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Constants and
Conversions

Contents
• Speed of Light and Sound
• Frequency, Wavelength, Period
• Background Noise
• Elecgromagnetic Waves
• Free Space Constants
• Radiation
• Temperature Conversions
• Angle Degrees and Radians
• Math Functions
• Decimal Multipliers
• Distance and Speed Conversions
• Acceleration g's and Conversions
Speed of Light and Sound
Speed of Light (c)
Vaccum
c = 299,792,458 m / s
= 983,571,056 ft / s
= 670,616,629 mph
= 186,282 mi / s
≈ 1 ft / ns
Speed of Sound
Sea Level
cs ≈ 765 mph
≈ 342 m / s
≈ 1,122 ft / s
≈ 374 yd / s
≈ 1 mi / 5 s

ft
m
yd
mi 		-
-
-
- 		feet
meters
yards
miles 		s
mph
kph 		-
-
- 		seconds
miles per hour
kilometers / hour
Frequency, Wavelength, Period
Sine Wave

Parameter Equations Unit Dimensions
Frequency f = c / λ = 1 / T Cycles / Second (Hz)
Period T = λ / c = 1 / f Time to Complete 1 Cycle
Wavelength λ = c / f = c T Distance 1 Cycle Covers
at the Speed of Light (c)

f = Frequency Hz = Hertz (1/s)
T = Period c = Speed of Light
λ = Wavelength


Calculate Wavelength and Period

Frequency

Wavelength in feet
Wavelength in meters
Period in seconds


Background Noise
Receiver Background
Noise Power
Noise = kTB
k = Boltzmann's Constant
T = Temperature in degrees Kelvin (°)
B = Receiver Noise Bandwidth in Herts (Hz)


Boltzmann's Constant
k = 1.380 649 x 10-23 Watt*sec/°K


TV Receiver Background Noise
kTB = -106 dBm
B = 6 MHz at 300°K (80°F)
See Television Minimin Signal.

Electromagnetic Waves
Power Density Pd = PERP / ( 4πR2 ) W/m2
Electric Field E = (Pd Zo)0.5 V/m
Magnetic Field H = E / Zo A/m
Free Space Impedance Zo = 377 ohms (Ω)

W/m2
V/m
A/m
PERP
R 		--
--
--
--
-- 		watts / square meter
volts / meter
amperes / meter
effective radiated power
range


Calculate Power Density
Power: kW
Range:

ERP
Range
Power Density
Milliwatts / Square Meter


Free Space Constants

Intrinsic
Impedance (Zo)
Ohms (Ω)
Zo = E / H Ω
= µo c Ω
= ( µ0 / εo )0.5 Ω
= ( εo c )-1 Ω
= 377 Ω
Electric Field (E)
Permittivity (εo)
Farads / meter
εo = µo-1 c-2 F/m
= 8.854 188 x 10-12 F/m
Magnetic Field (H)
Permeability (µo)
Henrys / meter
µo = 4 π x 10-7 H/m
= 1.256 637 x 10-6 H/m


c = Speed of Light
Radiation

Non-Ionizing and Ionizing Radiation

Radiation
A = Angstrom = 10-10 meters = 0.000 000 0001 m
Temperature Conversions
°C -- Degrees Celsius (or Centigrade)
Water freezes at 0°C and boils at 100°C
°F -- Degrees Fahrenheit
Water freezes at 32°F and boils at 212°F
°K -- Degrees Kelvin
Thermodynamic temperature
0°K is absolute zero
0°K = -273.15°C = -459.67°F
Temperature
Conversions
°C = (°F - 32) x 5/9
°C = °K - 273.15

°K = (°F - 32) x 5/9 + 273.15
°K = °C + 273.15

°F = (°C x 9/5) + 32
°F = (°K - 273.15) x 9/5 + 32
Convert
Temperature

Fahrenheit (° F)
Celsius (° C)
Kelvin (° K)


Angle Degrees and Radians

ANGLE
Degrees (°), Radians (Rad), milliradians (mR)

π Rad = 180°
1 Rad = ( 180 / π ) °
≈ 57.3 °
1° = ( π / 180 ) Rad
= 0.0175 Rad
= 17.5 mR
Degrees to / from Radians
Angle

Degrees (°)
Radians (Rad)
milliradians (mR)



Math Functions

TRANSCENDENTAL NUMBERS
Natural Logarithms (ln) base
e = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995...
Pi
π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510...


