve for the range of pressures 

encountered; the altitude readings from this 

instrument were accurate within the observational limit of 1 foot.

0.020" inlet orifice --*.,

Y///////////////////////

To controlled 

pressure chamber

and manifold

-Change-in-pressure indicator

Figure 3. Schematic diagram of barostat.
ACCURACY ATTAINABLE WITH PRESENT INSTRUMENTS AND METHODS

Atmospheric conditions on July 1 were 

especially favorable for the test survey. Low 

wind velocities made it possible to obtain accurate measurements of temperature and humidity over the entire survey area. (Light winds 

tend to make air density more uniform and also 

to nullify unequal heating effects caused by 

solar radiation.) The roving altimeters were 

used to determine elevations on 12 field 

stations, of which 11 were bench marks and the 

twelfth was a road intersection with an elevation 

previously established by stadia traverse. The 

average error of the elevations determined by 

altimetry was 1. 3 feet.

One of the altimetric elevations, 

however, was in error by 6 feet. The service

altimeter in question was later subjected to 

repeated calibrations, at 10-foot intervals, 

over the portion of its scale used in the field 

test. These detailed calibrations revealed an 

abrupt change in the instrument's calibration 

curve; when the true calibration correction was 

applied, the error of the elevation was reduced 

to I foot. It can thus be inferred that, when 

high accuracy is required, the present service 

altimeters may have to be calibrated at intervals smaller than 100 feet. Such detailed 

calibration can be very laborious.

The barostat. To provide a more accurate and convenient calibration standard for 

altimeters, a modified version of the Johnson 

barostat designed at the National Bureau of

Figure 4. Barostat (right) and test chamber with manifold system (left).
INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Standards has been constructed in the instrument shop of the Geological Survey at Silver 

Spring, Md. (See figs. 3, 4, 5.) The testchamber pressure is regulated by a set of 

precisely computed and machined weights, 

which produce absolute pressure intervals 

equivalent to 100-foot steps of elevation. The 

term "absolute" is used conditionally because 

1-foot absolute accuracy in altimetry is an 

elusive goal. Pressure datum for the barostat 

is established by comparison with a highly 

precise laboratory aneroid calibrated by the 

Bureau of Standards. Inasmuch as the elevation 

datum for field altimeter surveys is established 

by placing the base stations at bench marks, a 

slight difference between the pressure datum of 

the barostat and true sea-level pressure datum 

is not important.

The barostat is fast and relatively 

simple in operation and provides far more accurate and repeatable test-chamber pressures 

than any method of calibration used heretofore. 

Calibration with the barostat is expected to 

improve the results of altimetry substantially, 

by indicating the reliability of each service 

altimeter as well as by providing more accurate calibration corrections. Aneroid hysteresis is apparent from the calibration data 

because the barostat itself is virtually free of 

hysteresis and operates on an absolute rather 

than a comparative basis. Figure 6 illustrates the difference between the calibration 

curves for a service altimeter obtained by 

comparison with nine other service altimeters 

(dotted line) and by the use of the barostat 

(dashed line). Field tests have not yet been 

made to determine what effect calibration with 

the barostat has had on the accuracy of field 

elevations.

General conclusions. The results of 

regular supplemental control projects with 

altimeters, as well as laboratory research, 

indicate that the greatest need is for higher 

absolute accuracy in service altimeters, though 

the use of the barostat for calibration can be 

expected to bring about some improvement in 

the accuracy of field elevations. The sensitivity of present altimeters is adequate and 

should not be confused with absolute accuracy.

Figure 5. A. Sensitive unit of barostat; 

B. Weights for barostat.

Daily field comparison of the six or 

more altimeters used on a supplemental 

control project usually disclose unaccountable 

differences of several feet between instruments. 

A part of each of these discrepancies is 

assumed to be caused by the limitations of field
CHARACTERISTICS OF AN IDEAL SURVEYING ALTIMETER

Altimeter, correction in 8 5~o

y^'X.^ ''' *"*..'''

__./-x

 -by

 -by

/

barostat

compariso

-^

i with 9 ot

^,

ier service

^ ^ ^/"

altimeters

) 1000 2000 3000 400( 

Altitude, in feet

Figure 6. --Calibration curves for service altimeter T-25270.

comparisons. Moreover, field tests in which 

pairs of altimeters are used at each field station 

reveal discrepancies of several feet between 

instruments, after all corrections have been 

applied. Some of these discrepancies undoubtedly are caused by inadequate calibration.

Although the 6-foot calibration error 

discovered in the Bull Run test survey was 

particularly noteworthy, many similar anomalies in calibration curves have been demonstrated by laboratory calibrations. Altimeters 

with such irregularities require more careful

Skilled observers, using laboratory test 

chambers, can consistently check their readings 

to 1 foot. Field comparisons can seldom be 

made with such accuracy; however, simultaneous 

readings could be obtained by using a camera.

calibration, and the corrections determined 

for them are not dependable because the points 

of calibration do not necessarily coincide with 

the points of change of the optimum calibration 

curves. To obtain the high accuracy required 

in supplemental control surveys, there is a 

critical need for altimeters that can be calibrated quickly and accurately and that do not 

exhibit serious anomalies in their calibration 

curves.

CHARACTERISTICS OF AN IDEAL 

SURVEYING ALTIMETER

In describing an "ideal" surveying 

altimeter, some compromise must be made 

between the desirable and the practical. An 

altimeter accurate to 0.1 foot under all conditions is highly desirable, but practical

feet Drrection,in per

degree Fahrenheit

2 Po 

* 'i i 

/ ^

-^^" *-^*» --\

\

2000 4000

Altimeter reading. in feet

6000

Figure 7. --Temperature correction curve for a service altimeter. Corrections are algebraically 

additive for temperatures above 75°F and subtractive below 75°F.
INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

considerations limit the instrument to one of 

reasonable size and cost, for which instrumental and observational errors combined are small 

in comparison with atmospheric errors

Net accuracy. The altimeter should 

yield elevations correct within 1 foot under all 

conditions of temperature and pressure, after 

appropriate corrections have been applied.

Temperature characteristics. Altimeters are subjected to a constant temperature 

of 75°F while being graduated and therefore 

require no temperature corrections when used 

in the field at that temperature. Although the 

effects of variations from the standard temperature are largely compensated in the design and 

fabrication of the instrument, the manufacturer 

supplies a temperature correction curve, similar to figure 7, so that any residual error due 

to temperature variation can be eliminated. It 

should be emphasized that this correction is 

entirely separate from the air-temperature 

correction factor previously discussed and that 

it is valid only when the instrument is in thermal 

equilibrium or the temperature is changing 

slowly. Instrumental temperature corrections 

usually are quite small, seldom exceeding 

2 feet, a figure which may be taken as an 

acceptable maximum.

Only two temperature effects are consequential in a well-designed altimeter: 

dimensional changes in the mechanism and 

elasticity changes in the pressure-sensitive 

element. Temperature effects on the gas 

within the pressure-sensitive element are 

avoided by evacuating the pressure capsules to 

less than 0. 05 inch of mercury at 75°F?

When readings are taken on an altimeter 

that is not in thermal equilibrium, serious 

errors are likely to result. This can be demonstrated by placing an altimeter in a test chamber 

at a given pressure and a temperature of 100°F.

Peterson, J. B., and Freeman, J. R., Jr., 

1922, Precision altimeter design, in National 

Advisory Committee for Aeronautics Report 126, 

Altitude instruments: pt. 2, p. 36.

