Friden_1155_Program_Abstracts_Apr74 Friden 1155 Program Abstracts Apr74
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PROGRAM ABSTRACTS
FRIDEN MODEL 1155
ADVANCED PROGRAMMABLE
CALCULATOR
SINGER
BUSINESS MACHINES
PROGRAM ABSTRACTS
FRID-EN MODEL 1155
ADVANCED PROGRAMMABLE
CALCULATOR
Publication No. 52-0002-01
April 1974
SINGER
BUSINESS MACHINES
2350 WASHINGTON AVE
SAN LEANDRO
Copyright © 1972, The Singer Company
All rights reserved throughout the world.
CALI F
94571
PRINTED IN USA,
CONTENTS
BUSINESS
Amortization of a Loan
Annual Percentage Rate
Compound Interest
Budgeting . . . . . .
Life Annuities . . . .
Automobile Dealer Calculations
Job Cost Computations
Rebar Weight Summary . . .
Automobile Financing. . . .
Several Financial Calculations
Short Term Discount Note. .
Bond Price or Yield . . . .
Bond Price with Concessions
Tax Exempt Bond - General Program
Bonds - General Program (48% Tax Rate, Par Only)
Bonds - General Program (48% Tax Rate) .
Insurance Rebate: Short Rate or Prorate)
Interest on Loan for Tax Deduction .
Installment Loan - Payment Known
I
I
I
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
BIOCHEMISTRY
Quality Control Chart.
5
CHEMISTRY
Decay Constant and Half Life
Relative Elemental Percentages
Output Concentration - Varigrad
6
6
6
ELECTRICAL ENGINEERING
Flux Density - Circular Loop
Circuit Analysis . . . . .
Fourier Transform. . . . .
Fourier Transform - Pulse .
Euler-Fourier Formulas - Periodic Functions
Euler-Fourier Formulas - f(t) = Constant.
Current - Resonant RLC Circuit
Power Supply Design . . . . . . . . . .
4/74
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7
7
7
8
8
8
Friden 1155 Calculator - Program Abstracts
iii
Contents
MECHANICAL ENGINEERING
Cam Design . . . . . . . . . . . . .
Compression Spring Design - Round Wire
Cam Design - Modified Cycloid. . . . .
Extension Spring Design - Stress Concentration
Torsion Spring Calculations
Flat Spring Calculations . . . . . . . . . . . .
9
9
9
9
9
10
STRUCTURAL ENGINEERING
Cantilever Bean - Partial Uniform Load.
Stress and Strain - Elastic Bodies
Weibull Distribution Function. . . . . .
11
11
11
SURVEYING
Traverse Closure (revised program)
Traverse Calculations. . . . . . .
Coordinates of an Observer's Position
Area by Helon' s Formula
Cut and Fill Calculations . . . . . .
Manning's Equation . . . . . . . . .
Conversion between Azimuth and Bearing
Intersection of Two Lines . . . .
Intersection of a Line and a Circle
Intersection of Two Circles
Grade Elevations . . . . . . . .
Computation of Curve Data. . . .
Long Chord Data for Traverse Closure
Coordinate Geometry for a Traverse
Area of a Traverse . . . . .
Vertical Curve Equation . . . . . . •
Deflection Angle Calculations
Traverse Closure using Interior Angles
Curve Staking Calculation . . . . . .
12
12
12
12
12
12
13
13
13
13
13
13
14
14
14
14
14
15
15
CIVIL ENGINEERING
Hardy Cross Network Analysis
16
NUMERICAL ANALYSIS
Solution to Three Linear Equations
Solution of a Quadratic Equation
Simpson's Rule of Integration. . .
Calculation of Coefficients of a Polynomial
Evaluation of a Polynomial and its Derivatives
Inversion of a 3 x 3 Matrix. . . . . . . . .
iv
Program Abstracts - Friden 1155 Calculator
17
17
17
17
17
17
4/74
Contents
Multiplication of Two 3 x 3 Matrices
Determinant of a .3 x 3 Matrix . .
+, -, Product for Vectors . . .
X,-7-' l/x for Complex Numbers
Newton-Raphson Method . . . .
