I'm curious how some of you have your dope card set up for angular adjustments, do you have a column for say every 5 deg. from say 20 to 45 degrees. Just looking at ideas of how to add this to my present dope.
Let me preface by this: You may or may not know already what I'm about to say with regards to the geometry. I've been asked it before and how to account for it, so if you already know this please bear with me. I'm sure there's others out there who don't know it.
There's something in geometry called "Small Angle Theorem"
It says that (this is in radians, not degrees) that as the angle approaches 0, the sine of the angle ~= to the angle. Test this out, sine(0) = 0, sine(1*) is ~0.008 or something like that. Cosine is ~= 1.0
Generally it's held to +/-5* of 0* as an acceptable limit. I only bring up radians because that's what the theorem is based upon, unless it's on paper, I don't default to thinking in radians.
This is the background info for what I'm about to say.
I don't worry about the dope change until I'm shooting at least 600yd and/or 20* off horizontal. Some conditions apply depending on caliber and load data obviously.
I'll try to provide some examples and you can make the determination more completely for yourself.
EX 1. Let's try a 45* downhill shot on a whitetail deer at 350yd with a 300 WM and 210 VLD's @ 2975 fps. Assume the vital zone is a 6" circle.
"Gravity Range" is a term I'll use to describe the horizontal range, not the flight distance. This is because it's the component of the flight that is largely affected by gravity, the vertical component of velocity is affected but it's miniscule and can easily be ignored.
Look at your dope chart for 250yd vs. 350yd horizontal flight. Via JBM I see that the drop from 100yd zero is:
250 yd = 6.0 in
350yd = 16.3 in
Clearly if you shot your 350 yd dope here, you'd end up outside your kill radius (6"/2 = 3") from aim point and you might even put the bullet right over the back of the deer.
EX 2. Same load, same deer, same range, but the angle is 20* this time.
GR = R * cos(h) = 350 * cos(20) = 350 * 0.9396 = 329yd
Look at the JBM drop in inches again.
325 = 13.2"
350 = 16.3"
Ok, so it's 0.1" outside the vital zone and it's going to be just a touch high.
Long winded summary:
Plot a table of cosine values from 0-90* and take a look at the trend, compare this trend to the "danger space" at your various expected shots and make sure that your bullet still lands in the vital zone.
I don't think that there's a specific "always right" answer to say you need to be at a certain range or a certain angle. I think it depends on the danger space you're shooting in.
Interesting discussion of the numbers, but regardless of units, it still seems it can be summed up as: Worry about big angles...but I'm not sure why just as short ranges. My drops @ 500 and 1000 change 1.2 and 3.4 mils respectively on a 45 deg. shot.
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: azimutha</div><div class="ubbcode-body">Interesting discussion of the numbers, but regardless of units, it still seems it can be summed up as: Worry about big angles...but I'm not sure why just as short ranges. My drops @ 500 and 1000 change 1.2 and 3.4 mils respectively on a 45 deg. shot. </div></div>
Big angles are not a problem at 100yd. Extreme angles could be, but a 60* angle at 100yd is really a 50yd dope. It's a discussion on target size to flight path variation for whatever assumption is made.
Your vital zone size and respective "danger space" for that particular caliber and target size are important.
You could make a dope table up based on a deer target. Say a 6" target circle. Don't bother to put a correction down until a specific angle and range combo calculates out to a miss.
As you get out to longer adn longer distances you have to be dead on with the dope, so if you're off by 5% from ignoring an angle at 1000yd your shot will likely go over the target