LOGARITHMS
Base 10 Logarithm = log10(x) = log(x)
Natural Logarithm = loge(x) = ln(x)

Base 10 Logarithm
Log( )

Base 10 Logarithm

Natural Logarithm
Ln ( )

Natural Logarithm



Natural Log (ln) to/from Base 10 Log
log10 (x) = ln (x)
ln (10)
≈ 0.43429448 ln (x)
ln (x) = log10 (x)
log10 (e)
≈ 2.30258509 log10 (x)


Decimal Multipliers

Decimal Multiplier Prefixes > 1
Multiplier Power Prefix Symbol Name
1 followed by 100 zeros 10100 - - googol
1,000,000,000,000,000,000,000,000 1024 yotta Y -
1,000,000,000,000,000,000,000 1021 zetta Z -
1,000,000,000,000,000,000 1018 exa E -
1,000,000,000,000,000 1015 peta P -
1,000,000,000,000 1012 tera T trillion
1,000,000,000 109 giga G billion
1,000,000 106 mega M million
1,000 103 kilo k thousand
100 102 hecto h hundred
10 101 deka da ten
Decimal Multiplier Prefixes ≲ 1
Multiplier Power Prefix Symbol
1 100 - -
0.1 10-1 deci d
0.01 10-2 centi c
0.001 10-3 milli m
0.000 001 10-6 micro µ
0.000 000 001 10-9 nano n
0.000 000 000 001 10-12 pico p
0.000 000 000 000 001 10-15 femto f
0.000 000 000 000 000 001 10-18 atto a
0.000 000 000 000 000 000 001 10-21 zepto z
0.000 000 000 000 000 000 000 001 10-24 yocto y

In the U.S. sometimes g's or a grand refers to a thousand (1000).


Distance and Speed Conversions

DISTANCE
1 in = 0.0254 m
1 ft = 12 in
1/ 3 yd
0.3048 m
1 yd = 36 in
3 ft
0.9144 m
1 m = 1 / 0.0254 in
1 / 0.3048 ft
1 / 0.9144 yd
DISTANCE
1 km = 1 / 1.852 NM
1 / 1.609344 mi
1 / 0.0009144 yd
1 / 0.0003048 ft
1000 m
1 mi = 1609.344 / 1852 NM
1.609344 km
1760 yd
5280 ft
1609.344 m
DISTANCE
1 NM = 1852 / 1609.344 mi
1.852 km
1852 / 0.9144 yd
1852 / 0.3048 ft
1852 m
1 NM (UK) = 1853.184 m

in
ft
yd
m 		-
-
-
- 		inches
feet
yards
meters 		km
mi
NM
-
-
-
kilometers
miles (statute)
nautical miles


SPEED
1 m / s = 1 / 0.3048 ft / s
3.6 kph
1 / 0.44704 mph
900 / 463 knots
1 ft / s = 0.3048 m / s
1.09728 kph
15 / 22 mph
274.32 / 463 knots
SPEED
1 kph = 1 / 3.6 m / s
5 / 5.4864 ft / s
1 / 1.609344 mph
1 / 1.852 knots
1 mph = 0.44704 m / s
22 / 15 ft / s
1.609344 kph
402.336 / 463 knots
1 knot = 463 / 900 m / s
463 / 274.32 ft / s
1.852 kph
463 / 402.336 mph


knot = nautical miles / hour


Acceleration g's and Conversions

Acceleration
due to Gravity (g)
International Definition
1 g = 9.80665 m / s2
= 32.1740 ft / s2
≈ 21.9 mph / s
≈ 35.3 kph / s


ACCELERATION
Unit Exact Approximate
1 m / s2 = 1 / 0.3048 = 3.2808 ft / s2
9 / 2.5 = 3.6 kph / s
1 / 0.44704 = 2.2369 mph / s
900 / 463 = 1.9438 knots / s
1 / 9.80665 = 0.1020 g's
1 ft / s2 = 0.3048 = 0.3048 m / s2
15 / 22 = 0.6818 mph / s
1.09728 = 1.0973 kph / s
274.32 / 463 = 0.5925 knots / s
0.3048 / 9.80665 = 0.0311 g's
1 mph / s = 22 / 15 = 1.4667 ft / s2
0.44704 = 0.447 m / s2
1.609344 = 1.6093 kph / s
402.336 / 463 = 0.8690 knots / s
0.44704 / 9.80665 = 0.0456 g's
ACCELERATION
Unit Exact Approximate
1 kph / s = 2.5 / 9 = 0.2778 m / s2
5 / 5.4864 = 0.9113 ft / s2
1 / 1.609344 = 0.6214 mph / s
1 / 1.852 = 0.54 knots / s
2.5 / (9 * 9.80665) = 0.0283 g's
1 knot / s = 463 / 900 = 0.5144 m / s2
463 / 274.32 = 1.6878 ft / s2
463 / 402.336 = 1.1508 mph / s
1.852 = 1.852 kph / s
463 / (900 * 9.80665) = 0.0525 g's
1 g = 9.80665 = 9.81 m / s2
9.80665 / 0.3048 = 32.1740 ft / s2
9.80665 [ 3600 / (5280 * 0.3048)] = 21.9369 mph / s
3.6 * 9.80665 = 35.3039 kph / s
3600 * 9.80665 / 1852 = 19.0626 knots / s


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Constants and Conversions 		OTA DTv