NBSIR 77-1386

Problems in World-Wide

Standardization of the Units of

Altitude Measurement

Judith F. Gilsinn

Applied Mathematics Division

National Bureau of Standards

Washington, D C. 20234

February, 1978

Technical Report to: Office of Systems Engineering Management

Federal Aviation Administration

Washington, D.C. 20591

NBSIR 77-1386

PROBLEMS IN WORLD-WIDE

STANDARDIZATION OF THE UNITS OF

ALTITUDE MEASUREMENT

Judith F. Gilsinn

Applied Mathematics Division

National Bureau of Standards

Washington, D C. 20234

February, 1978

Technical Report to: Office of Systems Engineering Management

Federal Aviation Administration

Washington, D.C. 20591

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

The U.S. committment to a voluntary conversion to metric units raises

changeover problems in the fields of air traffic control and airspace management. This report begins by discussing current practice in altitude measurement and the rules for height maintenance now in effect worldwide. Four

desirable features are given for an altitude measurement system, encompassing

both the units of height measurement and the designation of cruising levels.

Three alternative bases for the design of such a system are discussed and

related to the desirable characteristics. Problems associated with each

of the approaches are discussed and the many factors to be considered and

the many interrelationships involved are examined.

Key Words ; Altimetry; altitude; aviation; height measurement; measurement

units; metric; standardization; vertical separation.
TABLE OF CONTENTS

Page

1. Introduction 1

2. Executive Summary and Conclusions 3

3. Current Height-Keeping Regulations and Practice 4

4. Desired Characteristics of an Altitude Measurement System 11

4.1 Linear Scale

4.2 Equally Spaced Flight Levels 12

4.3 Few Digits 13

4.4 Single System of Units 14

5. Discussion of Alternatives 16

5.1 Present Flight Levels 16

5.2 Metric Units 17

5.3 A Function of Pressure 19

6. References 20

LIST OF FIGURES

1. ICAO-Recommended Cruising Levels 6

2. Examples of Common Altimeter Displays 9

3. Metric IFR Height Level System 18
1 . INTRODUCTION

On December 23, 1975 President Ford signed into law PL 9^-168, the Metric

Conversion Act of 1975, which authorized the appointment of a 17-member

U.S. Metric Board to coordinate a voluntary changeover to the metric system. Metric units have been legal in the U.S. since 1866 , but have not

been in general use. In the last 25 years, the metric system has become

the dominant language of measurement in the world. Only the United States,

among the more developed nations, has not adopted its use officially. The

Metric Conversion Act of 1975 emphasized the country's determination even- tually to adopt metric units for most applications, particularly in areas having international impact. One such area is the regulation of international air traffic.

The basic metric units, from which all others are derived, are six [6]:

One of the units derived from these is the metric unit of pressure, the

Pascal (P^), measured in Newtons per square meter: in basic units,

m *kg*s . In addition to the basic metric units and those derived from

them, the International Committee of Weights and Measures (CIPM) recommended

[6] in 1969 the retention, for the time being, of several other units

including the nautical mile, the knot, the bar (l bar = lO'Ta) and the

standard atmosphere (l atm = 101,325 Pa).

In the U.S., aircraft altitude is currently expressed either in feet

or in hundreds of feet. The actual measurement process is more complicated than this and will be described below, but the units of measurement

in which altitude is expressed are length units. Conversion to the metric

system will require either transformation to metric length units (meters),

or the choice of an alternate physical quantity to express altitude.

The purpose of this paper is to explore the problems associated with

metrication of altitude measurement. Solution of these problems is difficult, perhaps involving equipment modification and changing human orientations in a safety-critical environment. In fact, the U.S. Metric Study

Report A Metric America - A Decision Whose Time Has Come [2, p. 129] noted:

'There is unlikely to be any early change in

air navigation practices, particularly in units used

for air-to-ground communications in traffic control

or for the calibration of flight instruments. International civil aviation uses two differnet sets of

standards; both include the knot and nautical mile,

but one set measures speed and vertical distances in

kilometers per hour and meters, the other in miles per

hour and feet .

length

mass time

electric current

thermodynamic temperature

luminous intensity

- meter

- kilogram

- second

- ampere

- degree Kelvin

- candela
The slowness of the world aviation community in changing over to metric

units results in part from U.S. dominance in this field. The Metric

Study Report [2, p. 131] notes in this vein that aircraft manufacturers

in Great Britian

’agreed to make every effort to comply with the

Defence Ministry's program. But they pointed out

that unless the U.S., the world's largest manufacturer and operator of civil aircraft, changes over

to metric, two sets of units are likely to he current for some time to come.'

With the U.S. committed to metric conversion, albeit a voluntary conversion,

it is appropriate to consider change in the measurement units of worldwide

aviation. Metric countries are already actively seeking such a conversion

(see for example [8]).

If the U.S. is to take an active role in the design and promulgation

of metric regulations in aviation, it must conduct its own study and

analysis of the various approaches and must assess impacts on the domestic

aviation community. This report is designed to assist in that task, by

presenting criteria for the units of height measurement and by identifying

problems associated with several plausible approaches.

