Applications: Sharp EL-5150
Note: spaces included for readability
Fan Laws
AER Equation:
1; f(BCDI) = B * ( C ÷ D ) Y^x ( 1 ÷ I )
Variables:
Calculate CPM_new
B = CPM_old
1st Fan Law:
I = 1
C = RPM_new
D = RPM_old
2nd Fan Law:
I = 2
C = SP_new
D = SP_old
3rd Fan Law:
I = 3
C = BHP_new
D = BHP_old
Example 1:
Fan Law 2:
CPM_old = B = 4000 CPM
SP_new = C = 48
SP_old = D = 36
I = 2
Result: 4618.802153
Example 2:
Fan Law 3:
CPM_old = B = 3500 CPM
BHP_new = C = 59
BHP_old = D = 52
I = 3
Result: 3650.488072
Ideal Shockley Diode Equation
I = I0 * e^((VD/(n* VT) - 1)
where VT = K * T/q
I = diode current (amps)
I0 = saturation current (amps)
VT = thermal voltage (V) - see notes below
VD = voltage across the diode (V)
n = ideality factor, in ideal situations, n = 1
Notes:
* The equation below assumes the ideal diode, n = 1
* The equation uses a ratio of scientific constants: k/q
* k = Boltzmann's Constant = 1.380649 * 10^-23 J/K
* q = Charge of an Electron = 1.602176634 * 10^-19 C (on some calculators, like the Casio fx-991EX, this constant is labeled e)
* k/q = 8.617332385 * 10^-5 J/(K*C) = 8.617332385 * 10^-5 V/K (volts/degrees Kelvin)
AER Equation:
1; f(IDE) = 8.617332385E-5 × E STO A, I ×(e(D ÷ A) - 1)
Calculate VT (stored in A), the I
I = I0
D = VD
E = temperature in Kelvin
Example 1:
I = 4E-6 A
D = 0.08 V
E = 280 K
Results:
A = 0.024128531, (I) 0.00001061
Example 2:
I = 4E-6 A
D = 0.06 V
E = 300 K
Results:
A = 0.025852000, (I) 0.00003674
Dot and Cross Product of Two 3D Vectors
For the two vectors [A, B ,C] and [D, E, F]:
AER Equations:
1; f(ABCDEF) = A × D + B × E + C × F ◣
2; B × F - C × E, C × D - A × F, A × E - B × D
Example 1:
[ A, B, C ] and [ D, E, F]
[ 4.5, -2.5, -8 ] and [ 1.6, 3.9, 6 ]
Dot Product: -50.55
Cross Product: [ 16.2, -39.8, 21.55 ]
Example 2:
[ A, B, C ] and [ D, E, F]
[ 4, 3, 2 ] and [ 2, 7, 0 ]
Dot Product: 29
Cross Product: [ -14, 4, 22 ]
Law of Cosines
Sides with lengths A, B, C with D as the angle opposite of A. Equation 1 finds the length of side A, while Equation 2 finds the angle D.
AER Equations:
1; f(BCD) = √(B^2 + C^2 - 2 × B × C × COS D) STO A ◣
2; f(ABC) = cos^-1 ((B^2 + C^2 - A^2) ÷ (2 × B × C)) STO D
Example 1 - find A:
Degree Mode Set
Input: B = 4.5, C = 3.7, D = 30°
Run 1:
Result: 2.258617731
Example 2 - find D:
Degree Mode Set
Input: A = 40, B = 56, C = 38
Run 2:
Result: 45.5579132°
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Eddie
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