The shorter the parking-lot light poles, the fewer lights you need?! Wha?

Factual Questions
1

Our township is working on writing a dark-sky ordinance. There is an astronomer from the local community college working with the committee. I’m told that he claimed that if one uses shorter poles on which to mount parking-lot lights, then one actually needs to use fewer lights to accomplish the same amount of lighting.

I don’t understand this. Would he be talking about not using fully shielded lighting fixtures, and then utilizing the light spill to illuminate the lot more horizontally than from a more verticle direction? Wouldn’t that increase light tresspass and glare? Would it be like the spill light from figure 10 as opposed to maximizing the useful-light range as in figure 9?

I’m confused as to why lower lights would be better. Is there a trade-off between the upward reflection of light from the light coming from closer to vertical, and glare & light tresspass from bulbs that need more horizontal spread? The person who reported it to me made it sound like ceteris paribus, lower lights means fewer lights, and I just don’t understand that.

2

The best explanation I can think of (and a reasonably plausible one) is that with shorter poles, there would be less illumination of areas outside the parking lot, therefore you wouldn’t need as much overall power.
The basic idea being that lower poles cast smaller pools of light, therefore you can cover the lot more precisely with less wasted illumination of other areas.
This is not actually using fewer lights – the opposite in fact – but it is using less power because each light pole can be lower powered.

But there may be other reasons based on illumination angles, upwards versus sideways reflection, and things I am as of yet still ignorant on.

3

Take a flashlight in a dark room and hold it 5 feet away from the wall. Now move it to 2 feet away. Notice how much brighter it appears. Even though the light farther away covers more area (possibly even unwanted area), the light is much dimmer on the surface. By placing the lights on shorter poles you get more light on the ground where you want it, and don’t have to overlap as many lights to get the same amount of brightness.

4

Now I’m going to have to get a bunch of pen lights and conduct an experiment. The Great Parking Lot Experiment of 2004.

5

Local Man Found Dead in Wal-Mart Parking Lot

Area man js_africanus was found dead this morning by two early shoppers in the parking lot of the local Wal*Mart. The deceased had three dozen maglites in his backpack and appears to have died of massive blunt trauma injuries after tripping and having the flashlight-filled backpack fall on top of him.

Several acquaintances of the deceased have commented loudly about his connection to the mysterious cult known as Dopers. “This is just the kind of thing those crazy internet cultists have always been egging him on to do…the amateur science thingie…”

6

Yeah, but to get the same ratio in a parking lot you’d have to lower a 20’ light pole to 8’ - clearly not an option.

It seems to me that higher poles may use more lumens each, but due to light spread would require fewer poles. Shorter poles may require less lumens but more poles to light the same area. Figure 10 in your second link seems to argue against lowering the light source for that reason. Also, the more horizontal the lighting the more one has to contend with dark areas caused by shadows.

It doesn’t make sense to me unless you’re not getting the full story. Maybe he wants shorter poles equipped with softer, more diffused, hooded and/or better aimed bulbs?

7

It seems to me that the scattered light from the lower towers would be more likely to be absorbed by surrounding buildings, trees and the like. Scattered light from higher towers would be more likely to light up the sky. Take Fat Bald Guy’s* flashlight, shine it at the wall and look at how much light hits an adjacent wall at the corner.

The shields help block sideways light, but the light that hits the shields will still reflect as scattered light.
*No offense, but it is your user name.

8

…And yes, I did miss the entire point. Sorry, I just pulled an all-nighter.

9

I’m not sure how you missed the whole point. It seemed relevant.

Regardless, acknowledging that I’m a lazy bastard and too cheap to buy the materials for a first-rate experiment, let my try to explain what’s causing me so much trouble, and try to think out loud.

First, we’re concerned with the quantity of light going up into the air. If we hold constant the intensitiy of the bulbs and the level of shielding, then the angle and quantity of light hitting the ground should be constant, in total, regardless of the height of the pole. Is this correct?