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2. EXECUTIVE SUMMARY AND CONCLUSIONS

The enactment of the "Metric Conversion Act of 1975” (PL 9^-168) has

made examination of the units of altitude measurement appropriate at

this time. The discussion in this document addresses the problems as- sociated with three possible approaches to revising the present system

of units. The impact of these changes on avionics and ground equipment

as well as the pilot, controller and operating procedures make it clear

that a selection of a satisfactory system of units will be difficult.

The three alternatives evaluated were:

1. use of the present flight level system without direct reference

to feet

,

2. measurement of altitude in meters and use of a metric flight

level system,

3. use of some function of the pressure measurement itself,

rather than its linear transform.

The suggested criteria for a new system of units were also delineated.

None of the three approaches reviewed meet all four of the criteria which

where that

1. the units used for expressing altitude should be a linear

function of height,

2. flight levels should be equally spaced or at intervals which

are small multiples of some basic spacing,

3. flight-level units should have as few digits as possible,

h. all altitude references should be based on the same units.

The selection of a new system of units will be complex task involving

trade-off study of the many factors involved. A most difficult area

will be the evaluation of the effect of changing human orientations in a safety-critical environment. A conversion of the altitude measurement

system to metric units is not practical in the near future.

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3. CURRENT HEIGHT-MEASUREMENT REGULATIONS AND PRACTICE

Current International Civil Aviation Organization (ICAO) regulations

related to altitude maintenance are given in [1]:*

5 . 2 Rules applicable to IFR flights within con- trolled airspace

5.2.2 An IFR flight operating in cruising flight

in controlled airspace shall be flown at a cruising

level, or, if authorized to employ cruise climb

techniques, between two levels or above a level,

selected from:

a) the Table of cruising levels in Appendix

C, or

b) a modified table of cruising levels,

when so prescribed in accordance with Appendix

C for flight above flight level 290,

except that the correlation of levels to track prescribed therein shall not apply whenever otherwise

indicated in air traffic control clearances or specified by the appropriate ATS authority in Aeronautical

Information Publications.

5. 3 Rules applicable to IFR flights outside controlled

airspace

5.3.1 Cruising Levels - An IFR flight operating in

level cruising flight outside of controlled airspace

shall be flown at a cruising level appropriate to its

track as specified in:

*The terms IFR, VFR and ATS authority appearing here are defined below:

IFR : Instrument Flight Rules. Under poor visibility conditions

or in certain airspace aircraft must fly according to instrument

flight rules. In addition, many aircraft, especially air carrier

craft, usually fly IFR in contact with an air traffic controller.

VFR : Visual Flight Rules. Aircraft may fly using these procedures

when visibility is acceptably clear at lower altitudes.

ATS: Air Traffic Services. This is used to refer to the formally

designated appropriate air traffic control authority.

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a) the Table of cruising levels in Appendix C,

except when otherwise specified by the appropriate

ATS authority for flight at or below 900 metres

(3000 feet) above mean sea level; or

b) a modified table of cruising levels, when so prescribed in accordance with Appendix C for flight

above flight level 290.

4.3 Unless authorized by the appropriate ATS authority,

VFR flights shall not be operated:

a) between sunset and sunrise, or such other period

between sunset and sunrise as may be prescribed by the

appropriate ATS authority;

b) above flight level 200;

c) at transonic and supersonic speeds

4.5 Except as provided in 4.5.1, VFR flights in

level cruising flight when operated above 900 metres

(3000 feet) from the ground or water, or a higher

datum as specified by the appropriate ATS authority,

shall be conducted at a flight level appropriate to

the track as specified in the Table of cruising levies

in Appendix C.

4.5.1 VFR flights operated in controlled airspace

(instrument/visual) shall select cruising levels from

those to be used by IFR flights as specified in 5.2.2,

except that the correlation of levels to track shall not

apply whenever otherwise indicated in air traffic control

clearances or specified by the appropriate ATS authroity

in Aeronautical Information Publications.

The table of cruising levels from Appendix C of [1] is reproduced as Figure 1. The definitions of "cruising level" and "flight level" (FL)

from [1] are given below:*

*The terms QNH and QFE used in Note 1 refer to the process used in calculating altitude. A QNH setting (NH stands for natural height) utilizes

the sea level barometric pressure for the local area in which the aircraft

is operating and results in a height measurement closely approximating

actual distance above sea level. A QFE setting uses the standard atmosphere everywhere and represents an approximate height measurement for

which the degree of approximation depends on the difference between the

actual and assumed sea level barometric pressure.

