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Put another way, draw a “cone” from the muzzle to the target area you list. The 3” @ 25 yard cone will expand (get ‘fatter’) three times as fast as the 10” @ 250-yard ‘cone’. If you extend the 3-inch, 25-yard cone out to 250 yards, it will cover 30 inches, not ten. (It will be 6” at 50, 9” at 75, etc).

Let’s take your example one step further. You use the number 3 inches @ 25 yards; that’s a circle that covers 7.068 inches. To get the same relative number of square inches at 100 times the distance, we need a circle that covers 100 times the area, (or 706.8 inches) at 2,500 yards, which is 1.4 miles. One hundred times the distance, one hundred times the target area; that’s the argument you’re making. A circle that covers 706.8 inches has a radius of 15 inches, or a diameter of 30 inches.

So if your approach is correct, shooting 3 inch groups at 25 yards is no less of a feat than shooting 30” groups at 1.4 miles. Mathematically inarguable conclusion, if we accept your premise of “number of square inches” being the key factor.

In addition to that, in the physical world, we have to allow for other influences:

- Bullet drop. Not only increased bullet drop, but increased (non-linear) RATE of bullet drop.

- Wind influence. With 10X the distance and 12-15X the flight time, the influence of the wind is increased almost exponentially, when compared to 25 yards.

Consider this. Pick a handgun you can put into 3” at 25 yards; 9mm, 22, whatever. A lot of handguns can do that easily. Are you saying you can get 10” at 250, if the best you’re getting is 3” at 25? It’s mathematically impossible, regardless of “split times”.

The “number of square inches” argument reminds me of an example one of my teachers once used, about a mosquito stopping a freight train.

A mosquito flying 30 mph east, hits head-on into a freight train running 30mph west. We all know what happens – the mosquito hits the train and loses the fight, instantly changing direction from east to west (stuck to the front of the train). Now picture a standard mathematical number line, with positive numbers on the right (east) and negative numbers on the left (west).

Now plot the mosquito’s course, speed and direction on that number line. He went from +30 (flying east) to –30 (traveling west, stuck to the train front); that’s demonstrable and inarguable. He switched direction 180 degrees when he hit (and became impaled on) the train. Here comes the rub: if he DID that, he at some point MUST have crossed “zero”, and at zero, he was standing still. Since he was stuck to the train while “at zero”, the train must also have been standing still, mustn’t it…?

If we use the seemingly-appropriate ‘number line’ approach to solve this, we have to accept that a freight train comes to a dead stop every time it hits a mosquito. What we need to realize is that even though the answer seems irrefutable, it’s extremely flawed because it was arrived at using the wrong type of approach. (You can solve the mosquito problem with a two-dimensional [four-quadrant] layout, but not with a one-dimensional number line.)

Wrong math, no matter how convincingly applied, is still wrong.

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I never took calculus (differential or otherwise); trig is as far as I got, and I remember very little of it. And even trig was pushing the limits of my gray matter, believe me.Magnum88C said:John in AR: differential calculus would be the easiest way to solve the train Vs mosquito thing -- in a one-dimensional model, no less. In fact that was one fo the "applications" in Calculus class. :dgrin:

My wife's the smart one. She used to take advanced math and physics courses as electives in college, just because she enjoyed them and she saw them as an easy way for her to keep her GPA up. Weird people, those kind.

Trying to explain things to me is one of her life's great challenges. My brother asked her a few weeks ago about "Splenda" sweetener, asking if it wasn't "made partly from sugar". Her response was "it

All we could do was look at each other, and then go back to picking bugs out of each other's hair like the apes we apparently are.

In answer to your rhetorical question )) I don't see how one arrives at the conclusion that it must have been standing still because it never experienced a turn? The only thing that would have changed (because of Newton) would have been the delta V, going from -30 to -29.99999999999 to compensate for the tiny amount it slowed when plowing into the mosquito. I guess I'm overcomplicating the use of the line?Here comes the rub: if he DID that, he at some point MUST have crossed “zero”, and at zero, he was standing still. Since he was stuck to the train while “at zero”, the train must also have been standing still, mustn’t it…?

Nonetheless,

that is correct.Wrong math, no matter how convincingly applied, is still wrong

BTW, Splenda replaces the -OH (hydrates) on the end of "sugar's" (technically sucrose) carbo

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krept said:...BTW, Splenda replaces the -OH (hydrates) on the end of "sugar's" (technically sucrose) carbohydrateswith -Cl (chlorines), thus rendering them metabolically inert.

Right... Grog go get coffee now...

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