LA-8819
UC-34
Issued: September 1985

The Yields of the Hiroshima
and Nagasaki Nuclear Explosions

—

-..

.~~

~b~~~

.— -.

-..

Los Alamos National Laboratory
LosAla.os,Ne..e.ic.87545

THE YIELDS OF THE HIROSHIMA AND NAGASAKI EXPLOSIONSbyJohn Malik

ABSTRACTA deterministic estimate of the nuclear
radiation fields from the Hiroshima and Nagasaki
nuclear weapon explosions requires the yields ofthese explosions.
The yield of the Nagasaki
explosion is rather well established by both
fireball and radiochemical data from other tests
as 21 kt.
There are no equivalent data for the
Hiroshima explosion. Equating thermal radiation
and blast effects observed at the two cities
subsequent to the explosions gives a yield of
about 15 kt.
The pressure-vs-time data, obtained by dropped, parachute-retarded canistersandreevaluated
using
2-D
hydrodynamic
calculations, give a yield between 16 and 17 kt.
Scaling the gamma-ray dose data and calculations
gives a yield of about 15 kt.
Sulfur neutron
activation data givea yield of about 15 kt.
The current best estimates for the yield of
these explosions are the following:
Hiroshima
15 kt
Nagasaki
21 kt
The outside limits of uncertainties in theseare believed
to be 20 percent forvaluesHiroshima and 10 percent for Nagasaki.

I.. INTRODUCTIONTheManhattan

Project

culminatedtypes of nuclear weapons--Little

in the design

Boy and Fat Man.

and fabrication

The first type was exploded

Estimatesof radiation exposuresover Hiroshima,

the second

over Nagasaki.

dependon explosive

yields, and much of the evaluationin parteffects upon man depends on data from the Hiroshima
The

yield

of

variously

from

the

Fat

19-24

Man

kt.

has

been

determined

13 kt.1)of radiation

and Nagasaki explosions.
ratherwell,(Present official yield is 23 kt.1)

for the Little Boy have ranged from 6-23 kt.

of two

being

given

Estimates2-7(The current official yield is

The data from which estimates may be made are fragmentary, and the1parameters

neededfor evaluation

have

been either missing,inconsistent,orerroneous.

Part of the problem arises from President Truman-s edict that theyields of both explosions were 20 000 tons of TNT; another part of the problem
arises from the inadequate and faulty documentation of the combat missions by
the Army Air Corps 509th Composite Group and the US Air Force historians.
Manywell-researchedbooks,8-21

resolvinginconsistencies.

There

Bombing(USSBS), 22

SurveyJapanese.21

particularly

Ref.

are

16,

usefulinis also documentation

the Manhattan

by the US StrategicDistrict, 8,15 and theEngineering

These sources are not particularly

useful for yield evaluation;

however, they contain clues.

II.

TRINITY TESTThe purposes of the Trinity Test of July 16, 1945, were to determine theperformanceof the Fat Man;

particularly

blast;

weaponsandto determine

overpressure
combatcamerathe fireball-s

from

The

growthof the fireball wason

gyrostabilizer

photographic

instrumentation

the

of

obtainedtelemeteredaircraft;of theData were to be obtained on theaircraftaccompanying

theto be recorded with
theNorden~bomb

strikea Fastax TM

sight

of

the

aircraft; the camera was to be operated on the first mission by

B. Waldman and by R. Serber on the second.
bethe yield of therate of growth and the time dependenceof the blast wave at altitude.

mountedeffects,

Yield was measured on the combat missions

missions

aircraft.

physicalto evaluate methods of determining

to be used against Japan.

by determining

the explosion-s

from

gages

to anotherinparachute-retarded

instrumented

this program was

Overpressure-vs-time

executed

aircraftindata were tocanisters

droppedformation

with

by

and

the strikeby a group headed by L. Alvarez, which

included H. Agnew and L. Johnston.
During the Trinity Test, excellent
the fireballationsandprevented

the aftermath.
collecting

photographic

Weatherrecords were obtained ofconditions and/or safety consider-

overpressure-vs-time

data, although

the aircraft

was in the area and observed the explosion.

111.

HIROSHIMA MISSION
The

missionagainstHiroshima

has been describedaircraft and equipment operating as planned.
of plan.

2

as textbook

with

all

The bomb was dropped within 15 s

Waldman believed he obtained good Fastax~

records from a point some

19 miles

out, and good overpressure-vs-timefrom the dropped
equipment

parachute-retardedthemalfunctioned,

data were obtained by telemetry

canisters.

Fastax~film

Because the film developing
was

torn,

the

emulsionwasblistered or was scraped off, and the film came out clear where emulsion did
exist; no image was visible.

The equipment had earlier successfully processed

the films from the cameras recording the canister data. 23

The overpressure-vs-time records24-25 were good.
The

locationsof the canisters

relative to the burst have been elusive

The historical records 26 of the mission by the 509th Composite Group of

data.

the Army Air Corps, the operationalgroup formed to deliver the weapons, areboth

For example,

incomplete

and inconsistent.

thoseparticular

of

the

and

bombardiers,thethe crew members”

logs, indebriefing

are

notes

not

missionA crucial fact, the aircraft altitude, is given for the Hiroshima
in the strike report 26 as 30 200 ft, in the historical narrative 26 as

31

ft,

and

in

Parsons-

navigator-s

log

on

the

included.

600

insideinconsistencies were resolved:
possibly a transposition.

loglo

as

32

covers

700 ft.

Uponofbook,16Marx-sdiscovery
many

of

the

of

the

the true altitude is given there as 31 060 ft,

Correction of the indicated pressure altitude gives

a value of 32 200 ft, in reasonable agreement with Parsons” log or the 31 600ft.

An interview by J. A. Auxier and L. J. Deal with General

Sweeney(thenMajor), who piloted the instrumentation

aircraft from which the canisters were

dropped,aircraftresolved

Uncertainties

theproblemofthespacing

intheformation.*

which still remain include the time from “bomb away” or release

tone to parachute deployment, the true altitude, and the gage calibrations.

Asummary of the missions is given in Tables I and II.

IV.