After an hour, all parts of the altimeter should 

have reached a uniform temperature, and the 

altitude reading, corrected for instrumental 

temperature, will equal the equivalent altitude 

of the test system. If the temperature is then 

suddenly dropped to 30°F at the same pressure, 

the pointer of the altimeter will swing away 

from the original reading for a few minutes, 

reverse direction, and swing back (some altimeters will go into full oscillation, with gradually decreasing amplitude). After some time, 

which depends on the time-lag constant of the 

instrument, the pointer will come to rest, and 

the corrected altitude reading will again agree 

with the equivalent altitude of the test system.

For maximum speed in field use, the 

thermal time-lag constant of the altimeter 

should be as short as possible. Moreover, 

temperature changes larger than 5 degrees 

should be avoided, and the altimeter should be 

shaded from the direct rays of the sun. If 

large changes in temperature cannot be avoided, 

the altimeter must be held at a constant ambient 

temperature for a suitable time before readings 

are taken.

Hysteresis. An altimeter should indicate the~same scale readings with pressure 

increasing or decreasing, regardless of the 

magnitude or rate of change of pressure. 

However, a small time lag is inevitable because 

of the imperfect elastic characteristics of the 

materials from which the pressure-sensitive 

element and flexural parts are fabricated. In 

a perfectly elastic material, strain would be 

exactly proportional to stress, as stated in 

Hooke's law; unfortunately, no such material 

is available.

The absolute accuracy obtainable in an 

altimeter is thus limited to a large degree by 

the elastic characteristics of metals. In the 

pressure-sensitive element, atmospheric 

pressure is balanced by the elastic forces of 

the element, and it is essential that the metal 

follow Hooke's law, within a few millionths of 

an inch, throughout the pressure range for 

which the element is designed. (Actually, it 

is necessary only that the elastic behavior of 

the metal be consistent and repeatable.)
CHARACTERISTICS OF AN IDEAL SURVEYING ALTIMETER

If a loading spring is used, its elastic performance must be correspondingly consistent. In 

general, the elastic error or inconsistency of 

metals is proportional to about the fifth power 

of the applied stress. If springs and elastic 

members are designed so that the applied stress 

does not exceed about three-tenths of the classified yield-point stress, hysteresis and elastic 

errors are held within acceptable limits.

Time is an important factor in analyzing elastic errors. If an elastic member is 

stressed a given amount, the resultant deformation will continue to increase for an indefinitely 

long period of time, toward a condition of equilibrium, as shown in figure 8. With the time 

abscissa plotted on a logarithmic scale, the 

curves approximate straight lines for a considerable distance but probably do not continue 

along straight lines indefinitely. Elastic error 

usually is plotted as a percentage of total strain 

or deformation, as in figure 8, the percentage 

being proportional to about the fourth power of 

the applied stress. Change in elastic error 

with temperature is not considered serious 

within the temperature range to which altimeters are subjected.

In a well-designed altimeter, the 

materials used and the stresses applied are 

such that the total elastic error is very small 

and deformation approaches the equilibrium 

point, within undetectable limits, in a few 

minutes. Five minutes after a change of 

pressure, an altimeter should not show lag 

exceeding 1/2000 of the pressure change.

Although for small stresses quartz has 

optimum properties of elastic performance 

and variation of elastic coefficient with temperature, it is not a practical material for altimeter pressure elements because it is difficult 

to fabricate and becomes fragile under the 

stresses required of pressure elements; also, 

it often fractures under shock or because of 

scratches on its surface. Materials widely 

used for pressure elements because of their 

superior elastic characteristics include beryllium copper, phosphor bronze, and Nispan C; 

however, they must be carefully heat treated 

and hardened to obtain the required elastic 

properties?

Stott, L. L., and Carson, R. W., 1938, 

Stability of some alloys for springs compared: 

Metals and Alloys, no. 9, p. 233-36.

\ of totaldeformation Elastic percent in error, c

Sfe £S8B

/^

-^

/

<^f

V*?*®**^ ^

Stress40,000p«i__. - 

""Stress 30.000 pai __

X

/"' "

/ ^

^^ ^^

"l Mill ______ 1 1 1 1 1 1 1 1 1 ______ L__. 1 L__l 1 II 1 _ .. 1

- x

^ ^

_ _ -~

1 1 1 1 II 1 1 L_ 1 1 1 1 1 1 1 1 ._!_

15 min 1 hour I day 1 month 1 year 10 years

Time

Figure 8. Generalized graph of change in elastic error with time and stress.
10 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Rapid response. The altimeter must 

respond as rapidly as possible to any change of 

altitude greater than 0. 5 foot, or 0.005 inch of 

mercury. For use under all field conditions, 

including helicopter transportation from station 

to station, it should track a change of altitude 

to an accuracy within 1 foot at any rate of change 

up to 1,000 feet a minute.

Controlled pressure equalization. -- 

Although inadequate circulation of air between 

the interior of the altimeter case and the external atmosphere can cause excessive lag in 

response, this effect can be controlled and used 

to advantage by proper design. In some types 

of altimeters, the case is airtight except for a 

capillary tube, permitting the instrument to be 

sealed for transportation at high altitudes. 

Such altimeters also can be connected into 

pressure-calibration systems that do not use 

vacuum test chambers.

A capillary tube that controls the rate 

at which the internal air reaches equilibrium 

with the surrounding atmosphere will largely 

eliminate the effects of small, rapid fluctuations in air pressure which are caused by 

local disturbances, such as a car or truck 

passing by along a highway or a door opening 

and closing in the office or laboratory. Atmospheric disturbances of this sort are shown in 

the barograms (App. B, p. 30 ).

Stability. Each time an altimeter is 

subjected to the same test conditions of pressure, 

temperature, and humidity, it should indicate 

the same scale reading. Some altimeters, 

however, exhibit a gradual change, usually 

constant over the instruments' range, which may 

amount to several feet a year. The rate of 

change should not exceed 2 feet a year. An 

abrupt change or a variation in the rate of 

change generally means that the altimeter has 

been intentionally disturbed or adjusted. A 

gradual increase in altitude readings for a 

given test pressure may indicate a leak in the 

pressure element.

Ease of calibration and regularity of 

curve. Surveying altimeters usually are calibrated in vacuum test chambers, but instruments

with sealed cases and outlet tubes also may be 

connected into a test system by means of 

vacuum lines, a procedure which is often used 

for field comparisons. Null-type altimeters 

are difficult to calibrate and require special 

test equipment because they must be adjusted 

manually before each reading; if these instruments were equipped with sealed cases, calibration would be simplified.

The calibration correction curve for 

each altimeter should be as nearly linear as 

possible. The differential between the corrections for adjacent 100-foot graduations should 

not exceed 1 foot. Altimeters with the physical 

characteristics previously described in this 

section could be expected to have nearly linear 

calibration curves. Moreover, they would be 

easy to calibrate because only a few points on 

their scales would have to be compared with 

the laboratory standard.

Adequate range.--To a considerable 

extent, the accuracy of an altimeter is 

inversely proportional to its range because the 

greater the range the greater the stresses, 

flexural deformations, and elastic errors. 

Therefore, wide range and high accuracy are 

essentially conflicting characteristics in an 

altimeter. If altimeter surveys on a given 

project are limited to an elevation range of 

2,000 feet, as previously discussed, and a 

factor of 1, 500 feet is allowed for variations 

in atmospheric conditions, the ideal surveying 

altimeter would have a range of 3, 500 feet. 

However, setting the range this low for maximum accuracy would require multiple models 

of the altimeter, each for use within a specific 

range of elevation. Economic considerations 

in manufacturing and the overlapping of elevation ranges in field operations will probably 

make it necessary to increase the range to 

5,000 or 7,000 feet.