3 x 3 Matrix Multiplied by a Column Vector.
Evaluate y = f(xl, x2' . . . x n). . . . . •
Root of a Non-linear Equation . . . . . .
Factorization into Primes . . . . . . . . . .
Evaluation of a Polynomial - Complex Value .
Root of a Polynomial - Real or Complex.
Division of Polynomials . . . . .
Solution of a Differential Equation
Binary - Decimal Conversions
Harmonic Analysis . . . . . .
Product of Two n x n Matrices
Solution of n Linear Equations
n x n Matrix Inverter . . . .
18
18
18
18
18
18
18
19
19
19
19
19
19
19
20
20
20
20
STATISTICS
Mean, S.D., S.E., T-Values . . . . .
Covariance, Correlation, and Regression
Fitting of a Quadratic to Data Pairs. • .
Linear Regression . . . . . . •
Fitting of y = AeBx to Data Pairs.
x 2 for a 2 x 2 Contingency Table
x 2for n x m Contingency Table
Paired -T Test . . .
Binomial Distribution . . . .
Poisson Distribution . . . .
Mean, S. D., S. E., Range for Data. •
Significance between Two Proportions
Likelihood Ratio . . . . . . . .
Combinations, Permutations. . .
Multiple Correlation Coefficients. .
Normal Distribution Ordinates . .
Least Squares Fit to y = axb . . .
One-way Analysis of Variance . . .
Anova Table - 2 x 2 Factorial Design
x 2 Distribution Ordinates . . • . . .
F Distribution Ordinates. . . . . .
Integrals for the Normal Distribution
Integral for the x 2 Distribution. . .
Reliability Testing - Test Period
Reliability Testing - Confidence Limits .
Reliability Testing - Confidence Level. .
Random Permutations of Sequenced Integer Values
Pseudo-random Number Table . . . . . . . • .
4/74
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Friden 1155 Calculator - Program Abstracts
v
Contents
24
24
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25
25
Check for Randomness of Digits in a Table . . . . .
Generation of a Set of Pseudo-random Integer Values.
Statistics of a Set of Groups . . . .
. . . .
Multiple Linear Regression . , , ,
Least Square Fit with a Polynomial.
REAL ESTATE
26
26
26
Real Estate Investment Projection Analysis
Depreciation Calculations
Mortgage Yield. . . , , , , , . . , . . ,
EDUCATION
Test Correction: Less than 40 fq!uestions .
Test Correction: 40 - 50 fq!uestions, ,
Determination of Grades . , . . , , ,
27
27
27
SUBROUTINE PROGRAMS
Pack Values . , .
Unpack Values . .
Round a Decimal Value
Vector Sorting Routines.
28
28
28
28
MrSCELLANEOUS
Navigational Course Calculation
Six Geometric Problems
Manual Mode Diagnostic . . . ,
vi
Program Abstracts- Friden 1155 Calculator
",
.
29
29
29
4/74
INTRODUCTION
INTRODUCTION TO ABSTRACTS
This publication contains abstracts of all programs prepared by Singer Business
Machines for use with the 1155 Programmable Calculator.
Programs may be ordered from the local Singer Business Mar-hines Office.
Publication numbers have been changed to reflect a new numbering system for
documents. When ordering, please specify the publication number in this
manual for the program wanted.
4/74
Friden 1155 Calculator - Program Abstracts
BUSINESS
ABSTRACTS
52-8003-001
AMORTIZATION OF A LOAN
There are several options available:
52-8003-002
(1)
Calculation of payment/period, X, necessary to amortize a loan if the
principal, P, annual interest rate, i, and number of periods, n, with m
periods per year are known.
(2)
Determination of n, the number of full payments of x dollars given P, i,
m and x. Also calculate the amount of the last payment.
(3)
For a given n 1 < n or n 5 n 1 5 n b , determine the interest payment for n 1 ,
payment on the principJl, total principal paid to date, total interest paid
to date, total amount paid to date, and the principal remaining.
