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COMPUTING DEVICE
Filed Nov. .14, 1944
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M, WAT-1m
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COMPUTING DEVICE
Filed Nov. 14, 1944
4 Sheets-Sheet 2
_March 30, Í948.
M_ WATTER
2,438,730
couPuTING DEVICE
Filed Nov. 14, 1944
4 sneets~sheet s
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NVENTÍDR
Michael Ñ, 'a D i,
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March 30, i948.
M. WATTER
2,438,273@
COBWUTING DEVICE
Filed Nev. ld, 1944
INVENTOR
Micha l W ’c l”
By ¿ß @/ÄÄZ.
Patented Mar. 30, 1948
aliarse
UNITED STATES
y PATENT
OFFICE
2,438,730
COMPUTING DEVICE
Michael Watter, Philadelphia, Pa.
Application November 14, 1944, Serial No. 563,343
ßclaims. (Cl. 23S-61)
This invention relates to a. computing device.
particularly to a device for solving vector prob
lerns, and has for an object the provision of lm
Drovements in this art. 'I'he device is herein de
scribed speci?cally in connection with the solu
tion of navigational problems for aircraft,
2
lems can be solved. These lined rotatable mem
bers -are preferably formed as circular plates,
sheets or disks and may be associated with a base
plate or disk carrying indicia of direction, for ex
ample, a compass rose. Also there is provided a
member which is similar to the lined disks but
which may be an incomplete disk, for example, a
narrow strip or arm carrying a single radial line.
The lines of the two associated disks thus may
form the sides o_f a. parallelogram; the arm may
form the diagonal or resultant; and the compass
rose may provide directional orientation.
These several members are shown connected
though without limitation to use in this or any
other definite ñeld.
One of the particular objects of the invention
is to provide a simple device for quickly solving
problems involving vector analysis, preferably a
device which can be operated by one hand, leav
ing the operator’s other hand free to manipulate
controls, as of an airplane in flight.
in Fig. 2 and separated in Fig. l. The base plate
Another object is to provide a device which 15 or compass rose is designated by the numeral l0.
can be inexpensively manufactured, yet will be
the tlrst lined disk thereabove by the numeral ll'.
very durable in service.
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the radial arm by the numeral I2, the' second
Another object is to provide a device having
lined disk by the numeral i3, and a hub pin by
few and small parts adapting it to be easily car
the numeral Il. The pin i4 holds the members
ried about, as for example. in the operator's 20 I0, ll, l2 and i3 together under friction but not
under sufiicient friction to prevent easy turning
The above and other objects of the invention
movement by the hand. Further frictional en
and various features of novelty will be apparent
gagement between the arm i2 and the disk I3
from the following description of an exemplary
is provided by a resilient clip i6 secured to the
embodiment thereof, reference being made to 25 outer end of the arm and embracing the outer
the accompanying drawings, wherein:
edge of the disk. When either the disk or the
Fig. l is an exploded isometric view of a device
arm is moved it moves the other unless held
embodying the invention;
against such conjoint movement.
Fig. 2 is an axial section through the device;
The top disk i3 is transparent so that its lines
Fig. 3 is'a plan view of the device showing 30 may be seen superimposed upon the lines of the
parts in position for the solution of a naviga
disk Il. The second lined disk l l may also be
tional problem:
transparent, although transparency is actually
Fig. 4 is a diagram of the computation illus
needed only near the circumference to reveal
trat-ed in Fig. 3;
indicia on the edge of the compass rose lll. If
Fig. 5 is a plan view of the device showing the 35 the disk Il is enough smaller in diameter than
parts in position for the solution of another navi
the disk l0 it need not be transparent in any
gational problem;
part; however, it is desired that disk li shall
Fig. 6 is a diagram of the computation illus
be of larger diameter than the compass rose so
trated in Fig. 5;
its edge will be exposed beyond the edge of disk
Fig. 'l is a plan view of the device showing the
l0, convenient for engagement by the lingers.
parts in position for the solution of another navi
The arm I2 is made of transparent material when
gational problem ;
' it is located in a position above one of the upper
Fig. 8 is a diagram of the computation illus
or rotary disks. as here illustrated. All oi' the
trated in Fig. 7;
transparent members may be formed of Celluloid
Fig. 9 is a plan view of the device showing the
or other plastic: the base disk I0 is preferably
parts in position for the solution of still another
formed of heavy cardboard. Preferably also the
navigational problem; and '
topmost disk I3 is formed with a mat surface
Fig. 10 is a diagram of the computation illus
iìnish in order that pencil marks may he made
pocket.
trated in Fig. 9.
