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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) is measured in a vacuum, and is slightly slower in the atmoshpere. Speed of sound (Mach 1) is measured in the atmosphere and varies with altitude. There is no sound in a vacuum (outer space). Speed of sound in water is much faster and varies with temperature (higher is faster), seawater or Fresh water (seawater is faster), and pressure (higher pressure is faster). All "speeds" are approximate.

Speed of Light (c)
vacuum
c = 299,792,458 m / s
= 983,571,056 ft / s
= 1,079,252,849 kph
= 670,616,629 mph
= 580,243,467 knots
= 299,792 km / s
= 186,282 mi / s
≈ 0.984 ft / ns

knot = nautical miles / hour

Speed of Sound (Mach 1)
Sea Level
Mach 1 ≈ 765 mph
≈ 665 knots
≈ 1231 kph
≈ 342 m / s
≈ 1122 ft / s
≈ 374 yd / s
≈ 0.21 mi / s
≈ 1 mi / 4.7 s
Speed of Sound
in Water
3219 mph
2797 knots
5180 kph
1439 m / s
4721 ft / s
5174 yd / s
0.89 mi / s
1 mi / 1.1 s

ft
m
yd
mi
NM 		-
-
-
-
-
- 		feet
meters
yards
miles
Nautical Miles 		s
ns
mph
kph
hr 		-
-
-
-
- 		seconds
nano seconds
miles per hour
kilometers / hour
Hours


Approximate Speed of Sound
Sea Level to 154,000 feet
Sea Level 36,000 to
82,000 feet		 82,000 to
154,000 feet
765 mph Linear
decrease to 		660 mph Linear
Increase to 		755 mph
1 mi / 4.7 sec 1 mi / 5.5 sec 1 mi / 4.8 sec


Thunder travels about 1 mile per 5 seconds.

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 Travels
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
= kTB
k
T
B		 =
=
=		 Boltzmann's Constant
Temperature in degrees Kelvin (°K)
Receiver Noise Bandwidth in Hertz (Hz)
All TVs have a 6 MHz noise bandwidth


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

Watt*sec (W*s) = Joules (J)

TV Receiver
Background Noise
kTB = -106 dBm
B
T		 =
=		 6 MHz
300°K (80°F)


Receiver sensitivity (minimum signal)
depends on receiver noise figure (NF)
& minimum signal-to-noise ratio (S/N).
See - Television Minimum Signal.
- The Decibel (dB) Scale

Television typical minimum signal is -65 dBm.
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 log10(x) or log(x)
Natural (Base e) loge(x) or ln(x)


Base 10 Logarithm of "x"
Log( )

Base 10 Logarithm

Natural Log (Base e) of "x"
Ln ( )

Natural Logarithm



Compute Base 10 Log
using Natural (Base e) Log
log10 (x) ≈ ln (x)
ln (10)
log10 (x) ≈ 0.43429448 ln (x)
Compute Natural (Base e) Log
using Base 10 Log
ln (x) ≈ log10 (x)
log10 (e)
ln (x) ≈ 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