المعادلات الحسابية لضبط التلسكوب (متميز)

[Aboyassin]

السلام عليكم،
الإخوه الأعزاء.
لقد قرأت بعض أسئلة و محاولات الأعضاء لتحديد أنسب السبل لضبط التلسكوب. و لقد وجدت هذه المقالة المتميزة على النت تحدد بالضبط ما ينبغى عمله بالنسبة لتلسكوب من نوع: MIL dot reticle>
أرجو أن تفيد إخوانى الصيادين و يمكننى تفسير أى جزء غير مفهوم منها حيث أننى مهندس ميكانيكا و قد كان علم البصريات جزءا من دراستى.
وجزاكم الله خيرا

Mathematics for Precision Shooters
Recently my old friend Steve Langford of Millett Sights and I discussed the many
formulas, measurements, math shortcuts and rules-of-thumb that are of value to
precision shooters. He and I jotted down quite a collection which I'm passing on
to you:
Equivalents and Conversion Factors
These are worth knowing so you can convert units of measurement -- especially
when using a meters-based map -- or employing a scope that uses metric
adjustments.
• One centimeter equals 10 millimeters
• One centimeter equals 0.3937 inches
• To convert centimeters to inches, multiply the inches by 2.54
• One inch equals 2.54 centimeters
• To convert inches to centimeters, multiply the inches by 0.3937
• 1 Yard equals 0.9144 Meter
• 100 Yards equals 91.44 Meters
• To convert yards to meters, multiply the yards by 0.9144
• 1 Meter equals 1.0936 Yards or 39.37 Inches
• 100 Meters equals 109.36 Yards
• To convert meters to yards, multiply the meters by 1.0936
Minutes-of-Angle and Mil-Dots
The Minutes-of-Angle is the standard unit-of-measurement for elevation and
windage on most riflescopes in America, while the mil (or milradian) is the unit-ofmeasurement
found in mil-dot reticles. In a previous column I dealt with both mils
and MOAs to a great extent, explaining how to calculate measurements and use
them in various ways. So here we're only contrasting mils and MOAs at 100-yard
increments all the way to 1000 yards to give you a sense of how these compare.
One Minute of Angle Equals One Mil Equals
100 Yards
200 Yards
300 Yards
400 Yards
500 Yards
600 Yards
700 Yards
800 Yards
900 Yards
1000 Yards
1.0 Inch
2.0 Inches
3.0 Inches
4.0 Inches
5.0 Inches
6.0 Inches
7.0 Inches
8.0 Inches
9.0 Inches
10.0 Inches*
3.6 Inches
7.2 Inches
10.8 Inches
14.4 Inches
18.0 Inches
21.6 Inches
25.2 Inches
28.8 Inches
32.4 Inches
36.0 Inches
*By the time you reach 1000 yards, an actual Minute of Angle equals 10.47
inches
Mil Ranging Estimates
Here are a variety of ways to calculate distances using a mil-dot reticle. The first
technique is especially useful because it enables you to base your calculation on
an object that is measured in inches rather than fractions of a yard.
TO FIND A DISTANCE IN YARDS: An object of known size IN INCHES x 27.8
divided by the object's size IN MILS equals its distance IN YARDS. Example: you
know an object at the target's distance is 12 inches wide; you measure the
object's width in your scope's mil scale and find it is 2 mils wide -- therefore, 12 x
27.8 divided by 2 equals 166.8 meaning the target is 166.8 yards away. [That
"27.8" is simply a constant – don't get wrapped up about why it's 27.8 but DO
NOT use this constant for computing a distance using meters! It won't work!]
Here's another way TO FIND A DISTANCE IN YARDS: At the target, identify an
object of known size IN YARDS and then measure it in mils. Now, multiply its
estimated size IN YARDS by 1000 then divide that by the object's measured size
in mils. Example: You see a fencepost that you know is two yards high;
measuring it in your mil-dot reticle you see it is 4 mils high. Thus, multiple its 2-
yard height by1000, which equals 2000. And since that post measured 4 mils in
your reticle, you divide the 2000 by 4, so you know it is 500 yards away.
And to find a distance IN METERS: Place your mil-dot reticle on an object whose
size is known size in inches. Measure it in mils. Now, Take the object's size IN
INCHES and divide by the constant 39.4 and then multiply the result by 1000 and
then divide that by the object size IN MILS. Try this example: You see an old tire
near your target, and know the tire is 34 inches wide. Measured in your mil
reticle, the tire is 1.5 mils wide. So, you divide the 34 inches by the constant of
