Transcript Using the hp33s

Using the HP35s
For Land Surveying
Computations
by Jon B. Purnell, PLS
©2010 Alidade Consulting
Synopsis
• Strategies
• Capabilities and
Limitations
• Operating Essentials
• Statistics Functions
• Traverse and Inverse
• Memory and Variables
• Equation Solver
Capabilities
and Limitations
• User programmable
– 30K of memory for
programs, variables and
user equations
• 800+ storage registers
– For variables/data
• Integrated equation
Solver utility
• RPN or Algebraic entry
modes
Capabilities
and Limitations
• 3rd Party surveying
applications are
available
– http://www.softwareby
dzign.com/
• Legal for LSIT exam
– http://www.ncees.org/
exams/calculators/
Capabilities
and Limitations
• No Polar-Rectangular
conversion functions
• HMS conversion
functions cannot be
used with Complex
Math “conversion”
functions
Capabilities
and Limitations
• Only 27 storage
registers are directly
accessible to the User
• A handful of Stats
registers are reserved
• Remainder are easily
accessible only to
running programs
0.00000000
0.00000000
The Keyboard
Press
[GOLD] + [key]
to access Gold
functions
Press [key] alone to
access“unshifted”
functions
Press
[BLUE] + [key]
to access Blue
functions
Press key when
prompted for “Alpha”
input
Press to power [ON] or to clear an entry
Press [GOLD] [ON] to turn unit OFF
0.00000000
0.00000000
The Keyboard
Press to select operating modes: DEGrees,
RADians, GRaDs, or ALGebraic and Reverse
Polish Notation
Press [GOLD] + key to select DISPLAY
formats: FIXed, ENGineering notation,
SCIentific notation, or ALL (automatic
formatting)
Cursor pad—click up, down, left or right to
choose menu options, or scroll amongst
options
10.00000000
FIX 2SCI
0.0000
3FIX
0.00000000
E N4 G 4 A L L
0.0000
Setting and Changing
Display Formats
Press [GOLD] + [<] key to open DISPLAY
menu
Options appear on menu. Underlined option
= current selection
Use Cursor Pad to select display mode, or
press [1] for FIXed, [2] for SCIentific, [3]
for ENGineering, or [4] for ALL
EXAMPLE: to set display to show 4 FIXed
decimal places:
1. Press [GOLD] +[DISPLAY], then [1],
then [4]
0.0000
10.0000
D E G 2 RAD 3 GRD
0.0000
40.0000
ALG
5 RPN
Setting and Changing
Angular Mode Format
Press to open MODES menu
Options appear on menu. Underlined option
= current selection
Use Cursor Pad to select mode, or press [1]
for DEGrees, [2] for RADians, [3] for
GRaDS, or choose [4] or [5] to select
between ALGebraic and Reverse Polish
Notation modes
EXAMPLE: to set unit to work in DEGrees:
1. Press [MODES], then [1]
Mode icons:
ALGebraic, RPN and EQuatioN entry modes,
GRADs and RADians angular modes
Program “Flag”
indicators
Icons: [Gold]
and [Blue]
keys
System Busy
“Alpha” keys
active
The Display
Programming
mode active
ERROR!
Current numeric system: HEXidecimal,
OCTal or BINary. Blank = Decimal
Two lines of data
HYPerbolic mode is active
Low
battery
Scrolling mode
is active
RPN: Reverse Polish Notation =
Math without Parentheses
• Evaluate 20 / 2+3
• RPN:
– 20 [ENTER] 2 [ENTER] 3 [+] [/]
(Result is 4)
• Algebraic:
– 20 [/] [(] [2] [+] [3] [)] [=]
(Result is 4)
Order of operations and your
calculator
=13
20  (2  3)
=4
=4
20  2  3
20
23
20
( 2  3)
Not all of these expressions yield
the same answer!
Be careful how you write and enter
the expression!
20
3
2
=4
=13
“ALG” should appear
here
Algebraic Mode
• Set up your calculator to operate in
the ALG (Algebraic) mode
1. Press the [MODE] key
2. Press [4]
20  2 + 3
13.0000
Back
to our problem…
• Evaluate the expression
20 / 2+3
1. Key in “20”
2. Press the [division]
key
3. Key in “2” and press
the [addition]
4. Key in “3” and press
[ENTER]
Did the calculator
evaluate the
expression using
the rules of the
order of
operations?
20  ((22) +3)
+3)
Let’s try it again…
4.0000
• Evaluate the expression
20 / (2+3)
1. Key in “20”
2. Press the [division]
key
3. Press the [( )]key
4. Key in “2+3”
5. Press press [ENTER]
Did the calculator
evaluate the
expression using
the rules of the
order of
operations?