ANNUAL PERCENTAGE RATE
This program uses the Muller iterative method to determine i such that
R
=P
i(1 + i)n
(1 + i)n-l
.--;'--~-
where
R = payment/period
P = principal
n = number of payments
i = interest rate/period
The process stops when the difference between two successive i values 510- 4 •
To determine the APR, it is necessary to multiply i by- the number of
periods per year.
52-8003-003
COMPOUND INTEREST
Evaluates the formula
A
= P(1 + i)n
p
where P = principal, i = annual interest rate, p = number of periods per year,
n = number of periods. For each period, the interest is printed, the total
interest to date, and the total amount to date.
4/74
Friden 1155 Calculator - Program Abstracts
1
Business
BUDGETING
52-8003-004
The distribution of payments on a principal is determined meeting specific
requirements. The year is divided into quarters. The payment during the first
month of each quarter is approximately equal to 1.25 times the latter 2 months.
Monthly totals and the grand total are printed.
LIFE ANNUITIES
52-8003-005
The program performs calculations for the values of whole life annuities and
temporary life annuities.
AUTOMOBILE DEALER CALCULATIONS
52-8003-006
Given the amount to be financed, the number of months, the number of extra
days and the add-on rate, the program calculates APR, the amount of life
insurance premium, the amount of accident and health insurance premium, the
total to be financed including insurance, the amount of the finance charge and
the monthly payment for each of five insurance options. It is easily tailored to
individual needs.
52-8003-007
JOB COST COMPUTATIONS
Consider a table consisting of fewer than 26 items, each having two associated
cost values - for example, price/item and labor (hr)/item. The user simply
keys in a quantity for each item and the machine will print total material cost
and total labor cost for that item. At the same time, it keeps running totals.
After all items have been entered, it will compute total job cost based on a
sales tax rate and an hourly labor rate.
52-8003-008
REBAR WEIGHT SUMMARY
The program accepts three input values: number of bars, size of bar, and
length per bar. Given the pound/foot for each size as a part of the program, the
machine determines total length and poundage for each size bar as well as the
grand weight total.
52-8003-009
AUTOMOBILE FINANCING
This program is set up to be tailored to the user's needs. The input includes
principal, number of months, odd days. add-on rate. There is an opportunity
to input other charges such as title or recording fee. Various rates for credit
life, AIH insurance, taxes, etc. are incorporated into the program by the user.
Included in the output are the total note value, the amount financed, the finance
charge, insurance charges, total other charges, monthly payment, and APR.
2
Program Abstracts - Friden 1155 Calculator
4/74
Business
52-8003-010
SEVERAL FINANCIAL CALCULATIONS
Amortization Schedule
Discounting a Note
Status of a Loan
Number of Payments to Pay Off a Loan
52-8003-011
SHORT TERM DISCOUNT NOTE
Given the face value, maturity and transaction dates, and one of the three values
discount rate, effective yield, or price, the program will determine the other
two values.
52-8003-012
BOND PRICE OR YIELD
Given the date of maturity, settlement date, bond rate, and gross yield, the program will calculate dollar price. If the former three values and dollar price are
known, it will determine the gross yield.
52-8003-013
BOND PRICE WITH CONCESSIONS
This program determines the bond price when given either the expected yield or
the straight price.
52-8003-014
TAX EXEMPT BOND - GENERAL PROGRAM
This program will determine the following.
1.
2.
3.
4.
5.
6.
7.
8.
52-8003-015
Dollar price required for a specified gross or true yield
Gross yield for a specified dollar price or true yield
True yield (after capital gains tax. if any) for a specified dollar price or
gross yield
Any of the above for a call date (with possibly a different redemption value)
Any of the above for a different tax rate
The dollar price and actual price after concessions
The accrued interest for the present coupon period
The total price
BONDS - GENERAL PROGRAM (48 C{ Tax Rate, Par Only)
The program determines 1 through 4 and 6 through 8 as for Business Program
014 above. It assumes a 489c; tax rate and that all bonds are redeemable at par
even on call dates.
52-8003-016
BONDS - GENERAL PROGRAM (48% Tax Rate)
This program is the same as Business Program 015 except that bonds redeemable
at premium are allowed.