39.4 to yield 0.86. Multiply that by 1000 to get 860, and divide that by 1.5.
Therefore, your target is 573 meters away.
Calculating Elevation and Windage Changes
Retired Navy SEAL Master Chief Jim Kauber, with whom I instructed at Gunsite
Training Center, developed this formula for determining sight changes at various
distances.
Let's say you've fired a shot at 436 yards and you observe it strike 15 inches low.
How much do you adjust your elevation? Here's Jim's formula for determining a
scope correction in Minutes of Angle:
Correction (in inches)
----------- = MOA Change
Distance (in hundreds of Yards)
Now let's use the numbers from our example:
15 (inches)
----- = 3.44 MOA (rounded to 3-1/2 MOA)
4.36 (hundreds of Yards)
Thus on a scope with 1/4-minute increments, we'd achieve this 3-1/2 MOA
change by raising our elevation fourteen clicks.
Here are ways to find the third factor when any two factors are present:
Inches
-------- = MOAs
Distance
OR
Inches
-------- = Distance
MOAs
OR
MOAs x Distance = Inches
To keep all these variations straight, Gunsite precision rifle graduate Frank
Zaluga devised his own formula graphic, which he forwarded to me. Frank
dubbed it, "The Doctor is in."
IN (inches)
------
M D
IN = Inches of change on target
M = Minutes of Angle
D = Distance in hundreds of yards
To use Frank's method, just place your fingertip over the factor you want to
determine, which tells you to multiply or divide the other two factors, to learn the
third factor. Let's say you want to see how many inches 5 MOAs are at 200
yards: Just place a fingertip over "IN" and you see that you must multiply the
MOAs by the Distance, which means 5 MOAs times 2 (Distance in hundreds of
yards). Therefore, the answer is 10 inches. And if you're trying to determine how
many MOAs to crank your scope when you want to raise the bullet impact ten
inches at 200 yards: put a fingertip on the "M" (for MOA), and you see you must
divide the inches by the distance. Frank's graphic formula is simple and easy to
remember.
An Old Marine Corps Method
Here's an old USMC formula for estimating windage compensation, in Minutes of
Angle. This only applies to .30-caliber rounds, such as the .308 Winchester and
.30-06 Springfield. In use since the days of the excellent 1903 Springfield rifle,
this formula is only employed for targets 500 yards or closer, after which the
math constant changes:
Range (hundreds of yards) x Windspeed (MPH)
------ = MOA Windage
15 (a math constant)
For example, your target is 300 yards away, and there's a 10 MPH crosswind.
3 x 10 = 30
------------ = 2 Minutes of Angle
15
If it's a full-value (90 degree) crosswind, click-in the two Minutes of Angle and aim
dead-on; if the wind is oblique, proportionally reduce your clicks. This formula
works well except when a target is farther than 500 yards – after that, the Math
Constant increases, as shown below:
At 600 Yards, Divide by 14
At 700 and 800 Yards, Divide by 13
At 900 Yards, Divide by 12
At 1000 Yards, Divide by 11
Compensating for Headwinds and Tailwinds
In theory, a headwind slightly increases drag on your bullet and thereby reduces
its velocity, while a tailwind has the opposite effect. Thus, a headwind requires
that you slightly raise your scope reticle, and a tailwind dictates that you slightly
lower it.
This formula, cited by W.W. Greener, is:
Wind Velocity (MPH) x Distance (Hundreds of Yards)
------------ = Yards (Range Change)
4 (Math Constant)
Let's see how exact this small compensation can be by calculating the
adjustment for a 10 MPH tailwind, when our target is at 300 yards
10 x 3
------------ = 7.5 Yards
4
Since it's a tailwind, we subtract these 7.5 yards from the 300, and set our sight
as if the target is 292.5 yards away - which translates (for a .308 Winchester
firing 168-gr. BTHP) to just one click -- one tiny 1/4-Minute of Angle click! Had it
been a headwind, we would have added that 7.5 yards to the actual distance,
and fired as if the target were 307.5 yards away.
This may seem like splitting hairs, but headwind/tailwind compensation increases
with distance because the bullet slows and its trajectory becomes a plunging arc.
At 900 yards, that same, mild, 10 MPH headwind or tailwind, would require a