Second, let’s imagine looking straight down on a surface. Suppose we pack the survace with basket balls so that they cover the surface maximally. There will be areas where the basket balls do not cover. If instead we use tennis balls, the amount of area not covered will be less, because the smaller balls pack more tightly. I don’t know the math behind this, so I don’t know if this is true; but it seems intuitively true. Is it correct?

Third, if point two is correct, then higher poles are analogous to the basketballs, and will require more overlap to light the areas not receiving enough light.

Fourth, it could then come down to a fun geometry problem that I should ask him to prove.

But that’s not what’s bothering me. What’s bothering me is that it was presented to me as a blanket statement. The fact is that the number of poles can’t be monotonically decreasing with pole height, because the logical conclusion is that we set the lights face down on the pavement for maximal coverage with minimal lights. Clearly that dog don’t hunt. So, there must be some sort of maximum, right?

Another thing that bothers me is his motivation. Astronomers like, I’ve discovered, the sodium bulbs that produce that uniform light that is so easy to filter out. But that light is particularly visible to the naked eye. So maybe from his perspective, he’s looking to set it up so that the number of photons going into the sky isn’t minimized, but instead to make them of such character that he can easily filter them out. But, this could be inimical to the desires of the average Dark-Sky Joe, who just wants to walk outside and see stars. He doesn’t have a handy filter to conveniently eliminate the light like the astronomer does.

I was hoping to get some collective knowledge from the group before I start asking questions. Any clues will be more than helpful.

10

This is not correct. Small balls will fill a region exactly as efficiently as large balls, provided that the region is large compared to the size of the balls. Two points here, however: First, you can fill a region more efficiently (arbitrarily efficiently, in fact) by using balls of a variety of different sizes (the small ones partially fill in the gaps between the larger ones). Secondly, how efficiently the space is filled might not actually be the issue for lighting a parking lot. If you have dark gaps a few meters across, that’s a problem, because a person of unsavory motivations could hid in such a gap. But if you scale everything down, you’ll have about the same area of gaps, in a larger number of smaller gaps, which a person couldn’t hide in.

On the topic of light pollution, no astronomer particularly likes any kind of light pollution. Most of us still like just gazing up with the naked eye, even if we don’t have time for it and it doesn’t pertain to our work. And even on a strictly professional level, you’d really rather not filter anything out. What if your filter’s band is a little bit wider than it needs to be? And what if you’re interested in looking at that very spectral line, from astronomical sources? Now, if you absolutely can’t get rid of light pollution, then yes, you’d prefer that it be easily filtered, but that’s a lesser of two evils.

11

Maybe the guy means lower poles combined with fixtures designed to direct all light downward, rather than the traditional globe that sends it everywhere.

For general information about light pollution issues, this might be helpful:

And this is their page of recommended light fixtures:
http://www.darksky.org/fixtures/fixtures.html

12

See?! That is interesting. Basically, if I’m covering one football field with pennies and another with dinner plates, then in the end both fields are about equivalently covered—percentage-wise. Is that correct? I would have never guessed that. Thanks!!

In this case we’re not dealing with pennies & dinner plates on a football field, however. It’s more like covering a cookie sheet with pennies vs. dinner plates.

However you make a good point. If we can specify a certain fixture that minimizes light spill, then couldn’t we have one big-ass light pole in the center of the lot and a few smaller ones scattered around the perimiter for best coverage? The lion’s share of the lot is covered by one light, and the rest can even be turned on and off to suit the situation.

It seems like you’re confirming my fear to some extent. The astronomer and the average slob have two different optimum condition, because the average slob doesn’t have to worry about the effect of light on the local community-college observatory.

In that regard, what I’m wondering is whether one type of light could be used to light a parking lot, but when it reflects (or difuses or whatever) into the sky, it is less visible to the naked eye, but more difficult filter. Is that a possiblity? That’s what went through my head when I read that the sodium bulbs are preferred since they’re highly visible but easy to filter. Does that imply that there are lights that will cause less pollution for the naked eye but be a bigger pain to filter?

