Technical question related to ballistics and bullet drop


September 13, 2007, 01:39 AM
Trying to figure out the least common denominator for determining trajectory... is it possible to find a certain trajectory with:

a) Knowing only the first couple hundred yards of a certain cartridge's trajectory, is it possible to know exactly the remainder of its flight path?

Say one knows that a particular round, sighted in at 100 yards with a muzzle velocity of 2800fps, will be -3.8 inches at 200 yards, and -13.9 inches at 300 yards. Is it possible, with only this information, to calculate the remaining trajectory data out to the end of its range?

or else:

b) If not, how many more variables do we need to add before calculating the remaining trajectory. Would knowing that the above bullet were a 150 grain .308, would that be enough? Or would we actually have to know the particular bullet composition (e.g., Nosler boattail), the BC, etc.?

I'm working through learning the ins and outs of reloading and bullet trajectory, and am trying to figure out how much needs to be known before a ballistic chart can be calculated.



Edited to ask one more question: On an online ballistic sheet I printed out (not particularly related to any cartridge combination I would use), it lists six categories: Range, Velocity, Impact, Drop, ToF, Energy, Drift. The first two, and the last two, are fairly obvious.

However, I don't know what ToF indicates. Secondly, I'm not really sure of the difference between Impact and Drop. At 0 yards, it shows -0.75 impact, while it shows 0 drop. At 200 yards, it shows -4.31 impact, while it shows 10.14 drop. For 525 yards, it -62.16, and 78.69 for impact and drop, respectively. For my use, lets say I range a target at 525 yards. Should I come up 10 MOA (for 62.16 inches impact variation), or should I come up aprox. 13.3 MOA (for 80 inches drop)?

Thanks, this is all new, but very interesting and helpful.

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September 13, 2007, 02:23 AM
You've probably got enough on hand (weight, velocity, drop at a couple of points downrange) to calculate out with reasonable assurance what the useful portion of the trajectory (before the accuracy opens up to where you can't hit targets with good assurance) is for the average highpower rifle bullet. You'll need to plug in Ballistic Coefficients on a trial and error basis till you find one that matches the known bullet drop data.

September 13, 2007, 03:21 AM
EDIT- Nevermind, I missed the point.

September 13, 2007, 03:50 AM
you could guesstimatewith what you've got, but haveing b.c. as well, you could deff do it. it is something like the old electronic standard of E=i/r , and you plug in the numbers.
tof is time of flight, usually.

September 13, 2007, 03:52 AM
go here to learn a bit
go to top right, where it says ballistik.

September 13, 2007, 04:26 AM
Impact is where it hit. Drop is measured either from the height of the bore or the peak of the bullet's arc.

Bullet trajectory is calculated from four things:
bore height
muzzle velocity
ballistic coefficient
peak height of bullet arc

The weight of a bullet is not important. Bullets drop due to gravity. The effect of gravity is calculated by the time in flight. Bullets climb because the bore was pointed upwards at a slight angle to the ground.

Time in flight is extended due to low ballistic coefficient, which means the bullet resists air more than a bullet with a high ballistic coefficient.

You could calculate the ballistic coefficient given the muzzle velocity, and assuming a 100 yard zero, and a point of impact at some distance other than 100 yards. You could reverse the math and determine the ballistic coefficient of the bullet, then calculate its path. You'd have to calculate deceleration due to air resistance, then determine the peak height of the arc by the reversing the formula for the two points you've already got. But you don't have to do this.

Numerous web pages provide a calculator if you have the ballistic coefficient and the muzzle velocity. IIRC, the Sierra reloading manual provides a chart of raw data, rather than specific drops for specific loads. You look up the ballistic coefficient of the bullet you're using, then the muzzle velocity and the point of aim. It shows the entire data set for the load. The program is included with their reloading software.

September 13, 2007, 11:23 AM
I prefer to work back into a BC from actual drop data. Published BC's are often fairly optimistic.


Zak Smith
September 13, 2007, 12:21 PM
Ask guys who calculate BCs regularly, and they say that using drop data is not a particularly good way to do it. I think TOF or difference in velocity are better measures.

Also, it takes quite a bit to change the short-range (300-500 yards) trajectory, so back-calculating from that data is going to be a rough approximation.

Jim Watson
September 13, 2007, 04:11 PM
What I have heard, Zak. Natural dispersion of the group makes figuring BC from drop very approximate unless you do a lot of shooting to build statistics.
I once calculated BC well enough to get on target with two chronographs, one at 3 yards, just in front of the firing line; one at 98 yards just in front of the 100 yd target.

BC of nearly all commercial bullets is published. Even if optimistic advertising, it will get you on target.

September 13, 2007, 07:15 PM
BC changes depending on velocity. Most publish only an average figure. Sierrea is pretty good about publishng BC at several velocities.

Delta V (change in velocity) is typically the most accurate way to determine BC. As noted, drop varies with the precision of the firearm.

Also note that you must adjust for station pressure. Most drop tables are calculated for Army metro - that is 59 degress F, 29.53 inches mercury and 78% humidity. If you are in an environment other than this, you need to make adjustments.

Zak Smith
September 13, 2007, 07:19 PM
As an experiement, run the ballistics using Sierra's multiple BC's, and then run them using the average BC over the velocity range. The difference in drop at 1000 yards should be very small. When I did this experiment, it was 0.25 MOA for the 175 SMK.

September 13, 2007, 07:33 PM
I used Norma's ballistic calculator, using Federal's published data. Overall, the averages were very close (though I only ran it out to 600 yards). I'll need to verify these on a real range.

.446 BC (average)

yards / Drop (inches) / Wind Drift (per inch w/ 10 mph @ 90dg)

100 yards / 0.0 / 0.7

125 / -0.4 / 1.1

150 / -1.1 / 1.6

175 / -2.1 / 2.2

200 / -3.5 / 2.9

225 / -5.2 / 3.7

250 / -7.3 / 4.6

275 / -9.8 / 5.7

300 / -12.8 / 6.8

325 / -16.1 / 8.1

350 / -19.8 / 9.4

375 / -24.1 / 10.9

400 / -28.8 / 12.6

425 / -34.0 / 14.3

450 / 39.7 / 16.2

475 / -46.0 / 18.2

500 / -52.9 / 20.4

525 / -60.3 / 22.7

550 / -68.4 / 25.1

575 / -77.1 / 27.7

600 / -86.5 / 30.4

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