Estimating Range With Gun Sight Triangles: Home Experiments

[rexford]

British trials during WW II showed that the average crew was capable of estimating range to a target tank with an average error of about 20%, when only the eyes were used. The distribution was bell shaped with a standard deviation of 25%.

To see whether those German gun sight triangles would improve things and to examine the ins and outs of the triangles, two trials were conducted.

The trials consisted of placing a scale model T34 M42 on the rug and estimating the range in meters using a homemade gun sight.

The gun sight actually had no magnification, but 2.5x and 5.0x magnification was modeled by increasing the size of the triangles and multiplying the actual scale range of the model by the appropriate multiplier (if the scale range to a perceived target was 300m using the straight model scale, it would represent 750m with a 2.5x gun sight).

65 trials were conducted with the 2.5x gun sight model, and 60 with the 5x sight, and both tests resulted in an average range estimation error of 10% from 350m to 1000m (bell shaped curve, standard deviation of about 12.5%).

The 5x magnification sight trials resulted in faster range estimation, due to a larger target size, clearer target image and larger triangles.

It is also likely that the 5x gun sight would retain a low average error to a longer range than the 2.5x sight, since an important aspect of the tests was a visual distinction between the front and side armor when both were in view, which would be evident longer with the 5x sight.

Various precautions were taken to assure that the person with the sight had as little knowledge about the new T34 placement as possible and relied totally on the sight triangles for the estimate.

Going by the triangle trials, which represent one case (target in open terrain), the Germans would have approximately halved the first shot average range estimation error of the British through use of the gun sight triangles.

The abovementioned trials were run in an empty house, and to see how commotion and an unfamiliar and uncomfortable setting impacted triangle estimate the model tank and tape measure were brought to the gym downstairs.

The average error from the mean for the busy gym was similar to the quiet house case (about 12.5%), but the center of the gym curve resulted in the most likely shots being 10% long at the center of the curve, while the quiet house curve was centered about the actual target range.

The noise, unfamiliarity and stress of the gym setting through off the accuracy, which suggests that crew experience and calmness would be important.

Note on using Triangles to Estimate Range:

The triangle at the center of the sight is 4 mils wide and 4 mils high, and a T34 M42 at 1000m has a 3 mil front hull width, 2 mil height and 6 mil hull length for estimating purposes (3 mils cuts a distance of 3m at 1000m).

If the T34 front hull width is measured at about 4 mils using the triangles, the estimated distance equals 1000m x (3 mils/4 mils) or 750m.

A 3 mil measurement for the height would result in an estimated range of 1000m x 2 mils/3 mils or about 650m.

[rexford]

For comparison purposes, it is useful to compare how much a 100m range estimate error misses the intended target mark by (center of mass aiming was followed by the Americans and British):

TRAJECTORY HEIGHT ABOVE AIM POINT FOR A 100m RANGE ESTIMATION ERROR

500m

====

75L40, 0.73m

75L48, 0.50m

50L60, 0.46m

88L56, 0.45m

75L70, 0.32m

88L71, 0.27m

1000m

=====

75L40, 1.63m

75L48, 1.11m

50L60, 1.13m

88L56, 0.97m

75L70, 0.72m

88L71, 0.57m

2000m

=====

75L40, 3.99m

75L48, 2.72m

50L60, 3.16m

88L56, 2.27m

75L70, 1.75m

88L71, 1.31m

3000m

=====

75L40, 7.11m

75L48, 4.84m

50L60, 6.00m

88L56, 3.93m

75L70, 3.12m

88L71, 2.22m

All rounds are APCBC except for 50L60 which is firing the APC round with a poor ballistic shape (high drag resistance and light weight combine for relatively rapid velocity drop-off with range).

For preliminary estimate purposes, the trajectory distance from the aim point is proportional to the 100m figures presented above times the actual range estimation error divided by 100m. Double the listed error for a 200m error in range setting, half for a 50m error.

A +10% range estimation error results in the following trajectory error with regard to the aim point for the 75L70 gun:

0.16m high at 500m

0.72m high at 1000m

3.50m high at 2000m

9.36m high at 3000m

A +20% range estimation error results in the following trajectory error with regard to the aim point for the 75L70 gun:

0.32m high at 500m

1.44m high at 1000m

7.00m high at 2000m

18.7m high at 3000m

Random dispersion or scatter would be added or subtracted from the average trajectory placement noted above.