seven click correction to place our .308 bullet on center-target. And recall that at
such extreme range, the bullet is plunging so sharply that even a small elevation
error can cause a complete miss.
Adjusting for Temperature Changes
This is another elevation adjustment, dictated by how much temperature variation
can change the trajectory of your bullet. Because powder inside your cartridge
burns at a higher rate when it's warm, and slower when it's cold, your rounds will
strike low in cold weather and high in hot temperatures. The following best
applies to .308 and .30 caliber rounds:
When the temperature changes 20 degrees from your zero temp, apply 1 MOA at
300 yards;
When the temperature changes 15 degrees from your zero temp, apply 1 MOA at
600 Yards;
When the temperature changes 10 degrees from your zero temp, apply 1 MOA at
1000 Yards
U.S. Army tests measured the following effects of changing temperatures on .308
ammunition,
Degrees
Fahrenheit
-10
+25
+59
+100
Muzzle
Velocity
2400 fps
2500 fps
2600 fps
2700 fps
Bullet Drop at 600 Yards (200-Yard
Zero)
-109 inches
-100 inches
-91 inches
-84 inches
A century ago, British firearms authority W.W. Greener developed a formula
based upon a "standard" temperature of 60 degrees Fahrenheit, which is very
close to today's 59-degree F. ballistic table standard:
Degrees +/- 60 Degree Standard x Distance (Hundreds of
Yards)
------------ = Range Change for Temperature
10 (Math Constant)
When the temperature is less than 60 degrees, add the result to your actual
target distance; when it's above 60 degrees, subtract this distance from the
actual distance. Here's an example: The temperature is 90 degrees F. (30
degrees hotter than Greener's 60- degree F. standard), and your target is 500
yards away.
30 x 5
------------ = 15
10
Deduct this distance (15 yards) from the 500 yards, then set your sights as if the
target is 485 yards away, aim dead-on, and fire. Altitude Effects
Altitude Effects
Since air is thinner at higher altitudes, there's less drag on a bullet and therefore,
in relative terms, a bullet flies faster with a flatter trajectory. Standard ballistic
tables assume a sea-level altitude, so already there may be a variance from
these tables and the altitude at which you zero your rifle.
Concern about altitude change usually involves travel - say you regularly fire your
rifle near St. Louis at an altitude of 450 feet, then you go to Colorado to hunt elk
at 10,000 feet. What's the difference? The basic rule-of-thumb is, add or subtract
one MOA for every 5000 feet of elevation change.
But what about changes in barometric pressure which can vary day-by-day, even
hourly, when high- or low-pressure fronts pass through? I don't think there's
enough variance to change your elevation except in extreme weather changes;
yet, W.W. Greener, in his 1901 classic, Sharpshooting for Sport and War,
suggested, "One inch of barometric pressure is equal to 15 degrees Fahrenheit
change in temperature. Treat a rise in barometer as a rise of the thermometer in
the above proportion."
Trajectory Changes for Barrel Length
When you consult an ammo manufacturer's rifle ballistic tables, you're actually
looking at the velocity when fired through a 24-inch barrel. The degree to which
your barrel is shorter or longer will respectively decrease or increase muzzle
velocity, and thus require elevation changes, a significant factor since some rifles
have 26-inch and even 20-inch barrels.
Here are the three rules of thumb, as disseminated by Remington Arms
Company:
• - For cartridges generating a muzzle velocity of 2000 - 2500 fps, each inch
a barrel is longer or shorter than 24 inches changes velocity 10 fps;
• - For cartridges generating 2500 - 3000 fps, one inch will vary velocity 20
fps;
• - High velocity cartridges, generating 3000 - 3500 fps, will change muzzle
velocity 30 fps per inch of barrel.
While these velocity differences seem minimal - at 100 yards there's almost no
noticeable change in trajectory - the effect becomes significant at long range. For
example, the .308, 168-gr. BTHP Match round will impact six inches lower at 500
