Re: V54 Lumen & Throw Measurements
Justin--Is there a formula to find the multiplier for the distance(m) being tested
You use the inverse square law.
I gave an example (Above) where you can multiply the lux at 20 meters by 400 to get the lux at 1 meter, which is the light's cd.
The Inverse Square Law
The inverse square law defines the relationship between the irradiance from a
point source and distance. It states that the intensity per unit area varies in inverse proportion to the square of the distance.
E = I / d2
In other words, if you measure 16 W/cm
2 at 1 meter, you will measure 4 W/cm
2 at 2 meters, and can calculate the irradiance at any other distance. An alternate form is often more convenient:
E1 d12 = E2 d22
Distance is measured to the first luminating surface - the filament of a clear bulb, or the glass envelope of a frosted bulb.
Sooooo, if you have a reading of lux at a distance, and want to back calculate back to the cd...
...just remember that at half the distance, its 4x as bright (lux), and that at double the distance, its 1/4 as bright, and so forth.
So, a measurement at 20 m would require multiplying the measured lux by 400.
A measurement at 5 m would require multiplying the measured lux by 25.
A measurement at 10 m would require multiplying the measured lux by 100.
A measurement at 100 m would require multiplying the measured lux by 1,000.
And so forth.
Again, the beam needs time to form...so, a measurement at a given distance may not represent a number you can plug in to get it at other distances.
IE: If I want the cd of a good throwing light (Its lux at one meter), and I MEASURE its lux AT one meter, I will NOT, ironically, have measured its cd (Lux at one meter).
So, you HAVE TO BE FAR ENOUGH AWAY,
FOR THAT LIGHT, to get a representative cd value.
The way to be SURE the cd is representative, is if it DOES allow prediction of lux at farther distances.
So, if you measure the lux at say 5 meters, and at 10 meters, the measured lux at 5 will be more than at 10 meters, BUT, the cd calculations may give DIFFERENT numbers....if 5 m was too close...for that light.
You need to measure so far away that you "Know" the beam has had room to form...or, simply take a second measurement farther away to see if the cd is improved, or not.
If the cd gets better on the farther distance, you then do a THIRD measurement at yet still FARTHER away...to see if THAT calculated cd is better than the 2nd one.
If its the same cd at the 3rd point, then, the second point WAS far enough, for that light...because it predicted the measurement at the third point, and so forth.
If the second point's cd is the same as the first point's...you don't need a 3rd point, as the 1st point was representative, and so forth.
Example:
I measure 7,500 lux at 5 meters. I multiply that by 25, to get the cd, which would work out to 187,500 cd
If I measure again at 10 meters and get 2,500 lux, and multiply that by 100, to get the cd, which works out to 250,000 cd....I know 5 M was too close.
(Notice I measured a lower
LUX, but that lower lux, because of the longer DISTANCE, calculated out to a higher
cd)
If I measure a 3rd time at 20 meters...and get 625 lux, and multiply that by 400 to get the cd, which works out to 250,000 cd...I KNOW that I got 250k cd on the second and third measurements, and that 5 M was too close and that 10 m was far enough....because it predicted the lux at the farther (20 m) distance.
Does that make sense?
The entire reason for wanting to know a light's cd, is TO be able to predict the lux at any other distance....so, that's why you want a representative number for the cd...as when that representative cd is plugged into the inverse square law...you DO get the predicted lux on distant targets.
