Equations and Definitions

Equation #1.
"Water Heat" MBH = 0.5*gpm*T Where: MBH is thousand btu/hr gpm is gallons per minute T is differential temperature. Example: We use 3 gpm of water and we wish to heat it to 110ÞF. If it is available at 50ÞF from the ground, what size of demand water heater is required? MBH = 0.5*3*(110-50) = 90 Therefore a demand heater with a 90 MBH output is required. This matches the output of the Aquastar 125.

Equation #2
"Electrical Direct Current" (Ohm's law) P=IV Where: P is Power expressed in Watts (joules/second) I is current expressed in Amps (coulombs/second) V is electric potential expressed in Volts Example: An appliance that draws 2.5 amps at 12 Volts draws how many watts? P = 2.5*12 = 30 Watts. Note: 1 Watt hour (WH or WHr) is equal to 3600 Joules of energy. If the appliance runs for 4 hours at a rate of 30 Joules/sec (watts), how much energy will it draw? It will draw 4hrs * 60min/hr *60sec/min *30 joules/sec = 432000 Joules (or 30 W * 4 Hrs = 120 watt*hrs).

Equation #3
To estimate available power from a hydro site multiply the head (vertical fall in feet) x flow (gpm) Š 10 = potential watts.

How much propane does a particular gas appliance use? divide 90,000 by the btu rating (1 gallon of propane = 90,000 Btu) HP = flow (cfs) x head (feet) x .8 8.8 448 gal/min = 1 cubicfoot/sec (cfs)

Photometric Units Candela
Systeme International (CI) unit of luminous intensity. The modern calibration reference is a platinum radiator heated to just below its melting point: each square cm of such an object has 60.0 candela luminous intensity! (In old-fashioned parlance, each sq. cm of the hot platinum emits as much light as 60 standard candles.) A point source of 1 candela radiates 1 lumen into a solid angle of 1 steradian. A 1 sq-cm source of 1 candela produces an illumination level of 1 foot candle at a distance of 1 foot. It gets a little confusing at times, because there are 3 ways of measuring the light output of sources:

1) Total luminous flux,

2) Luminous intensity or surface brightness per unit area (Summing this up over a surface gives total flux, but a point source has no area so you can't really calculate its intensity.) See below.

3) Illumination level at some distance away, sometimes measured in foot-candles. Luminous intensity is surface brightness, sometimes measured in candelas. Note that a big surface can have a high luminance at the same time that it has a low luminous intensity and vice-versa. An example will make this clear (I hope):

A 40W fluorescent tube is a lot easier to stare at than a 40W incandescent. Why? The light output of the incandescent is spread over a much smaller area, so it has a much higher luminous intensity. The 40W fluor. puts out about 2000 lumens spread out over about 2500sq-cm. Meanwhile, the incand. puts out only about 750lumens, but it's spread over only about 150sq-cm (assuming a frosted bulb). So, the surface of the incandescent will have about 6 times greater luminous intensity. Imagine how bright the filament itself is, with its much smaller surface area. So, as you look at a CRT or other display, its surface brightness can be measured in candelas. It it has 60candela brightness, it's as bright as the Pt standard. Another way to look at it is that each sq-cm would emit the same luminous flux as 60 candles! However, the intensity of a candle flame is another matter: it depends on the size of the flame! Here's an example of a practical problem:

Q. What's the luminous intensity of a white screen illuminated by 9 ft-cd lighting? (This is like slightly dimmed office lighting..I chose the value 9 to make calculation easier, see below.) [Here's the significance of this question: In order to see images projected onto the white screen under such conditions, the display projector must produce at least a comparable level of luminosity.]

A. There are about 900 sq-cm per sq ft. For 9 ft-cd illumination, it's as if each sq ft of the screen were illuminated by a 9 candle source at a range of 1 ft. Those 9 candles of flux are spread over 900 sq-cm of area, so each sq-cm has an intensity of 10 millicandelas! In order to be seen clearly, the display device should provide a luminous intensity significantly higher than 10 mcd.

0) Standard candle - a point source of light having a particular radiance spectrum (power vs wavelength) and total power output which are approx. that of an 'ordinary' candle. Point sources radiate uniformly into a sphere.

1)1 Lumen - the amount of visible light emitted by a standard candle through a solid angle of 1 steradian. Since a sphere has 4pi = 12.57 steradians, the standard candle emits a total of 12.57 lumens. (Of course, 1 Steradian is just that solid angle over which the subtended area is exactly equal to the radius of a sphere, so, 1 sq-ft of surface area on a 1 ft sphere covers exactly 1 steradian.) Foot candle = 1 lumen/sq-ft, which is the illumination from 1 standard candle at 1 foot range.

2) 1 Lux = 1 meter-candle, i.e., illumination from 1 std cdl at 1 meter range. Since there are 10.76 sq ft per sq meter, it follows that there are 10.76 lux per foot candle.

3) Illuminance of noonday sun - ~ 10,000 ft-cd, which is 107,600 lux. Since the sun is about 1,116,000,000 ft away, it's visible energy output must be about 1.245456e+18 candles!

4) Illumination levels in various other settings: Office illumination: 50 to 200 ft-cd Art galleries 10 to 50 ft-cd Hospital operating table 1000 ft-cd Moonlight, full moon 0.01 ft-cd Major league baseball 100 ft-cd

5) Lumen outputs of various sources: Incandescent lamps, inside frosted 20 lumens/Watt Fluorescent lamps, cool white 50 lumens/Watt

6) Calculating illumination level: In general, if the light from an x lumen source is spread over y square feet, the average illumination level will be x/y ft-cd.

CRI Definition
CRI (Color Rendering Index) is defined as the effect that a light source has on the appearance of an objects color. In short, CRI is how the lamp makes an object appear.

Measurement
CRI is a universal measurement system numbering from 0 - 100, with outdoor light having a CRI of 100. Generally, the higher the CRI the better the color rendering properties of the lamp. However, a correct judgement can not be made based upon CRI alone. A second measurement also needs to be considered, Kelvin Temperature. Kelvin Temperature Background Information: History of Kelvin Temperature (K) originally comes from the incandescent lamp. In order to understand Kelvin (K) one needs to look at the following example: When you heat an iron bar the color of the bar changs from dull red, to red-orange, to white as the temperature of the iron bar increases. In an incandescent lamp the tungsten filament goes through similar color changes as the voltage increases. Thus K measures the change in color appearance.

Definition
Kelvin Temperature (K) is defined as the appearance of a light source. Simply put, how the light source itself appears. Measurement: Kelvin is measured in degrees. Less than 3000 K are considered warm colors and have a reddish appearance. ie: Warm White, Warm White Deluxe, Design Spec 30. 3400 K to 4500 K are considered to be white or neutral in appearance. ie: Natural, Design Spec 35 and 41, and Cool White. Greater than 4600 K are cool or bluish in appearance. ie: Artic Lite, Sign Lite, Chroma 50, Chroma 75, True Lite, and Daylight.

Copyright 2001 by Paul Mathews from the LED FAQ PAGES used with permission.