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upon and removed from it.
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The device comprises a plurality of rotatable 50 The compass rose lll is divided and marked
members, some transparent in whole or in part,around the circumference in degrees, the major
provided each with a series of parallel lines which
points being designated, as usual, by letters such
are so disposed, as for example, parallel to a base
as N, E. S, W, and >the terminal cipher of each
diameter. that the lines of two or more members
degree number marking being omitted. Thus 3d
form parallelograms from which various prob 55 designates 360 degrees, etc. 'I'he members ii, i2
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3
.
assenso
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and -I3 have- radial base lines marked to a comsî
solved and it is onlynecessary to «read the an» '
mon scale, the full disks II and I3 each hav-,
ing two aligned base line radii forming a diame
trai base line. Ali radial lines are divided into
spaces of uniform length and are. marked from
zero at the center upward toward the outer edge.
swer), the “heading" direction is read on the
The parallel lines of disks II and I3 are spaced
~ "airplane" arm base line is followed to its inter-v l,
compass rose disk and found to be approximately f ‘ _
139 degrees. Finally, while `continuing to hold
all parts against turning, the line on the “wlnd"
disk which puses through the point at 8 on the
apart to the same scale as the markings on the
section with the base line of the "ground" disk
radii. These markings may represent miles per
and the value of this point is read and found to
hour. the terminal cipher being omitted. The 10 be approximately 9 (for 90 M. P. HJ. The oper»`
markings shown run from zero to 160 M. P. H..
common for private airplanes. For faster craft
different markings or larger disks may be pro
vided. 'I‘he lines and indicia on the diil’erent
-
. ator now knows that in order to ñy due east with ' y
._ '
the given wind direction and velocity and the '
selected airspeed he must head toward 139 de-.
greesand that he will travel due east relative
disks are preferably mutually distinctive, as by 15 to the ground at about 90 M. P. H.
f , '
Where lines do not exactly correspond to a -,
The upper disk I3 is conveniently used to rep
given unit the operator must interpolate, as is
resent the direction and velocity of the wind,
usual with other computing instruments. such
hence for convenient reference it is marked
as slide rules and the like. In the above and `
"Wind" or “Wind vector" on the edge. The arm 20 other vexamples given herein the approximate
>I2 conveniently represents the direction and
instrument readings are given rather ,than math
speed of the aircraft relative to the air, hence
ematical calculations.
being made ordiüerent colors.
is markedl “Airplanef’ "Airplane heading.” “Air
speed” or "Path"
'I'he lower movable disk Il
conveniently represents the direction and speed
of the airplane relative to the ground, hence is
marked “Ground” "Ground speed," "Track" or
“Course” On the edge of disk II there are also
marked certain indicia of altitude in feet such
as “2000,” u4om'u “8000,” llßoœ’lr «10000:» etc.
30
The device can best be understood from a con
sideration of the solution of some representative
problems on the device. -
afmazn-wma-zmck relationship, Figs. 3 «ma 4
‘ Given any two of the above three factors. the -
third can be determined quickly with the device
without extraneous notations or computations.
Fig. 4 graphically illustrates the above problem> .
in «usual vector analysis form. Here OA or CB ’
represents the direction and velocity of the wind,
_or wind-travel, or wind vector; OB represents
the direction or heading and speed of the air->
plane relative to the air, or air-travel, or pro
jected air path; and OC or AB represents the
direction or _course and speed of the airplane
relative to the ground, or ground-travel, or
track.
Radius of action, Figs. 5 and 6 '
The radius of action (for a round trip along
35 the same course) is the distance or‘vjtrack along
la. given course that an airplane can- îlyì andv return
with a given supply of fuel at a given speed. The
fuel consumption at a given air speed for one
More precisely. given any four of the six ele
hour's flight being known for any given airplane,
ments of the three pairs of factors (1) heading 40 it is only necessary to determine the distance
airspeed, (2) wind direction-velocity, and (3)
out and in along a given course that the airplane
course-groundspeed. the other two can readily. - can ily in one hour. This range for -one hour is
be computed.
here referred to as the radius of action. The full `
Assume that the direction and velocity of the
radius of action, then is simply the'number of
windA are known; that the airspeed of the air 45 hours fuel supply multiplied by the radius of
craft is known; and that the desired course is
known; the problem is to determine the necessary
heading forthe aircraft and the speed it will
make along the plotted course.