Size, weight, and ruggedness. For 

field use, an altimeter should be convenient to 

on foot over difficult terrain. With carrying 

case, it should weigh not more than 5 pounds. 

The carrying case should be waterproof, wear 

resistant, shock absorbent, and insulating.
CONSIDERATIONS IN ALTIMETER DESIGN 11

The altimeter should be rugged enough 

to withstand the normal jars and shocks of field 

use. If the case is sealed, it must withstand 

differential pressures, such as those encountered 

when the altimeter is tested at low elevations or 

when it is sealed off at high elevations and then 

carried to low elevations.

Ease of use. Although precedures 

have been developed to guard against blunders 

in reading, much depends on the ease with which 

the scales can be read. The scales should be 

clearly graduated, adequately illuminated, and 

free of parallax. It should not be necessary to 

level the altimeter precisely.

Cost. Although cost is an important 

consideration, and high cost would restrict the 

potential market, a surveying altimeter meeting 

the requirements described above could command 

a price several times that of present instruments.

CONSIDERATIONS IN ALTIMETER DESIGN

Improved methods of forming the 

diaphragms.

Improved methods of heat treatment.

Improved methods of joining the

diaphragms to form the vacuum box.

Older designs for pressure-sensitive 

elements incorporated auxiliary springs to 

keep the vacuum boxes from collapsing under 

atmospheric pressures. The springs were 

either helical or leaf shape and were placed 

either inside or outside the vacuum box. 

However, the auxiliary-spring designs are now 

relatively obsolete, and the surveying altimeters 

used by the Topographic Division have vacuum 

boxes that are stiff enough not to require auxiliary springs. Consequently, the pressuresensitive elements are under relatively heavy 

stress at sea level.

Freedom from constraints

Pressure-sensitive element

Of the three general types of pressuresensitive elements, the vacuum box (Naudet type) 

is most widely used in altimeters and is the only 

one which will be discussed here. The bellows 

(Sylphon type) is employed in the barostat. The 

third type is the Bourdon tube.

The vacuum box consists of two corrugated elastic diaphragms joined together at 

their rims. Because of the needs of aviation 

for accurate altimeters, much research and 

development work has been directed toward 

perfecting the performance of vacuum-box 

pressure-sensitive elements. Significant 

results of this research include the following:

Materials with better elactic characteristics and smaller temperature effects, 

providing greater displacements for 

given pressure changes. Also, some 

pressure-sensitive elements have been 

designed so that the displacement of 

the element is linear with respect to 

changes in altitude.

To minimize elastic errors, the 

pressure-sensitive element must move without 

constraints. The displacement-indicating 

mechanism should be designed so that all its 

parts are as light in weight and as free of 

friction as practicable. When two or more 

vacuum boxes are connected in tandem to 

increase the magnitude of displacement, some 

constraint is unavoidable because the weight of 

one box acts on the other. (Another consideration in tandem mounting is the mechanical 

instability of the system.) As a result, more 

than three vacuum boxes are seldom used in 

tandem.

It is often erroneously assumed that, 

aside from gravitational forces, the displacement of the vacuum box is affected only by

"It can be proved that the elastic time 

effects in an aneroid barometer can be reduced 

if a. spring with good elastic properties is used 

in conjunction with a relatively very flexible 

diaphragm, although the diaphragm had large 

elastic time effects." M. D. Hersey, 1916, 

Theory of stiffness of elastic systems: Jour. 

Washington Acad. Sci., v. 6, p. 569.
12 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

unknown, negligible constraints. The elastic 

performance of the altimeter would be markedly improved if the displacement of the pressuresensitive element were measured without in any 

way constraining the movement of the element. 

One theoretically possible solution to the 

problem would be to use monochromatic light 

and an interferometer. Such a device, used in 

conjunction with a good pressure-sensitive 

element and designed to measure vacuum-box 

axial displacements as small as 0. 000001 inch 

with negligible error, could provide altitude 

readings accurate to 0. 1 foot. However, as an 

instrument of this type would hardly be considered practical for field use, other approaches 

to the problem must be considered.

Electronic methods. --Although practical considerations make it necessary to 

accept some compromises in design, the use of 

electronic devices holds some promise of 

approaching the ideal in measuring displacements 

ments of the pressure-sensitive element.

One electronic method is to mount one 

of the electrodes of a capacitor, known as the 

pressure plate, on the free end of the pressuresensitive element or vacuum box.7 This electrode is in the form of a lamina or plate, with 

its two surfaces plane parallel, and must be as 

light in weight as practicable. The plate is 

mounted so that its plane surfaces remain perpendicular to the central axis of the vacuum box 

when the free end of the box and the plate are 

displaced by pressure changes. The opposite 

or fixed end of the vacuum box is rigidly 

attached to the frame or chassis of the altimeter. Also mounted on the frame is a micrometer mechanism which holds and moves the 

opposing plate (or plates) of the capacitor, 

called the measuring electrode. The measuring plate and micrometer system are alined to 

keep the surfaces of the measuring plate .parallel and in close proximity to those of the pressure plate. The micrometer is used to measure 

displacements of its electrode from a standard 

-position relative to the pressure electrode.

The term "vacuum box" is employed when 

the box itself is considered, without accessory 

mechanisms, linkages, or springs. The term 

"pressure-sensitive element" denotes the entire 

unit, with accessories.

The pressure and measuring electrodes 

constitute a variable capacitor, which is connected into an electronic micrometer circuit, 

usually a bridge circuit. By suitable displacement of the measuring plate, the capacitance is

adjusted and the associated circuit brought to a

standard condition (either maximum or zero

current, as :

static force oxerted on the pressure plate by the

measuring p] ate can be reduced to a negligible

amount through careful design of the electronic 

circuit. The system therefore approaches the

ideal of a fre 

free of error 

springs.

i-movement vacuum box and is 

s due to friction, linkages, and

In c,n alternative electronic method, 

movement of the vacuum box could be measured 

by means of :he variations of inductance between 

two coupled coils.

Botft

here require 

adjustments 

might not be 

use, but 

cult.

Des

electrical 

placement ha 

of variations 

contact, 

resistance

Null

ead on a meter). The electrothe electronic methods described 

either manual or servomechanical 

o obtain altitude readings. This 

i disqualifying objection for field 

calibration procedures would be diffigns employing micrometers and 

contacts to measure vacuum-box disve proved unsatisfactory because 

in the pressure needed to make 

Errors also result from variations in 

due to corrosion of the contact points.

methods. --One well-established

means of red icing elastic errors is to apply the 

null principle, in which stops restrict the center 

connections cf the vacuum box from moving more 

than a few thousandths of an inch under any 

pressure conditions. In field instruments of the 

null type, spring tension is applied to the 

box; for each altitude measurement the tension 

is adjusted to bring the sensing end of the 

vacuum box to the null position between the 

stops, by centering the null-indicating needle 

over its index mark. The altitude reading is 

obtained by means of a micrometer system, 

which measured the amount the equalizing 

spring has been extended to bring the vacuum 

box to the null point. Although the vacuum-box
THE OPTICAL ALTIMETER 13

connections do not move apprec 

on the diaphragms changes con: 

extreme variations in atmosphe 

as can be seen in figure 9. The 

viously described, can be consi 

merit of the null type in which tl 

measurements are based on weiyms 

than spring movement.

Performance requirements

An average vacuum box is displaced 

0.1 inch by a 10,000-foot difference in altitude. 