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FIGURE 1 ICAO -Recommended Cruising Levels

APPENDIX C.—TABLE OF CRUISING LEVELS

The cruising levels to be observed when so required by this Annex are as follows:* TRACK**

From 000° to 179 » * * From 180° to 359' * * •

IFR Flights VFR Fliciits IFR Flights VFR Flichts

FL

Altitude

FL

Altitude

FL

Altitude

FL

Altitude

Metres Feet Metres Feet Metres Feet Metres Feet

-90

10 300 1000 — — — 020 600 2 000 — — —

30 900 3 000 35 1050 3 500 40 1200 4 000 45 1 350 4 500

50 1 500 5 000 55 1700 5 500 60 1850 6000 65 2000 6 500

70 2150 7000 75 2 300 7 500 80 2 450 8 000 85 2 600 8 500 90 2 750 9 000 95 2 900 9 500 100 3 050 10 000 105 3 200 10 500

110 3 350 11 000 115 3 500 11 500 120 3 650 12 000 125 3 800 12 500

130 3 950 13 000 135 4 100 13 500 140 4 250 14 000 145 4 400 14 500

150 4 550 15000 155 4 700 15 500 160 4 900 16 000 165 5 050 16 500

170 5 200 17 000 175 5 350 17 500 180 5 500 18 000 185 5 650 18 500

190 5 8C0 19 000 195 5 950 19 500 200 6100 20 000 205 6 250 20 500

210 6 400 21 000 215 6 550 21 500 220 6 700 22 000 225 6 850 22 500 230 7 000 23 000 235 7150 23 500 240 7 300 24 000 245 7 450 24 S00 250 7 600 25 000 255 7 750 25 500 260 7 900 26 000 265 8 100 26 500 270 8 250 27 C90 275 8 400 27 500 280 8 550 28 000 285 8 700 28 500

290 8 830 29 000 300 9 ISC 30 000 310 9 450 31000 320 9 750 32 COO

330 10 050 33 000 340 10 350 34 000 350 10 650 35 000 360 10 950 36 000

37C 11 300 37 000 380 11 6C0 38 000 390 11 900 39 000 400 12 200 40 000

410 12 500 41 000 420 12 800 42 000 430 13 100 43 000 440 13 400 44 000

45C 13 700 45 000 460 14 000 46 000 470 14 350 47 000 480 14 650 48 000

490 14 950 49 000 500 15 250 50 000 510 15 550 51000 520 15 850 52 000

etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc.

• Except when, on the basis of regional air navigation agreements, a modified table of cruising levels based on a nominal vertical separation minimum of less than 600 metres (2 000 feet) but not less than 300 metres (1 000

feet) is prescribed for use, under specified conditions . by aircraft operating above flight level 290 within desig- nated portions of the airspace. •* Magnetic track, or in potr areas at latitudes higher than 70° end within such extensions to those areas as may be prescribed

by the appropriate ATS authorities, grid tracks as determined by a network of lines parallel to the Greenwich Meridian

superimposed on a polar stereographic chart in which the direction towards the North Pole is employed as the Grid North.

•** Except where, on the basis of regional air naiigatinn aqreements, from 090 * to 269° and from 270 * to 089° is prescribed to accommodate predominant traffic directions and appropriate transition procedures to be associated therewith are specified

- 6-
Cruising level . A level maintained during a significant portion of a flight.

Flight levels . Surfaces of constant atmospheric pressure which are related to a specific pressure datum,

1013.2 mb ( 29.92 inches), and are separated by specific

pressure intervals.

Note 1 A pressure type altimeter calibrated in accordance

with the Standard Atmosphere:

a) when set to a QNH altimeter setting, will indicate altitude;

b) when set to QFE altimeter setting, will indicate height above the QFE reference datum;

c) when set to a pressure of 1013.2 mb ( 29.92 inches),

may be used to indicate flight levels.

Note 2 The terms height and altitude used in Note 1

above, indicate altimetric rather than geometric heights

and altitudes.

Altimeters do not determine height directly by a length ("geometric")

measurement. Rather, an altimeter measures a pressure difference, between the ambient air pressure outside the aircraft and some sea-level

reference atmospheric pressure. If the aircraft is flying at a lower

altitude (below FL180 in the U.S.), the reference pressure will be

sea-level barometric pressure supplied by local weather stations. For

altitudes at and above FL180, the reference pressure used is the standard atmosphere, 1013.25 millibars or 29-92 inches of mercury, the millibar definition being the one preferred by ICAO.

The altimeter instrument translates the pressure difference to an ('altimetric') height above sea level. This height would be actual

geometric height if the reference barometric pressure were the true

sea-level barometric pressure at that point, and if the ambient air con- ditions (temperature and density) happened to equal exactly the ideal

conditions used in the equation of transformation from pressure differences to height. Since these special circumstances will in general

not obtain, the pressure altitude calculated by the altimeter will

differ from true geometric height. However, as long as they use the same reference barometric pressure, altimeters in all aircraft should measure

the same pressure altitude, and differences between adjacent flight

levels should approximate the true geometric height differences.

The table in Figure 1 lists the pressure altitudes in both feet and

meters for the cruising levels which are to be used by all flights.

Note that while meters and feet are given equal status (with meters

- 7 -
even listed first), the flight-level designations are actually the altitudes expressed in hundreds of feet . Thus the ICAO-supported altitude

designations of cruising levels are implicitly based on the customary,

rather than metric, units.