Are the results the
same as before?
What’s different?
8 keystrokes!
“RPN” should appear
here
RPN: Math without
parentheses
• Set up your calculator to operate in
the RPN (Reverse Polish Notation)
mode
1. Press [MODE]
2. Press [5]
Using RPN
0.0000
20.0000
2.0000
20
4.0000
52.0000
20.0000
3
• Evaluate the expression
20 / (2+3) using RPN
1. Key in “20”
2. Press the [ENTER]
key
3. Key in “2” and press
[ENTER]
Did the calculator
evaluate the
expression using
the rules of the
order of
operations?
4. Key in “3” and press
the [addition] key
5. Press the [division]
key
8 keystrokes!
The Stack
0.0000
0.0000
0.0000
0.0000
T register
Z register
Y register
X register
• Four “registers” (X,Y,Z
and T) for temporary
storage of values and
intermediate results
• X and Y registers
visible on the display
• Z and T registers, not
visible
• Operations performed
on values in X and Y
registers
20 / (3+2) on the Stack
0.0000
20.0000
0.0000
3.0000
20.0000
0.0000
0.0000
20
20.0000
23.0000
5.0000
4.0000
T register
Z register
Y register
X register
• Key in “20”
• Press [ENTER]
• Key in “3”, Press
[ENTER]
• Key in “2”
• Press [+]
• Press []
Stack Functions
“Roll Down” (values in stack drop down 1
register, value in X register goes to top
(T register)
“X-Y Exchange” (values in X and Y registers
trade places)
“Last X” (recalls last value stored in X register)
Press [BLUE] [ENTER] to execute
Some Functions that
Operate on Values
in the X Register
• Key in a number, execute
the function
“1 over X” [1/X]
“Square root of X” [√X]
“X Squared” [X2]
“Trig Functions” [SIN]
[COS] [TAN]
[ASIN] [ACOS]
[ATAN]
Unit Conversions
• The HP35s ships with several built in
unit conversions
– Sexagesimal Units (Decimal Degrees and
Degrees Minutes and Seconds)
– Centigrade and Farenheit
– Inches and Centimeters
– Miles and Kilometers (US or
International definition?)
Sexagesimal Units
• When finding the Sine, Cosine or
Tangent of an angle, you must:
– Enter the value in degrees, minutes and
seconds…
– …then, convert the value to decimal
degrees…
– …then get the Sine, Cosine or Tangent
0.0000
20.0910
20.1528
0.9388
Finding a Sine,
Cosine or Tangent
Find the Cosine of 20º09’10”
Key in the value in D.MS format: 20.0910
Convert the D.MS value to Decimal
degrees: Press the [GOLD] key, then
press [HMS] (think from HMS to
Decimal)
Result is 20.1528°
Press [COS]
Result is 0.9388
(rounded!)
Sexagesimal Math
• When adding, subtracting, multiplying
or dividing, (etc.) an angle, you must:
– Enter the values in degrees, minutes and
seconds…
– …then, convert the values to decimal
degrees…
– …then perform the operation
– …then convert the result to D.MS
format
5.2515
5.2514
0.0000
5.2514
2.5
1.2500
6.5643
6.3351
Problem: Find the angle from a PC to a
POC at
525.14 feet from the
PC
Sexagesimal
Math
(degree of curvature = 2°30’)
Example
1
Solution: Angle = 5.2514 x (2°30’) /2
Key in the value “5.2514”, press [ENTER]
Key in the value “2.30”, press the [GOLD]
key, then press [HMS]
Key in the value 2, press the [] key
Press the [x] key. Result is 6.5643°
Convert result to D.MS format:
Press [BLUE] key, then press [HMS]
Result is 6.3351
which is 6°33’51”
0.0000
0.0000
Sexagesimal Math
Example 2
Problem: Find the Weighted Mean
Azimuth of Line 1 and Line 2
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
Solution =
Weighted _ Azim uth
 Azm1 Dist1   Azm2  Dist 2
Dist1  Dist 2
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
97.0892
0.0000
63776.9027
92.9347
63,776.9027
97.0521
97.0892
656.89
63776.9027
92.9347
2607.0000
242280.8208
306,057.7235
Sexagesimal Math
Solution =
Example

 

Weighted _ Azim uth
Azm1  Dist1  Azm2  Dist 2
Dist1  Dist 2
Key in the value “97.0521”, press the [GOLD]
key, then press [HMS], then press [ENTER]
Key in the value “656.89”…then press the [x] key
Key in the value “92.5605”, press the [GOLD]
key, then press [HMS], then press [ENTER]
Key in the value “2607.00”…then press the [x] key
….next, press the [+] key
The result, 306,057.7235 is the numerator in the
equation….