If 0.1-foot sensitivity and 0. 5-foot accuracy are 

sought, the measuring system must be sensitive to 0. 000001 inch and accurate to 0. 000005 

inch. These extreme degrees of response have 

been attained in electronic altimeters (note 

agreement between the barograms in Appendix 

B), and there is good evidence that the best 

vacuum boxes will respond with comparable 

accuracy in field instruments.

In a surveying altimeter of the indexing type, the multiplying mechanism causes the 

needle, to -traverse about 40 inches of scale for 

the 0.1-inch displacement of the vacuum box, 

thus providing a multiplication factor of 400. 

Two different methods of improving the performance of pressure elements have been outlined. In one method the pressure-sensitive 

element is allowed the freest possible movement; in the null method, movement is restricted to a very small amount. Although either

^ At high altitude

Figure 9. --Cross-sectional diagram of vacuum 

box in null-type altimeter, showing elastic 

movement of diaphragms (exaggerated) 

under extreme of pressure when center 

connections are restricted by stops.

method may bring the performance of pressure 

elements within the standards sought, the 

micrometer and other measuring mechanisms 

thus far investigated (weight systems excepted) 

seldom have performed with the desired accuracy. Therefore, it has been concluded that an 

optical magnification system will provide the 

most practicable approach to the ideal surveying 

altimeter.

THE OPTICAL ALTIMETER 

Optical magnification

The use of optical, rather than mechanical, magnification offers many advantages, the 

most significant being a great reduction in the 

number of mechanical parts, so that the design 

approaches the ideal of free movement, in which 

nothing touches the free end of the vacuum box 

in the course of the measurements. Figure 10

Focus adjustment

Graduated scale 

on glass

Illuminator

Vacuum 

boxes

Frame

Reticle scale

_ 400X microscope

Figure 10. Schematic diagram of direct-reading optical altimeter.
14 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

illustrates a design of this type, in which a 

scale attached directly to the free end of the 

vacuum box is viewed through a microscope. 

However, to provide 400X magnification, a 

relatively high-powered microscope, with its 

minute depth of field, and an adequate system 

of illumination are needed. If built to laboratory standards, the microscope would require 

an 8-mm objective and a 20X eyepiece and 

would have a depth of field of about 0.000002 

inch.

The possibilities of this basic design 

have not yet been exploited. It would not be 

necessary to follow the strictest laboratory 

standards in building the reading microscope. 

Nevertheless, the requirements for depth of 

field, illumination, and other factors indicate 

that a completely free-moving pressure-sensitive element could not be used because a very 

slight lateral restraint would be needed to 

maintain or adjust the focus.8

A modification of the free-movement 

optical-reading design has been explored to a 

limited extent. (See fig. 11.) This modified 

design employs a small tilting mirror, linked 

to the moving end of the vacuum box, which 

reflects the image of a finely divided glass 

scale into a 50X reading microscope. Although 

artificial illumination would not usually be necessary, the size of the mirror (a problem 

requiring careful consideration) could be reduced if artificial illumination is used. 

Moreover, the altimeter could then be used 

regardless of natural lighting conditions. To 

avoid adverse effects on the pressure-sensitive 

element, all the heat produced by an illuminating lamp, except that of the pencil of light 

passing through the glass scale, could be kept 

outside the instrument case.

Q

This lateral restraint could be negligible, 

It is assumed that the scale would have 100-foot 

divisions, that the microscope would have a 

reticle with 5-foot or smaller divisions, and 

that the scale would be adjusted laterally into 

focus instead of moving the microscope.

Eyepiece 

Index reticle s 

Graduated scale 

on glass

Illuminator

Objective

Tilting mirror 

Flexure elements 

Push rod

Vacuum 

boxes

Frame

Figure 11. Schematic diagram of tiltingmirror optical altimeter. Flexural elements shown below proper position for 

clarity.

Experimental optical altimeters

Two of the three experimental altimeters, models X-l and X-2, thus far constructed by the Geological Survey are illustrated in 

figures 12 through 15. Although these prototypes have not been temperature compensated 

and are not ready for field use, their performance in the laboratory indicates excellent
THE OPTICAL ALTIMETER 15

'! ", si US I* 1 «* "f

Figure 12. Experimental optical altimeter, 

model X-2.

possibilities. A further indication is that only 

a minor part, rather than the major part, of 

instrumental error in commercial altimeters 

is caused by the vacuum box. A brief discussion of the principal parts of model X-2 follows.

Microscope. The reading system 

consists of a 32^mm, f:4 achromatic objective, 

a pentaprism to bend the light rays 90°, a glass 

reticle with a single index line, and a well-corrected 25X eyepiece. As the objective is 2.4X, 

total magnification is about 60X. Model X-l is 

generally similar but has no pentaprism, its 

design being more nearly as shown in figure 11. 

Model X-3 (not illustrated) differs only in 

minor details from model X-2.

For "best resolution the objective should 

be designed specifically for this application, but 

stock achromats usually will give a fair degree 

of resolution. Adequate resolution probably

Figure 13. Experimental optical altimeter, "model X-l, showing internal 

construction through structural plastic top which supports altimeter.

could be obtained with an aperture of 6 mm. 

This would permit the use of a smaller, lighter 

mirror and also would increase the depth of 

focus. Maintaining focus over the entire scale 

range has not been a serious problem in the 

prototype altimeters, but it must be carefully 

considered in future designs.

Mirror. It is highly desirable that 

the mirror be as small and light as practicable 

because flexure-element stiffness and the resulting load on the vacuum box are approximately proportional to the size of the mirror. 

Decreasing the size of the mirror will improve 

ruggedness and reduce sensitivity to tilt. The 

1 x 8 x 12 mm first-surface mirrors used in the 

prototype models probably can be reduced in 

size in future models, with beneficial results. 

The mirror must, of course, be large enough to 

reflect the light rays from the graduations to the 

objective lens and must be sufficiently flat to 

have no degrading effect on image quality. The 

mirror supports in the experimental models 

were fabricated from solid aluminum alloy, and 

the mirrors were attached to the supports with 

an adhesive.
16 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Figure 14. --View of model X-2 with case removed, looking toward objective.
THE OPTICAL ALTIMETER 17

Figure 15. --View of model X-2 with case removed, looking toward mirror.
18 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Graduated scale. A tilting mirror 

microscopic reading system requires graduations on a cylindrical or spherical surface 

whose center of curvature lies on the mirror's 

axis of rotation. Although it is more difficult 

to produce graduations on a curved surface than 

on a flat one, the problem is not serious. In 

the experimental altimeters, spherical glass 

elements of ophthalmic quality and with concentric surfaces were used, rather than cylindrical elements, because the spherical elements 

were readily available and easy to mount. Graduations were photographically processed onto the 

glass blanks by contact printing from a 20X reduction of a millimeter scale. The scales are 

about 30 mm long and contain 20 lines per mm; 

line width is about 10 microns. As each graduation represents 10 feet, total range is 6,000 

feet; the operating range is about 5,000 feet.

Scales with as many as 40 lines per mm 

and line widths as small as 3 microns are 

available commercially. These limits seem 

adequate for the present; but, should the need 

arise, laboratory microscope stage scales with 

100 lines per mm and a line width of 1. 5 or 2 

microns can be obtained. For altimeters with 

a 5,000-foot range, limitations of magnification, 

mirror rotation, and .focus will also limit the 

length of the scale and probably will not permit 

graduations at intervals of less than 5 feet. 

Even though a unit-foot scale could be included 

in the reticle, it is doubtful that such a reticle 

is superior to a single index line and interpolation between 5- or 10-foot graduations. Tests 

with other optical instruments have shown that 

the average individual can, without special 

training, interpolate to tenths of intervals with 

errors averaging 1/20 interval.