13

Turns out I had actually spent some time there before I wrote the OP. Ironically, it wasn’t until I googled for “inverse square law” and light pole height (no quotes) this morning that I found their info sheet # 78.

14

I wouldn’t mind seeing more about this also. It seems obvious to me that filling a large volume with sand fills more of it than filling it with beach balls. Or did you mean that the space left is equivalent, compared to the size of the particle being used? I could see their being less send in some exact proporition to the ratio of beach ball to sand particle size.

15

muttrox – what Chronos was saying (correctly) was that, apart from what happens at the edges, you get the same amount of coverage with the same shape, no matter what the size of the shape is. In other words, 1 inch circles and one yard circles have the same proportion of covered and empty space.
Yes, the spaces between the one-yard manhole are larger, but there are a lot more spaces between the one-inch pennies, and it exactly balances out.

If you think about it, it makes sense. Arrange a bunch of pennies, close packed. Now take a picture of the pennie (so you can’t see the edges of the arrangement), and blow the picture up so the pennies are the size of manholes. The proportion of covered and uncovered space has to be the same before and after enlargement, right?
For a parking lot though, there is a difference, because the edges matter: Unless it’s a round lot, you’ll be able to cover the lot more exactly with small circles than with large ones.

But I still don’t know if there’s more going on than the simple geometric considerations.

16

I honestly didn’t believe this until I sketched it out and did the math. Cool!

17

Ironically, today at lunch I was thumbing through an old book and came across a problem similar to the Buffon needle problem (IIRC) that involved dropping grains of sand on a surface covered with uniform circles. Low and behold! The radius dropped out of the percentage coverage calculation. Funny coincidence.

I don’t know if my problem relies on simple geometry. Info sheet discusses spacing in terms of lighting fixtures and how fully they shield the light source. But nothing about height.

I broke down and emailed the guy. Waiting to hear back.

18

I’d be hesitant to make such a general statement, since it depends on the exact shape and size of the area and of the circles. Consider a square, with four circles fit into it as tight as possible. If we make the circles just a tiny bit larger, we’ll only have room for three, and our coverage will therefore decrease significantly. On the other hand, if I make the circles just a tiny bit smaller, there won’t be enough room for another one at first, so again, the coverage would decrease (since we have the same number of circles, but they’re smaller). But if I make the circles 2/3 of their original radius, then I’ll be able to fit nine circles in, and cover the square with exactly the same efficiency. Similarly, if I make the circles twice the original radius, only one will fit in the square, but again fill it the same amount as the original four. So here we have four cases, one where increasing the size decreased the coverage, one where decreasing the size decreased the coverage, and two where changing the size didn’t affect the coverage at all.

Not at all. The astronomer and the average slob (or at least, average stargazing slob) have the same optimum condition: No light pollution at all. And even for the average slob, narrow-band light is no worse than wide-band.

19

Now don’t go taking things out of context. People are going to use exterior lighting, so dreamily ignoring that constraint ain’t gonna fly with me. More importantly, however, is that any light going into the sky is equally bad for the average slob. It’s a fair question, I hope, since, for example, high-pressure sodium & metal halide lamps hit in different areas of the spectrum which then affects how we see depending on the light levels. But it sounds like they affect the observatory and the average slob the same way, so that’s the end of that concern.

Thanks!

BTW, whenever I read you screen name, I think of that Johnny Bravo episode with that really grumpy, hibernating bear.

20

The Figures 9 & 10 in your earlier cite are for spotlighting, not typical parking lot area lighting.

I went thru GE’s Roadway Lighting Instute workshop many years ago in Hendersonville, NC, where they make/made all their street and other types of lights, but haven’t used the date/info much since then and I was never really into it (lighting) in my work.

Try www.ge-lightingsystems.com.

It’s mainly product oriented but there are photometric data available.

I personally think your astronomer is thinking wishfully to minimize spillover competing with his targets.

High mast lighting is used at Interstate highway interchanges so that the entire interchange can be lit with very few poles.

Good luck.