A question for you math wizards

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A question for you math wizards

Post by joy2shoot on 4/6/2017, 5:32 pm

I hope the following makes sense.
 
I use blank wall dry fire, target dry fire and eyes closed dry fire as part of my training routine.  I would like to create a dry fire target whose black looks the same diameter at 12 feet as the black on a B-6 target looks at 50 yd.
 
As we know, the B-6 50 yd slow fire target has the 8, 9, 10 and X rings black with the 8 ring having a diameter of 8".  And when we are standing on the firing line looking at this target on the 50 yd line, the black looks small indeed.  What diameter black ring would give me the same perceived diameter at 12 feet?
 
Why 12 feet?  That is the distance from my always-keep-a-gun-pointed-in-a-safe-direction wall to a fixed table.  What wall is that?  It is the wall in my basement that if heavy forbid the gun actually goes bang, the bullet will go through the dry wall, into concrete block and if it gets through the concrete block, into soil.
 
Thank you.

p.s. A formula where you enter the distance and it tells you the diameter would be really great.

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Re: A question for you math wizards

Post by Magload on 4/6/2017, 6:10 pm

Hope this helps

Example 1 
 
3 inch target at 33 feet distance. Scale down distance to 20 feet > What is new smaller target size?
 
20-ft / 33-ft (or 20 ÷ 33) = .61 or 61% of original distance, next > .61 x 3 inch (original target size) = 1.83 inch, new target size
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Re: A question for you math wizards

Post by Multiracer on 4/6/2017, 6:12 pm

Unrelated question........if you are dry firing how could the gun go bang ?

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Re: A question for you math wizards

Post by LenV on 4/6/2017, 6:14 pm

8" divided 150' = .05333" per ' x 12= .639996" give or take a little for your pupil size.
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Re: A question for you math wizards

Post by dronning on 4/6/2017, 6:26 pm

Used SCATT software (free), 3.7 meters and here's what printed out:

https://drive.google.com/open?id=0B0bQ6jtAb47rdXpoa1p2RmpCV3M

- Dave
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Re: A question for you math wizards

Post by Froneck on 4/6/2017, 6:30 pm

Lots of things will enter the appearance, perception well make it look bigger or smaller. However if you interested in actual size similar to a cone with the diameter at 50 yards of 8" and want to know the diameter at 12 feet. It's a simple trig. equation.To determine the angle lets use a simple straight line to the center, the rise above will be the radius or 4", distance of the straight line to the target at 50 yards is 1800" so 4"/1800" =.00222 (Tangent of the angle) Then X 144" = .32" radius so the diameter of the circle will be X 2 = .64"
 If a calculator is used as I did the accuracy is good to 32 places.
 Note 33 ft target is not a scaled down B6 also SCATT is probably scaled down 9 ring

 This was the first time I used the calculator on Windows 10, for trig functions, does anyone know how to determine the angle if the sine, cosine or tangent is known? What is the angle with the tangent .002222??? With all my calculators at my shop it's a simple push of the correct button.


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Re: A question for you math wizards

Post by joy2shoot on 4/6/2017, 7:03 pm

Magload, LenV, dronning and Froneck; thank you for your information.
 
Multiracer, the #1 gun safety rule (per the NRA) is Always Keep The Gun Pointed In A Safe Direction.  Why?  In case it does accidently go bang.  I have seen where a customer walked into a gun store with a gun they want worked on/sold on commission/sold outright, etc.  The clerk asked the customer if it is unloaded and the customer said yes.  The clerk cycled the slide and out popped a live round.  We all want to believe we are super safe, but the #1 rule exists in case we make a mistake because if we do, it is no longer called dry firing.

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Re: A question for you math wizards

Post by Multiracer on 4/6/2017, 7:09 pm

Gotcha

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Re: A question for you math wizards

Post by Tim:H11 on 4/6/2017, 7:19 pm

What I did was - at the range, I held up my thumb (Imagine giving the target a thumbs up), and with a pen made two lines the width of the target. Then at home I created different size black dots until I found one that fit within the marks on my thumb thus creating the same picture. The trick to making this work is that at home, the distance you stand away from the dot must be the same every time. So maybe memorize the spot in the room where you stand. Or mark the floor some how..... for those married folks like me, marking the floor is only good so long as the wifey doesn't notice. Once wifey notices, things get complicated. Explaining to her if she's not a shooter will not go over well. Good luck! Im not a mathematician.
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Re: A question for you math wizards

Post by joy2shoot on 4/6/2017, 7:34 pm

Thanks Tim.  I have actually placed a piece of removable tape (painters tape) on the fixed table to mark the 12' distance.

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Re: A question for you math wizards

Post by Wobbley on 4/6/2017, 8:02 pm

12 feet = 4 yards

8 inches x ( 4 / 50 )  = 32 / 50 = .64 inch.  Call it 5/8.

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Re: A question for you math wizards

Post by james r chapman on 4/6/2017, 9:03 pm

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Re: A question for you math wizards

Post by Froneck on 4/6/2017, 9:24 pm

That system is designed to take bullet diameter in determining target diameter is order to add difficulty for training. Also the writer states that the 50ft target is so much harder. It is harder I read someplace because it's a gallery match and designed to be quite a bit smaller to avoid tie scores. I have shot the B-16 targets at ranges that didn't have a 50 yard range. I feel the B-16 at 25 yards is easier than the B-6 at 50 yards.
 However the OP is looking for a scaled reduction to dry fire at 12'. .64 or about 5/8" is what he should be using

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Re: A question for you math wizards

Post by LenV on 4/7/2017, 10:55 am

It's not .64. It is .639996. Ok, I guess I could have rounded up a little bit.