NAGASAKI MISSION
The plans for the second mission, with the primary target of Kokura, weresimilar to those for Hiroshima, but the execution did not go as planned.g

The

problems

andstartedbeforetakeoff-- a fuelfuel in one bomb-bay tank was unavailable;transfervalve wasinoperative

further, R. Serber, who was to haveoperated the FastaxTM camera in the photographic plane, when drawing equipment* Lord Penney 27 said he questioned the bombardier of the canister aircraft after the mission as to the spacing. He was’’completely sure he
was very close -- 100 yd.” Beahan, the bombardier, confirmed this.

3

TABLE IMISSION SUMMARIES FOR STRIKE AIRCRAFT

Hiroshima
Bomb designation

L-n,

Little Boy

Nagasaki
F-31, Fat Man

Mission number

13

16

Strike aircraft

v-82, Enola Gay

V-77, Bock-s Car

Aircraft commander

Col. P. W. Tibbets

Maj . C. W. Sweeney

Pilot

Capt. R. A. Lewis

1st Lt. C. D. Albury

Navigator

Capt. T. T. Van Kirk

Capt. J. F. Van Plet

Bombardier

Maj. T. W. Ferebee

Capt. K. K. Beahan

Weaponeer

Capt. W. S. Parsons (USN)

Cdr. F. L. Ashworth

Time of detonation

0815, August 6, 1945

1102, August 9, 1945

Indicated air speed

200 mph

200 mphTrue air speed

328 mph315 mphWind

8 knots at 170°l-knot head wind

True heading

262°

True course

265°

Indicated altitude

30 200 ft

28 000 ft

True altitude

31 600 ft (34 640 ft)a

28 900 ft

TemperatureInd. -22°C, True -33°C

Height of burst28
Time of falla4

580 ~ 15 m
44.4

S

(46.9

S)

503i3m47.0

Quantities in parenthesis have been derived from canister pressuretime records and test drop data.

(USN)TABLE 11
MISSION SUMMARIES:INSTRUMENT AND PHOTOGRAPHIC AIRCRAFT

Hiroshima

NagasakiInstrument aircraft

V-89, Great Artiste

V-89, Great Artiste

Position

300 ft behind V-82

300 ft behind V-77

Aircraft commander

Maj. C. W. Sweeney

Capt. F. Bock

Bombardier

Capt. K. K. Beahan

1st Lt. C. Levy

Scientists, observers

L. W. Alvarez

L. Johnston

H. M. Agnew

W. Goodman

L. Johnston

J. Kupferberg
W. Laurence (The New York Times)

Photo aircraft

V-91, Strange Cargo

V-90, Full House

Aircraft commander

Capt. Marquardt

Maj. J. Hopkins

Scientists, observers

B. Waldman

Dr. W. G. Penney
Gr. Capt. G. L. Cheshire

for the mission, was given two life rafts instead of a raft and a parachute.
When

this

was

discovered

the

plane

took

off

without

he attempted to obtain a “chute;him. 29
Instead of three aircraft

rendezvousing

over

YakoshimaIslandbeforephotographic

plane

however,

beforecircledtakeoff,

the wrong

proceeding

toisland and never joined

Japan,

thethe formation;

the strike and the instrumentation aircraft , after a 45-minute wait, proceeded
Kokura was obscured by smoke and after three aborted

to the primary target.
bombingruns

without

secondary target:

seeingNagasaki.

the two aircraft

the target,

proceeded

to the

The target was obscured by clouds; the bombing

run was made by radar with a late decision to drop by radar even though theoperationorder

specified

only visual

bombing;

however,a holethroughtheThe strike aircraft barely madeThe
Okinawa with the remaining fuel (an excess of seven gallons). 9,14,16,20
clouds opened and the drop was made visually.

photographic

plane not only was not near Nagasaki

did not havean operator

pictures.

An

for the Fastax~

overpressure-vs-time

recordcanisters, but that record was off-scale. 24
The position

at detonation time, but it
9
There were no fireballcamera.
was

obtained

from

the

droppedparameters

for the second mission are even more uncertain

than for the first mission.

For example, the altitude is given as 28 000 ft

in the strike report, as 28 900 ft in the final report, and as 31 600 ft (thesame as the Hiroshima mission) in the summary report. 26
Admiral Ashworth(then Commander),the weaponeer

on a glide from Kokura
under 28 000 ft.
evaluators

to Nagasaki to conserve fuel and that the altitude was

It seems clear that the 31 600 ft altitude used by previous

is incorrect.

Because the crew members- logs have not been found,
However, one source 26 states that there was a l-knot

there are no wind data.
head wind.
theSimilarly,

separation

was

Hiroshima mission.

v.

The evaluation
mountedinstrumentationdata:

Laurence14 states

the aircraft separation is unknown.

one-half

mile,

but

it

probably

was

about

that

of theTables I and 11 present a summary of the mission.

THE OVERPRESSURE-VS-TIME

gages

of the mission, states that the aircraft wereDATAof the pressure-vs-timeintheaircraft,data obtained from the condenser

parachute-retarded

the Great Artiste,canisters

droppedfromrequires at least the following

1) distance of canister from the explosion, 2) altitude of canister, 3)

definition of the atmosphere, 4) calibration of the gages, and 5) calculationsof the overpressure expected at the gage altitude with yield as a parameter.

6As

impliedearlier,

may have been

resolved

for Hiroshima.

Three

the aircraft
adequately

altitudeis a necessary

parameter;itfor the Nagasaki mission but is uncertain

values are given:

31 600 ft from the AF historical

records,26 32 700 ft from Parsons” log,l” and 35 000 ft from Alvarez” letterand from working backward from the timing of the Hiroshima

to McCrae25
record.

p(t)These and the other assumed parameters for the two missions are given

in Table 111.

The estimated bomb ballistics

at Site M (Muroc) (Appendix),

are derived from drop test dataand projectile calculations using the classicalsolution assuming the projectile drag is proportional to the square of its
speed. 30(The test data for Thin Man, an earlier longer gun device withcross-sectional

area and weight similar to the Little Boy, were used for the

Little Boy; test data for Little Boy have not been located.)
the test drop conditions determined
used for the combat conditions.
given

in

Table

IV.

The

Calculations forthe drag (terminal speed), which was thenA summary of these data andsummaryofthecalculations isdata and calculations

givingthecanister position is given in Table V.
The

time of fall of the Little

Muroc plus trajectory calculations
derive a drag coefficient.

