Schneier on Security

Roger • August 3, 2005 9:07 PM

@Dave:
Minor nitpick, but inverse square law means you quadruple the power to double the range (i.e., square the ratios); squaring the power to double the range would be an exponential law. But your example calculation was correct.

@ECMpuke:
“an antenna with 30 dB gain has a beamwidth so narrow that pointing it becomes a serious problem”

Well, certainly the higher the gain, the more accurately it must be pointed, but 30 dB isn’t really in the realm of a “serious” problem. The “half power beamwidth” of a 30 dB antenna of typical type, is about 5 degrees, or about a 50 cm spot on the other side of a 6 metre room. Most people can point more accurately than that by hand, and with any sort of tripod mount it’s trivial. It’s more difficult (especially in elevation) if you can’t see the exact location of the target, but we’re still only talking a few minutes of fiddling about.

Roger • August 11, 2005 4:28 AM

(For those who don’t know, the steradian is the unit of solid angle. It’s defined as the area outlined by projecting the solid angle onto the surface of a unit sphere, or equivalently, the area projected onto any sphere, divided by the square of the sphere’s radius. Thus, a full sphere is 4 pi steradians. It is abbreviated sr, or more often msr for millisteradian because a whole sr is quite a lot.)

@ECMPuke:
“You do the pointing”.

I have. We often use 35 dBi antennae at work, and pointing just isn’t as hard as you seem to think. Even a 40 dBi is (just barely) doable by hand.

“One millisteradian is a lot less than one.”

I don’t think you finished this sentence, but in any case I’d point out that you only need 12.6 msr (4 pi sr in a sphere, divided by 1000). 12.6 msr is the solid angle subtended by a 3 inch circle at 2 feet, i.e. a baseball held at arms length. It is not a particularly fine angle. (Actually, because the beam doesn’t have a sharp cutoff, we normally work with the half power beamwidth — I’m sure you know that, just for other readers — which is a bit more restrictive; it calculates to about 6 msr in this case.)

“It’s like searching the world through a soda straw. Try it some time. It’s far from trivial.”

Well no, it isn’t like searching through a soda straw. The analogy is wrong two ways, first because in “bluesniping” type applications most of the time you would be “searching” with the Mk I eyeball and only using the 30 dB beam for “target acquistion”. That’s more like pointing the straw at something and then seeing if you can see the target through the straw, a task which in fact is trivial (try it).

Secondly a straw is much tighter than what is required here. A typical soda straw (about 8 in by 0.2 in) gives a solid angle of 0.45 msr. That’s an order of magnitude tighter than this requirement. To get a 12.6 msr (30 dB) beam, an 8 in straw would need a diameter of an inch.

Having said that, to “keep myself honest”, I did just try some “searching the world through a soda straw” (the same one). Forming a fist around the straw so I couldn’t peek around it, I spun myself around on my chair with my eyes closed, opened one eye to look through the straw, then timed myself to find a certain spot of light on the wall (a spot much smaller than 12 msr). By nodding the straw up and down while slowly rotating, I found it in 11 seconds. Not quite trivial, but not very challenging, either. (Yes, it helps quite a bit that I knew it was roughly in the horizontal plane, but that’s usually the case for non-aerial targets.)

“By the way…that 30-dB aperture at 2.4 GHz is bigger than a Pringles can. It would take a dish about 4 feet in diameter, in fact.”

Ah, good point, well made. Nasty unwieldy 12 cm waves 8^) (We mainly use Ku band at work!)

“You might find the tripod to hold it a little unwieldy.”

Well, if we only want good gain and don’t care about suppressing sidelobes, you can go with a grid parabola. By no means hand held but practicable to tripod mount; the lightest commercially available 24 dBi one that I have seen was 2 kg, presumably a 30 dBi one would be about 8 kg.