**PCalc 42 User Functions ( iOS )**

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

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

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.