Using a Stadiometer to Estimate Distance

Introduction
The most important factors in military long-distance marksmanship, after learning to load and fire a rifle, were aiming and judging distance.  If a soldier didn’t know how to use and adjust his sights he would never hit his target, but as or more importantly, if he didn’t know how to judge the distance to his target he wouldn’t be able to set his sights correctly no matter how well he understood the mechanics of doing so, and at any range past 200 yards he was very likely to miss no matter how perfect his sight picture.

Soldiers spent a great deal of time training in distance estimation using techniques based on the appearance of targets at various distances, but in this article we will discuss a tool used in period for estimating distance using trigonometric principles called, among other things, a “stadium range finder,” or a “stadiometer.”

Trajectory
 In order to shoot well it is necessary to understand what bullets do. The slow speed of black powder rifle bullets and their heavy weights produced large, rainbow-like trajectories. With modern firearms we expect nearly flat trajectories, but black powder weapons had much more extreme parabolas. This means it is necessary to understand the bullet’s path and to judge the distance well in order to make a good hit.

The line of fire is a straight line extending through the centre of the barrel, indefinitely produced.  The line of sight is a straight line passing through the middle of the notch of the rear-sight and the top of the front-sight. A ball describes a curved line in its flight, which line is called the trajectory. When fired from a gun, the ball crosses above the line of sight after going a certain distance,—according to the arm used,—it crosses below the line of sight: this point is called the point-blank. Suppose the point-blank of your carbine to be one hundred yards: to hit an object at that distance, aim at it; if the object is closer, aim below it; if farther off, aim above it. (Congdon 1864 pp. 34-35.)

Every weapon, and every load used with that weapon, will have a different trajectory, so it is important to understand the specific trajectory of one’s own rifle and ammunition in order to learn to use the weapon well.

Point Blank
The idea of the point blank is important for good black powder shooting but is often misunderstood today; people mistakenly think “point blank” means “so close you can’t miss.”  As Congdon said, the bullet trajectory crosses the line of sight twice, once when it first leaves the muzzle and a second time when it drops down to cross the line of sight again at a farther point, and it is this second point that is the point blank.

Thus, when using adjustable sights, every sight setting will have a different point blank; “by the use of the hausse or raised sight, the number of points-blank are increased” (Heth 1862 p. 18), so when using the rear sight with the back sight folded down the point blank of many mid-nineteenth-century rifles is 100 yards, but if the slider on the back sight is set for, for example, 500 yards, then the point blank is 500 yards (assuming the use of government ammunition—changing the bullet or load will throw this off).  Understanding the point blank when shooting modern rifles is less important because of their flat trajectories, but it is far more so when shooting black-powder firearms with their highly curved trajectories. 

The Dangerous Space
The dangerous space (called the “margin” in British sources) is the area from “first catch” to “first graze” at any particular sight setting.  First catch is the range at which a bullet fired at a given sight setting will hit a standing man at the top of his head, and first graze is the range at which that same bullet would hit a man on his foot.  Thus, the dangerous space is the range over which a bullet would hit an enemy somewhere from the top of his head to his foot when aiming at his waist (which is where soldiers were taught to aim) with the back sight set to the correct range.

At normal rifle ranges the trajectory will pass over an average soldier’s head for quite some distance (e.g., when shooting the Pattern 1853 Enfield the apex of the trajectory when shooting at 600 yards was more than 25 feet from the ground), so knowing the dangerous space is quite important.  With black powder rifles dangerous spaces start very wide, but at longer ranges the space shrinks dramatically because of the parabolic nature of the bullet trajectories.  As this demonstrates, the ability to estimate range is critical for achieving hits at longer ranges.

With the Enfield musket’s back sight set for 600 yards and the weapon fired at a target 565 yards away the target would be hit in the head, whereas if the target was at 600 yards he would be hit at the waist (the point blank), while if the target was at 635 yards he would be hit on the feet.  If the target was closer than 565 yards or if he was farther than 635 yards, he would not be hit at all.  Thus, if the back sight on a P-53 Enfield is set for 600 yards, a target would be hit somewhere from his head to his feet within a 70-yard space; this is the “dangerous space” for that sight setting with that weapon.  At 300 yards the dangerous space for the P-53 was 145 yards, but at 600 yards it shrank to a mere 70 yards, meaning that to have any chance of hitting an enemy at that range the soldier had to be able to estimate the range to within 70 yards (Walker 1864 p. 131).  This demonstrates how critical was the need to be able to judge distance accurately.

After Walker 1864 p. 131.