Boy is basedon test data of tests at

for other altitudes using the test data to

The calculations

are very well fit by the free-

fall equation with g reduced to 30.1 ~ 0.1 ft/s 2 from the perfect bomb case of
32.16.

This good fit and the l.72-s difference that the S-Cubed calculations*show between

the acoustic

and shockarrivaltimes as a result of their 2-D

hydrodynamic

calculation permit a parameter study.

To simplify calculations,

I have used an average sound velocity derived from a fit to the 1945 Japanesemeteorologicalobservations

used by ORNL

and S-Cubed.

Thatvalue is 1.087

kft/s.
There are two possible evaluations
fromthe canister

directandrecord:of canister position using the timing

1) one based on the time difference

reflected shocks as well as the arrival

between thetime of the direct shockand 2) another using only the time of arrival of the direct shock.

With thefirst, there is agreement with the record timing if the canister altitude wasabout 34 kft

in agreement

previous work.

with

the S-Cubed

calculations

by Penney, and my

As the reflected shock traverses previously

shocked air, theacoustic reflection time is longer than for the reflected shock (2.55 s).

* Information from L. W. Kennedy of S-Cubed.

April 25, 1984.

To

TABLE IIIMISSION PARAMETERS

Height-of-burst(ft)

Aircraft altitude (ft)Ground speed (mph)Head wind speed (mph)Aircraft separation (ft)Hiroshima

Nagasaki

1 903 (Ref. 28)

1 650 (Ref. 28)

31 600 (Ref. 26)
32 700 (Ref. 10)35 000 (Ref. 25)

28 900 (Ref. 26)

328 (Ref. 26,16)

315 (Ref. 26)

O (Ref. 10)

1 (Ref. 26)

300 (Ref. 27)

3ooaTime delay from bomb tocanister releasea andstart of record 25 (s)11Parachute opening time (s)a11Canister drop speed (ft/s)(?)

16

16

a Estimates.

1
TABLE IV
TRAJECTORY PARAMETERS

Hiroshima
Height-of-burst(ft)

Aircraft altitude (ft)Nagasaki

1 903 (Ref. 28)

1 650 (Ref. 28)

31 600 (Ref. 26)

28 900 (Ref. 26)

328 (Ref. 26)

315 (Ref. 26)

Ground speed (mph)Dataa

Calc30

Dataa

Calc30Site M test
Altitude (ft)

28 06528 026Air speed (mph)

315

300

Time of fall (s)

43.11

43.4

47.70

Vertical speed (fps)

1 138

1 116

901

2 030

Terminal speed (fps)

47.71

1 005

Angle at impact

12°

17°

10°

11.5°

Trail (ft)

1 441

1 449

5 005

5 068

Combat conditions
Time of fall (s)

44.4

47.0

Angle from verticalat explosion

17°

12°

Trail (ft)

1 330

5 200

Vacuum time-of-fall (TOF) = 43.0 s
Tone signal switched on by Ferebee at -15 s (Ref. 20, p. 256).
Tone break at release.

a Appendix Table A-I.

TABLE V
CANISTER LOCATION SUMMARY

Canister locations for Hiroshima and Nagasaki as estimated from“historical” records for the aircraft altitudes, ground speeds,
and drop test data. Aircraft altitudes are based on shock arrival
times at the canisters taken from the pressure-time records(together with aircraft ground speed from “historical” records,
drop test data, and Tokyo pressure-temperaturesoundings forAugust 6, 1945).

Hiroshima
Historicalp(t)ac altitude (kft)ac separation (kft)ground speed (kft/s)
time-of-fall (s)canister altitudea (kft)vertical separation(kft)
horizontal separation(kft)
slant distancea (kft)
6 (kft/s)
acoustic reflection t (s)shock arrival time (s)height of burst (kft)trail (kft)

34.6

31.6

p(t)
28.7

28.9
0.3
0.462

0.3
0.481
46.9
33.8
31.9
21.5
38.4

44.4
30.5
28.4
20.3
35.1

NagasakiHistorical

1.087
80.6
1.903
1.33
1.45

47.0
46.7
27.78
27.65
26.0
26.1
16.0
16.7
30.9
30.6
1.087
72.9
1.65
5.2

a Canister location relative to burst at shock arrival.
Location assumes 2 s from bomb release to parachute opening and
16 ft/s canister fall speed.
Canisters found 12.5 m north of ground zero at Hiroshi~~. 22
Canisters found 12 km east of ground zero at Nagasaki.

10

obtaina reasonable

trail

time is about 3.0 s.

(lag overthat for a perfect bomb), the acoustic

To bring agreement with the 30.5 kft altitude requires

an average sound speed of about 0.91 kft/s or a time of arrival of the shock
about 5.5 s less than given by the record.
again agreementwiththe record

Using the second method there is

if the higher

altitudes or a reduced shock

time-of-arrival are used.
The delay between bomb release and canister release is not known but wasestimatedby Alvarez as about 1 s. 25

canisters

was

opening

of

also

the

probably

parachutes

less

is

The time separation between the three

than

also

1 s.

The

not knowntime between

but Wieboldt

releasestatesandthat theexpected g-loading during parachuteopening at these altitudes and air speeds

was in the range of 20 to 50 g.*

Assuming uniform deceleration,

time must have
havingbeen about 1 s.

it open in the bomb

bomb-bay

shacklesTo minimizebay,parachute opening time but avoid

the lanyards

low in the bomb bay.

the opening

were

short

and looped around

Thus , the time delay between bombrelease and parachute deployment must have been in the range of 2 to 3 s.
parachutes

werestandard

personnel

were “baseball” parachutes,

was 16 ft/s at 30 000 ft.
onthetransmitter

power

increase in fall rate.

The measured

Hirschfelder

evaluation
andfor Crossroads,

the parachutes

24 ft in diameter with 40-ft shrouds and stopped

with no more than one oscillation.

Alvarez‘chutes;

The

hence

of

fall rate on that operation

used 15 ft/s in his May 1945 memo tothecanisterbattery

weightmethod.
wereSubsequently,

increased

with

the

probable

For Crossroads the transmitter power was reduced fromabout 20 W to 3 W with reduced weight.

Sixteen to twenty-eight ft/s seem tobe possible fall rates.
Thesystem was based

California

group).

It used a condenser microphone as the capacitor of a radio-frequency
a verysimpleoffrequency-modulated

frequency was proportional to the pressure.
by CIT.