Field readings should be taken in sets 

of three or more. One accepted procedure is 

to take three readings at each field station, at 

timed intervals of 1 or 2 minutes, and use the 

mean of the readings. This procedure reduces 

errors of interpolation and errors due to local 

disturbances and provides a check against 

blunders. If such a reading procedure is 

followed, interpolation to unit feet between 5- 

or 10-foot graduations is considered adequate.

Flexural elements. --As it is believed 

that a serious amount of instrumental error is 

caused by improper design of the flexural elements and the use of solder to hold them, the 

flexural supports for the mirrors in the experimental altimeters were fastened to milled surfaces with 1/8-inch square washer-type pads 

and No. 2 machine screws. The supports are 

of beryllium copper, 0.004 x 0.125 x 0.5 inch, 

with a flexural length of 0. 25 inch. The mirror 

rotates a maximum of 11° from the unstressed 

position, producing maximum stresses of about 

28,000 psi (pounds per square inch). It was 

assumed that the axis of rotation is situated at 

the center of the flexural section, and the lack 

of any serious focusing problems indicates that 

the assumption is justified though not theoretically exact.

Tilt of the instrument, weight of the 

mirror unit, and forces exerted by the push rod 

all tend to shift the axis of rotation from an 

exact position. Further stabilization of the axis, 

by adding two similar flexural strips outside and 

at right angles to the strips actually used, was 

considered, but tests have not shown this refinement to be necessary. Although other types of 

pivots, such as jeweled pivots, could be used, 

flexural pivots are considered decidedly preferable because they do not involve lost motion or 

sliding friction. It may be practicable to fabricate the mirror support and its flexural elements 

from a single strip of beryllium copper.

Connecting element. The connecting 

element links the vacuum box to a lever arm on 

the mirror support. Partial and perhaps adequate temperature compensation can be obtained 

by using suitable material and dimensions for 

the connecting element. The length of the lever 

arm on the mirror support is inversely proportional to the value of a graduation interval (in 

feet of altitude). Provision is needed for adjusting this value so that variations in pressuresensitive elements can be compensated; an 

alternative possibility is to vary the width of the 

flexural strips. The elements used in the experimental models reduce the vacuum-box displacement about 5 percent; an increase in this percentwould be justified as a means of adjusting the 

vacuum-box displacement.
THE OPTICAL ALTIMETER 19

Instrument feet corrction, in 

^ to ooO) ro ^° !?o 

/

f

/

 altitude

 - --altitude <

Service

/-\_/c^r^

X-1 deviation from

'^X

Optical altimeter X-1

increasing in 100 foot

lecreasing in 200 foot

altimeter T-25270

 ^-^ ^

uniform curve -^-.--^.^ ^

\

\

\

v

\ increments \

 \ 

increments \

\

\

-^^x/\._./AV"

\

.»

) 1030 2000 3000 \

Altitude, in feet

Figure 16. Calibration correction curves for optical altimeter X-1 and service altimeter T-2527C.

The calibration curve of model X-1 is 

parabolic in shape (fig. 16). The curve could be 

made to approximate a straight line by raising 

the effective pivot point between the connecting 

element and the lower arm. In the experimental 

altimeters the connecting arm was constructed 

of stainless steel wire for convenience, but a 

material such as an aluminum alloy should be 

used to provide temperature compensation.

Lighting unit. After the prototype 

models were constructed, it was found that the 

high power of the reading microscope plus the 

rather small objective aperture made artificial 

illumination highly desirable in laboratory use. 

Auxiliary lighting units would be needed for field 

use under adverse lighting conditions. Moreover, 

the use of artificial illumination exclusively will 

permit greater freedom in designing optical 

Figure 17. Cross-sectional diagram of altimeters. The lighting unit constructed for use

lighting unit for tilting-mirror

optical altimeter.

mercury 

battery
20 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

with the prototype altimeters provides adequate 

light together with long battery life. (See fig. 

17.) The lamp is held over the part of the scale 

to be read, and the light is directed toward the 

mirror.

An important consideration in designing future optical altimeters is adaptability for 

use in automatic photorecording instruments of 

the Alticorder type. This use will require a 

lighting unit that covers a wide portion of the 

scale or an automatic device for positioning 

the illuminator.

Frame. No particular effort was made 

to provide lightweight frames for the prototype 

altimeters, except to construct the frames from 

an aluminum alloy. The relatively massive 

frames do not add an excessive amount to the 

weight of the instruments. Moreover, they 

improve ruggedness, deform very little under 

variable temperatures, and conduct heat quickly 

to bring the instruments to thermal equilibrium. 

The complete altimeters weigh 2 pounds each.

Case. --The altimeter case consists of 

a commercial deep-drawn aluminum cup, modified to permit the top piece to screw into the 

flange of the cup. The top piece serves both as 

a part of the framework and as an airtight top 

for the case. This combination forms a strong 

protective case but gives no protection against 

shock. The joint is sealed with an O ring to 

make the case airtight. For ease of reading, 

the microscope should extend several inches 

above the top of the case, but this complicates 

the problem of providing adequate shock protection. Shock protection can be provided by a 

sponge-rubber cover that extends up over the 

top rim, plus a padded canvas carrying case 

that will also protect the microscope.

The vent tube, which extends half an 

inch above the top of the case, allows the altimeter to be connected into testing and calibrating 

systems with plastic tubing.

Vacuum boxes. The experimental 

altimeters employ pairs of vacuum boxes in 

tandem. No adverse effects due to the tandem 

mounting have been observed. Although

pressure elements in which displacement is proportional to altitude rather than pressure are 

preferred for use in altimeters, the relative 

merits of the two types of elements have not yet 

been carefully studied.

Performance of experimental models

Even though the experimental optical 

altimeters are not temperature compensated, 

and no attempt was made to obtain linear calibration curves, their performance in the laboratory has been unusual in regularity of calibration surves, repeatability of results, and 

freedom from hysteresis. The calibration 

curve for altimeter X-l is shown in figure 16. 

Although the magnitude of the correction exceeds 

100 feet at some points.along the curve, the 

curve itself exhibits a regularity not hitherto 

observed in the calibration curves of surveying 

altimeters. Deviations from a uniform parabolic curve are shown at the lower edge of 

figure 16; at a few points, these deviations are 

as great as 2 feet per 100-foot difference in 

altitude. A significant part, perhaps half, of 

the deviation may be charged to reading error 

because the scale graduations in this instrument 

are quite crude.

The almost total lack of hysteresis, as 

indicated by the difference between the up and 

down curves, suggests that perhaps altimeter 

X-l, the barostat (with which the altimeters 

were tested), and the change-of-pressure indicator (with which the barostat was monitored) 

may have small and approximately equal amounts 

of hysteresis. In undergoing a large difference 

in pressure, the corrugations of the bellows 

element of the barostat are subjected to strains 

corresponding to those illustrated for a vacuum 

box in figure 9. In a recent modification of the 

barostat system, the change-of-pressure indicator was fitted with a three-way valve so that 

it can be left at atmospheric pressure when the 

barostat is used at high-altitude pressures, 

thereby providing an accurate check on hysteresis when the barostat is returned to zero-altitude pressure.
THE OPTICAL ALTIMETER 21

The duration of the calibration plotted 

in figure 16 was about 3 hours. The two altimeters were held at the pressure equivalent to 

3, 500 feet of altitude for 15 minutes before the 

series of decreasing-altitude readings was begun.