4/74
Friden 1155 Calculator - Program Abstracts
3
Business
52-8003 -017
INSURANCE REBATE: SHORT RATE OR PRORATE
This program will determine the rebate factor commonly found on an insurance
rebate 'wheel'. This may be either the short rate factor or· the prorate factor.
It then multiplies this factor by the annual premium to determine the actual
amount of the rebate.
52-8003-018
INTEREST ON LOAN FOR TAX DEDUCTION
This program will compute the amount of interest paid on a loan during one tax
year. If the loan was not prepaid during the year, the finance charge is prorated
by month. If it was prepaid, the amount of tax-deductrule interest is the finance
charge minus the rebate on the finance charge minus the interest paid in previous
years.
52-8003-019
INSTALLMENT LOAN - PAYMENT KNOWN
Given a principal balance, add-on rate, payment per period, number of periods
per year (52, 26, 24, 12), and an insurance\Qption, the program will determine
term, amount financed, finance charges, last payment, APR.
4
Program Abstracts - Friden 1155 Caclulator
4/74
BIOCHEMISTRY
ABSTRACTS
52-8004-001
QUALITY CONTROL CHART
This program prepares a quality control chart for a given set of data for a
particular parameter (preferably greater than 30 observations). It determines
the number of observations (N), the mean (x), standard deviation (S. D.),
x ± 2 S. D., and the coefficient of variation (v). It includes an error routine for
incorrectly entered data.
4/74
Friden 1155 Calculator - Program Abstracts
5
CHEMISTRY
ABSTRACTS
52-8005-001
DECAY CONSTANT AND HALF LIFE
This program calculates the decay constant and half-life given a number of
activity readings at various times. There is an option available to calculate
1:: ( for ta';; t "tb where M, is initial mass and Mt ~ mass at time
t. There
is an error routine for incorrectly entered data.
52-8005-002
RELATIVE ELEMENTAL PERCENTAGES
The program determines the % of an element in a particular compound. The
atomic weights of twelve common el~ments are already incorporated into the
program (the user may elect to add others). An element number and the
number of atoms of that particular element present are entered for each element.
An error routine is available for incorrectly entered data.
52-8005-003
OUTPUT CONCENTRATION - VARIGRAb
This program calculates the output concentration of a variable gradient device
consisting of a number of identical chambers (not more than 12) connected in
series in hydrostatic equilibrium.
6
Program Abstracts - Friden 1155 Calculator
4/74
ELECTRICAL ENGINEERING
ABSTRACTS
52-800S-00l
FLUX DENSITY - CmCULAR LOOP
The program calculates the flux denSity along the axis of a circular loop.
52-8009-002
cmCUIT ANALYSIS
Given a circuit containing two nodes and five branches, the program determines
the voltages at the two nodes. The user inputs a topology matrix which
describes the circuit; resistances, and voltages.
52-8009-003
!
FOURIER TRANSFORM
The program evaluates:
g( w) =
f
00
F(t) cos w t dt - j
-00
f
00
F(t) sin w t dt = Af - j
Bf
-00
for frequency, f ~ 0 (w = 23t'f) in increments of M (f may increment
arithmetically, geometrically or logarithmically).
52-8009-004
FOURIER TRANSFORM - PULSE
This program performs the same function as 003 except that it is especially
written for a pulse and is faster in execution.
52-8009-005
EULER-FOURIER FORMULAS - PERIODIC FUNCTIONS
The program determines an (n=O, 1, 2 ... ),
btl (n=l, 2, ... ) such that (t=time)
00
f(t) = a20 + n~l (an cos 2 3t' nt + b n sin 2 3t' nt)
where
.5
an = 21 f(t) cos 23t'nt dt (n
=
0,1,2 ... )
-.5
bn
=2
f
.5
f(t) sin 23t' nt dt (n = 1, 2, 3 ... )
-.5
4/74
Friden 1155 Calculator -Program Abstracts
7
Electrical Engineering
then
c n (amplitude) = ~ a n2 + b n2
'l'n (phase)
= tan -1
(:~)
itt) is defined by the user and each of the integrals may be a sum of integrals
of functions defined on sub-intervals.