The transmitters

Technology

(CIT)

for

by

providingInstitute(FEI) developed

the Navy

oscillator

theon the Firing Error Indicator(W.

systemPanofsky”sin whichthe

The receivers were units suppliedand packaging were built at Los Alamos.

The gageitself was modified at Los Alamos to provide a slow vent to equalize pressuresfor changes in altitude(this was nominally 30 s but the Hiroshima gage had a* This and much of what follows are extracts from a Crossroads handbook
and the notebooks of participants on the combat missions.
These
remain classified.

18se-foldingtime).24

Also

added

were

two

spring-actuatedpistons(snappers) to provide known volume changes and provide a direct calibration of
the gage

One piston rotated inward, the other outward toafter deployment.

restoretheoriginal

volume;motionshadsome overshoot,

they

were

The

set to trip at 30 and 40 s.

and extrapolation

to zero time was necessarytoThe operating frequencies of the units were 52,

determine the volume changes.

54, and 56 MHz; the receiver output was expected to be about 10 V with about a
60-kHz frequency deviation.
The

recordersphotographing

a

were

Kodak

cathodeCine

Ecamerasray oscilloscope.

modified

The

for

strip

time scale wasfilm useby blanking

markers derived from pip sharpening of the output of a Wien bridge oscillator;
calibrationwasin terms of a model

200C Hewlett-Packard

which had an accuracy of about 1 percent.

signalgenerator,

Johnston states the calibration was

There were two checks on the timing accuracy--film“quite adequate.”

speed

and the settings of the snappers.
A.

Calibration

Three

independent

methods

Luis” weight plus volt-box,
Agnew box. 24

ofcalibration

of

the

gage

were

provided:snappers, and the Firing Error Indicator (FEI) or

For the Luis” weight plus volt-box calibration , small weights were placedon the gage diaphragmmeasured.

The volt-box

the resultant
voltage.

andthe resultant

voltageintroduced voltages,

deflections

on the film gave

output of the receiver wasin steps, into the recorder andthe conversionof deflectionto

For the Hiroshima mission, the weight used was equivalent to 10.0 cm

of water or 0.142 psi at 30 kft to produce 9.0 V from the receiver.

The volt-

box data were:
volts

Deflection, V/mm

16.0

2.44

12.0

2.15

8.0

2.07

4.0

2.16 I

2.13

It was noted the calibration using the 16-V step indicated the system was not
linearat the largest step.

4.5 V, it seemedsteps.

appropriate

Full-scale

deflection

As the voltage produced by the shock was about
to discard
was

combination yields 0.0336 psi/mm.

12

10 V.

this value and use the three lower
Theaverage was

2.13 V/mm.

The

For the Hiroshima mission the snappers were set to trip at about 30 s and
40 s.

Only the first snapper worked on the record analyzed.

The resulting

calibration was 0.0336 psi/mm, 24 the same as the weight plus volt-box value.
Another

voltagecalibration

This

unit was developed

This

unit

injected

receiver.

used

at CITasignalthe FEI or Agnew box supplied by CIT.

as the field calibration unit for the Navy.
with

a

known

The unit was used on the mission

remembers the unit.

frequency

deviation

this unit

that

of

the

temperature

The calibrations were not used in the field analysis of

disagreed

other

two

difference

by a large(greaterThe

problemthan 60°C) between

probably

was

the

large

the setupconditionson

The relative linear contraction would have

As inductance of a coil is proportional to about the squareof the diameter, and the frequency is proportionalof

The calibration

factor (3.1 V/mm vs 2.13 V/mm)24 fromtechniques.

Tinian and the operating altitude.
been about 10-3.

thethough now no one on the mission

the data, nor were they used on the Crossroads measurements.
using

into

the inductance,

the frequency

to the inverse square root10‘3 of the operating

shift would be about

frequency, which was 54 MHz; a frequency shift of 0.5 MHz could have occurred.
The bandwidth of the system was about 0.1 MHz and the receiver was retuned onthemissionprobably

to match

not,

the

therefore

receiver frequency.

transmitter

the

FEI

frequency,

calibration

whereasbox maythe

not haveThis is conjecture but it seems plausible;

FEI
been

box

was

at thethe value isin the right direction.
B.

Zero-Time Signal

It has been conjectured by some that an electromagnetic
may have been recorded to provide a zero-timebythose,

Tinian.
modulated

including
Nor would
50+

both

Alvarezandit be expected.

MHz

receivers

Such was not noted

indicator.

Penney,who

signal (the EMP)

examinedthe

The systems had narrow-band,

inherently

insensitivefrequency-

amplitude-modulated

Further,

weapons,

the Little Boy, would lie well below the frequency bandof the receivers.
c.

componentsonsignals such as EMP.
particularly

the frequency

torecordsof the EMP from such

In any case, the complete records have not been found.

The Canister Data

The original films from the missions have not been located; reproductions
exist in LAMS-377.24

The films have been read at least twice--by the originalteam with the readings contained in W. Goodman-s
by Wieboldt summarized by LAMS-377. 24

notebook

and a reevaluation

A copy of the original plot of the data13

from the Hiroshima

missionreproduced in Brode. 2
I

have

the

used

was

attached

to Alvarez-

LAMS-377

readings

but

calibration

factorsbycorrection

for

gage

the

notes

made

leak

by

the

and,

have

letterbeen

original

followingato McCrae25

guidedteam.

Isuggestion

and

in

choosing

have

made

by

Reed

a

and

Bannister, made a correction for the time resolution of the gage of the form
given by Reed.31
The

1 and 2.
Alvarez25

The readings and corrections to the data are given in Figs.

time scale on the figures is the time from canister release.

suggests

adding

1 s for the time from weapon release.

With thistime scale it is possible to get both the slant distance to the gage from thedirect pulse time and the altitude of the gage above ground from the reflected
pulse

using

the knownmust

traverse

height-of-burst

previously

shocked

The reflected pulse, however,(HOB).

air,

requiringathecanisterdata

two-dimensionalhydro-

dynamics calculation.
Penney,inhisevaluationofon

Tinianafter

themission, took the canister release altitude as 35 kft, probably based upon thetime-of-arrivalof the direct shock.

(Alvarez, on the plot of the data madeon Tinian, gives the canister altitude as 30.5 kft). 25

Based upon the data,

the canister altitude must have been about 34 kft, putting the aircraft at analtitude of about 35 kft, an improbable altitude for a B-29 with that fuel andbomb load.