To take a specific example, assume that the
wind blows from 210 degree point of the compass
at a velocity of 7o M. P. H.: that the aircraft
action for one hour. In mathematical terms,_as
given in any textbook on -aerial navigation, the
radius of action R is ground speed out multiplied
by ground speed in, divided'by ground speed lout 5
plusground in; or
V1 X V2
airspeedis80M.P.H.; andthatthecourseisto
be due east. i. e.. toward the 90 degree point. In
Assume that the airplane airspeed is 100
allcasesthewindis assumedtoblowinwardor 55 M. P. H.: that the wind is 30 M. P. H. fromdue
toward the central axis; and the directions of
east; and that the course out and in'is along the
travel along the course and heading are assumcd
30-210 degree line.
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to be outward or away from the central axis.V
First. set the "wind” disk I3 base line at E.
First, the "wind” disk I3 is turned until its
Next, set the "ground” disk li base line on 3-21.
diametrai base line is directed toward the mark 60 Next. set the "airplane" or “heading” arm i2 at
ing "21" (for 210 degrees) on the margin of the
a point above the "wind” disk lhase line where
compass rose disk Il. Second, while holding the
l0 (100 M. P. H.) intersects the wind velocity
arm I2 to keep disk I3 from turning (through
line 3 (30 M. P. HJ. which is parallel to’ the
the frictional connection between the arm and
."ground” base line and passes through 3 on the
the disk), the “ground" disk II is turned until
“wind” base line; then follow back along a par
allel "wind" disk line from the point of intersec
tion to the “ground" base line. This. is approxi
mately 8 or 80 M. P. H. ground speed along the
course or track. This may be called the "track
its diameter'is directed to the marking "E" on
the compass Arose disk. i. e., to the 90 degree point.
Third, whlleholding both disks II and I3, the
"airplane” or “heading" arm I2 is turned until
the point on its radial base line at 8 (for 80 70 in" and "ground speeed in" for reference. Next, -' »- `
M. P; H.) falls upon a line on the "groun " disk
set the “airplane” arm I2 at the point below the
Il which passes through the point 7 (for 'l0
“wind" disk base line where 10 (100 M. P. H.) in
M. P. H.) on the diameter or base line of the
„ tersects the wind velocityline 3 (30 M. P. H.) and
“wind” disk I3. Fourth, while holding all parts
follow back along a parallel line from the inter
against turning (since the problem has been 75 section to the “ground" base line. This isapß
2,438,780
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proximately 11.2,.or 112 M. P. H. ground speed
along the track. This may be called the “track
out” and "ground speed out” for reference.
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lines intersect locates one end oi' the wind vec
tor, the other end being at the center of the disks.; ‘
_ It may be necessary to mark one oi these inter
There has now been charted the Ground speed
secting 'lines on the disk or to place a straight
in, V2, 80 M. P. H.. or distance ior one hour’s
edge on the disk while moving the “airplane”,
flight against the wind, and the ground speed
arm to the second position to locate the second
in, V1. 112 M. P. H., or distance for one hour’s
intersecting line. However, with some practice
night with the wind.
one can note the crossings oi’ the losse line inode
Now, by a_ system of triangles which can readily
_by the intersecting lines and remember their
vbe set up on the device as thus held, and by 10 values until the problem has been solved.
the use of a single straight edge (which is prac
rig. s graphically illustrates this problem.> ’
tically always available in some convenient
Here 0C is the north heading: 0B is the eastv
form), the radius of action can readily be read
heading; and A is the point of intersection of the
oir. Make a base line through V1 (112 M. P. H.)
determining lines AC and AB which are drawn`
parallel to the "wind” base line and equal to V1. ~ 15 parallel to the two tracks in the manner set
This can bev done by compass oi- can be done
forth above. AO then, is the wind vector sought.
visually by ilnding the point 11.2 on the "wind"
The wind direction. of course, is known by rea
base line and following down a line parallel to 'the ' son of the direction oi dritt in the two nights.
“ground" base line -until it intersects a line
through 11.2 on the “ground" base line which is
parallel to the “wind" base line. Keeping this
point in view, either by observation or by mark
ing it with a dot. a straight edge is placed through
the dot and the point V2 (80 M. P. H.) on the
The wind velocity is approximately 55 M. P. H. '
Airspeed at altitude and sea level, Figs. 9 and 10
If the airspeed at sea level or at a given altitude
is known. it may be desirable to compute the
other for assumed standard temperature values.
