Need help doing some math (looks to be engineering)

[RIGorous1]

Ok I'm doing a project for LED lighting and I came across this diagram

candlefoot compared to height

LED light specs

The minimum requirement for Lighting is 2 footcandles and obviously from the diagram 20 feet high only produces 1.64 footcandles so I'm under. However, as the diagram progresses from 40 feet down to 20 feet the footcandles increase. I'm thinking that if I drop the lighting down to 10-15 feet that I can achieve 2 footcandles at the cost of a smaller illumination area. Is it safe to assume this?

I'm no engineer, but I need some mathematical support that lowering the height to 10-15 feet will allow me to get 2 footcandles. I was thinking of using volume of a cone, but the numbers didn't work out.

Thanks for your help

 

[RIGorous1]

does this question need more information? no help?

 

[Goosemaster]

I don't know much about illumination, but try this http://www.cs.fredonia.edu/~barneva/classes/csit462/lect9.ppt

 

[dullard]

I bet that wouldn't be too difficult to figure out. However, why bother? Just fit the three points to a curve and extrapolate. Extrapolation is dangerous if you extrapolate very far, but in this case we aren't. Those three data points fit quite nicely to this function:

(Max ft-cd) = (290 ft-cd) * (h^-1.73) where h is in feet.

Thus 17.5 feet would get just to 2 ft-cd maximum. Of course that maximum is just at one point directly under the bulbs. Add in a 20% fudge factor since we extrapolated, since the angle might not be perfect, and since the bulb may eventually get dirty. Thus you really want 2.4 ft-cd to be really safe. If the extrapolation holds, that would be a height of just under 16 ft.

 

[RIGorous1]

Originally posted by: dullard
I bet that wouldn't be too difficult to figure out. However, why bother? Just fit the three points to a curve and extrapolate. Extrapolation is dangerous if you extrapolate very far, but in this case we aren't. Those three data points fit quite nicely to this function:

(Max ft-cd) = (290 ft-cd) * (h^-1.73) where h is in feet.

Thus 17.5 feet would get just to 2 ft-cd maximum. Of course that maximum is just at one point directly under the bulbs. Add in a 20% fudge factor since we extrapolated, since the angle might not be perfect, and since the bulb may eventually get dirty. Thus you really want 2.4 ft-cd to be really safe. If the extrapolation holds, that would be a height of just under 16 ft.

Wow! Thanks for help! However, I'm uncertain what you mean by "just fit the three points to a curve and extrapolate." what curve did you use? how did you get these numbers ((290 ft-cd) * (h^-1.73)) Sorry for the layman questions, but I would like to try to "punch in" these numbers into my calculator so that I can see what you mean.

 

[notfred]

WTF is a footcandle?

 

[dullard]

Originally posted by: RIGorous1
Wow! Thanks for help! However, I'm uncertain what you mean by "just fit the three points to a curve and extrapolate." what curve did you use? how did you get these numbers ((290 ft-cd) * (h^-1.73)) Sorry for the layman questions, but I would like to try to "punch in" these numbers into my calculator so that I can see what you mean.

I could go into a whole lecture on this (I've taught curve fitting in a college course before). But I don't think you really want that much detail. So I'll give you the easy way. Type the data - height and ft-cd - into Excel. Plot it. Then add a trendline that appears like it fits the expected results and the data. Hint: a quadratic equation fits the data, but doesn't fit the expected results. The result is that only one of Excel's built in functions meets both criteria - the curve I gave you.

That doesn't mean the function is the true function, but it is decent enough for a simple extrapolation.

Note: I know very little about light and light intensity. But I think in this problem you don't need to know about it. As the light gets closer, the light hits a smaller area, and thus that area must be brighter.

 

[notfred]

Originally posted by: dullard

Originally posted by: RIGorous1
Wow! Thanks for help! However, I'm uncertain what you mean by "just fit the three points to a curve and extrapolate." what curve did you use? how did you get these numbers ((290 ft-cd) * (h^-1.73)) Sorry for the layman questions, but I would like to try to "punch in" these numbers into my calculator so that I can see what you mean.

I could go into a whole lecture on this (I've taught curve fitting in a college course before). But I don't think you really want that much detail. So I'll give you the easy way. Type the data - height and ft-cd - into Excel. Plot it. Then add a trendline that appears like it fits the expected results and the data. Hint: a quadratic equation fits the data, but doesn't fit the expected results. The result is that only one of Excel's built in functions meets both criteria - the curve I gave you.

That doesn't mean the function is the true function, but it is decent enough for a simple extrapolation.

Note: I know very little about light and light intensity. But I think in this problem you don't need to know about it. As the light gets closer, the light hits a smaller area, and thus that area must be brighter.

I'm sure you'll get one hell of an accurate trend line from three data points.

 

[dullard]

Originally posted by: notfred
I'm sure you'll get one hell of an accurate trend line from three data points.

For a simple problem, it is enough. That is why I also put in a fudge factor. And by the way, it is 4 data points. At a height of infinity, the maximum ft-cd should be zero. 😉 That is why a quadratic fit is a poor choice.

Of course my solution would be to just add another light if it is extremely critical to get to that value.

 

[Semidevil]

what is extrapolate?

 

[dullard]

Originally posted by: Semidevil
what is extrapolate?

Given this data:

[*]At x = 0, y = 0.00,
[*]at x = 1, y = 2.01,
[*]at x = 2, y = 4.00,
[*]at x = 3, y = 6.02,

What do you estimate will happen at x=4? A reasonable estimate would be y = 8. That estimate is called extrapolation. We don't know for certain that y = 8. But it is a good guess.