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
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
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
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.