52-8009-006
EULER-FOURIER FORMULAS - f(t)
=
CONSTANT
This program performs the same function as 005 except that f(t)
value for an interval of t and thus the execution time is faster.
52-8009-007
=
a constant
CURRENT - RESONANT RLC CIRCUIT
Given voltage (V). resistance (R), inductance (L), capacitance (C), the program
calculates i (current) for time t between a and b in increments of t:, t.
2Ve -Rt/(2L)
i
52-8009-008
~4L/C - R2
~
+ Ri + ~
Ji dt
when
L
and
i = 0, L.di/dt =V
at
= 0
t =0
POWER SUPPLY DESIGN
This program is an aid to the designing of power supplies - series or shunt.
The user supplies the voltage and current values. The suggested values for
capacitor, resistor, and transformer ac may be accepted or replaced. The
machine prints out the appropriate values for low, nominal, and high for
either series or shunt or both if so desired.
8
Program Abstracts - Friden 1155 Calculator
4/74
MECHANICAL ENGINEERING
ABSTRACTS
52-8012-001
CAM DESIGN
This program determines the displacement, velocity. and acceleration for the
following types of curves for cams with (1) a radial translating roller follower,
or (2) an offset translating roller follower:
a. parabolic
b. harmonic
c. cycloidal
52-8012-002
COMPRESSION SPRING DESIGN - ROUND WIRE
Find various spring parameters given the values of other parameters.
8PD
S
= -;or
H
52-8012-003
Gd 4
P
; F =
8D31\l
(N+1)d + 2(D-d)
CAM DESIGN - MODIFIED CYCLOID
The program determines the velocity and acceleration of various points
(values of 8).
52-8012-004
EXTENSION SPRING DESIGN - STRESS CONCENTRATION
Find anyone of the parameters given the values of the others.
32PR
SB= --;d3
ST=
52-8012-005
16PR
rod 3
• !.1
r3
•
(~)
4c - 4
c
=
TORSION SPRING CALCULATIONS
Given all but one of the parameter values, find the remaining one:
S
4/74
=
32PR
--;(iT
M
=
Ed 4T
10.8 DN
Friden 1155 Calculator - Program Abstracts
9
Mechanical Engineering
52-8012-006
FLAT SPRING CALCULATIONS
Given all but one of the parameter values, find the remaining one for either
(1) a cantilever type (rectangular section). or (2) an elliptical type (rectangular
section).
(1)
s =
10
6PL
bh 2
Program Abstracts - Friden 1155 Calculator
(2)
S
3 PL
2" bh 2
4/74
STRUCTURAL ENGINEERING
ABSTRACTS
52-8008-001
CANTILEVER BEAM - PARTIAL UNIFORM LOAD
Given the following parameters: the modulus of elasticity of the material (E);
the moment of inertia (I); the load (W); and L, a, b (refer to diagram), the
program calculates VAB (shear A to B), MAB (bending moment A to B), YAB
(deflection A to B), V BC ' MBC ' Y BC ' VCD' MCD ' YCD ' Mmax ' Ymax '
e (end slope) for any x value. It contains an error routine for incorrectly
entered data.
Y
b
----I~
a
O~--~========~--~~D~X
~------L -------I~
A
52-8008-002
STRESS AND STRAIN - ELASTIC BODIES
Given Rl and R 1 ' (max and min radii of curvature for body 1; R2 and R 2' for
body 2; modulus of elasticity for each body; Poisson's ratio for each body;
total pressure; and the angle between the planes containing 1/R 1 and 1/R 2 , the
program calculates the maximum unit compressive stress, the major and
minor semi-axes of elliptical contact area and the combined deformation of
both bodies at each contact along the axis of load.
52-8008-003
WEIBULL DISTRIBUTION FUNCTION
This program may be used for anal~'sis of failure data. It performs a
regression analysis on the number pairs (x, F(x», where x is the time to
failure and F(x) == median rank c:: i - .3 [i == the failure order number
n +.4
(1, 2, 3, - - -); n= size of the samples].