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
656.8900
306,057.7235
0.0000
656.8900
2607.00
3263.8900
93.7708
93.4615
Sexagesimal Math
Solution =
Example

 

Weighted _ Azim uth
Azm1  Dist1  Azm2  Dist 2
Dist1  Dist 2
Next, key in the value “656.89”,and press [ENTER]
Key in the value “2607.00”…then press the [+]
key…the result, 3263.8900 is the denominator
in the equation….
Press the [] key…the result 93.7708° is the
weighted mean azimuth of the line in Decimal
Degrees
Convert result to D.MS format:
Press [BLUE] key, then press [HMS]
The result is 93°46’15”
Statistics functions
•
•
•
•
•
Entering observations
Getting n
Getting the mean of the set
Standard deviation of a population
Standard deviation of a sample
Statistics Functions
Function Description
Keystrokes
S
Enter observations into stats registers
[
S-
Delete observations from stats registers
[GOLD] [ S-]
Clear stats registers
[BLUE] [CLEAR] [4]
View SUMMATIONS Menu
[BLUE] [SUMS]
n
Number of observations in data set
Access via SUMS menu
Sx
Sum of x values
Access via SUMS menu
Sy
Sum of y values
Access via SUMS menu
Sx2
Sum of squared x values
Access via SUMS menu
Sy2
Sum of squared y values
Access via SUMS menu
SCLEAR
SUMS
S]
Summary Statistics Functions
Function Description
Keystrokes
View MEANS Menu
[GOLD] [ x, y ]
x
y
Mean of x values
Access via MEANS menu
Mean of y values
Access via MEANS menu
xw
Weighted mean of x values
Access via MEANS menu
View Standard Deviation Menu
[BLUE] [S,s]
Sx
Sample Standard Deviation of x values
Access via SD menu
Sy
Sample Standard Deviation of y values
Access via SD menu
sx
Population Standard Deviation of x values
Access via SD menu
sy
Population Standard Deviation of y values
Access via SD menu
xy
S,s
Problem: Find the Weighted Mean
Azimuth of Line 1 and Line 2
Statistics Example 1
10.0000
656.8900
x2607.0000
X y x2WVARS
30.0000
656.8900
97.0892
1.0000
2607.0000
92.9347
2.0000
93.7708
93.4615
ALL 4 S
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
Clear STATS Registers, press: [BLUE] [CLEAR] [4]
Key in “656.89”, press [ENTER]
Key in “97.0521”, press [GOLD] [HMS]
Press [ S]
Key in “2607.00”, press [ENTER]
Key in “92.5605”, press [GOLD][HMS]
Press [ S]
Press [GOLD] [+], and select 3rd option…result is
weighted mean azimuth in Decimal Degrees
Press [ENTER], then [BLUE] [HMS]…result is
weighted mean azimuth in Deg.MinSec format
Problem: Find the 95% Standard Deviation
of the following set of 20
observations:
Statistics Example 2
Sx Sy sx sy
0.0000
1.9541
0.0000
20.0000
1.9541
1.96
3.8300
No.
1
2
3
4
5
Value
50
51
52
50
59
No.
6
7
8
9
10
Value
52
52
53
52
52
No.
11
12
13
14
15
Value
51
52
52
55
52
No.
16
17
18
19
20
Value
53
52
51
52
54
Clear STATS Registers, press: [BLUE] [CLEAR] [4]
Key in each value from the table, press
[ S] after each entry
Press [BLUE ], [S,s] to view Sample
Standard Deviation (or Sx) at the
1 Sigma level
Press [ENTER] to copy the result to
the X register.
Key in “1.96” and press [multiply].
Result is Standard Deviation of set
at 95% confidence level
Vectors and vector addition
(Traverse and Inverse)
• You can do these COGO computations
with your hp35s (with the Equation
Solver-no programming required)
– Compute latitudes and departures, given
the azimuth and length of a line
– Compute azimuth and distance, given the
coordinates of the end points of a line
– Carry coordinates (traverse)
Using Equations
for Problem Solving
• Equations are sets of instructions
that the HP35 can use to perform
computations
• Equations can use values stored in
variables A though Z for their
computations, or they can prompt you
to supply values for the variables
Using Equations
for Problem Solving
• Equations can be used to solve
repetitive problems
• Equations can be used to solve for any
unknown in the equation
• Equations can be stored for future
use, or input on-the fly
• Not all functions are available, see pg.