Conclusion

It is hoped that this discussion will lead 

to a better understanding of the accuracy and

possibilities of altimeters and altimetry in 

general. The laboratory performance of experimental optical altimeters holds considerable 

promise that the optical design is a practical 

approach to the ideal surveying altimeter. 

However, further engineering research and 

development work is needed to adapt the prototype designs to practical field instruments. 

It is hoped that this work will be undertaken by 

commercial instrument manufacturers.

APPENDIX A 23 

THE AIR DENSITY CORRECTION FACTOR IN ALTIMETRY

The two-base method of altimetry does not take into account the change in air density due to 

the variation of air temperature with altitude. To provide a check on air density, air temperatures 

usually are recorded at all base stations although the two-base formula does not require this information. If the difference in elevation between the high and low bases exceeds 500 to 1,000 feet, the 

variation of air temperature with altitude should be taken into account. The following article, written 

by us in 1955, explains a method for doing so.1

The determination of altitudes from altimeter readings in mountainous areas is less accurate than in areas of low relief for several reasons. Probably the main reason is that the two-base 

formula as presently used does not take into full account the variation in pressure of the air column 

between the low and high bases, there being no consideration of the variation in density due to the 

decrease in temperature with increase in altitude. The error from this cause is of the order of 

1 foot for a difference in elevation between high and low bases of 500 feet to as much as 15 feet for 

base altitude differences of 2,000 feet.

Corrections must be made for the deviation in air density from 50°F and zero percent relative humidity, the conditions assumed in Smithsonian Meteorological table 51, to which W&T altimeters are calibrated. In the single-base and traveling-base altimetry methods these corrections are 

applied directly to the observed altitude differences between two stations as obtained from the altimeter readings at each of these stations. These two corrections are often combined in correction 

tables or by nomograms. The factor desired is known as Air Temperature and Relative Humidity 

Correction Factor for Altitude (fig. I, p. 2). In the following discussion this factor is designated as 

the air density correction factor.

The air temperature is the most important factor to be used in the evaluation of the air 

density correction factor. In the field the determination of air temperature is often a difficult matter. 

For this reason an investigation has been made to determine the comparative accuracy of the air 

density correction factor computed from only the altimeter readings. This is done in the two-base 

method and produces satisfactory results for elevation differences less than 500 feet. For elevation 

differences greater than 500 feet the variation of the air density with elevation becomes important 

because the air is compressible and air temperature varies with elevation, a variable not considered 

in the two-base formula.

Only the average air density correction factor for the air column can be determined from 

two altimeter readings made at locations that differ in elevation. The greater the elevation differences between the two stations, the less the effect of the altimeter observational and instrumental 

errors. Therefore, the accuracy of the determination of the average air density factor is increased 

with the increase of the vertical separation of the stations. However, because of the variation of air 

density with altitude, the greater the difference in elevation, the greater the possible departure of 

the actual air density correction factor at a given elevation from the average air density correction 

factor as determined from the altimeter readings.

The average variation of the air density with altitude can be determined for the present 

purpose from tables used to compute the performance of aircraft and missiles. Several available 

tables give the values of the air density at different elevations. The table of air density factors 

prepared from values of air density at different elevations in a manual of the International Civil 

Aviation Organization^ gives the ratio of the density at the elevation designated in the table to the 

density under standard conditions at sea level.

See also Kissam, Philip, 1944, Precision altimetry: Hiotogramm. Eng., v. 10, no. 1, p. 25-43.

2 National Advisory Committee for Aeronautics, 1954, Manual of the ICAO Standard Atmosphere: 

Tech. Note 3182, 132 p.
24 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

The average air density correction factor is the same as that employed in the two-base 

method and computed as (7) on the U. S. Geological Survey computation form "Altimeter Elevations"

as follows:

Average air density known difference in elevation

^ = correction factor = difference in altimeter readings

The adjustment factor may be determined from three altimeter readings; those at the upper base, the 

lower base, and at the requested point.

If /o s = Density factor at the upper base 

^ = Density factor at the lower base 

^ = Density factor at the requested point

the adjustment factor may be computed by the following formula:

/3 j. £> /LO -i- rap 

K. = Adjustment factor = ^ 

+

If we now represent by

(7)' = Actual air density factor = K/o (7) 

An example will illustrate the computation and application of (7)'.

The following are values used for an altitude computation by the two-base method on the 

form, "Altimeter Elevations. "

UNITED STATES

DEPARTMENT OF THE INTERIOR

GEOLOGICAL SURVEY

ALTIMETER ELEVATIONS

Computed By________________-__

State _ _.-.___________-_ Quad.______________________ Obs.Date__

Lower Base____ ____________. Work By _____-.. ____--___--- Upper Base.

lnst.No.__________________ Field Inst. No.______ __________ Inst. No.___

(T) = Lower Base Rdg

= Ele», Lower Base

. 7 /"/.

U-Elev, Upper Bo

2320.2 f+.

- 25 /

@- Field Rdg.

Zg3?.^

2063.5"

®= Upper Base Rdg.

303?

ev. = -

2063-^

now Elev. 2 O 7 7'

I = Elev, Lower Bose m=E-I I = Elev., Upper Bose

S ration Time

(T) = Lower Bose Rdg.

®=-® + ®

E, W .I*@.®

©= Field Rdg

® = m ^®

©=®-CD

(D- Upper Base Rdg.

©--©-©

EleVr®'®+D

Ad] Elev. Known Elev.
APPENDIX A 25

The adjustment factor K^ can be determined by a number of procedures from the altimeter 

readings at the upper base, lowerbase, and the requested point or field reading. One method is as 

follows:

Numerical Computation of K^ 

By entering the table (p. 26) with these values we obtain

Upper base reading 3089.0 /°ua from table = 0.9403

Lower base reading 1496.5 /i e ..do.. = .9855

Requested point 2839.5 f ..do.. = .9472

For computation from lower base

0.9855 +0.9472

x, . /«. _/, ~ 0.9855 + 0.9403 ft.a + /Tit, / "- e ^/Ve

= 1.

(7)' = 19, (7) = 1.0035 x 1.0289 = 1.0325

Elev = I + (7)' (4) = 681.7 + 1343 x 1.0325 = 2068.4

The same result will be obtained and the computation checked if the correction factor is 

computed from the upper base as follows:

0.9403 + 0.9472 

^ JU* +rt, = =0.9802

/°<a */°«« 0.9855 + 0.9403 

(7)' = K^ (7) = 0.9802 x 1.0289 = 1.0085 

Elev = II - (7) 1 (5) = 2320.2 - 249. 5 x L. 0085 = 2068. 6

A comparison of the elevation value for N-251 as computed by form "Altimeter Elevations" 

with the above results is presented as follows:

Known elev Elev by Elev using 

of N-251 form factor (K^)

2077. 9 2063. 5 2068, 5 

Error -14.4 -9.4

The evaluation of the actual air density factor (7)' for application to two-base method computations may be accomplished by the employment of the accompanying graph, figure 18.3 The ordinates 

of this graph represent the value of b = (K^ -1). The abscissas are the values of (4) of form, 

"Altimeter Elevations." The values of (6) are represented by the diagonal straight lines on the graph.

