NATIONAL BUREAU OF STANDARDS REPORT

NESS PROJECT NBS REPORT

1103-40-5X18 1? July 19£6 lj.78X

Progress Report for January^®June 195*6

on

Research in Applications of Mathematical Statistics

to Problems of the Chemical Corps

(KBS Project 1103«4|.0«£ll8)

NATIONAL BUREAU OF STANDARDS

The publication, reprinting, or reproduction of this report in any form, either in whole or in part, is prohibited

unless permission Is obtained in wrltingfrom theOfRce of the Director, National Bureau of Standards, Washington

25, D, C, Such permission is not needed, however, by a Government agency for which a report has been specifically prepared if that agency wishes to reproduce additional copies of that particular report for its own use,
I t V i 4
Progress Report for January-®June 1956

on

Research in Applications of Mathematical Statistics

to Problems of the Chemical Corps

(KBS Project 1103-40-5113)

This report contains a summary of the work done during

the quarter,. Results of this work are briefly stated,. Technical reports written in connection with this project are

mentioned but are transmitted separately©

( 1 ) Computation of atmospheric diffusion

Two basic codes have been written for SEAC for evaluating the dosage of a grid point as a function of the

distance from the source© The first of these computes values

x < 0

Lx

j

x > 0

for given values of 0, P* L at a rectangular grid

Xq ( Ax)x_, f) y^ (&y)Ym

o This code was used to compute a

table of 64 X 2,40 - X5*3&Q entries in about If hours 0

The second code computes the effects of N sources on

a grid point 0 The code calls for the following quantifies

as input

M, a,# $ 9 P, L s constants related to type of

source

a5 b s length and width of area of

interest

f

(x ty) exp f p _.2 «ad

j -P y x
-
h

X o o o % X coordinates of grid points 2

2 initial Y coord in at

increment in Y0

The code computes the sum of the effects from the N

sources at each point on the grid? X, , Xo0O oo, Yr (AY) Y 0 1 c, 0 ZH (See Figure)

(0,b) (a,b)

Yfj + 4&Y o o o

Y

0 + 3&Y o 6 0

Y

q

+ 2L\Y o o o

Y

0

+ &Y O O O

T

o

0 0 o

- 0 X^ X. O o o ;a o 0)

The X and Y coordinates of the N point sources are

tandem numbers from rectangular distributions with ranges

0 < X < a and 0 < Y < b respectively0 The computation time is proportional to the number of

source points to the left of a grid point 0 For the case

P on which tests were made the following table gives the

computation time required for each grid point 0

Distance of grid point

from origin

(meters)

Time (minutes)

per grid point

100 0 2

5oo 0 8

1 5,000 io5

2j>Q0Q 3o

5*000 8 o 10^000 i5o

12j,000 18 0

A manuscript on "'Some Examples of the Use of High Speed

Computers in Statistics'9 by J© Mo Cameron prepared for inclusion in the Proceedings of the "Conference on the Design

of Experiments in Army Research Development and Testing"

was submitted

o

NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

1103-40-51.18 1? July 195>6 b?Bi

Progress Report for January®®June 195*6

on

Research In Applications of Mathematical Statistics

to Problems of the Chemical Corps

(IBS Project Ii03»[>0-5X13)

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication, reprinting, or reproduction of this report In any form, either in whole or in part, is prohibited

unless permission Is obtained in writing from the Office of the Director, National Bureau of Standards, Washington

25, D. C, Such permission is not needed, however, by a Government agency for which a report has been specifically prepared If that agency wishes to reproduce additional copies of that particular report for its own use.
-
Progress Report for January—June 1956

on

Research in Applications of Mathematical Statistics

to Problems of the Chemical Corps

(MBS Project 11 03-40-5118)

This report contains a smamary of the work done during

the quarter o Results of this work are briefly stated „ Technieal reports written in connection with this project are

mentioned but are transmitted separately 0

(1) Computation of atmospheric diffusion

Two basic codes have been written for SEAG for evaluating the dosage of a grid point as a function of the

distance from the source 0 The first of these computes values

x < 0

P y

d 7.°^ - Lx

I

x > 0

for given values of M, P, L at a rectangular grid

x

Q

(Ax)x^ 9 yn

o This cod© was used to compute a

table of 61j. X 240 ~ 15^360 entries in about Ij- hours 0

The second socle computes the effects of H sources on

a grid point 0 The code calls for the following quantities

as input

P* P» L : constants related to type of

source

a, b : length and width of area of

interest

}i

a

2

o o o

CD 2

% X coordinates of grid points

Y , AY ? initial Y coordinate

,

u increment in Y©

The code computes the sum of the effects from th© N

sources at each point on the grids J 9 X {0 oo» Y (AY) Y 0

JL c?L l i l (See Figure)

(O/o) (a^b)

Y

q * bAY o o o

Y

Q

3AY O O O

T

q

+ 2AY €> 0 0

Ya + AY

U

9 0 0

T

o

© 0 O

_ 0 X

j Xg o o o ( a o 0 )

The X and Y coordinates of the U point som^ces are

tandom nnmbers from rectangular distributions with ranges

0 < X < a and Q < Y < b respect Ively 0 The computation time is proportional to the number of

source points to the left of a grid point 0 For the case

P on which tests were made the following table gives the

computation time required for each grid point 0

Distance of grid point

from origin

(meters)

3

Time (minutes)

per grid point

s

100 0 2

500 0 8

X 9 QQ0 Xo5

2*000 3o

5 2 ooo 8c

10*000 X5o

X2 0 OQQ X8 0

A manuscript on w Some Examples of the Use of High Speed

Computers in Statistics'® by J 0 Mo Cameron prepared for in®

elusion in the Proceedings of the "Conference on the Design

of Experiments in Army Research Development and Testing”

was submitted

o