yards when fired from a 20-inch barrel, then when fired from a 24-inch barrel.
After determining your round's muzzle velocity for your barrel length, consult a
good ballistic software program to chart how it changes the bullet's trajectory.
A Quick-Fix for Up/Down Situations
When your target is uphill or downhill, your round will impact high if you aim
dead-on. (The explanation is complex and worthy of a future column, but for now,
just trust me.) There are several methods to determine the amount of
compensation, but the quickest involves these simple Rules of Thumb:
• - For a target 45 degrees up or down, multiply the actual distance by 0.7,
set your scope elevation for this distance and aim dead-on;
• - When the target's 30 degrees up or down, multiply its range by 0.9, set
your scope for this distance and aim dead-on;
• - If the target angle is less than 30 degrees, aim dead-on.
Another Rule-of-Thumb, suggested to me by Sergeant Neal Terry, a longtime
sniper instructor and police SWAT sniper, is to draw an invisible vertical line
through the up or down target, and where this line intersects the earth's surface,
range it! Disregard the angle, ignore the direct distance from muzzle-to-target,
concentrate only on adjusting elevation for the distance to where that vertical line
touches the earth. Compensate for that distance, aim dead-on and fire. We've
worn out several pads of paper comparing Neal's math to other kinds of up/down
calculations - it works and it's the essence of simplicity!
Exit Pupil and Lowlight Observation
At dusk and at night, your eye's pupil dilates, or widens, to 6 or 7 millimeters, so
you can see better. Ideally, your riflescope or binoculars should generate a cone
of light of this measurement to allow the best lowlight viewing. How to calculate?
Divide the objective (forward) lens diameter in millimeters by the optical device's
magnification. Say you have fixed-power 7x binoculars with 35 mm objective
lenses -- thus 35 mm divided by 7 equals an exit pupil of 5mm, meaning the cone
of light reaching your eyes will be 5 millimeters wide. Not quite as wide as your
eye pupils. Thus, 7 x 50 mm binoculars would be better, because the exit pupil
would be 7mm. Here are the best riflescope magnifications for shooting in low
light, depending upon the size of your objective lens.
Objective Lens Diameter
56 mm
50 mm
44 mm
40 mm
Best Night Magnification
8-9x
7-8 x
6-7 x
5-6 x
Calculating a Barrel's Rate-of-Twist
Known as the Greenhill Formula, here's how to calculate the most compatible
rifling rate-of-twist for a given projectile. First, determine the LENGTH of your
bullet in "calibers" which is a measurement in hundredths-of-an-inch, the same
way we measure bullet diameters. (ie., a .50 caliber bullet is 0.50 inches in
diameter). Now divide the length in calibers/hundredths by its diameter caliber.
Next, take this figure and divide by 150, which is simply a math constant. And
finally, take that result and divide again by the diameter caliber and you'll have
the rate-of-twist in inches. Here's an example: Your .30 caliber, 200-grain bullet
measures 1.35 calibers (or inches) in length. Take the 1.35 length and divide by
the .30 diameter, which equals 4.5. Divide 150 (the constant) by that 4.5 which
equals 33.33 Now take that and multiply by the caliber diameter, thus, 33.33
multiplied by .30 caliber equals 9.999 or a 1-in-ten inch rate of rifling twist.
Bullet Length Versus Diameter
Today's Very Low Drag bullets are disproportionately longer than Whitworth
recommended, a reflection, I think, of our higher velocities leading us ever farther
from round balls, and further from rules-of-thumb of past ages.

[mohamed_salam]

بما ان حضرتك متخصص ليه مسهلتهاش و ترجمتها فى جدول صغير زى اللى بيجى بيه التليسكون
و بخصوص الضبط لاول مره سهله جدا انت بس تحط هدف على المسافه المراد الضبط عليها و تضرب و تعدل بمقدار الخطاء زى ما هو مذكور فى المانوال و بعد الضبط لو هدفك على نفس المسافه اضرب و لو ابعد اضرب لريشه فوق و لو ااقرب اضرب لريشه تحت و هتلاقى الموضوع بالممارسة سهل
تقبل مرورى

[Aboyassin]

السلام عليكم
أشكر لك مشاركتك
سأحاول فى الإجازة القادمة العمل برأيك.

[BooGY]

انا رأيي من رأى محمد سلام لو امكن يا باشمهندس ننرجم لنا المعلومات دى يكون افضل