While the Germans initially aimed the gun at the target bottom they added an adjustment to the initial range estimate to bring the ideal shot placement near the center of the target height.

[ September 01, 2004, 03:52 PM: Message edited by: rexford ]

[flamingknives]

Classic! I've now got a mental image of a grog sighting down a toilet roll at a toy tank in the middle of a gym.

The lengths people go to for their hobby!

[flamingknives]

Incidently, have you tried ranging said toy eyes only? It might be that you're above average at guessing range.

[Mr. Tittles]

Yeah and stop playing with these F_Knives and go do your homework.

[Mr. Tittles]

The noise, unfamiliarity and stress of the gym setting through off the accuracy, which suggests that crew experience and calmness would be important.

But the crew would be under this even during training. Being in a AFV is such a noisy uncomfortable thing that it is the norm. You are secluded from the world (gunner anyway) by the walls of the armor. You are much better off than a PAK40 gunner who would be subjected to the atmospheric disturbances of HE and supersonic bullets as well as clods of dirt raining down/dust/etc.

You also want to survive and the adrenalized intensity of concentration IS focused through the sight. Its a unique isolation by noise and headphones (your only source of information in a noise storm). Hits on the external armor might not even be percieved unless close to your station.

An AFV like a tank is very unique in the level of control by a commander (TC) that takes place. They are level to his morale in most cases. The concentration of training, firepower, will, effort and ability is such a close mesh that they are truly a team in effort.

For the gunner, seeing an enemy directly target his vehicle has to be the greatest shock. Especially when you know your own armor is inferior.

[ September 01, 2004, 05:13 PM: Message edited by: Mr. Tittles ]

[c3k]

Rexford,

Well done. I've been repeatedly opining that SIGHTS are more important than OPTICS. The well designed German sights would help their accuracy when compared to the somewhat crude Allied designs. Your experiment bears that out. Thanks for the devotion. By the way, how many dumb-bells were "accidentally" dropped your way?

Ken

[Mr. Tittles]

Sights are Optics. German sights were excellent optics at that. his test bears out the value of a triangle with precision being built into the optics.

Having excellent optical qualities only enhances the ability to read the 'triangle'.

[ September 01, 2004, 07:02 PM: Message edited by: Mr. Tittles ]

[Alkiviadis]

Well done rexford

[Tero]

Interesting.

Now, when can we see these test results put to practise using a BB-gun on 1/35 scale models ?

[rexford]

Additional stats for British, American and German ammo trajectory errors per 100m range estimation variation:

500m

====

17 pdr APCBC, 0.35m

2 pdr AP, 0.54m

2 pdr APCBC, 0.42m

6 pdr APCBC, 0.46m (2600 fps muzzle velocity)

6 pdr APCBC, 0.41m (2725 fps muzzle velocity)

U.S. 76mm APCBC, 0.45m

U.S. 76mm HVAP, 0.27m

U.S. 37mm APCBC, 0.37m

German 50L42 APC, 0.68m

German 75L46 APCBC, 0.45m

1000m

====

17 pdr APCBC, 0.75m

2 pdr AP, 1.39m

2 pdr APCBC, 0.96m

6 pdr APCBC, 1.03m (2600 fps muzzle velocity)

6 pdr APCBC, 0.94m (2725 fps muzzle velocity)

U.S. 76mm APCBC, 1.00m

U.S. 76mm HVAP, 0.63m

U.S. 37mm APCBC, 0.85m

German 50L42 APC, 1.68m

German 75L46 APCBC, 1.00m

2000m

=====

17 pdr APCBC, 1.75m

2 pdr AP, 4.01m

2 pdr APCBC, 2.42m

6 pdr APCBC, 2.58m (2600 fps muzzle velocity)

6 pdr APCBC, 2.35 (2725 fps muzzle velocity)

U.S. 76mm APCBC, 2.44m

U.S. 76mm HVAP, 1.61m

U.S. 37mm APCBC, 2.19m

German 50L42 APC, 4.69m

German 75L46 APCBC, 2.44m

3000m

=====

17 pdr APCBC, 3.01m

2 pdr AP, 7.59m

2 pdr APCBC, 4.39m

6 pdr APCBC, 4.68m (2600 fps muzzle velocity)

6 pdr APCBC, 4.25 (2725 fps muzzle velocity)

U.S. 76mm APCBC, 4.34m

U.S. 76mm HVAP, 2.97m

U.S. 37mm APCBC, 4.00m

German 50L42 APC, 8.91m

German 75L46 APCBC, 4.34m

The interesting aspect of the trajectory displacement per 100m range estimation error is that the U.S. 37mm APCBC is more accurate than the Tiger 88L56 to almost 3000m, and U.S. 76mm HVAP is a better round in terms of trajectory accuracy than every round except 88L71 APCBC.