Using a Stadiometer
The stadiometer or “stadium rangefinder” is a device used for estimating distances based upon the principle of similar triangles. This means that, for a triangle with a given angle, the ratio of opposite side length to adjacent side length (tangent) is constant. Thus, if you know the height of an object you can estimate the range to that object because the ratio of its height to the distance at which it lies (which form the horizontal and vertical legs of a right triangle) will be a constant.

After Walker 1864 p. 147.

Several texts of the period give detailed instructions for using stadiometers, including Busk, Heth, and Walker, among others.  In general, few individual soldiers probably would have had them (although Heth suggested giving silver ones as prizes in company shooting contests), so they would more than likely have belonged primarily to officers.

To use a stadiometer, put the attached string in your mouth (or at the eye, or on the tip of the nose, depending upon the source) and extend the device to the fullest extent of the string.  Busk said the string should be 25 inches long (p. 97), but you actually need to calibrate it by checking a partner at a known distance.  Look through the opening to see the target and hold the unit so that the upper edge of the opening is at the top of the target’s head, then move the slide (on models that have one) up until it is at the target’s feet; if the device doesn’t have a slider, you just find where the target fits in the gap. The approximate distance to the target can then be read from the scale engraved on the side of the stadiometer.

An extremely crude representation of a stadiometer.  This should not be taken as accurate, nor to scale, and is only intended to show how to use such devices.  Look through the opening and move the slider (when available, not all had them) until it just contains the target figure and read the range in yards from the sale.  In this case, the range is 100 yards.

After Walker 1864 p. 148.

Note that most original devices had two scales, one for infantry and one for cavalry. They were calibrated to assume that infantrymen are six feet in height while mounted cavalrymen are eight feet. Naturally, in real life the target may be taller or shorter than exactly this height, so this is only an approximation.

This example was taken from Busk (p. 97) and represents a fairly crude device which simply has a triangle cut into the plate with a scale engraved on it.

After Busk 1860 p. 97.

The next device is also pictured in Busk and shows a more sophisticated device with a slider for getting a more precise estimate.  It was manufactured by Holtzappfel & Co. in London and was also sold to the Frankford Arsenal in the U. S. for use in our Civil War (Huggett 2023 p. 163).

Drawing after Busk 1860 p. 97.

Photograph courtesy Jon Huggett; used by permission.

This next unit was manufactured by Geo. W. Simmons & Bro. of Philadelphia, PA. and is very similar to the drawing below it from Heth.

After Heth 1862 pl. 7.

The final device was made by Chadburn & Co., an optical maker in Liverpool, England and was patented in 1860.  It is different in having cut outs for each range and not having a slider.  Note that it has two holes; a right-handed person would put the string into the hole on the right, and vice-versa.

After Huggett 2023 p. 162; used by permission of the author.

Modern Reproductions
Stadiometers were ingenious tools, and we are very fortunate to have several good reproductions available today that shooters can experiment with in order to get a better feel for historical shooting.  There are three modern reproductions of which I am aware, although period texts showed more designs than this.

My Holztapffel-style stadiometer (see below) is a crude copy of the style shown in Busk and others sold by Cash Manufacturing (q.v.), but this one does not include a scale for cavalry.

The next reproduction is a copy of the style used during the Civil War as pictured by Heth and was purchased from Capandball.com (q.v.).  The chain and toggle was intended for attaching to the user’s button hole for carrying.

Finally, my Chadburn-style stadiometer is a faithful copy of the original shown above and was manufactured by Jon Huggett (q.v.).

Works Cited
Busk, Hans. Hand-Book for Hythe: Comprising a Familiar Explanation of the Laws of Projectiles, and an Introduction to the System of Musketry, now Adopted by all Military Powers. London: Routledge, Warne, and Routledge, 1860.

Congdon, James A. Congdon’s Cavalry Compendium. Philadelphia: J. B. Lippincott and Co., 1864.

Heth, Henry. A System of Target Practice for the Use of Troops When Armed with the Musket, Rifle-Musket, Rifle, or Carbine. New York: D. Van Norstrand, 1862.

Huggett, Jon.  Knowing The Enfield – Pattern 1853 to 1865. Volume 1.  United Kingdom, Privately Published, 2023.

Walker, Arthur. The Rifle; its Theory and Practice. Westminster: J. B. Nichols and Sons, 1864.

Sources
Ted Cash Mfg.: www.tdcmfg.com/product-page/range-finder

Capandball.com: www.etsy.com/listing/815854052/us-arsenal-stadia-19th-century-range

John Huggett stadiometer: www.curiouscasper.co.uk/product/chadburns-rifle-distance-gauge/

Judging Accuracy: Analyzing Shot Groups (Take 2!)