6-16 of the Users Guide
Using Equations
for Problem Solving
• Northing = Northing+(Dist x cos(Azm))
–
–
–
–
Variable assignments:
N = Northing
D = Distance
G = Azimuth
• N = N + (D x cos (HMS(G)))
Using Equations
for Problem Solving
• Easting = Easting+(Dist x sin(Azm))
–
–
–
–
Variable assignments:
E = Easting
D = Distance
G = Azimuth
• E = E + (D x sin (HMS(G)))
Store an equation for computing
Northings
N = N +(D x cos (HMS(G)))
1. Press [EQN]
2. Press [RCL] then [N]
3. Press [GOLD] then [=]
4. Press [RCL] [N] then [+]
5. Press [( )] then [RCL][D]
6. Press [Multiply]
7. Press [COS]
8. Press [GOLD] then [HMS] then [G]
0.0000
EQN
LIST
EQN
LISTTOP
TOP
N=N+(DxCOS(HMS(G)))
0.0000
N=
N=N+(D)
N=N+(D
x COS(
N=N+
x)
EQN LIST
TOP ))
0.0000
EQN
N=
D?
G?
N? LIST TOP
N=N+(DxCOS(HMS(G))
0.0000
1083.8432
85.31
10.3824
1000.00
Use Stored Equation for finding
Northing of a new point
Northing 1 = 1000.0000
Distance 1-2 = 85.31 feet
Azimuth 1-2 = 10°38’24”
Using a
Stored Equation
Press [EQN]
Scroll up or down if necessary to select
desired equation, and press [ENTER]
At the prompt “N?” key in the starting
Northing, or 1000.0000, and press [R/S]
At the prompt, “D?” key in Distance from point1
to point2, or 85.31 and press [R/S]
At the prompt, “G” ken in the Azimuth from
point1 to point2 in D.MS format or 10.3824
and press [R/S]
New Northing, N is displayed
Selected Equation Mode Operations
Function
Description
Keystrokes
EQN
Enter and leave Equation mode
[EQN]
ENTER
Evaluates displayed equation, stores result
in variable on left of equals sign
[ENTER]
RUN/STOP
Prompts for next variable in the equation
[R/S]
CLEAR
Deletes displayed equation from memory
[BLUE] [CLEAR]
SOLVE
Solves for a user-specified variable in an
equation
Select an Equation via
[EQN], press [SOLVE]
DELETE
Deletes rightmost character in an equation
[]
SCROLL
UP / DOWN
Scrolls up/down through list of stored
equations
Cursor pad 
SCROLL
TOP / BOTTOM
Jumps to top/bottom of equation list
[BLUE] + Cursor pad

SHOW
View Checksum and length of equations
[GOLD] [SHOW]
Leaves Equation mode
[C]
Exit
Basic Coordinate Geometry
Name
Equation
Variables
Horizontal
Curve
Equations
Northing*
N = N + (D x cos (HMS(G)))
N = Northing, D = Distance,
G = Azimuth in D.MS
Easting*
E = E + (D x sin (HMS(G)))
E = Easting, D = Distance
G = Azimuth in D.MS
Latitude
N = D x cos (HMS(G))
N = Delta N or Latitude, D = Distance
G = Azimuth in D.MS
Departure
E = D x sin (HMS(G))
E = Delta E or Departure, D = Distance
G = Azimuth in D.MS
Distance
D = SQRT(SQ(N)+SQ(E))
D = Distance, N = Delta N or Latitude
E = Delta E or Departure
Bearing
B = ATAN(E/N)
B = Bearing of line with respect to N or
S axis. Determine quadrant from sign
of Latitude (N) and Departure (E)
Test Data
D = 630.40, G = 198°30’24”
N = -597.80, E = -200.10, B = 18º30’24”
*Equation can also be used to find latitude and
departures by setting initial Northing and
Easting values to Zero at prompt.