The vertical trajectory displacement per 100m range error is only one piece of the overall accuracy puzzle, and would be supplemented by wind effects (lighter rounds are more impacted), trunnion cant, lateral jump and random dispersion. Just plain bad shooting would also play a part, although the projectile characteristics might play a minor role in how bad the shot ended up being.

The trajectory displacement for a given range estimation error approximately equals:

4.936 x (flight time to target x flight time to aim range - (flight time to target squared))

The flatter the trajectory the less flight time to the target (gravity does not pull the round down as much), and the less variation from the aim point for a given gun setting error. Even though 76mm HVAP loses a higher percentage of its initial velocity at all ranges than 76mm APCBC, the high velocity of the HVAP results in a flatter, lower trajectory.

[ September 02, 2004, 05:17 AM: Message edited by: rexford ]

[rexford]

The trajectory displacements per 100m gun setting error suggest that hits might be rare at many ranges, since a 100m error may result in an aim error of more than 1.20m. Hits will still occur with very large aim errors due to two factors:

A. random dispersion, which adds to or subtracts from the mean trajectory to cause high and low diversions from the average flight path

B. the bell shaped nature of the range estimation curve

Looking at the range error distribution, a 20% average range estimation error is a bell shaped distribution that varies from the maximum individual probability at 0% error, with 68.3% of the errors within 125% of the average (+/- 25%) and a few at 50% or more.

The following factors convert the average range estimation error to a random distribution if one rolls a 20 sided dice (1-20):

A. range error = range x average error x 1.25 x dice roll factor

Roll/Dice Roll Factor

01/0.03*

02/0.09

03/0.16

04/0.21

05/0.28

06/0.34

07/0.42

08/0.49

09/0.56

10/0.64

11/0.72

12/0.80

13/0.89

14/0.98

15/1.09

16/1.22

17/1.36

18/1.54

19/1.79

20/2.22

Note: *- suggested that a small percentage of these scores be associated with 0% error, 0.2 to 0.33 might be reasonable.

For the Tiger 88L56 APCBC at 1000m, the trajectory displacement from the aim point is 0.97m per 100m gun setting error. If one is firing on a 1.2m high target, this allows for a maximum range error of 1.2m x 100m/0.97m or 124m to place the average trajectory on the target vertical height (aim at center).

Using the above dice roll factor table, if the Tiger crew averages a 10% (0.10) range estimation error the "range x average error x 1.25 x dice roll factor" must be 124m or less:

124m = 1000m x 0.10 x 1.25 x dice roll factor, resulting in a factor of 0.99 or less to place the average trajectory on the target. According to the above table, a roll of 1-14 would be successful (70% probability).

If the average range estimation error was 20%, the equation would be 124m = 1000m x 0.20 x 1.25 x dice roll factor, and the dice score range for a success would be 1-8 (40% success).

The 1000m vertical success rate against a 2m tall target with a 1200m range estimate would be 30% (roll 1-6), which only applies to having the average trajectory cross the vertical height of the target at 1000m.

Due to random dispersion, the final hit percentage would be less due to up and down variations from the average trajectory and left and right misses. The overall hit probability would also be lowered by nervous and unpredictable errors by the gunner, who might have the gun aimed far in error and still fire, hitting nothing but air even at close ranges.

[ September 02, 2004, 06:14 AM: Message edited by: rexford ]

[rexford]

Originally posted by flamingknives:

Incidently, have you tried ranging said toy eyes only? It might be that you're above average at guessing range.

Good question. Previous studies showed that my guessing ability is about average.

We've done similar experiments tossing pennies and trying to guess the range, looking at cars or trees at some distance on the street and guessing range, and the average range estimation error was 20% to 25% using the eyes alone. We compared our estimated ranges to measured distances using a yard stick or tape measure where possible, or used a laser range finder.

Having a 4 mil triangle to compare the perceived height or width of a T34 against is a great aid.

[rexford]

Originally posted by Mr. Tittles:

Sights are Optics. German sights were excellent optics at that. his test bears out the value of a triangle with precision being built into the optics.