VI.

POSTSHOT SURVEYS
Estimates of an explosion-s yield can also be made from observationsits

effects.

Directcomparisonof equal effects

undersimilarofdetonation

conditions from two explosions will give an estimate of one explosion, if theyieldof the otherexplosions
becausewere

is known.

indeedof ground

The conditions of the Hiroshima and Nagasaki

similar,surveysandconducted

a

few

after

such

directcomparisons

the two explosions.

exist

One survey,

headed by W. G. Penney, was on a time scale of a few days, and surveys by a
BritishmissionJapanese

also

Engineeringand the USSBS wereon a time scale of a few months.

The

made

observations, and there were surveys by the Manhattan
District. 8,15,21
All of these surveys form the basic data forevaluation of the yield of the Hiroshima explosion scaled to the rather wellknown

yield

Trinity14

withof the Nagasaki
excellent

explosion.

photographic

The Fat Man was tested not only atcoverageand radiochemistry, but also

5

I

I

I

I

I

HIROSHIMA
4o READINGSCANISTERFROM-CORRECTED

I

LAMS

DATA

- 377

FOR GAGE RESPONSE

3 t psl
0.071 b
2 o
0
1 -

o

0 ~

0
\

-1 I
80

-2 I
79

0

0

0
00

1

1

I

81

82

83

0

00

1
84

I
85

Seconds After Units Dropped(Add -1 s For Time After “Bomb Away”)
Fig. 1.

Hiroshima canister pressure data.

I

10

1

1

NAGASAKIO READING

8
Psl
0.148

—CORRECTEDJUMP=6.90

I

I

CANISTER
FROM

LAMS

DATA

- 377

FOR GAGE RESPONSE

6

4

2

0

-2
“o 00

-4
1

I

I

I

1

I

72

73

74

75

76

Seconds After Units Dropped(Add -1 s For Time After “Bomb Away”)
Fig. 2.

Nagasaki canister pressure data.

7

Crossroads,

duringwhereradiochemical

radius-vs-time data were obtained.

debriswascollected

andfireball(Unfortunately, the large bombing error ofAble, the air burst, put the burst outside the prime fireball cameras- fieldof view; only a streak camera record was obtained, however those data are very
good.)

Table VI summarizes the data relative to the measurements of the yieldof Fat Man.

VII.

LITTLE BOY YIELD FROM BLAST DATA (HIROSHIF@A.

Canister pressure-vs-time measurements

The

shock

overpressure-vs-time

retardedcanisters
strike aircraft. 24

droppedThefrommeasurementanaircraftused

flying

in

gages

in

parachute-formation

with

the

three canisters were toggled by the bombardier uponnoting “first motion” of the bomb.
One good record was obtained on each missionon

the Nagasaki);

the record

shows both(the signal went off-scale

shock(about 1 s after bomb release). 2,25

timed from the start of the recorderthe direct

and reflectedasIn

principle there is enough information on the records to determine the canister
range and altitude.
bomb drop altitude

For the Hiroshima mission, historical

records give theas 31.6 kft26 and the canister altitude at shock arrival

time (?) as 30.5 kft,24’25 consistent values.

Values obtained from the record

give the drop altitude as about 35 kft and the canister altitude as about 34
kft.

The difference

has not been resolved.
These data have recently been32
reanalyzed by Kennedy et al. , who used meteorological data taken over Japanin August1945 to describe the atmosphere and used a combination of two- andone-dimensionalhydrodynamic

calculations

the record and the shock magnitudes.
phase duration and the impulse.
themethodestimateisshouldto attempt

to match the timing ofThey put most reliance upon the positive

For these slant ranges and low overpressures,

not be sensitive

16.6 f 0.3 kt whereto the canister

the error

quotedlocation.

Theiris the precision

yieldof thecalculation and not the overall error, which must be greater than 10 percent.
As their slant range to the canister is greater than the probable range, thisyield is probably an upper limit.
B.

Equivalent blast effects scaling

Surveys after the explosions
effects due to the blast wave.
few comparisons16

noted distances from ground zero of similar
The data set for comparison is limited but aby the same observers

and with documentation exist.

DamageTABLE VI
YIELD OF THE FAT MAN

Radiochemical yield (kt)Trinity

20.3

Crossroads A

20.4

Crossroads B

21.7

Fireball yield (kt)Trinity

20.8

Crossroads A

21.4

Calculated yield (kt)a22

Recommended yield21

a By R. Osborne, Los Alamos National Laboratory Group X-4.

due to drag effects has been excluded; only those comparisons of damage due tooverpressure with a significant number of objects observed were retained.

The

ground surfaces were far from “ideal;” thermal effects would have produced aprecursor to the blast wave and added both smoke and dust loads.
mechanicalIn addition,effects due to the many buildings would have absorbed energy fromthe wave as well as providing debris to further load the blast wave. 33

Thesummary of blast data and the comment by Brode 34 suggest simpler models of theheight-of-burst

effect may be more

appropriate.

Twosuch models have beensuggested:using scaled ground ranges and using scaled slant ranges.

by

range

groundallows

for

some

HOB

effectsbutisindependent

Scalingof

HOB.

Scaling by slant range implies that the effect of the direct shock results inmoredamagethan does the reflected shock.

have the same

Brode prefers the first but the second appears to be more

yield dependence.
appropriate.

Both postulations

These relations are‘@N= (x@N)3or(RH/RN)3,
where the subscripts refer to Hiroshima and Nagasaki, W to the yield, X to theground

range

(GR),

and

R

to

the

slant

range

(SR).

Takingthe

Nagasaki

explosion yield at 21 kt, Table VII gives the data set and the derived yields
for Hiroshima.

The averagefor the Hiroshima yield is about 14.3 kt using

ground range scaling and 14.9 using slant range scaling.

The average of theseis about 15 kt when rounded.

c.