Separation between adjacent IFR levels is an even 1000 feet below FL290

and an even 2000 feet above FL290, where adjacent levels on the same track carry traffic in opposite directions. (Compare entries on the same line in the two "IFR Flights" columns of Figure 1.) The difference, in

meters, between adjacent IFR levels below FL290 is generally 300 meters

but sometimes is 350 meters. Above FL290 the metric difference is usually

600 but occasionally may be 650. This variation in the metric flight

level makes them much more difficult to remember and use. In fact, the

controllers and pilots generally refer only to the cruising-level designation, not to the equivalent height. Altimeters in most aircraft, ex- cept those of the Soviet Union and Eastern Europe, use feet so that the

pilot can use the altimeter reading directly in communicating with the

controller about altitude. Thus the current practice in use throughout

the world, outside of Eastern Europe and the Soviet Union, involves the use of nonmetric altitude designations.

Figure 2 shows two types of altimeter displays. One, a clock-type

which is the most common, has a short hand indicating the coarse altitude

reading (1000's of feet) and a long hand indicating the fine altitude

reading (100's of feet). The second, which is becoming more common,

gives the coarse reading in a digital odometer-type display and the fine

reading by a pointer indicating 100's of feet. Other altimeter displays

exist (for examples see [ 9 ] )

but these two are the most common types in use today. Both types of display also show the reference barometric

pressure on the face.

Because of the number of dials and guages in the cockpit, the pilot

cannot consult each in detail at every glance. Rather, he carefully scans the few of the instruments most appropriate during any maneuver, and only

glances at the others for deviation from expected position. To ease this

process, the instrument displays (including that of the altimeter) are designed so that pointers will be in a vertical position (i.e. "pointing

up") when the instrument recording is the desired value. Thus when the

pilot is exactly at one of the cruising levels given in Figure 1 (for

IFR traffic), his altimeter fine pointer will be straight up, if he has

either of the two displays in Figure 2. During climb or descent the pilot

will consult both coarse and fine altimeter readings to insure correct

altitude is attained, but during level flight he need only maintain the

fine pointer in a vertical position.

Altitude information is relayed to controllers on the ground by the airborne Mode € transponder. This instrument, when triggered by a radio

signal, sends a 3-digit altitude code which is received at the point which

sent the triggering signal. Most aircraft in upper altitudes or in highdensity IFR terminal areas are equipped with transponders with Mode C

- 8-
FIGURE 2 Examples of Common Altimeter Displays

Clock-type Display

- 9-
capability. Equipment associated with the radar processes the signal,

and the 3-digit altitude code is included in an alpha-numeric display on

the radar scope of the controller who is handling this aircraft. The

transponder encodes and transmits only the 3-digit coarse altitude

reading rounded and smoothed to eliminate frequent changes in the last

digit when an aircraft is in between two hundred foot levels.

In the U.S., or any other place in which the coarse 3-digit reading is

the altitude in hundreds of feet, the controller can consult the rightmost of the three digits. If it is 0, the pilot is exactly on one of

the cruising levels (below FL290) . Otherwise, the last digit indicates

how far in error the pilot is. Above FL290 the controller must also

consult the second digit to determine that it is odd, in ascertaining

whether the aircraft is at an appropriate flight level. Thus for altimeters reading in feet, the 3-digit Mode C altitude can be used by the

controller both as a positive indication that the aircraft is maintaining

correct altitude, and if not, as an indication of the magnitude of the

deviation.

The controller is not required to monitor constantly the Mode C altitude

displayed on his scope. Rather, keeping track of the appropriate altitude is an advisory service provided on an 'as available' basis. However, if a U.S. controller does notice a discrepancy of more than 300

feet between assigned altitude and Mode C displayed altitude, he must check with

the pilot to ascertain whether the cockpit altimeter agrees with the Mode

C response (and the aircraft has indeed wandered from its correct cruising

level) or the discrepancy is one between the cockpit altimeter and Mode C.

In the latter case, the cockpit reading is assumed correct, and the pilot

is requested to turn off Mode C. This check is usually done, where necessary, at handoff from one sector to another. Therefore, although checking

of altitude by controllers is not a required activity, the procedures assure

that it is usually done at least at handoff. In addition, the structure of

the altitude display code (which makes recognition of altitude deviation

easy) aids continuous monitoring.

It is clear, from this description of current practice, that changeover to metric altitude reporting would require more than just redesigning

altimeter dials, adding a second set of units on the dial or overlaying

current units with metric values. Some consideration must be given to

changing the cruising-level structure, perhaps to represent constant metric

differences. Changed cruising levels must be coordinated with vertical

separation standards to assure that any reduction in separation resulting

from the change is safe. Changes in the units of altitude measurement

will also have an impact on Mode C transponder encoding, and on the display

of the Mode C altitude upon the controller's radar scope. In addition,

other altitude references in charts and handbooks must be changed to en- sure compatiability . All references to altitude, whatever the source or application, must be expressed in the same units. In the remainder of this

report we will use the term 'altitude measurement system' to denote the

system elements involving altitude units and the interactions among them.

This includes the units used to express altitude, the scheme of assigned

flight levels, and the relationships among the units used by the various

instruments, such as altimeter, Mode C transponder and controller radar

display.