Having excellent optical qualities only enhances the ability to read the 'triangle'.

Well said. German sights had superior light gathering ability and clarity, and when that is added to the triangles one gets a very good sighting system.

[rexford]

Originally posted by flamingknives:

Classic! I've now got a mental image of a grog sighting down a toilet roll at a toy tank in the middle of a gym.

The lengths people go to for their hobby!

The sight was slightly longer than a toilet roll, being 12" long. The treadmill folks did not like my constant walking between them to take measurements and adjust the T34 position on the floor.

The T34 was not just pointing at the sighter, it was placed at angles from straight-on to a pure side view and everything in between.

One thing, I forgot to wear my long pants and skinned my knees crawling on the harsh rug trying to estimate range from the T34 height (get down as low as possible for that estimate).

Got same general results whether range was estimated using the height, width or length.

One thing that stuck out was that a tank at 1000m with 5x magnification looks the same as a tank at 200m with naked eye sighting. It is possible to clearly make out the front and side aspects at 200m with unaided vision, which is an important requirement when one is basing the triangle measurement on the front view and quite a bit of the side armor is visible.

The wheels and shadows give away the side aspect.

With 2.5x magnification, a 1000m target is the same as a 400m target with unaided eyes, which still allows for a somewhat clear division of front and side armor. I peered out my window at home looking at the Macy's ring road, which is 400m way, and tried to estimate range to the UPS trucks with a ruler with mils markings drawn on it for 2.5x magnification.

Not easy, but possible.

[ September 02, 2004, 04:59 AM: Message edited by: rexford ]

[rexford]

Originally posted by Mr. Tittles:

Yeah and stop playing with these F_Knives and go do your homework.

How does one add a drawing or scanned page to their posts?

One other problem at the gym was the neanderthals who kept walking on the 25' long tape measure. They must have been working through the pain and entered the numb zone.

[flamingknives]

On the full reply form there is an 'Image' button in the instant UBB. It give a dialogue box into which you put the web address of the picture. It produces this:

{IMG}web address{/IMG} replace the squirly brackets '{}' with square ones '[]'.

[flamingknives]

Originally posted by Mr. Tittles:

[image snipped]

Yeah and stop playing with these F_Knives and go do your homework.

Hey, you're just jealous that I can do that, make a website to put the picture on and still do my homework.

Anyway, I start proper work in a couple of weeks.

[FM Paul Heinrik]

I don't really remember much from my econometric studies, but isn't a standard deviation above 2-3% basically, means that the data sample is too small or that what is being hypothesised needs to be redefined. 20%+ is a huge standard deviation.

Also, range estimation is an aquired skill, are the tests preformed using controlled testing or AARs? The more you estimate range the better you get at it, ask any hunter. In Vietnam there were reports of VC mortar crews consistantly hitting targets on their 1st shots (now they might have been infiltrating and pre-marking targets, I don't know).

Regardless, I highly enjoy reading all the gronard info from Rexford.

[Mr. Tittles]

One thing that isnt modeled is atmospheric effects like dust, smoke, mist, heat shimmer that might throw off the triangle method.

[Mr. Tittles]

My question would be..Who has a superior method of guaging range..The gunner with a monosight w/triangles or a TC with binoculars with reticles? The TC has a stereoscopic enhancement typically with binoculars. This increases his depth perception. Did German binoculars have some sort of triangle built in?

I was thinking of a range measuring aid the other day. Imagine a flat stick, like a ruler, that has a sliding device that can run its length. The sliding device has a small clear square with a outline of a tank engraved in the clear material. You sight a tank in the distance. You then put the end of the stick against your face under you eye. You then slide the tank outline till it overlaps the distant tank (you are lining up your eye, the tank outline and the target tank). The stick has ticks on it that designate range.

Could accuracy be read to 100m or less? I would want something that could get ranges between 300m and perhaps 1000m. Basically for ATGs in fixed positions.

[ September 02, 2004, 09:15 AM: Message edited by: Mr. Tittles ]

[c3k]

Okay, a digression on OPTICS vs. SIGHTS.

Mr. Tittles is taking me to task on a pedantic definition of the two terms. As the terms have been used on this forum, OPTICS usually refers to the quality of manufacture of the glassware. SIGHTS refers to the actual reticle and how the optical device is attached to the weapon and used.