Introduction
Shooters often talk only about their group size when discussing the accuracy of a group of shots, but group size is a relatively unimportant factor for understanding accuracy.  I have written about this subject previously but have heard from several people vociferously insisting that “group size is king,” and nothing else matters, so this article is intended to try to help folks like that understand.  I jokingly entitled my last article on this subject “No One Cares About Your Group Size,” and I’ll admit that was somewhat unfair (as I tried to make plain in the article) and only intended as a humorous way of making my point, but hopefully this article will make things clearer.  Group size isn’t entirely valueless—in general, a small group is, of course, better than a large one—but it would be more fair to say that group size is the least important gauge of accuracy because it fails to take into account two more important factors:  Mean Radial Deviation and the distance from the Mean Point of Impact to the Intended Mean Point of Impact, so let’s explore those two factors.

Mean Radial Deviation
Consider a group in which almost all of the hits are packed closely together with one flyer, and another group of the same overall size but in which the hits are much more widely spaced out: how tightly the hits are grouped in general is more telling than the mere overall size of the group.  We term this a question of the precision of the group, and it is measured by “mean radial deviation,” i.e., how far the shots average from the center of the group.  Look at groups X and Y below; here we see that Group X is obviously a better group because almost all the hits are packed tightly together, with just one flyer, and yet it has precisely the same group size as does Group Y.  Obviously, just knowing the group size does not tell us anything about the important difference between these two groups.

NB:  Precision, taken by itself, is a measure of the weapon and the load being used, not the shooter, and is usually tested from a rest to take the shooter out of the equation as much as possible, but it is also, when taken in context, an overall part of judging accuracy, or how well the shooter does with that specific weapon and load.

MPI vs. IMPI
In the target diagram below we see two groups of shots, A and B, each with five hits, numbered 1 to 5.  The small black circles indicate bullet hits, the red circles indicate the center of the group or its Mean Point of Impact (MPI), and the large black circle with the red cross indicates the bullseye, with the cross showing the exact center point (known as the Intended Mean Point of Impact, or IMPI).  The black lines show the distance of each hit from the IMPI, the red lines show the distance from the MPI’s to the IMPI, and the dashed rectangles show the group size of each group.  Note that Groups A and B are literally identical in all ways except one: Group B is farther from the bullseye than is Group A, with the distance from MPIa to the IMPI being 1.77 in. and the distance from MPIb to the IMPI being 2.72 in.

Looking at this comparison, we see that the group size of both groups is the identical, as is the mean radial deviation—again, the groups are identical.  The difference is that Group A is much closer to the bullseye, 0.95 inches closer, meaning it’s a better group, and the group size is not as important.  Someone pointed out that me that this is meaningless, all you need to know is the group size and then for the next group you just aim off to make up for the difference.  Unfortunately, that approach doesn't say anything about this group of shots.  If you were aiming at a deer’s heart and sent five bullets six inches over its withers but the group size of those five shots was only one square inch, that’s still five misses despite the excellent grouping—how close the MPI is to the IMPI obviously matters, and Group A is obviously better than Group B.

Conclusion
Ultimately, what matters is hitting the thing you’re trying to hit.  Look at the third diagram below.  Here we see two groups, Black and Red.  Group Red is obviously superb, and no measurement is needed to see how tight it is, it is obviously much better than Group Black in terms of group size.  But despite that, Group Black is still a better group because four of the five shots all hit the heart, the thing the shooter was trying to hit.

As this explanation should make obvious, to judge accuracy we need to examine two things:  How closely packed together the shots are in a given group relative to the center if that group (which is different from the group size), and how close the group is to what the shooter was actually trying to hit, with the latter being far more important, as the heart diagram should make plain.  Group size isn’t meaningless, but it runs a poor, weak third, and can actually be ignored for all practical purposes.

For those thinking that even if all this is true, figuring it all out is too complicated and it’s easier to just measure the group size, fear not, there is a simple, powerful tool that will do all of this very clearly and simply:  The String Test.  I have written about this at length, and even posted a video about it, so I won’t go over it again here except to say that all you have to do is measure the distance from the center of each hit to the IMPI and divide that total by the number of shots and the result will give you the important figure, since it takes both the mean radial deviation and the distance from the MPI to the IMPI into account in one simple number—that’s what the red line in the diagram above really is.  To learn more about this historically authentic method of calculating the String Test, read the article I have posted here:  https://historicalshooting.blogspot.com/2020/12/the-string-test-measure-for-historical.html