UK Yield Evaluation

A group from the Manhattan District, composed of W. G. Penney, R. Serber,and G. T. Reynolds,

was

sent

to both Hiroshima

explosions to report on physical effects.
theinformation

explosions.

upon

which

to

make

and Nagasakisoon after the

These surveys have provided much of

estimatesoftheyields

of

the

two

The results of the survey and samples of damaged objects from theblast wave were analyzed by Lord Penney et al., 5 who concluded that the yieldof the Hiroshima

explosion was 12 k 1 kt and that of the Nagasaki explosion

wasThey used data from objects damaged

18

22 ~ 2 kt.

from the pressure pulse

TABLE VII
SCALING EQUIVALENT BLAST DAMAGE

WH =WN(~h)3, orWN(

H
.

)3

‘h

%

Ground Distance (km)

‘H/wN

H

N

GR

SR

Collapse or complete
destruction of y~odenframe buildings

2.0

2.4

0.579

0.612

Severedamage
Ref.
Ref.

1.98
2.41

2.44
2.62

0.562
0.778

0.568
0.802

structural
to homes:
15
36

Damage to buildings (Ref. 36)a
One story brickWooden buildings(except residences)
Wooden residences

2.19

2.55

0.633

0.662

2.61
2.19

2.82
2.46

0.793
0.706

0.813
0.735

10 to 20% of empty 4-gal.
petrol cans undamaged (Ref. 5)b

1.74

1.95

0.710

0.755

0.68

0.71

AverageBest estimate, based on WN = 21 kt:

a The damaged
circular area.

area

was

observedb The petrol can data are believedbuildings as next best.

15 kt

to

be moreellipticalto be the more

than

the

impliedcredible with damage to

19

and

by drag. *tests.

Calibration

Unfortunately,

Hiroshima

in terms of scale models

in high-explosive

the scale used was for a full-scale explosion

height-of-burst

explosions.

wasbut at 9 kt,

requiringan extrapolation

They also assumed ideal surfaces in the two cities.

at thefor both

Lord Penney

has recently reevaluated the data of Reference 5 using US blast data and finds
the same

results.

He also suggests that the vertical velocity gradientcanproduce turbulence and this may in part explain the nonideal shape of recordedpressure-time

records

inadditiontothedistortion

producedbythermaleffects on the surface.
Heareasuggeststhat a measure

on

the

telegraphdistancesofthermalbetterinformation.

poles

of

may

the anglebeeffects.

Better

He

the

notes

a

of the sector of the scorchedbetterway

photographs

distances

toofquoteddetermine

limiting

the poles may
in

the

USSBS

yield

may

be

reversed for the two cities (assuming they are reversed, then scaling in themanner of Sec. VIII.A below gives 14.3 kt for the Hiroshima explosion yield).

for

He has added

to information

Sec.

he

VII.A;

conjectures
dependence

that

confirms

shockneeded for evaluation

thereflection

spacing
from

of

the

the

two

parachute(The method of correctingof the record.

of the canister data
aircraft.

He

also

may

the

time

alter

the record should haveremoved the effect.)

VIII.

LITTLE BoY YIELD FROM THERMAL DATA (HIROSHIMA)
Equivalent thermal effects scaling

A.

Surveys subsequent

to the explosions

noted distances from ground zero of
The data set issimilar effects due to thermal radiation in the two cities.

limited, but four comparisons by the same observers and with the documentation
have been selected by Kerr. 37

The same set is used here.

Scaling is on thebasis that the thermal fluence at slant range R is proportional toW cos i e

-ER

R2
where

W

is

the

yield,

i

the

angle

‘
of

incidence,

and

E

the

extinction* An evaluation of the Hiroshima yield using the observation of damageof drag-sensitive objects-- lightning rods, flagpoles, etc.--was madeat Sandia Corp. in the early 1950s by Shelton. Calibration was byscaled models exposed in a supersonic wind tunnel. Documentation
has not been located but the value of yield obtained was 16 kt.
F. Shelton, Kaman Sciences, Jan.10, 1984.
20

The extinction

coefficient.
visibility

coefficient

may be obtained

from the measured

the relation e = (ln 50)/V used by meteorologists, where V is
For the data
the visibility, given as greater than 20 km in both cities. 21

set

used

by

and

when

all surfaces

are taken as vertical

exceptfor the roof

tiles, the ratio of the yields in the two cities WH/WN is given in Table VIII,
resultingin an average of 0.64.

Taking the Nagasaki explosion yield as 21

kt, this scaling gives a yield for the Hiroshima
If

a

30-km

observations

visibility
of

the

is

explosion

used,

the

derivedyieldisexfoliationofgraniteobservationsof about 13.4 kt.

about

13.7 kt.

areomittedIfassuggested by Tajima because of the paucity of these data, the yield ratio is0.68, or a yield scaled to Nagasaki of 14.3 kt.

TABLE VIIISCALING EQUIVALENT THERMAL EFFECTS

Ground Range (m)WH/WNaH—

N—

Watanabe et al.38
Melting of roof tilesb

600

950 - 1000

0.575 - 0.526

Exfoliation of granite 38c1000 - 1100

1600

0.473 - 0.545

British Mission39
Charring of poles
Lord Penney 5,39,40

2740

3050

0.782

Charring of poles

2900

3350

0.707

Averagea

0.64d

WH/WN, ratio of the explosion yield at Hiroshima to that at Nagasaki.
b Ridge tiles: normal incidence.
c The quantitative (and qualitative) data for this effect are oflower value compared with that of the roof tile data. This entry
has low weight; omitting it results in an average of 0.68.
d With 30-km visibility WH/WN = 0.65.

B. Charring of Cypress on Chugoku Electric Power Building
Charringofcypress

reported

Building,

byoffers an evaluation

on a shrine

Kimura,the Chugoku Electric Powerand Tajima 41 and again by Tajima, 42

Akutsu,of the Hiroshima

atop

explosion yield in absoluteterms.

It

that there were two charred layers, one a completely carbonized

was observed

layer 0.10 mm thick(1.38 mg/cm2) and a brown incompletely

To produce

0.35 mm thick.
exposure

wood

the completelyfrom a 1200°C electric hot plate.

charredlayer

carbonized

requiredlayer

3.3 s ofThis is a thermal fluence of 21.1.

cal/cmz assuming block body radiation at this temperature.

The thickness ofthe second

intensity

layer

was

observed

to bedependent

upon

the

of theradiation and not on the exposure time from a carbon arc furnace.

To obtain

the 0.35-mm

a fluence

thicknessof the incompletely

charredlayer

requiredrate of 14 cal/cm2 per s; with this fluence rate it required 1.4 s to produce
theO.10-mm-thickcal/cm 2 .
Thecompletely

distanceto

carbonizedtheChugoku(hypocenter) was about 676 m.

layer.