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4. DESIRABLE CHARACTERISTICS OF AN ALTITUDE MEASUREMENT SYSTEM

From the preceding discussion of the current regulations applying to

altitude and the accompanying description of operational aspects of the

altitude maintenance system, several desired characteristics arise:

1. It is desirable that the units used for expressing altitude

be a linear function of height.

2. Flight levels should be equally spaced, or at intervals which

are small multiples (i.e., by 2 or 3) of some basic spacing.

3. Flight-level units should have as few digits as possible.

4. All altitude references should be based on the same units.

Further elaboration and justification of these criteria will be given below, in the respective Sections 4.1 through 4.4.

The Military Standard - Human Engineering Design Criteria for Military

Systems, Equipment and Facilities [5] contains specifications for visual

displays, such as the pilot’s altimeter gauge or the controller’s radar

scope. These specifications are relevant to the units used and how they

are to appear on such a display. General requirements concerning the information to be displayed include [5, p. 25]

Content - The information displayed to an operator shall be limited

to that which is necessary to perform specific actions or to make

decisions

.

Precision - Information shall be displayed only to the degree of

specificity and precision required for a specific operator action

or decision.

Format - Information shall be presented to the operator in a directly

usable form. (Requirements for transposing, computing, interpolating,

or mental translation into other units shall be avoided.)

The same document recommends that coding techniques be used, among other

things, to identify critical information within a display. The four

criteria enunciated above apply these general principles, together with

other well-recognized desirable characteristics, to the problem of altitude measurement.

4. 1 Linear Scale

It is generally believed that people understand linear units and can read

linear displays much more easily than others. The Military Standard [5,

p. 35] recommends, for instance, that

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'Except where system requirements clearly

dictate nonlinearity to satisfy operator information requirements, linear scales shall be used

in preference to nonlinear scales.'

In addition to the general desirability of linear scales, a specific reason for requiring altitude units to be a linear function of height

is that climb and descent rates are usually expressed in vertical units

per time period (feet or meters per second or minute). If a non-linear

function of height were used, climb and descent rates would depend on the

altitude, and the time to fly from one flight level to the next would

also vary. This would be confusing for pilots and would impose an additional mental burden, involving translation or calculation, in an en- vironment sometimes requiring split-second decisions.

Non-linear units would also violate the second criterion enunciated

above. Separation between flight levels should either be constant, or should only involve low multiples of the base separation; units which were

a nonlinear function of height would probably lead to non-constant separation intervals (when the intervals were expressed in those nonlinear

vertical units). This again would put upon the pilot and the controller

the great burden of retaining mentally the expanded information-base

required by such a system.

4 . 2 Equally Spaced Flight Levels

The second and third criteria relate the units of altitude measurement

to the specification of cruising levels (as in the table of Figure 1).

Although aircraft can fly at any altitude (within their performance

range) , pilots are requested — either by rules such as the ICAO regulations quoted in Section 2, or by controller instructions — to fly at one of the specified cruising levels when in level flight. Even ascent

and descent are often accomplished in stages, chosen to alternate a priod of altitude change with a period of level flight at one of the

cruising levels.

Equal spacing between cruising levels makes the levels easier to remember

and easier to use during climb or descent, for reasons similar to those

for use of a linear scale. The equal-spacing requirement is in part a response to the need for the simplest design compatible with functional

specifications. In this vein the Military Standard [5, pp . 15 and 17]

notes that

'Design shall also be directed toward minimizing personnel and training requirements within the limits of time, cost, and performance

trade-offs .

'The equipment shall represent the simplest

design consistent with functional requirements and

expected service conditions.'

- 12 -
Another justification for using flight-levels which are equally

spaced, or based on multiples of a basic separation, is found in the

cockpit procedures used by pilots to monitor their instruments: they

fly "pointers up". This also is in accordance with the Military

Standard for human factors design of instruments which states [5, pp

.

38-39]:

Zero Position and Direction of Movement - When positive and

negative values are displayed around a zero or a null position

the zero or null point shall be located at either 12 o'clock

or the 9 o'clock position. Positive values shall increase with

clockwise movement of the pointer, and negative values shall in- crease with counterclockwise movement.

Alignment of Pointer or Fixed Reference Line - Alignment of

pointer or fixed reference line shall be in the 12 o'clock

position for right-left directional information and in the 9

o'clock position for up-down information. For purely quantitative

information, either position may be used.

Pointer Alignment - When a stable value exists for given operating

conditions in a group of circular-scale indicators, they shall be

arranged either in rows so that all pointers line up horizontally

on the 9 o'clock position under normal operating conditions or in

columns so that all pointers line up vertically in the 12 o'clock

position under normal operating conditions. If a matrix of indicators is needed, preference shall be given to the 9 o'clock position.

If each complete rotation of the pointer corresponds to the same number

of units, then having each cruising level represented by a 12 o'clock

position requires that the cruising levels be separated by multiples of

the number of units in one complete pointer sweep.

In summary: for reasons of simplicity and compatibility with cockpit

procedures, equally-spaced cruising levels are desirable.