3 The main purpose of the graph is to avoid the multiplication operation of K^ x (7). As the 

values of (7) and K,^ are always within a few percent of unity, we can make use of the well-known 

approximation (l + a)(l + T3)»l + a+T3 when "both a and "b are small compared with unity.
26 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

AIR DENSITY FACTORS

Mean

Altimeter

Reading

0

100

200

300

400

500

600

700

800

900

1,000

100

200

300

400

500

600

700

800

900

2,000

100

200

300

400

500\

600

700

800

900

3,000

100

200

300

400

500

600

700

800

900

4,000

100

200

300

400

500

600

700

800

900

0

1.0296

1.0266

1.0236

1.0206

1.0177

1.0147

1.0118

1.0088

1.0059

1.0029

1.0000

.9971

.9942

.9912

.9884

.9854

.9826

.9797

.9768

.9739

.9711

.9682

.9654

.9625

.9597

.9568

.9540

.9512

.9484

.9456

.9428

.9400

.9372

.9344

.9316

.9289

.9261

.9234

.9206

.9178

.9151

.9124

.9097

.9069

.9042

.9015

.8988

.8961

.8934

.8908

20

1.0290

1.0260

1.0230

1.0200

1.0171

1.0141

1.0112

1.0082

1.0053

1.0023

.9994

.9965

.9936

.9907

.9878

.9849

.9820

.9791

.9762

.9734

.9705

.9676

.9648

.9619

.9591

.9563

.9534

.9506

.9478

.9450

.9422

.9394

.9366

9339

.9311

.9283

.9256

.9228

.9200

.9173

.9146

.9118

.9091

.9064

.9037

.9010

.8983

.8956

.8929

.8902

40

1.0284

1.0254

1.0224

1.0194

1.0165

1.0135

1.0106

1.0076

1.0047

1.0017

.9988

.9959

.9930

.9901

.9872

.9843

.9814

.9785

.9757

.9728

.9699

.9671

.9642

.9614

.9585

.9557

.9529

.9501

.9473

.9444

.9417

.9389

.9361

.9333

.9305

.9278

.9250

.9222

.9195

.9168

.9140

.9113

.9086

.9059

.9031

.9004

.8977

.8951

.8924

.8897

60

1.0278

1.0248

1.0218

1.0189

1.&159

1.0130

1.0100

1.0071

1.0041

1.0012

.9982

.9953

.9924

.9895

.9866

.9837

.9808

.9780

.9751

.9722

.9694

.9665

.9636

.9608

.9580

.9551

.9523

.9495

.9467

.9439

.9411

.9383

.9355

.9327

.9300

.9272

.9244

.921^.

.9190

.9162

.9135

.9107

.9080

.9053

.9026

.8999

.8972

.8945

.8918

.8892

80

1.0272

1.0242

1.0212

1.0183

1.0153

1.0124

1.0094

1.0065

1.0035

1.0006

.9977

.9947

.9918

.9889

.9860

.9831

.9803

.9774

.9745

.9716

.9688

.9659

.9631

.9602

.9574

.9546

.9518

.9489

.9461

.9433

.9405

.9377

.9350

.9322

.9294

.9267

.9239

.9212

.9184

.9157

.9129

.9102

.9075

.9048

.9021

.8994

' . 8967

.8940

.8913

.8886

Mean

Altimeter

Reading

5,000

100

200

300

400

500

600

700

800

900

6,000

100

200

300

400

500

600

700

800

900

7,000

100

200

300

400

500

600

700

800

900

8,000

100

200

300

400

500

600

700

800

900

9,000

100

200

300

400

500

600

700

800

900

0

0.8881

.8854

.8828

.8801

.8774

.8748

.8722

.8695

.8669

.8643

.8617

.8591

.8565

.8539

.8513

.8487

.8461

.8435

.8410

.8384

.8359

.8333

.8308

.8282

.8257

.8232

.8207

.8181

.8156

.8131

.8106

.8082

.8057

.8032

.8007

.7983

.7958

.7933

.7909

.7884

.7860

.7836

.7812

.7787

.7763

.7739

.7715

.7691

.7667

.7643

20

0. 8875

.8849

.8822

.8796

.8769

.8743

.8716

.8690

.8664

.8638

.8611

.8585

.8559

.8533

.8508

.8482

.8456

.8430

.8405

.8379

.8354

.8328

.8303

.8277

.8252

.8227

.8202

.8176

.8151

.8126

.8101

.8077

.8052

.8027

.8002

.7978

.7953

.7928

.7904

.7880

.7855

.7831

.7807

.7783

.7758

.7734

.7710

.7686

.7663

.7639

40

0. 8870

.8844

.8817

.8790

.8764

.8737

.8711

.8685

.8659

.8632

.8606

.8580

.8554

.8528

.8502

.8477

.8451

.8425

.8399

.8374

.8348

.8323

.8298

.8272

.8247

.8222

.8197

.8171

.8146

.8121

.8096

.8072

.8047

.8022

.7997

.7973

.7948

.7924

.7899

.7875

.7850

.7826

.7802

.7778

.7754

.7730

.7706

.7682

.7658

.7634

60

0. 8865

.8838

.8812

.8785

.8759

.8732

.8706

.8680

.8653

.8627

-.8601

.8575

.8549

.8523

.8497

.8471

.8446

.8420

.8394

.8369

.8343

.8318

.8292

.8267

.8242

.8217

.8191

.8166

.8141

.8116

.8091

.8067

.8042

.8017

.7992

.7968

.7943

.7919

.7894

.7870

.7846

.7821

.7797

.7773

.7749

.7725

.7701

.7677

.7653

.7629

80

0. 8860

.8833

.8806

.8780

.8753

.8727

.8701

.8674

.8648

.8622

.8596

.8570

.8544

.8518

.8492

.8466

.8441

.8415

.8389

.8364

.8338

.8313

.8287

.8262

.8237

.8212

.8186

.8161

.8136

.8111

.8086

.8062

.8037

.8012

.7988

.7963

.7938

.7914

.7889

.7865

.7841

.7816

.7792

.7768

.7744

.7720

.7696

.7672

.7648

.7624

Mean

Mtimeter

Reading

10,000

100

200

300

400

500

600

700

800

900

11,000

100

200

300

400

500

600

700

800

900

12,000

100

200

300

400

500

600

700

800

900

13,000

100

200

300

400

500

600

700

800

900

14,000

100

200

300

400

500

600

700

800

900

0

0. 7620

.7596

.7572

.7549

.7525

.7502

.7478

.7455

.7431

.7408

.7385

.7362

.7338

.7315

.7292

.7269

.7246

.7224

.7201

.7178

.7156

.7133

.7110

.7088

.7065

.7043

.7021

.6998

.6976

.6954

.6932

.6910

.6888

.6866

.6844

.6822

.6800

.6778

.6756

.6735

.6713

.6692

.6670

.6649

.6627

.6606

.6585

.6564

.6542

.6521

20

0.7615

.7591

.7567

.7544

.7520

.7497

.7473

.7450

.7427

.7403

.7380

.7357

.7334

.7311

.7288

.7265

.7242

.7219

.7196

.7174

.7151

.7128

.7106

.7083

.7061

.7038

.7016

.6994

.6972

.6949

.6927

.6905

.6883

.6861

.6839

.6817

.6796

.6774

.6752

.6731

.6709

.6688

.6666

.6645

.6623

.6602

.6581

.6559

.6538

.6517

40

0.7610

.7586

.7563

.7539

.7516

.7492

.7469

.7445

.7422

.7399

.7376

.7352

.7329

.7306

.7283

.7260

.7237

.7215

.7192

.7169

.7146

.7124

.7101

.7079

.7056

.7034

.7012

.6989

.6967

.6945

.6923

.6901

.6879

.6857

.6835

.6813

.6791

.6770

.6748

.6726

.6705

.6683

.6662

.6640

.6619

.6598

.6576

.6555

.6534

.6513

60

0. 7605

.7582

.7558

.7534

.7511

.7487

.7464

.7441

.7417

.7394

.7371

.7348

.7325

.7302

.7279

.7256

.7233

.7210

.7187

.7165

.7142

.7119

.7097

.7074

.7052

.7030

.7007

.6985

.6963

.6941

.6918

.6896

.6874

.6852

.6831

.6809

.6787

.6765

.6744

.6722

.6700

.6679

.6657

.6636

.6615

.6593

.6572

.6551

.6530

.6509

80

0.7601

.7577

.7553

.7530

.7506

.7483

.7459

.7436

.7413

.7389

.7366

.7343

.7320

.7297

.7274

.7251

.7228

.7205

.7183

.7160

.7137

.7115

.7092

.7070

.7047

.7025

.7003

.6980

.6958

.6936

.6914

.6892

.6870

.6848

.6826

.6804

.6783

.6761

.6739

.6718

.6696

.6675

.6653

.6632

.6610

.6589

.6588

.6547

.6526

.6504

Proportional Parts

oat.