This

is a fluence

Building

Electric

from

of

19.6

groundzero

The height of the building (and shrine) was 21

m, giving a slant range of about 877 m.
of 20 km (Ref. 21) was about 0.84.

The transmission using a visibility

The measured angle between the burst andthe normal to the surface was given as 62°360.

The fraction of the explosion

energy allottedtaken as 0.35. 33

values,to thermal energy is generally

the yieldof the Hiroshima

explosion

mustWith thesehave been about

15.1 kt

using the first calibration method or 14.0 kt using the second.
The evaluations
intheoriginal

neglect conduction

article 41 that withand reflection effects.
the longer

irradiation

It was noted

times from thecalibrating sources as compared with the weapon thermal pulse (time of maximum
tmax is about 0.14 s; at 10 times this value or 1.4 s, 0.80 of the total isdelivered),more heat is lost into the wood by conductance,

obtained are upper values.

and the fluences

Reflection from the surface is an opposing effectand would be greater from the bomb thermal fluence; the reflection coefficient
probablyvariedfrom 0.7 to 0.05 during

examineconduction,a calculation

the irradiation.

In an attempt towas made of temperature and flux into thematerial, using reasonable values for the thermal parameters (conductivity K =2.8.10-3

cal/cm2s/°C/cm,densityp = 0.46

g/cm3,

specificheatc = 0.40

cal/g°C, and diffusivity k = K/cp = 0.015 cm2/s).43

The fluence rate peaks at

about 1 tmax

Penetration at 10 max is

22

and the temperature at about 2 tmax.

The calculation assumed constant values and no phase changes (noabout 4 mm.

equation-of-state

was

For

found).

constantafluence

rate

as

from

the

calibrating source at a time of 1.4 s and a distance of 4 mm, the fluence rateis down to 0.05 of the fluence rate ,at the surface versus about 0.01 for thebombthermalReflection

pulse.

fromthesurface

opposestheconduction

effect, but no estimates have been made.
The average yield obtained by the two calibrations
the morereliablecalibration

value

using

from

the completely

more modern

thermalcharredsourcesis 14 kt or 15 kt if
Repeatlayer is used.

with approximately

the proper

time dependence would likely produce a better estimate from these data.

IX.

GAMMA-RAY DOSE SCALING
Scalingenhancement
as

one

km),

gamma-ray

dose

at

where

rangeshydrodynamic

shock

and cloud rise effects are small has long been used by Los Alamos

methodmethodology
3.0

integratedofdetermining

the

yield

of

a

nuclearThe

explosion.

was to scale at a range at which these effects are small (2.5 toforcorrectthedifference

in atmosphericconditions,andsimplyBetter agreement was obtained if

scale the measured dose linearly with yield.

the reference data were from a similar device.

It has worked well for yields

less than about 40 kt using similar film badges housed in similar packages.
Methods

have

been

developedat

Science

Corporation(SAIC)

forcalculating

the

dose

nitrogencaptureand fission

product

Applications

fromcomponents,

fissionInternational

devicesforthethe latter consideringthethree main fissionable materials. 44,45
The

data

on

thermoluminescence

provides a useful set of measurements

of

roof

tiles

reportedfor estimating a yield.

byIchikawa

46

In particular,

the tiles from the Hiroshima University Building HU-2 are of known orientationanddistances.

SAIC

has

calculated

the

TLD

(horizontal) with an assumed yield of 15 kt.
evaluation*

are givenin Table

IX.

The

dose

consideringorientation

The results of their preliminary

calculated

directly with yield for the same bomb and atmosphericdose willcondition.

scale

nearlyThe data

are better fit by calculations with an assumed yield of 16.6 kt.

* W. A. Woolson, Science Applications
October 18, 1984.

International Corporation,

23

TABLE IXCALCULATED AND MEASURED TLD DOSE
AT HIROSHIMA UNIVERSITYTLD Dose (rad(Si))

GroundRange (m)Calculateda

Measuredb

w=

1377

75

83

-0.11

1382

77

84

-0.09

1411

65

69

-0.05

1439

68

68

-0.14

a Yield:

15 kt. March 1985 calculation; the calculated doseat these ranges ought to scale linearly with yield.

b Ichikawa,46 horizontal samples from building HU-2
rad (silicon) = 0.87 roentgen.
c (Calc-mess) / mess.
Note: To bring the average of the deviations
values to zerorequires that 16.6 kt be used in the calculations.

X. SULFUR NEUTRON FLUENCE EVALUATION
For
above
has

similarbombs

the fluenceof high-energy

the sulfur threshold), corrected

been

used

to scale measured

neutrons

for atmosphericfluencesto reference(that is, thosetransmission effects,
datafrom a similar

device to determine the yield of a nuclear explosion.
A

yield

the activation of
32P.
Revision of
sulfur by high-energy neutrons in the reaction 32S(n,p)
48
Yamasaki”s47
Calculations of thedata have been reported by Hamada.
activityatdetermination

Hiroshima

may

have

be

made

using

been

made

by

data

SAIC,

from

includingthegeometriccorrections for tilt angle (TA) of the weapon and bomber heading (BH) of thedropaircraft.*

The data

and calculations

are summarized

weapon yield was assumed to be 15 kt in the calculations.

* D. C. Kaul, Science Applications
March 13, 1985.

24

International Corporation,

in Fig.

3.

The

L--

~

A(l?ASUREDBACKCROUIVD

HAMADA DATA (1983)
NEW RERF GZ, BH=265,

TA=15,
f.z

0.0

c#hvD
Fig. 3.

XI.

YAhT&KIL&A&)

Sulfur activations at Hiroshima.

CONCLUSIONS
The

yieldsfor the Little

Boy usedon Hiroshima,as derived

various methods, are summarized in Table X.

From these evaluations,ofuncertainty.

15 kt

uncertainty

isestimatedwitha20-percent

applied to radiochemical

data and seems appropriate

This

from

the

the value

is twicetheand fireball yield evaluations with goodfor the indirect methods

required to estimate theyield of the Hiroshima explosion.
The recommended yields for the two explosions are as follows:

where

the

value

is

Hiroshima

15 kt

Nagasaki

21 kt ,

believed

to

have

an

outside

limit

of

20

percent

for

Hiroshima and 10 percent for Nagasaki.

