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Pistol sights

There are some things about handgun sights which I’ve never seen explained properly — that is to say, so that even someone without any gun experience can look at the explanation and check that it is correct, rather than having to take something on faith. Yet they do have reasonably simple explanations.

One of these is the dictum to always focus on the front sight. This is in regard to “iron sights”, the usual type, which most often feature a post as the front sight and a notch as the rear sight; you align the sights by putting the post in the middle of the notch, and put the target right in the middle of the post, as shown below (rear sight in gray, front in black, and the target is the red X):

The nominal sight picture

Or at least that’s the nominal sight picture. But of course really you can only focus at one distance, so at least two out of those three things have to be out of focus. Focusing on the middle one (the front sight) should yield the best overall results, and that’s always been a good enough explanation to satisfy me personally, but for expository purposes I’ll calculate exactly what this looks like.

To pick a reasonably representative set of numbers, let’s say the rear sight is 300mm away from your eye, the front sight is another 150mm away, and the target is 5 meters away. And say the front sight post is 3mm wide and the rest of the image is to scale. And suppose your eye pupil is opened to 4mm diameter. (That last number might be twice as large in the dimmest of light or half as large in bright light; and the blurriness from being out of focus scales in direct proportion to it. So if you’re shooting in full daylight, you might have only half as much blurriness as shown in the following images. But your enemies may not do you the courtesy of attacking in full daylight.)

If you focused on the target, the 4mm of pupil diameter yields almost the full 4mm of blurriness diameter for both the sights: 3.76mm at the rear and 3.64mm at the front. With this image, the 3mm width of the front sight is 37 pixels, so 3.64mm of blurring is 45 pixels’ worth. The rear sight is closer, so a pixel translates to fewer millimeters: one pixel equates not to 3/37 mm but to (3/37) * (300/450) mm. So its blurring diameter is 70 pixels.

Now, lots of graphics packages offer a “Gaussian blur” feature, but that’s not what we want here; it would look sort of vaguely correct, but really out-of-focus blur is not a convolution with a Gaussian, aka Gaussian blur; instead it’s a convolution with a sharply-defined circle. (To illustrate this, if you take a point source of light and focus it onto a wall with a magnifying glass, then move it a bit out of focus, what you’ll see is an evenly-illuminated circle, not a Gaussian pattern of illumination, which would be a “bell curve” with the highest intensity in the middle, fading to the outsides.)

Performing those convolutions (this time with the rear sight being fully black), we get this sight picture:

The sight picture if you focus on the target

So if you focus on the target, the sights are almost completely blurred out. Looking at the above picture, one might think it was still somewhat possible to aim using them, but a red X on a pure white background is close to the best possible scenario; practical scenarios involve much less contrast and more variation in the background.

Alternatively, if you focus on the rear sight, the front sight gets 2mm of blur (25 pixels), and the target gets 63mm (70 pixels), the result being:

The sight picture if you focus on the rear sight

This time it’s the target’s turn to get blurred out.

Now for the recommended focus on the front sight. This gives 1.3mm of blur on the rear sight (11 pixels), and 40mm (45 pixels) on the target:

The sight picture if you focus on the front sight

This is obviously the winner, though the target is still pretty blurry. Of course it’s still inferior to optical sights, where you focus on the target and the crosshairs or red dot are superimposed optically and in perfect focus. But optical sights small and robust enough to be mounted on a pistol slide are a recent development, and are costly; very few handguns have one mounted. Laser sights, which project a laser beam onto the target, offer the same freedom to focus on the target, plus the freedom to actually see the whole target rather than having it blocked by the view of your gun. They are cheaper and more widely used. But if it’s dark, the laser gives away your position; and if it’s bright daylight, the laser has a very limited useful range.

There is another advantage, too, of laser and optical sights, which I have not seen remarked on much, but which is huge. With iron sights, you have two things to align: the front sight with the rear sight, and the front sight with the target. With optical or laser sights, you have only one: the reticle with the target. This is not just half the difficulty; it is much less than half, since with iron sights both alignments have to be accomplished at the same time. Now, if you really were super-adept with iron sights, you might recognize that this sight picture:

The sight picture with both sights moved

and this one:

Second sight picture with both sights moved

actually represent shots that will land dead center on the target, since in both cases the error in front-sight to rear-sight alignment cancels out the error in front-sight to target alignment. But calculating this is not to be expected from anything like an ordinary handgun user — who, if he needs the accuracy, must correct both errors rather than calculating that they cancel.