4/74
Friden 1155 Calculator - Program Abstracts
11
SURVEYING
52-8007 -001
(revised)
TRAVERSE CLOSURE
This is a S€t of 17 programs designed to solve the general problem of determining the successive coordinates of the points as well as the amount of error of
closure, and then of balancing the traverse using compass, transit, or Crandalls
Rule if the error is too large. The data may be in the form of bearings, azimuths, or field deflection angles along with a distance. The traverse may be
either 'closed' or 'open' and may contain curved legs. Up to 39 (if all straight)
legs may be accepted as input. The area will be printed in square feet and
acres. Surveying programs 013, 014, and 015 are designed to be used in conjunction with this program to perform various coordinate geometry functions.
52-8007-002
TRAVERSE CALCULATIONS
Given the coordinates of two successive points of a traverse, the program
determines the bearing, the changes in latitude and departure and the distance
between them.
52-8007-003
COORDINATES OF AN OBSERVER'S POSITION
Finds the coordinates of an observer's position by measuring two angles and
the coordinates of three points.
52-8007-004
AREA BY HELON'S FORMULA
Find the area of a triangle given the lengths of its three sides, using the
formula:
S=
52-8007-005
YI (l-a)(l-b)(l-c)
CUT AND FILL CALCULATIONS
This program will calculate cross-sectional areas, volume of earth between two
cross-sectional areas separated by a length L, I volume, and I L. The
input is series of number pairs describing the contour.
52-8007-004
MANNING'S EQUATION
This program calculates Q; volume of water flow not under pressure, where
12
Program Abstracts - Friden 1155 Calculator
4/74
Surveying
Q:;:::1.49 A'R2/3'Sl/2
n
A:;::: end area
R :;: : hydraulic radius
n :;: : roughness factor
S :;::: drop per foot.
52-8007-007
CONVERSION BETWEEN AZIMUTH AND BEAmNG
This program will convert the azimuth of a line, measured from the north meridian in a clockwise direction, to a bearing and vice versa.
52-8007-008
INTERSECTION OF TWO LINES
This program will determine the coordinates (N. , E.) of the point of intersection
of two lines, each defined by a point and a bearing or azimuth.
52-8007-009
INTERSECTION OF A LINE AND A CIRCLE
Given a line described by a point (N., E.) and a bearing or azimuth and a circle
defined by the coordinates of its center and a radius, the program will calculate
the coordinates of the point(s) of intersection.
52-8007-010
INTERSECTION OF TWO CIRCLES
Given two circles described by the coordinates of their centers and the lengths
of their respective radii, the program will determine the points of intersection.
52-8007-011
GRADE ELEVATIONS .
Given a starting stake number and elevation, the program will determine the
grade % change and the elevations at all 50-foot stakes in between.
52-8007-012
COMPUTATION OF CURVE DATA
Consider the following diagram:
Given a value for A or R and one of the other five values, the program will
determine the four remaining values as well as the area of the segment.
4/74
Friden 1155 Calculator - Program Abstracts
13
Surveying
52-8007-013
LONG CHORD DATA FOR TRAVERSE CLOSURE
This program can be used to prepare for option (-1) of Surveying Program 001;
i. e., it finds the bearing and length of the long chord of an arc. The following
values must he known: the radius of the arc, either the delta angle or length of
the arc, either a tangent to one of the ends of the arc or the tangent to an arc
that eventually connects tangentially to the arc.
52-8007-014
COORDINATE GEOMETRY FOR A TRAVERSE
Using the information stored by one of the Surveying Program 001 programs, the
following coordinate geometry functions may be performed.
1. Find the bearing and distance between any two points.
2. Given a point and a bearing of a straight line from that point determine either
a. the point of intersection of that line with a straight line or with a circular
arc defined by two other points, or
b. the coordinates of a point at a gi ven distance along that straight line.
3. Determine the intersection of two lines each defined by two point numbers.
4. Add a point to the set of points already defined.
5. Calculate the area of a portion or all of the traverse, accumulating areas if
so desired.
52-8007 -015
AREA OF A TRAVERSE
This program may be used in conjunction with Surveying Program 001 or independently. The user may find the complete area of a traverse defined in the
aforementioned program where the data represents the balanced or unbalanced
state, or he may key in the coordinates himself. The area of portions of the
traverse may be determined by referencing individual point numbers or a number of consecutive points. A routine for finding the area of a segment of a
circle is included.