Joytoshoot,  If you have an extra 2' you can stretch your shooting position the 3/4" repair stickers are the perfect size to be used at 14' (14.07). I was curious how close they were to the .64 so I measured one. Just more info you probably don't need.

Len
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Re: A question for you math wizards

Post by Froneck on 4/7/2017, 11:42 am

Not really Len, 8/150 is .05333333333333333333333333333333 1/3 X 12=.64
If you use .0533333333333333 X 12" = .6399999999999996" but your dropping 1/3 
Simpler form is 8/150 = .053 and 50/150 X 12" = .64"
 Your rounding down by dropping the numbers past .05333


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Re: A question for you math wizards

Post by ric1911a1 on 4/7/2017, 11:52 am

You lost me at the bakery....................
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Re: A question for you math wizards

Post by Froneck on 4/7/2017, 12:10 pm

Get me a dozen Bavarian Cream Donuts while your there ric lol!

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Re: A question for you math wizards

Post by Wobbley on 4/7/2017, 12:27 pm

Froneck wrote:Not really Len, 8/150 is .05333333333333333333333333333333 1/3 X 12=.64
If you use .0533333333333333 X 12" = .6399999999999996" but your dropping 1/3 
Simpler form is 8/150 = .053 and 50/150 X 12" = .64"
 Your rounding down by dropping the numbers past .05333
Why make it harder than it is..?  

12 feet is 4 yards exactly.

So the ratio of the distance is 4/50.  

The size needed is 8 x (4/50) = 32/50 = 64/100 = .64.

Froneck I thought you were a machinist?

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Re: A question for you math wizards

Post by Froneck on 4/7/2017, 12:40 pm

Wobbly Yes I'm a machinist we deal in 1/1000" not yards. Besides your making it too simple and I can't impress anyone!!

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Re: A question for you math wizards

Post by Chris Miceli on 4/7/2017, 12:49 pm

Froneck wrote:Wobbly Yes I'm a machinist we deal in 1/1000" not yards. Besides your making it too simple and I can't impress anyone!!
Lol
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Re: A question for you math wizards

Post by Magload on 4/7/2017, 1:32 pm

What ever it is it is a lot smaller then my wobble pattern.  Don
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Re: A question for you math wizards

Post by Froneck on 4/7/2017, 1:47 pm

While tinkering with the Windows 10 calculator and clicking on all the buttons I found the answer to converting the Trig functions of an angel to the angle. I then answered my own question and impressed myself since Wobbly wants to make everything too easy Laughing
 The angle of the cone is .2546+ degrees
 Though Len was .000004" off! How can anyone train with that amount of error lol!

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Re: A question for you math wizards

Post by bdas on 4/7/2017, 2:34 pm

Froneck wrote:... the writer states that the 50ft target is so much harder. It is harder I read someplace because it's a gallery match and designed to be quite a bit smaller to avoid tie scores.

I'm pretty sure that the targets aren't "perfectly scaled" to account for the bullet diameter.  The problem is that a bullet makes the same size hole at every distance, whether 50 feet, 20 yards, 25 yards, or 50 yards.  

If the bullet hole was scaled, a .45 hole at 50 feet is like making a 1.35" hole at 50 yards!  How often would that improve your score?  (Answer: Pretty often, actually... it's basically like moving every shot on your 50 yd target a half inch closer to the center of the target.  Who wouldn't love that?)  To compensate for that, they made the rings on the closer targets slightly smaller than "perfectly scaled", so that the scores would be approximately equivalent for good shooters.  Obviously, .22 bullets have the same basic problem, but it's slightly less pronounced.

If you look at the very nice graphs that indecorous made, when you click on the links to show the graphs adjusted for .22 or adjusted for .45, notice how the lines are pretty close to each other around the 10 and X rings (even though the unadjusted lines suggest that the scaling is way off) .  That way, the good shooters (the ones with lots of 10s and Xs) will end up with approximately the same scores at any distance.  Shooters who are not so good will suffer more due to the scaling, but they get compensated by the addition of the 4 ring on the 20yd and 50ft targets.  The shooters who suffer the most from the scaling are the ones who tend to shoot lots of 6s, 7s, 8s, and 9s, but don't have lots of 10s and Xs, and rarely put shots into the outermost ring or just beyond it (these are generally going to be the better Marksman and lesser Sharpshooters, with averages around 75-87).

If you ask me, what we have with the current targets, is actually a pretty reasonable compromise.  (It would get rather confusing (and expensive) to have different sets of reduced targets for 22, 32, 38, 40, 44, and 45 calibers.)

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Re: A question for you math wizards

Post by Wobbley on 4/7/2017, 2:40 pm

Next thing you know, Froneck will be making a request to NASA to borrow a super computer to get the millionth trailing zero.  "Just to be sure"

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Re: A question for you math wizards

Post by Magload on 4/7/2017, 2:47 pm

Just DF @ a blank wall you don't need math for that.  Don
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Re: A question for you math wizards

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