But to return to the case of iron sights, which still are the only sort of sight mounted on probably upwards of 99% of the handguns in existence in the world, the fact that both alignments need to be performed doesn’t mean they are equally important. They aren’t: the front-sight to rear-sight alignment is more important than the front-sight to target alignment. For instance, with the above numbers for sight distances it is twice as important: a given angle of deviation from alignment between front and rear sights produces twice the error that as is produced by the same angle of deviation between front sight and the target. (“Angle”, here, refers to the angle as perceived by the eye, and “error” is the error in the angle of departure of the bullet.) How this comes about is shown in this diagram:

Sight error diagram

The factor of two in importance comes directly from the ratio of the distance from the eye to the rear sight to the distance from the rear sight to the front sight, which by the numbers I used is also a factor of two (300mm vs 150mm). Two is a reasonable ballpark number for a full-size pistol held with a normal two-handed hold by an average-size adult, but with a snubnose revolver it might be four or more. Or in the other direction, an unusual hold that brings a handgun close to the face can reduce the number.

Here’s what the factor of two looks like from behind the sights. This is the case of sights lined up but pointing in the wrong direction (impact point superimposed in yellow):

Impact point 1

and this is the unaligned sights case:

Impact point 2

I was told once by a proficient pistol shooter that he ignored where the front sight was on the target, and paid attention only to the alignment of the two sights relative to each other. Since he did in fact hit the target, and quite accurately too, he couldn’t have been entirely ignoring it; at the time, I filed his comment under “mysterious things people say”, but now I realize that what he was trying to get at was this difference in importance: the alignment of the front sight with the target was so much less important that he could relegate it to a background task in his brain and spend all his active concentration on the alignment of the two sights.

People also are referring to this difference in importance when they speak of the “sight radius” of a weapon (the distance between the two sights) and of a short sight radius making it hard to aim, but I don’t think I’ve ever seen anyone explain exactly why, or mention that when one does have to deal with a short sight radius, a partial remedy is to concentrate more attention on the alignment of the two sights.

So clearly this difference in importance is something that is known on some level, or at least used to be, though it is so seldom explained that I had to figure it out myself.


Files and hacksaws

Files and hacksaws were two tools that were around the house when I was a kid, and puzzled me quite a bit: I couldn’t figure out how anybody did much with them. Later I learned: the secret is in what was missing: the vise. The piece being filed or hacksawed should be clamped firmly in a heavy, solid vise which is bolted down tightly — or some other arrangement that is equally rigid. (If the workpiece is big and heavy enough, nothing is needed to hold it, but that’s uncommon.) Then you can apply the sort of force that is needed to remove metal fast, without the workpiece escaping or getting into a mutual dance of vibration with the cutting tool.

There are of course various fine points to using these tools, but the workholding arrangement is what makes the difference between usability and unusability. It is not out of place to have a vise that costs more than all one’s files and hacksaws put together and weighs ten times as much as them.

(This is one of those things that people with a mechanical background know so well that they couldn’t even imagine not knowing it; but that still leaves the other >95% of the population.)

Oh, and while vise manufacturers seem to love to make toothy vise jaws, for civilized work a flat-faced jaw is usually best; that way it’s holding the workpiece with clamping force, not by digging its teeth in and damaging the surface.


From slavery to COBOL

Recently Yale University renamed one of their “residential colleges” (dorms): it had previously been named after John C. Calhoun, and now is named after Admiral Grace Hopper. The administration explained that although they don’t intend to go around renaming everything to satisfy every politically correct complainer, this was a particularly egregious case: the original naming after Calhoun had been not because of any strong link to Yale, but to honor Calhoun’s career as a politician, notably his advocacy of slavery as a “positive good” and of white supremacy. The college had featured a stained glass window depicting happy slaves on a plantation, recently smashed in protest. The original naming was done in 1931, long after Calhoun’s death, long after the Civil War, and at a time when white supremacy was, in the terms of today’s social networks, “strongly trending”.

Today, of course, one thing that is “strongly trending” is advocacy of women in technology. But skepticism as to such trends should not stop one from honoring people who truly deserve it. And for all I know Hopper does: I have not made any real examination of her career, but the occasional things I have heard of her have been positive. Still, the particular grounds called out by the Yale administration for naming the college after her are problematic. They seem to center around her efforts in advocating “word-based computer languages”, of which COBOL is the prime example, and one which she was instrumental in.

COBOL today is almost as dead as slavery was in 1931; and just as the namers in 1931 seem not to have asked the descendants of slaves to weigh in on Calhoun, programmers seem not to have been asked what we think of COBOL. Personally, I never had to suffer through COBOL (it was before my time), but suffering was the word. For one thing, the language was quite verbose. A dominant language today is C++; the name of that language is not only its name but a statement you can write in it. The corresponding statement in COBOL is “ADD 1 TO COBOL GIVING COBOL”. Now, admittedly nonprogrammers likely will be able to guess what the latter statement means, whereas with the former statement you just have to know. But programmers do know, and we object to having to write mountains of text to convey what to us has become simple. To force us to do so isn’t humane, it is inhumane: it denies us one of the main human powers, that of learning and developing skills.

So while Yale has changed the name of the college, it is still named in honor of a failed effort to crush the human spirit.


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