PCalc 42 User Functions ( iOS )

PCalc 42 User Functions ( iOS )

Programs for the iOS App PCalc 42 from Previous Posts (during May 2014):

http://edspi31415.blogspot.com/2014/05/pcalc-programming-introduction.html

Mohr’s Circle:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-mohr-circle.html

Period of Orbit Around the Sun:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-period-of-orbit-around.html

Horizontal Pipe Discharge:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-horizontal-pipe.html

Newton’s law of Gravity Solver:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-newton-law-of-gravity.html

Distance of a Star by Parallax:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp50g-distance-of-star-by.html

Escape Velocity:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-escape-velocity.html

Time to revisit this app:

PCalc42 Decimal to Degrees-Minutes-Seconds (d.mmssss form): 

D > DMS

Switch to Decimal

Set R0 to X

Truncate X

Set R1 to R0

Subtract X from R1

Multiply R1 by 60

Set R2 to R1

Subtract X from R1

Multiply R1 by 60

Set R2 to R1

Truncate R1

Multiply R1 by 0.01

Add R1 to X

Set R3 to R2

Truncate R3

Subtract R3 from R2

Multiply R2 by 0.006

Add R2 to X

Example:   1.85 in DMS form is 1.51 (1° 51’)

PCalc42 Degrees-Minutes-Seconds (d.mmssss form) to Decimal

DMS > D

Switch to Decimal

Set R0 to X

Truncate X

Set R1 to R0

Subtract X from R1

Multiply R1 by 100

Set R2 to R1

Truncate R1

Subtract R1 from R2

Divide R2 by 60

Multiply R2 by 100

Add R1 to R2

Divide R2 by 60

Add R2 to X

Example:  1.3052 (1° 30’ 52”) in decimal form is 1.514444444

PCalc42 Snell’s Law of Refraction

Input: Y: n1, X: n,  n1 ≤ n2

Switch to Degrees

Invert X

Multiply Y by X

Inverse Sine X

Example:  n1 = 1.33, n2 = 1.50.   Output:  62.4573248455

PCalc42 Doppler Effect (RPN)  (SI Units)

Input:  Z:  emitted frequency (Hz), Y:  receiver velocity (m/s), X: source velocity (m/s)

Output:  observed frequency (Hz) on stack X

Negate X

Add Y to X

RPN Swap

RPN Roll Down

Divide X by 299752458

Add 1 to X

Multiply Y by X

RPN Roll Down

Example: 

Z:  Emitted Frequency:  525 Hz

Y:  Receiver Velocity:  214,000,000 ft/s

X:  Source Velocity:  208,000,000 ft/s

Output:  Observed Frequency:  535.5086711249 Hz

PCalc42 Sums (RPN) Σ m, Σ m^2, Σ m^3

The sum of Σ m^X from m = 1 to m = Y, where X is the power, Y is the power (up to 3).  If Y > 3, an error condition occurs. 

Formulas:

Σ m = (X^2 + X) / 2

Σ m^2 = (2*X^3 + 3*X^2 + X) / 6

Σ m^3 = (X * (X+1))^2 / 4

Set R0 to Y

Truncate X

Skip 3 if X = 1

Skip 7 if X = 2

Skip 16 if X = 3

Error

RPN Roll Down

X To Power of 2

Add R0 to X

Divide X by 2

Stop

RPN Roll Down

X To Power of 3

Multiply X by 2

Set R1 to R0

R1 To Power of 2

Multiply R1 by 3

Add R1 to X

Add R0 to X

Divide X by 6

Stop

RPN Roll Down

Add 1 to X

Multiply X by R0

X To Power of 2

Divide X by 4

Example:

Y = 6, X = 1:  Sum is 21

Y = 6, X = 2:  Sum is 91

Y = 6, X = 3:  Sum is 441

PCalc42 Present Value Factor of a Single Sum

PV:  (1 + Y/100)^-X

Y:  interest rate

X:  periods

Negate X

Divide Y by 100

Add 1 to Y

Y To Power of X

RPN Roll Down

Example:  Y = 7 (7%), X =  5 (n = 5)

Output:  0.7129861795

Happy New Year’s Everyone! See you in 2017!    

Eddie

This blog is property of Edward Shore, 2016.