E~UATION
52-8007-016
VERTICAL CURVE
52-8007-017
Given two grades, the length of the curve, and the station and elevation of the
point of intersection of the grades, the program will determine the station and
elevation of the high point and the elevations at desired station increments along
the curve.
DEFLECTION ANGLE CALCULATIONS
Given the radius, beginning and ending stations, and station increment, the program will determine deflection angles as well as the chord lengths for the successi ve stations beginning with the first even station after the initial one.
14
Program Abstracts - Friden 1155 Calculator
4/74
Surveying
52-8007-018
TRAVERSE CLOSURE USING INTERIOR ANGLES
Given the interior angle measurements for a traverse, the program finds the
sum, compares it against the theoretical sum, distributes the error, and determines azimuths and bearing given the first known azimuth or bearing.
52-8007-019
CURVE STAKING CALCULATION
This program determines the total deflection angle from initial stake point and
the chordal distance between successive stakes when the radius of the staked
curve, the radius of the stationing curve, and the station numbers are given.
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Friden 1155 Calculator - Program Abstracts
15
CIVIL ENGINEERING
52-S013-001
HARDY CROSS NETWORK ANALYSIS
This program performs a standard hydraulic network analysis using the Hardy
Cross method. The total number of loops and pipes handled by the machine can
be calculated from the following formula.
n
[2 . (total no. of pipes in a system of n loops) + 1/4
.I (Pi
+ 2)] m.
A
52-8002-027
RANDOM PERMUTATIONS OF SEQUENCED INTEGER VALUES
Given two integers a and b, the program finds a pseudo-random permutation of
all the integers between a and b, inclusive.
52-8002-028
PSEUDO-RANDOM NUMBER TABLE
.
This program generates a table of ten-digit integral numbers, printing them in
groups of ten. A different starting value produces a different table.
52-8002-029
CHECK FOR RANDOMNESS OF DIGITS IN A TABLE
This program provides a frequency distribution of the occurrence of the digits
0, 1, 2, . . . , 9 in the table generated by Statistics Program 028.
52-8002-030
GENERATION OF A SET OF PSEUDO-RANDOM INTEGER VALUES
This program will generate n pseudo-random integer values between two
52-8002-031
li~its.
STATISTICS OF A SET OF GROUPS
This program will determine the mean and standard deviation for n values in a
group. It will them compute the overall mean and SD for a set of up to five
groups. Each time that a new groups is added, the lowest numbered group will
be dropped from the statistics for the next set of groups.
24v
Program Abstracts - Friden 1155 Calculator
4/74
Statistics
52-8002-032
MULTIPLE LINEAR REGRESSION
This program will determine the values for Bl, B2, B3, and A such that
1 = Blxl + B2x2 + B3x3 + A will be the best fit for n data points (xt>x2,x3'y).
It
will also determine the standard error of the estimate. If the data points consist of (xl' x2' y), then the regression equation will be ~ = Blxl + B2x2 + A. The
program will save up to 18 data points for three independent variables or 24 data
points for two independent variables. Any points above these limits will be used
in the calculation of the regression coefficients but then are destroyed. After the
regression coefficients have been determined, the user may elect to have the
machine automatically print Xl' x2' x3' y, 9, (y - y) for each data point stored.
Then additional data points may be entered to be included in the standard error.
52-8002-033
(Not written)
52-8002-034
LEAST SQUARE FIT WITH A POLYNOMIAL
This program will fit a polynomial to data pairs (x, y): that is, determine
A
AO' AI, . . . ,An such that y = An
y = Anx n + An_Ix n-l + . . . +Alxl + AO
is a least squares fit. The value of n may be between 2 and 11, inclusive. The
number of data pOints stored depends upon the order of the polynomial to be
fitted. The standard error of the estimate is determined.
A
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Friden 1155 Calculator - Program Abstracts
25
REAL ESTATE
52-8014-001
REAL ESTATE INVESTMENT PROJECTION ANALYSIS
This program accepts such input values as purchase price, down payment, conditions of up to ten mortgages, itemized income, itemized expenses, tax bracket,
vacancy factor, depreciation method and percent, and will print for whatever
number of years selected the following information among others.