"ground” base line. Where the straight edge
For this computation, some other markings on
the disks and other assigned values will be fol
lowed. The "ground" disk. as stated above has
line crosses the "wind" base line marks the limit
of the radius of action R.
'I'hisisseentobetruebyacomparisonoislml
certain altitude markings placed at given _points
lar sides of similar triangles. Referring to Fig. 6,
the triangle BOI#I is similar to BCA; hence 0B is
on its edge over the edge markings of the com
pass rose. These altitude markings are original
ly so placed as to be east of a N-S line, hence
toOBplusOCasOFistoAC. Now,since0Bis
V2, or 80 M. P. H.; and OC (or AC) is V1, or 112
M, P. H.; then 0F or R. equals V2xV1 divided by
for this computation the "ground” disk diametral
V V2-|-Y1, or 80)(112 divided by 804-112. Reading i
on the _“wind" base line. the radius of action-is
approximately 4.7 or 47 M. P. H.
base line is placed on the N-S line oi the com
pass rose in such position that the altitude mark
ings Ille to the east oi' the N-S line. 'The mark
ings and scales are so selected that the'degree
markings on the compass rose now represent alti
Determination 0f wind vectOr, Fiat'. 7 and 8
tude, N representing sea level. 1 (or 10 degrees)
An example will .be given for determining the
representing 1000 feet altitude, 2 (or 20 degrees)
wind vector by the double drift method, that is 40 representing 2000 feet altitude. and so on.
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to say, by ilying along two diii'erent headings,
To take a specific problem, assume that the
preferably at right angles to each other. The
true indicated airspeed at 8000 feet altitude
angle of _drift may be determined by a standard
under standard temperature conditions is 1-00
drift indicator. In the absence of a drift indi
ML P. H. The problem is to ilnd what the air
cator. and for simplicity, it will be assumed that 45 speed at sea level would be.
the pilot illes a ilrst heading from some monu
Having the "ground” disk base line properly
ment or landmark directly north; then illes a
oriented on the N-S line oi the compass rose
second heading directly east from the same
monument. It at any time after leaving the
as above-described, the base line of the “wind”
disk is placed on the altitude marking.- here at
monument the pilot sights back on it and meas 50 8000. This sets up a system of parallelograms.
sures the angie between the sighting and the
The “airplane" arm base line is now placed on
' heading, he has found the drift angle. Suppose
the degree marking on the compass rose which
.when he heads north he finds that the dritt angle
represents this altitude, here at 8. From the
is 20 degrees toward the east: and that when
point 10 (100 M. P. H.) on the “alrplane" arm
he heads easthe ñnds that the drift angle is 10 55 base line. a line on the “wind" disk is followed to
degrees toward the north. The alrspeed will be
its point of intersection with the N--S base line
assumed to’be 100 M. P. H. and it will also be
of the "ground" disk. This point of intersection
assumed that he flies each heading for one hour,
represents the airspeed at sea level.
though actually to determine the angle of drift
This problem is diagrammatically illustrated
he need fly only a very short time.
00 in Fig. 10. where OA represents the airspeed at
In solvingI this problem the "wind" disk is used
the given altitude and OB represents the airspeed
in a manner dinerent from that denoted by its
at sea level.
marked designation. It is used as a ground disk,
The above examples illustrate certain uses of
the “ground” disk itself retaining its usual func
the device but they are not exclusive of other
tion, and the same of the "airplane” arm.
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65 uses, many of which are known but which can
The base line oi one of the disks is turned
not be described within the limits of anl illustra
to one of the courses (that is. one of the head
tive exposition.
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ings plus or minus the angle o! drift as required)
Moreover, while one embodiment of the inven
and the base line oi the other disk is turned to
tion has been described, it is to be understood
the other course. The basic system o! paral 70 that there may be various embodiments within
lelograms has now been set up. The "alrplane”
the limits of the prior art and the scope of the
arm base line is in succession set on the head
subloined claims.
ings N and E and lines are followed back from
I claim:
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the airspeed 10 (for 100 M. P. E.) parallel to
1. A computing device comprising in combina
the two base lines. The point where these two 75 tion, a compass rose disk. and a plurality of upper