**fx-260 Solar Algorithms Part I**

All results are shown to screen accuracy.

**Sphere: Surface Area and Volume**

With the radius r,

the surface area is S = 4 * π * r^2

the volume area is V = 4/3 * π * r^3

Algorithm:

r [SHIFT] (Min) [ x² ] [ × ] [EXP](π) [ × ] 4 [ = ] // surface area is displayed

[ × ] [ MR ] [ ÷ ] 3 [ = ] // area is displayed

M = r

Example:

Input:

r = 3.86

Results:

3.86 [SHIFT] (Min) [ x² ] [ × ] [EXP](π) [ × ] 4 [ = ]

Surface Area = 187.2338956

[ × ] [ MR ] [ ÷ ] 3 [ = ]

Volume = 204.9076123

**Monthly Payment of a Mortgage or Auto Loan**

Input:

A = amount of the mortgage/loan

I = annual interest rate

N = number of months

The monthly payment can be found by:

PMT = ( 1 – (1 + I/1200)^-N) / (I/1200)

Algorithm:

I [ ÷ ] 1200 [ = ] [SHIFT] (Min) // stores I/1200 into M

1 [ – ] [ ( ] 1 [ + ] [ MR ] [ ) ] [ x^y ] N [ +/- ] [ = ]

[SHIFT] (1/x) [ × ] [ MR ] [ × ] A [ = ] // monthly payment

Example:

Input:

I = 4 (4%)

N = 360

A = 85000

Result:

4 [ ÷ ] 1200 [ = ] [SHIFT] (Min) // stores I/1200 into M

1 [ – ] [ ( ] 1 [ + ] [ MR ] [ ) ] [ x^y ] 360 [ +/- ] [ = ]

[SHIFT] (1/x) [ × ] [ MR ] [ × ] 85000 [ = ] // monthly payment

PMT = 405.8030014 ($405.80)

(I/1200 = M = 3.333333333E-03)

**Electromagnetic Field Strength **

Given the EIRP (effective isotropic radiated power) of a microwave (in Watts), we can calculate the following:

Power Flux Density:

S = EIRP / (4 * π * d^2) (W/m^2, d = distance from the wave source in meters)

Electric Field:

E = √(30 * EIRP) / d (W/m)

Magnetic Field:

H = √(EIRP / (480 * π^2 * d^2) ) (A/m)

Algorithm:

Calculating Power Flux:

EIRP [ ÷ ] [ ( ] 4 [ × ] [EXP](π) [ × ] d [ x² ] [ ) ] [ = ]

Calculating Electric Field:

[ ( ] EIRP [ × ] 30 [ ) ] [SHIFT] (√) [ ÷ ] 0.5 [ = ]

Calculating Magnetic Field:

[ ( ] EIRP [ ÷ ] [ ( ] 480 [ × ] [EXP](π) [ x² ] [ × ] d [ x² ] [ ) ] [ ) ] [ √ ] [ = ]

Example:

Input:

EIRP = 1800 W

d = 0.5 m (distance)

Results:

Calculating Power Flux:

1800 [ ÷ ] [ ( ] 4 [ × ] [EXP](π) [ × ] 0.5 [ x² ] [ ) ] [ = ]

Power Flux: 572.9577951 W/m^2

Calculating Electric Field:

[ ( ] 1800 [ × ] 30 [ ) ] [SHIFT] (√) [ ÷ ] 0.5 [ = ]

Electric Field: 464.7580015 W/m

Calculating Magnetic Field:

[ ( ] 1800 [ ÷ ] [ ( ] 480 [ × ] [EXP](π) [ x² ] [ × ] 0.5 [ x² ] [ ) ] [ ) ] [ √ ] [ = ]

Magnetic Field: 1.232808888 A/m

Source: Barue, Gerardo. __Microwave Engineering: Land & Space Radiocommunications__ John Wiley & Sons, Inc. Hoboken, NJ ISBN 978-0-470-08966-5 2008

**Slope and Intercept with Two Points**

Given two points of a line (x1, y1) and (x2, y2) we can find the slope (a) and y-intercept (b) of the general linear equation y = a*x + b.

The trick is to use the rectangular to polar conversion to find the slope:

θ = atan((y2 – y1)/(x2 -x1))

tan θ = (y2 – y1)/(x2 -x1) = slope = a

Once the slope is found, we can solve for the y-intercept:

y = a*x + b

b = y – a*x

Algorithm:

[ ( ] x1 [ – ] x2 [ ) ] [SHIFT] (R→P) [ ( ] y1 [ – ] y2 [ ) ] [ = ] [SHIFT] (X<>Y) [ tan ]

// slope is displayed

[ × ] x1* [ +/- ] [ + ] y1* [ = ]

// intercept is displayed

*x2 and y2 can be used instead

Example:

(x1, y1) = (8, 5.5)

(x2, y2) = (4, 9.5)

Result:

[ ( ] 8 [ – ] 4 [ ) ] [SHIFT] (R→P) [ ( ] 5.5 [ – ] 9.5 [ ) ] [ = ] [SHIFT] (X<>Y) [ tan ]

Slope: -1

[ × ] 8 [ +/- ] [ + ] 5.5 [ = ]

Slope: 13.5

Tomorrow will be Part II.

Eddie

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