1. Net operating income
2. Equity and interest on all loans as well as total
3. Net spendable before taxes
4. Net income after interest
5. Depreciation
6. Taxable net income and taxes
7. Net spendable after taxes
8. Capitalization rate
9. Return on equity
Grand totals and averages per year are printed at the end.
52-8014-002
DEPRECIATION CALCULATIONS
This program calculates depreciation by any of three methods:
Straight line
Declining balance
Sum of integers
52-8014-003
MORTGAGE YIELD
Given the value of the note, the interest rate, the time due (years), monthly
payment, and the. yield or discount rate, the machine will determine either of
the latter two rates not given. If the time = 0, the machine will use that time
that will completely amortize the loan.
26
Program Abstracts - Friden 1155 Calculator
4/74
EDUCATION
ABSTRACTS
52-8010-001
TEST CORRECTION: LESS THAN 40 QUESTIONS
Given a test of less than 40 multiple choice questions each having 9 or less
choices (numbered 1-9), the program screens student responses for wrong
answers, assigns a score, determines the group mean, the number of students,
the standard deviation and a frequency distribution for all questions of the
number of incorrect answers per question. There is an error routine for
incorrectly entered data.
52-8010-002
TEST CORRECTION: 40 - 50 QUESTIONS
Performs the same functions as 001 but the corrections are made on 13
questions at a time rather than the entire test. There is an error routine for
incorrectly entered data.
52-8010-003
DETERMINATION OF GRADES
This program will average the test scores for a student [eliminating the x
lowest scores (x<7)]. It will find his standard deviation: also, the over-all
class average and standard deviation. Error routines are included.
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Friden 1155 Calculator -' Program Abstracts
27
SUBROUTINE PROGRAMS
ABSTRACTS
52-8006-001
PACK VALUES
This subroutine accepts values through the keyboard and packs them beginning
with Register 01. The number of values packed per register depends upon the
number of significant digits per value (x) and = 12/(x + 1). Each value has a
sign digit = 1 for negative or = 0 for positive. The subroutine uses Register 00,
16-19. It is usually used with subroutine 002.
52-8006-002
UNPACK VALUES
Given up to 15 packed registers (Register 01-15), containing from 1-6 values
(depending upon the number of significant digits) the subroutine will return a
particular value from the register to which Register 00 is pointing. It is
usually used in conjunction with subroutine 001.
52-8006-003
ROUND A DECIMAL VALUE
This is a small routine to round a decimal value to x decimal places.
52-8006-004
VECTOR SORTING ROUTINES
It arranges a vector of up to 18 elements in ascending or descending order,
storing the results in Register 01-N.
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Program Abstracts - Friden 1155 Calculator
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MISCELLANEOUS
ABSTRACTS
52-8011-001
NAVIGA TIONAL COURSE CALCULATION
The program calculates a navigational course consisting of one or more
adjoining legs. Output variables include: compass heading; ground speed;
distance of the leg; cumulative distance; flying time; cumulative flying time;
fuel consumption; cumulative fuel consumption, given input variables: initial
latitude and longitude; destination latitude and longitude; magnetic variation;
wind direction and speed; air speed; fuel consumption rate.
52-8011-002
SIX GEOMETRIC PROBLEMS
(a) Given distance d and 6.. 9 from a known point K(x, y) find the coordinates
of the unknown point U.
(b) Points on a line from Po to P n in increments of D. x.
(c) Points on a Circle, given a starting angle, stopping
4 and
D.
4
(d) Point of intersection of 2 lines.
(e) An angle in degrees, minutes and seconds converted to decimal degrees.
(f) Distance between 2 points and the -4 made by a line connecting them and
the x axis.
52-8011-003
MANUAL MODE DIAGNOSTIC
This procedure is designed to test the operability of the machine. It should be
used in conjunction with 001 to make sure that the machine is functioning in the
manner it should be.
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Friden 1155 Calculator - Program Abstracts
29
SINGER
BUSINESS MACHINES
Publication No. 52-0002-01
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