4 . 3 Few Digits

As noted under the heading of simplicity, the Military Standard re- quires that the information displayed be the minimum needed to meet functional requirements. Current cruising-level designations require only

two digits, with a third used to indicate deviations. Metric levels

based on the values in Figure 1, or based on a fixed 300/600 meter separation, would require 3 digits since successive levels may have different

third digits. Deviation from level would thus become more difficult to

spot. In addition, it is intuitively clear that requiring three digits

rather than two, places an additional burden of memory and recognition

and communication on both pilot and controller. This intuitive idea is

reinforced by a study [7] conducted by the National Bureau of Standards

for the U.S. Postal Service in which operators were found to require

0.89 seconds on the average to recognize two digits of a Zip-code, but

1.17 seconds to recognize 3 digits. (This difference was statistically

significant at the .0005 level.)

- 13-
It is clear that a cruis ing-level system should have designations with

as few digits as possible. Also, as will be discussed in Subsection

3.4, all references should use the same units. That is, the system should

not use one set of units for display on a controller's scope or for as- signed flight levels, and a second set on cockpit instruments.

Another principle stated in the Military Standard [5, p. 30] which is

applicable to the use of the cruising-level designations is:

Positive Feedback - The absence or extinguishment of a signal

or visual indication shall not be used to denote a "go-ahead", "ready",

"in-tolerance", or completion condition, nor shall such absence be

used to denote a "malfunction", "no-go", or "out-of-tolerance" condition.

In the current cruising-level system, the third digit is always zero. Therefore, a non-zero value for that digit on the controller's display indicates

a deviation, and the value of the digit indicates the magnitude of the deviation. This makes it fairly easy for the controller to scan his display for

altitude errors. The third digit therefore satisfies the principle stated

above. In the case of a metric curising-level system, the value of the

third digit by itself does not provide a positive feedback. It must be com- bined with the two preceding digits, and the whole triple examined to obtain

the same information as that provided by the third digit alone in the

current system.

In summary: the current cruising-level system is particularly well-designed

to exploit the greatest information in the fewest digits, giving both a positive indication of "on assigned level" and a positive indication of

deviation and its magnitude. Loss of these advantageous features would

be a serious matter.

4.4 Single System of Units

This requirement seems particulary straightforward for any safety-critical

application like aviation, in which communication between various system

elements is a major factor. Pilots use their altimeters in responding to

requests from controllers. The controllers assign pilots to altitudes and use displayed Mode C responses to monitor actual altitude. Handbooks

listing airport heights are used by pilots in checking the altimeter instrument readings. Charts list minimum safe altitudes and heights of possible

obstructions. "Altitudes" appearing in all these contexts must be in

the same units. Other aspects of altitude usage which must be considered

include units of climb and descent, the cruising-level system and vertical

separation standards. The units chosen for altitude measurement will

limit choice of separation values, which in turn will determine cruising

levels. All must then be coordianted to meet criteria 1-3 (see the beginning of this Section) as well as criterion 4.

Our discussion of these four criteria has exhibited the complexity of

the factors which must be considered in choosing units. It has also

served to show the many inter-relationships involved in the use of alti-

-14 -
tude units. New units should not be such as to rule out or hobble any

of the current uses, and should neither degrade the quality of information

now available nor increase the quantity required. These constraints are particularly difficult to satisfy if metric units are to be employed and

if current separation values (whose magnitudes are determined independently

of the length units used) are to be retained.

- 15-
5. DISCUSSION OF ALTERNATIVES

Sections 2 and 3 have described the current regulations and operating

procedures affecting altitude measurement and maintenance, and have presented criteria for the design of a system for altitude measurement and

cruising levels. In this section we will examine three alternative

approaches to such a system:

1. Use the present flight-level system without direct reference

to feet.

2. Measure altitude in meters and use a metric flight-level system.

3. Use some function of the pressure measurement itself, rather than

its linear transform. (This is suggested in [3].)

We will discuss the advantages and disadvantages of each approach, re- lating these to the criteria given in Section 4.

5 . 1 Present Flight Levels

Because of variations in local barometric pressure and deviations from

the ideal conditions relating pressure and altitude, it is only by pure

chance that any aircraft would actually be flying at the geometric height

indicated by its altimeter. It has therefore been suggested that the

current altimeter readings in feet should be replaced. Instead, altitude

would be measured in artificial units called (perhaps) "flight levels",

and in fractions thereof. An altimeter reading of 27315 would be read

as 273.15 flight levels, for instance. This approach has the advantage of

retaining all the desirable characteristics of the current system: its

linearity, equal spacing, and especially the use of fewest digits to ex- press the information. The main advantage of this approach is the economy

with which it expresses the actual altitude, an indicator of "on flight

level" and an indication of the magnitude of any deviation, all within

three digits.

There are serious disadvantages, however. The U.S. is committed to the

eventual adoption of metric units, with exceptions where necessary. Divorcing "flight level" from "feet" does not change the fact that "flight

level" is not a metric unit. It would seem particularly strange for such

a high-technology industry as aviation to retain archaic non-metric units.

