Aimed Fire Issues (Perceived Target Height)

[rexford]

One aspect of aimed fire which places limits on successful targeting is the size of the perceived target on a gunsight.

At 100m range with a 2.5x magnification gunsight, a 2.2m target would appear to be 0.66 inches high, or 16.8mm.

Hold a ruler out 1 foot (30.5cm) infront of you and look at a height of 16.8mm or 0.66 inches. The target is fairly large and would allow for aimed fire.

So Wittmann was able to aim at T34 turret rings in his StuG IIIA and hit them, but the range was, and had to be, very close to raise the success probability to the point where the time taken aiming at and hitting T34's was less than the T34 reaction time.

At 1000m range, the perceived target height is one-tenth as high as the 100m case, 0.066 inches or 1.68mm for a 2.2m target. One is lucky if they can repeatedly place the crosshairs on the target center of mass at 1000m let alone aim at the center of the turret.

Perceived height at 12 inches (or 305mm) from the eyeball equals:

(actual height in meters x 12 inches (or 305mm) x gunsight magnification) divided by (range to target in meters).

At 100m, a 2.2m high target with 2.5 magnification would be 2.2m x 305mm x 2.5/100m, or 16.8mm in perceived height.

Having a 10x gunsight changes things for aimed fire at 1000m. 2.2m high target at 1000m appears to be 6.71mm high (0.26 inches) in 10x gunsight. A Jagdpanther with an educated and nerves-of-steel crew might be able to aim at the center of the IS-2 turret front if background contrast made the target stand out enough for aimed fire (which is another limit on high efficiency aimed fire, you have to be able to clearly make out the target outline).

Aimed fire ability at range is limited by gunsight magnification and other factors, which answers the question as to why 75mm and 88mm guns were needed when 37mm guns could aim at turret rings and land a hit or two given a large number of shots (or an incredibly short range). With the 75mm L70 gun a hit on the front of a T34 at 1000m is a kill most of the time and the perceived target is fairly small, with a 37mm gun aimed fire probabilities are ridiculously low at 1000m.

Perceived Height of 2.2m High Target with 2.5x Magnification Gunsight vs Range

25m, 67.1mm

50m range, 33.6mm

100m, 16.8mm

200m, 8.4mm

500m, 3.4mm

1000m, 1.7mm

1500m, 1.1mm

2000m, 0.84mm

3000m, 0.56mm

Takes good eyes and a steady hand to repeatedly aim at center of mass at 3000m,

let alone try to hit the gun mantlet center.

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To test the validity of the perceived height equation, measure the actual height of an object across the room, such as a 220mm high lampshade at 8.5' or 2.591m.

Hold a ruler 1' or 305mm away from your eyes and measure the perceived height, which is about 25mm (my hand shakes early in the morning so greater accuracy in reading the scale is not possible).

According to the equation, the perceived height at 305mm infront of the eye would be:

220mm x 305mm/2591mm, or 25.9mm.

Aiming at the center of the lamp or a specific point on it at 2.6m distance is possible, place the lamp at 1000m and things change radically even with 2.5x gunsights.

[Jussi Köhler]

Great post Rexford.

This was new information for me. Certainly puts things into perspective.

Jussi

[Jarmo]

Cool! I've been looking for a formula that'd tell the apparent sizes of objects far away. And it's simple one too. :cool:

[Bruno Weiss]

Oh man, I can do adds and takeaways, but them times and goesinta's are tough.

[rexford]

Originally posted by Jarmo:

Cool! I've been looking for a formula that'd tell the apparent sizes of objects far away. And it's simple one too. :cool:

I went outside with my 4x laser rangefinder binoculars and tested the theory.

A 30' high pole at 600' was found, which was measured at 15mm with a ruler held 305mm infront of my eyeball.

When the 4x binoculars were used and a ruler was used to measure the perceived height, the measurement was 60mm, while theory predicted 61mm.

[Lumbergh]

So, if I can follow up to your post, how does the amount of ambient light affect what you see through the gunsight? Does a higher-magnification gunsight require relatively more or less light to function?

Reeeally interestion post, thanks. Should be titled " Fun With Gunsights "

[SFJaykey]

One thing I think of when I read of "aiming at the turret rings," is that the turret ring is pretty close to the center of the target for most tanks....especially since the lower part of the hull and track will most likely be obscured by grass/whatever, even when not hull down. So I wonder: when German gunners cited this as their strategy for dealing with tough Soviet tanks, maybe they had tongues half in cheek. Or maybe they were saying, seriously, that they were just trying to aim quickly and fire first, and hit the darn things with as much AP as possible, and the historians and armchair tankers (like me) have taken the bit about the turret rings too literally.

MattT

[SFJaykey]

Lumbergh- I will jump in as optics is something I have some experience with.

Higher magnification in an optical system will dim the apparent image unless the objective lens (the lens pointed toward the target) is increased in size to compensate.

This is one reason why sizes of binoculars are usually described as "AxB". A is the magnification and B is the size of the objective lens, in mm, and by dividing B/A you can get a good idea of how bright the image will be: the image in 7x35s will be about as bright as that in 10x50s, and 10x25s will be much dimmer than 7x50s. (This assumes optical quality is constant, a _big_ assumption).

So, the designers of higher powered sights could increase the size of the objective in their system to maintain brightness. But, since that means a bigger window, which means a bigger chink in your front turret armor, designers may have compromised and settled for dimmer optics. Those with access to detailed specs on the gunsights in AFVs may be able to contribute here.

Dimmer views are more difficult to use for aiming. Another very important factor is image contrast, which is determined largely by optical quality. Poor optics should suffer a much greater handicap when shooting into the sun, or at backlit targets...I wonder if CMBB models this in the Dusk/Dawn environments?

- Matt

[Lumbergh]

Verrry interesting Matt, thanks for the post!