So, Mr. Tittles, if a magnification tube is attached to a large bore gun, exactly parallel to the barrel, and it has magnificent light gathering, magnification, field of view, etc., characteristics, but has absolutely no aiming device on it, is it a good SIGHT? Or does it represent fine OPTICS?

How about a device with an illuminated aim-point, manufactured such that the round will ALWAYS impact on the aim-point, regardless of range, motion or obscuration. (TOW missle aiming system.) Unfortunately, the OPTICS aren't very good. Low magnification, cloudy lens, etc.

Obviously these are extreme examples. The quality of production of the mirrors and glassware and the associated gears, bevels and rings can, and are, called OPTICS.

The design and manufacture of the aiming part (reticles, etc.) can be called SIGHTS.

Combine high quality OPTICS with well designed SIGHTS and you have a winning combination.

If you refuse to see the difference betwixt the two terms, that's your decision.

Ken

[rexford]

Originally posted by FM Paul Heinrik:

I don't really remember much from my econometric studies, but isn't a standard deviation above 2-3% basically, means that the data sample is too small or that what is being hypothesised needs to be redefined. 20%+ is a huge standard deviation.

Also, range estimation is an aquired skill, are the tests preformed using controlled testing or AARs? The more you estimate range the better you get at it, ask any hunter. In Vietnam there were reports of VC mortar crews consistantly hitting targets on their 1st shots (now they might have been infiltrating and pre-marking targets, I don't know).

Regardless, I highly enjoy reading all the gronard info from Rexford.

The curve which resulted from the 60 and 65 trial data formed a nice bell shaped normal distribution curve, and the standard deviation was around 12.5%. The data was input as percent error.

Normal distribution curves are defined by the mid-point (0% error in our case) and the standard deviation (12.5%), while range estimation by naked eye has the same mid-point but a 25% standard deviation.

The standard deviation does not indicate correlation or the niceness of fit in this case, it just defines how the curve spreads out away from the mid-point.

[Mr. Tittles]

Originally posted by c3k:

So, Mr. Tittles, if a magnification tube is attached to a large bore gun, exactly parallel to the barrel, and it has magnificent light gathering, magnification, field of view, etc., characteristics, but has absolutely no aiming device on it, is it a good SIGHT? Or does it represent fine OPTICS?

What is being discussed is actually a rangefinder. It is not a sight. But something altogether different. Its function, as rexford agrees, is highly dependant on having good optics also. The clarity, magnification, etc. all being part of its proper function. And Germany had some decent optics AND sights AND a built in range finder feature to boot.

[c3k]

Mr. Tittles, thank you. I enjoy keeping the tone of these things civil. At most, this would be a mild disagreement on terms.

I certainly don't want to hijack this thread which Rexford has started. His information is too highly regarded to be casually dismissed.

You have re-focused the discussion on the RANGEFINDER. I agree that all three (SIGHTS, OPTICS , and RANGEFINDERS) are often closely interrelated. The better each of them are, the higher a chance of a hit.

The German use of sighting triangles ( a RANGEFINDING device) is a highly specialized style of reticle. Some of the sights utilizing this function were monocular. (Yes, others were binocular). Forgive me for not quoting the terminology involved - my references are not handy.

The triangles in and of themselves cannot yield a range. This is quite different than the RANGEFINDERS used by FlaK units, i.e., stereoscopic rangefinders. In fact, the pictures you posted in similar thread were quite good in highlighting the calibration knobs on a rangefinder.

A well-trained gunner, able to use the known width of the triangle bases, also knowing the dimensions of the most commonly encountered Soviet AFV's, could use those two pieces of information to come up with a very close range estimation. That is similar to my use of the front blade on iron-sights to estimate the distance. (If a man is taller than the front blade, he is closer than 100 yards.)

So, I disagree that what is being discussed is a RANGEFINDER. Rather, I think the reticle is part of the SIGHT. Because it is well-designed, it can assist in RANGEFINDING. So, perhaps we're both being pedantic.

Pulling this all together, one of BF.C's founders has a deep background in OPTICS. It seems to me that the CM series, while paying due regard to differences in OPTICS, has completely disregarded the differences in SIGHTS (reticle design, training use, etc.) and how some SIGHTS can help the critical task of RANGEFINDING. It also seems that the higher incidence of German units being equipped with, and using, RANGEFINDERS has also been overlooked. I would like to see this rectified.

Quite wordy, but only so I can fully explain the differences I see in the terms being used.

Thanks,

Ken