100 Foot Arc Definition
Horizontal
Equations
Horizontal Curve
Curve Equations
Name
Equation
Variables
Arc Length
L = 2 x π x R x I ÷ 360
L = Arc Length, R = Raduis,
I = Central Angle in Decimal degrees
SemiTangent
T = R x tan( I ÷ 2 )
T = Semi-tangent, R = Radius
I = Central Angle in Decimal degrees
Long Chord
C = 2 x R x sin( I ÷ 2 )
C = Long Chord, R = Radius
I = Central Angle in Decimal degrees
External
E = ( R ÷ cos(I ÷ 2 )) - R
E = External distance, R = Radius
I = Central Angle in Decimal degrees
Middle
Ordinate
M = R – ( R x cos(I ÷ 2 ))
M = Middle Ordinate, R = Radius
I = Central Angle in Decimal degrees
Degree of
Cruvature
D = 5729.578 ÷ R
D = Degree of Curvature in Decimal
degrees, R = Radius
Test Data
R = 818.51, I = 22°50’28”
L = 326.30, T = 165.35, C = 324.14,
E = 16.53, M = 16.21, D = 7°
Triangles
Name
Equation
Variables
Horizontal
Curve
Equations
Area of Right
triangle
Q=1/2*B*H
Q = Area, B = Base,
H = Height
Area of
Oblique
triangle
Q=.5*A*B*sin(C)
Q = Area, A = Side a, B = side b,
C = Angle C in Decimal degrees
Coslaw
T=acos((B^2+C^2-A^2)
/(2*B*C))
T = Angle A in Decimal degrees, B = side
b, C = side c, A = side a
Hero’s
Formula
Q=SQRT(.5*(A+B+C)*(.5*(A
+B+C)-A)*(.5*(A+B+C)B)*(.5*(A+B+C)-C))
Q = Area, A = side a, B = side b,
C = side c
Pythagorean
Theorem
C = SQRT(A^2+B^2)
Trapezoid
Area
Q=(A+B)*H/2
Q = Area, A = Base 1, B = Base 2, H +
Height
Test Data
Right triangle: a = 60, b = 80,
c = 100, A = 36°52’12”,
B = 53°07’48” C = 90°
Area = 2400
Trapezoid: Base 1 = 100, Base 2 = 80,
Height = 95, Area = 8550
A = side A, B = side B, C = side C
Sliding Area Equation for TI-89 Numeric Solver
11/09/2006 – Jon B. Purnell, PLS
Area of sub-trapezoid to be segregated
from a larger whole – this equation will
compute the height of the height of the
sub-trapezoid given the pre-determined
area of the sub-trapezoid and the height
and two bases of the larger parent
trapezoid.
Enter this in “eqn:” field of TI89 Numeric Solver
Works for all trapezoids. Use to find the distance a parallel line must fall (height of a sub-trapezoid) from
base1 to get a given area, or to find the area of a sub-trapezoid having a given height.
Input Data:
sub-trapezoid area = 3,000,000.00
base1 = 4076.7189
base2 = 1763.1192
ht = 1713.2353
Output: solve for height of sub-trapezoid, h = 857.7407
(NOTE: the computed value “h” is measured from base 1 )
Derived from standard “area-of-a-trapezoid formula”: area = (base1+base2)*height/2 The sliding area
equation substitutes “base1+(base2-base1)/ht*h” for “base 2” in the standard trapezoid area equation (see
standard equation, above).
In a trapezoid, the lengths of the bases are dependent upon their separation (height of the trapezoid) and
upon and the difference in their lengths. It is a linear relationship: (base2-base1)/height describes it; and
it can be thought of as the change in base length per unit of trapezoid height. The relationship can be used
to compute the length of an unknown base of a sub-trapezoid, whose area is given as a fixed value. Then
it is possible to compute the height of a sub-trapezoid whose area has been defined, as in the sample
above.
These kind of problems are often referred to as “sliding side area problems” or “pre-determined area
problems”
• Sample equation
documentation
– Sample problem
– Sketch
– Variable
definitions
– Equation
formatted for
input
– Explanation
– Sample data
– Solution
Memory
• Hp35s has 30K of memory
• You can store
– Numbers
– Equations
– Programs
• 27+ directly addressable
– Registers A though Z, i, (plus STATS registers)
– Additional storage is available via Indirect
Addressing (available to running programs only)
- Ask presenter to explain, or see Chapter 14 of
the Users Guide
Meters to US Survey Feet:
1 meter ≈ 3.2808333333 US
Survey feet
Storing an
often used number
STO _
You can store this number in a
storage register for later use
Key in value you want to store…
3.28083333333, then press [BLUE] [STO]
Next, choose a register in which to store the
number (select a letter, from A to Z… We
will store this value in register U):
Press [U] to store the value in register U
Using the stored Meters-to-US foot
conversion, convert these metric
coordinates
to State
Plane values:
Stored
numbers
Math with
119,521.1550
0.0000
392,128.9894
337,663.4730
0.0000
119,521.155_
392,128.9894
RCL
337,663.473_
3.2808
1,107,817.5777
_
119,521.155mN, 337,663.473mE
Key in 119521.155
Press [RCL], then [U]
Press [Multiply]
Key in 337663.473
Press [RCL], then [U]
Press [Multiply]
Thanks for your kind attention!
• Contact: Jon B. Purnell, PLS
– [email protected]
• 360-460-8565
• Download this
presentation at
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