25

TABLE XYIELD EVALUATIONS FOR LITTLE BOY (HIROSHIMA)

MethodYield (kt)

Canister P(T) Data

16

Equivalent Thermal

14

Cypress Charring

15

Equivalent Blast

15

Lord Penney, et al.

12

Thermoluminescenceof Roof Tile

17

Sulfur Activation

15

Design Predictions (Schiff)

15

ACKNOWLEDGMENTS
Assistanceparticularlyin the preparationof this report is gratefully acknowledged,that of Harold Agnew, Luis Alvarez, Don Barr, Gil Bininger, Don

Eilers, Bill Hereford, Dean Kaul, Jack Kelso, Lynn Kennedy, George Kerr, Lord
Penney, Jack Reed, Eizo Tajima, George Trimble, and Paul Whalen.

26

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3d

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Nagasaki, Radiation Effects Research Foundation, p. 1, 8-9 November 1983.

43.

CRC Handbook of Chemistry and Physics, 64th ed. 1983-1984, p. E-5.

44.

W. H. Scott, “Delayed Radiation at Hiroshima and Nagasaki, Reevaluationsof Dosimetric Factors: Hiroshima and Nagasaki,” DOE Symposium Series 55,
CONF-81O928 (V. P. Bond and J. W. Thiessen, Eds.) pp. 159-178 (1982).

45.

W. H. Scott, “Delayed Radiation
Nucl. SOC. ~, 472 (1982).

46.

Y. Ichikawa and T. Nagatomo, “Measurement of Gamma Ray Dose from theAtomic Bomb by the Quartz Inclusion Technique.”Second US-Japan Joint
Workshop for Reassessment of Atomic Bomb Dosimetry in Hiroshima andNagasaki, Radiation Effects Research Foundation, pp. 30-31 (November1983).

47.

F. Yamasaki and A. Sugimoto, “Radioactive 32P Produced in Sulfur in
Hiroshima,” paper No. 5, pp. 46-48, Collection of Investigative Reports
on Atomic Bomb Disaster,Vol. 1, Radiation Effects Research Foundation.

48.

Inducedin Sulfur in Hiroshima:
Reevaluation of
T. Hamada, 1132PActivity
Data by Yamasaki and Sugimoto,” Second US-Japan Joint Workshop for
Bomb Dosimetry
Reassessmentof Atomic
in Hiroshima
and Nagasaki,
Radiation Effects Research Foundation, p. 52 (8-9 November 1983).

at Hiroshima and Nagasaki,” Trans. Amer.

29

APPENDIXEXTRACTS FROM LOS ALAMOS HISTORICAL FILES

30

INTER-OFFICE tfEN09ANDUH

Oppenheimer

TO:

R. J.

Flml:

Hirschfelder

SUBJECT:

ENERGY OF ilIROSHINA SHOT, 6000

●nd He~ee

TONS TNT

The perachutegauge was supposed to be located ● t an
feet
above the ground ●nd 23,000
feetin● horizontal
direction●way from the pointof explosion.
We
Littler,●nd Sheard (LA-316)
used the formulaeof Hirochfelder,
record. According
to interpretthe ●xperimental
to the record,
chock (sndthe reflected
chock had not caught up to the primarywould, ●ince the reflected
shock ustravelfog
in thenever●uctionphase wake of the prfmaryshock).
●ltltudeofprimary

shock

30,000

theprimary
shock we find (realizing thathas not been compounded with the reflected wave):

From theEnergy ●stimated from meximum preosure.
.
.
po8itive
impulee.
.
.
●nergy left
in blast
Similarly from theEnergy estimeted
,,
.
.

.

frtau

.

.

reflected

3526 tons
6233

TNT

4635

chock we find:meximum pressure

6030 tone

impuleepositivein blsct●nergy left

9409
7310

TNT

It is difficult to know how much credence to placereflected
chock wave result..
Rouever, it uould seem thatour beeteetimeteof the blast●nergy vould come from combining
in the positive
pheseof the primary chock withthe ●nergy left
in the poeitive
phase of the reflected
blast.
the energy left
This leads to:on theEmergyblaet

Niroohime shot

5970

J.
J.

ton9

TNT

O. Nirechfelder
Mecee

jsh
cc

-

Bethe
Iarkin?araons31

INTER-OFFICE F!E140RANDU?tTO:

J. R. Oppenheimer

FROH

W. S. ?araonm

SUBJECT:DATE

Paraphrased

TeletypeTo

forIarkin,Reference

Oppenheimer,

NR-302frcm

13 August 194s

dated 13 AugustManleyEstimates of tonnage heve been made by Penney for the two units.
However, they ●hould not be circulated. The relative valuee
Zlve
much
more meaning than the ●baolute values. Thie information compriees
allthat has been forwarded
frma Destination.
On the firstunit,
the ground equivalent walue was 15,000 tons,●nd on the second, was 30,000 tons. The peak pressure
on the firet unitft.
from
was 0.076# per ●quare inch from ● blaet pressure at 39,000
detonation ● t an ●ltitude of 30,500 ft.

On unit No. 2, the peak pressure was 0.055 lba. per square inchfor● durationof 1.44 ●econde.
Thle blast pressure
positive pressure,was taken ● t 32,000 ft. from detonation, and an altitude of 29,000 ft.,
and was a free air wave. The reflected wave gave 0.178 lbc. per ●quareinch as peak pre~~ure on the ●econd unit.
Betweendirect and reflected wave, the time interval was 2.55 aeconda
of detonation wae 8,000 ●ndfor both units. The ●quivalent at the point
16,000 tons for units one ●nd two, respectively.

32

f’
I

28 September
Norman

R.

F.

1945

Remwy

B. Brode

Units L-II ●nd

F-31

—

NeightofOperationme ●stimated ●ltitude of operation of Unitor minus 50 feet.
The ●stimated height
50 feet.

ofoperation of F-31

L-n

was 1885 feet,was 1650 feet,plus

plus or minus● re made on the basisof data obtained both ●tThese height estimatesslightly from
Destination and at Ringmen. These values may differ
previous ●stimates due to the fact ttut we have included here more
recent data than was ●vailable to the crew ●t Ikmtfnatlon.

R.

cc:

B. Brodem

Bradbury

33

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