An even more serious problem is that use of flight level would perpetuate

a dual system of units, with Eastern Europe and the USSR using meters and

others using the new flight-level units. The increasing pressure from

metric countries to use meters (see for example [8]) could result in even more countries using meters, again leaving the U.S. "odd man out".

The use of non-metric units, however disguised, is contrary to the intent

of the Metric Conversion Act.

- 16-
5.2 Metric Units

Perhaps the most direct approach to world-wide standard altitude measurement is to use the metric unit of length as the unit of altitude, and to

define flight level in terms of multiples of some basic number of meters.

The table in Figure 1 displays metric equivalents for levels which are based on increments expressed primarily in feet. An alternative table, with

increments based on 300 and 600-meter steps, would be more appropriate.

Such a table is displayed in Figure 3. The flight-level designations used

are 10' s of meters, so that the final digit has the desirable characteristics of positive feedback of "on-level" indication, and of estimation

of deviation-f rom- level using the final digit. The first 3 or 4 digits

also agree with the altimeter reading, so no translation would be required.

The main disadvantage of such a system is that it requires more digits

(4 rather than 3) to convey the same amount of information as does the

current feet-based flight level system. In addition, whereas the leading

digits in the current system progress in increments of 1 or 2, those of

the flight level system in Figure 3 progress in increments of 3 or 6,

violating an additional principle stated in the Military Standard [5, p. 35],

namely

Graduations - Scale graduations shall progress by 1, 2, or 5 units

or decimal multiples thereof.

The progression by 3 or 6 is clearly more difficult to remember, placing

an additional burden on both pilot and controller.

The extra digits required by a metric flight-level system would require

redesign of Mode C transponders and of the on-ground equipment which pro- cesses the transponder digital signal: the additional digit would require

a lengthening of the transmission interval, as well as additional altitude codes. The controller's display would also be affected by the need

to include the additional digit. Aircraft owners would thus incur a cost

for equipment purchase or modification, and the FAA would incur design,

development and hardware costs associated with the changeover. Other costs

would result from altimeter modification (the metric altimeter for such

a system would probably have a fine pointer rotating every 300 meters and

would utilize a digital display for the coarse measurement) . New charts

and handbooks would have to be preapred, published, and pruchased.

Many of these costs are similar to those incurred in metric changeover by

other industries. Whether they are warranted in the present case depends

on the degree to which the aviation community, here and internationally,

is committed to metric units. Should other countries make the changeover,

the U.S. aviation industry, the acknowledged world leader, could ill-afford

to remain aloof and isolated.

If a decision is made to proceed to metric altitude units, then the changeover process must be analyzed and planned with great care. Gradual changeover presents the difficulties resulting from having both systems concur- rently in use, with dual communication putting an intolerable burden on controller and pilot. Having dual flight-level systems in concurrent use would be confusing and would decrease safety by having a mix of aircraft

following different levels.

- 17 -
FIGURE 3

Metric IFR Flight Level System

From 000° to 179° From 180° to 359°

FL

Altitude

FL

Altitude

Meters Feet Meters Feet

30 300 990 60 600 1980

90 900 2970 120 1200 3960

150 1500 4950 180 1800 5940

210 2100 6930 240 2400 7920

270 2700 8910 300 3000 9900

330 3300 10890 360 3600 11880

390 3900 12870 420 4200 13860

450 4500 14850 480 4800 15840

510 5100 16830 540 5400 17820

570 5700 18810 600 6000 19800

630 6300 20790 660 6600 21780

690 6900 22770 720 7200 23760

750 7500 24750 780 7800 25740

810 8100 26730 840 8400 27720

870 8700 28710 930 9300 30690

990 9900 32670 1050 10500 34650

1110 11100 36630 1170 11700 38610

1230 12300 40590 1290 12900 42570

1350 13500 44550 1410 14100 46530

1470 14700 48510 1530 15300 50490

etc

.

etc. etc

.

etc

.

etc

.

etc

.

- 18-
An abrupt changeover in a safety-critical environment can proceed smoothly,

as evidenced by the Swedish switch from left to right drive on the highway.

However, the Swedish example did not involve simultaneous modification of

equipment. An abrupt changeover would necessitate an interval of dual

systems in the cockpit, since equipment installation requires time. This

might be difficult in aircraft whose control panels are already crowded

with instruments.

This discussion has been included to point out some of the problems implicit in a changeover to metric altitude units. It should not be con- strued as implying that we see no possibility of solving these problems,

but does serve to emphasize that such a decision should reflect careful

study of the whole system of altitude measurement and maintenance.

5.3 A Function of Pressure

Since altitude is not calculated directly as a length, it is natural to

suggest that the units of altitude reflect more directly the measurement

being made. This has led Du Feu, for instance, to suggest in [3] an alternative unit system based directly on ambient air pressure at altitude. He

suggests that the units y to be used to measure altitude be expressed as

y = y

Q

+kPx

where P is the measured pressure and k and x are parameters chosen in such

a manner as to assure that appropriate minimum separations between flight

levels are maintained. In [3] he obtains values of

y y

0

-!.39P0.57597

( 1 )

for values below 11 km (36,089 feet). The value of yn is chosen to make

y=0 at sea level (where P=1013.25 mbar) . Equation (1; is based on separation values suggested by IATA, which are less than those currently used.