4

5

6

1

6

0

0

J)

0

0

1

3

1

1

1

4

i

i

i

5

1

1

2

6

1

2

2

7

1

2

2

8

2

2

2

9

2

2

3

10

2

3

3

11 '

2

3

3

12

2

3

4

13

3

3

4

14

3

4

4

15

3

4

4

16

3

4

5

,,11.

3

4

5

18

4

5

5

19,

4

5

6
APPENDIX A 27

m

i I

S 8

5 I

11 2

CM

I -

s I

>|V 9*

Q 1

uoijaftMOD
28 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Correction to Air Density Factor tyj, - I
APPENDIX A 29

Graphical Evaluation of b = K^ - 1

To illustrate the use of the graph, the values used in the above numerical computation of K 

will be employed.

For evaluation from lower base

(4) = 1343 (6) -1592.5

On the graph, a point which has the abscissa value (4) = 1343 and which would be on a 

diagonal straight line represented by (6) = 1592.5 is situated just under the line (6) = 1600. It will be 

found from the graph that the ordinate value (b) is 0.0035. The value 0.0035 + 1 = K/o is found to be 

the same as the one obtained by the numerical computation. Computation of altitude determination by 

the use of value b.

Elev = I + (4) (7). (See computation form)

(7)' - (7) + b. Substitute (7)' for (7) in the equation above

Elev = I+(4) [(7) + b] = 681.7 - (1343) (1.0289+0.0035)

Elev = 681. 7 + 1343 (1 + 0. 0324)

-681.7 + 1386.5

- 2068.2 feet

By numerical computation: 2068.4 feet 

For evaluation from upper base

(5) = -249.5 (6) = 1592.5

On the graph, a point which has the abscissa value (5) = -249. 5 (,disregard the sign of this value for 

evaluation purposes) and which would be on a diagonal straight line represented by (6) = 1592. 5 we 

find the value b to be 0.0202. Because the value of (5) has a negative sign this value must be subtracted from (7).

Computation of altitude determination from upper base by use of value b (check computation). 

Elev - (5) (7) - II

(7)' = (7) - b Substitute (7)' for (7) in the equation above 

Elev = 11-(5) [jV)-b] =2320.2-249.5(1.0289-0.0202)

Elev = 2320. 2 - 249. 5 (1.0087) 

= 2320.2 -251.7 

= 2068. 5 feet

Summary of results of altitude determinations of Station N-251: Known elevation; 2077.9
30 INSTRUMENTAL IMPROVEMENTS IN ALTIMETRY

Computations from Computations from

lower base upper base

(feet) (feet)

USGS Form 2063. 5 2063. 5

From table 2068.4 2068.6

From graph 2068.2 2068.5

The error of an altitude determination is usually considerably reduced when the tilt of the 

equal-pressure surfaces over the survey area is taken into account.
APPENDIX B 

PRECISION ALTIGRAMS

31

Figure 20 shows sections of altigrams taken,in the same room at the same time on two 

United Geophysical electronic altigraphs. The upper record was made by altigraph 14, and the lower 

record (superimposed on the same time scale as the upper graph) was made by altigraph 15. Each 

vertical division represents 1 foot of altitude, and each horizontal division represents 1 minute of 

time. The altigraphs recorded an altitude reading every 2 seconds.

Atmospheric conditions were ideal, with the pressure remaining constant within about 

2 feet of the average for a period of 1 3/4 hours. However, local disturbances caused variations in 

altitude readings as great as 3 feet in 30 seconds. Such disturbances obviously can cause errors in 

comparing instruments or in taking field readings.

Figure 20. --Electronic altigraph records.
32 APPENDIX C

A METHOD FOR CALIBRATING ALTIMETERS

A method developed and formerly used by the Topographic Division of the Geological Survey 

for calibrating altimeters consists in comparing sets of six or more altimeters. The altimeters are 

placed in a test chamber, and the pressure is reduced in steps to give instrument readings approximately at even 100-foot altitude intervals. The pressure is held as nearly constant as possible while 

all the instruments in the set are read. Readings are taken at each successive interval to the upper 

altitude limit of the altimeters' range, and then similar sets of readings are taken as the pressure is 

increased to the lower altitude limit. For each set of readings at each pressure step, the correct 

value is assumed to be the average of the individual readings, and the error for each altimeter is the 

difference between its reading and the average. Each calibration thus gives two tabulations of 

averages and errors, one obtained with altitude increasing and the other obtained with altitude 

decreasing. Comparison of the two tabulations provides some indication of the hysteresis and hence 

the reliability of each altimeter. The pair of average values for each step is then averaged to obtain 

the final accepted value, and a correction curve is plotted for each altimeter. The main weakness of 

this method of calibration is that it operates on a comparative rather than an absolute basis; the 

errors of the poorer instruments are given full weight in obtaining the averages. Moreover, this 

method indicates relative rather than absolute hysteresis.
APPENDIX D 

STRAIN IN FLEXURAL ELEMENTS

33

A simplified method of computing the 

maximum safe strain in a flexural element can 

be used if the minimum radius of curvature to 

which the element is flexed can be determined. 

In figure 21 the neutral axis or unstressed part 

of the section is, for practical purposes, at its 

center. The maximum strain, which occurs at 

the inner and outer surfaces, is equal to (t/2)/R. 

For beryllium copper, we assume a classified 

yield stress of 100,000 psi and a,maximum safe 

stress of 30,000 psi for use in altimeter 

f lexural elements. The modulus of elasticity, 

or ratio of stress to strain, is 18,000,000. 

The permissible strain 1s therefore 

30,000/18,000,000 = 1/600.

Strain =

t/2

I..M! J..

R

t/2

R=radius to neutral axis

t=thickness of flexural element

Maximum _ Peripheral length Length along neutral axis 

strain ~ Length along neutral axis

""~ t/2)-27TR _ t/2R

Figure 21. Strain in curved flexural element.

660' andma*R = 36o

For beryllium copper, then, the minimum radius of curvature for a normally uncurved flexural element should be no less than 300 times the thickness of the element. These limits may be exceeded 

under some conditions; for example, if a flexural element has very small effect on vacuum-box displacement, a slightly higher stress can be tolerated. However, care must be exercised in designing 

for higher stresses because the elastic effects at a stress of 40,000 psi are about 4 times as large as 

those at 30,000 psi. For a large elastic member, such as a loading spring, the stress limit of 

30,000 psi may be somewhat excessive.

Sometimes, of course, it is necessary to use standard engineering beam formulas or spring 

tables and formulas in designing flexural elements for stress and strain.