Flight levels would be 1 unit of y (which Du Feu calls a Cayley) apart.

This system has the advantage of relating directly to the pressure measurement being performed, and the variable separation interval reflects measurement accuracy more directly than does the linearized altitude now used.

However, this approach violates criterion 1 of the previous section, since

Cayleys are not a linear function of height. It is true that the units

would appear on a linear scale in the cockpit, and that separation between

flight levels, when measured in Cayleys, is constant. However, climb and

descent rates will vary with altitude, and time to travel between flight

levels will be difficult to estimate. Thus this approach would put an additional burden on pilots requiring retraining and familiarization with

a new system. The particular flight level system derived in [3] is un- desirable because of the reduced separation involved, but this alone is

not reason to reject the underlying approach. The main difficulty is still

the non-linearity with height, and the resultant requirement for modifications in flying practice. This approach would also require redesign of the

airborne altimeter system.

- 19-
5. REFERENCES

[1] Annex 2 - Rules of the Air, International Civil Aeronautics Organization, Montreal, Canada, September 1975.

[2] Daniel V. De Simone, Director U.S. Metric Study, A Metric America - A

Decision Whose Time Has Come, National Bureau of Standards Special Publication 345, U.S. Government Printing Office, Washington, D.C. 20402

(SD Catalog No. C 13.10:345, Price $2.25), July 1971.

[3] A. N. Du Feu, Metres, Feet or Cayleys?, Tech Air, Vol. 26, No. 7, pp. 2-7,

July 1970.

[4] Judith F. Gilsinn and Douglas R. Shier, Mathematical Approaches to

Evaluating Aircraft Vertical Separation Standards, National Bureau of

Standards Report NBSIR 76-1067, National Bureau of Standards, Washington,

D.C. 20234, August 1976.

[5] Human Engineering Design Criteria for Military Systems, Equipment and

Facilities, Military Standard MIL-STD-1472B , U.S. Government Printing

Office, Washington, D.C. 20402, (SD Catalog No. 603-131: 1460),

December 1974.

[6] Chester H. Page and Paul Vigoureux, editors, The International System

of Units (SI), National Bureau of Standards Special Publication 330,

U.S. Government Printing Office, Washington, D.C. 20402 (SD Catalog No.

C 13.10: 330/3, Price $.80), July 1974.

[7] J. J. Persensky and J. R. Cornog, Digit Data Entry Study, performed by NBS

for the U.S. Postal Service, December 1971.

[8] Review of the Results of Studies Regarding the Feasibility of Reducing

the Vertical Separation Minimum Above FL 290 and Determination of Further

Measures to Be Taken to Facilitate Such Reduction, paper presented by

France at the Ninth Air Navigatior Conference, Montreal, International

Civil Aviation Organization Ihper AN Conf /9-WP/38 , April 1976.

[9] Jack J. Shrager, A Summary on Altitude Displays with an Annotated Bibliography, Federal Aviation Administration Report Number FAA-RD-72-46

National Aviation Facilities Experimental Center, Atlantic City, N.J.

08405, May 1972.

- 20-
N8S II4A iREv ?./.)

U.S. OEPT. OF COMM

BIBLIOGRAPHIC DATA

SHEET

1. PI Ml. It ATI ON OR REPORT NO. 2. Cmv’t Accession

No.

3. Ret ipu ni's Ai ( c.ssion V>.

4. TITi.i AND SI HTI 1 1.1 5. Publ u at ion D.itc Problems in World-wide Standardization of the Units of

Feb. , 1978

Height Measurement 6. Performing Org.im /at ion ( ode

7. ALTHOR(S)

Judith F. Gilsinn

8. Performing Organ. Report No. NBSIR 77-1786

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234 ...

10. Project Task Work Unit No. 2050491

11. Contract Grant No. DOT-FA76WAI-594

12. Sponsoring Organization Name and C omplete Address (Street. City. State, ZIP)

Office of Systems Engineering Management

Federal Aviation Administration

13. Type of Report & Period

C overed Interim

Washington, DC 20591 14. Sponsoring Agency ( od<

15. "I PPI.I Ml N I ARY NOTES

16. ABSTRACT (A 200- word or less tactual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The U.S. committment to a voluntary conversion to metric units raises

changeover problems in the fields of air traffic control and airspace management. This report begins by discussing current practice in altitude measurement and the rules for height maintenance now in effect worldwide. Four desirable features are given for an altitude measurement system, encompassing

both the units of height measurement and the designation of cruising levels.

Three alternative bases for the design of such a system are discussed and

related to the desirable characteristics. Problems assoc iated with each of

the approaches are discussed and the many factors to be considered and the

many interrelationships involved are examined.

17. k 1 Y VU)R l)S (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name, separated by semic olons ) Altimetry; altitude; aviation; height measurement; measurement units; metric;

standardization; vertical separation

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