I need a mathamatician

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mugsie

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Need someone with some math background. I don't have a chrony so I can't measure the spped of my bullets. However I do know the drop between 100 and 200 yards. Knowing the drop and knowing gravity affects an object at 32 feet/sec/sec, can I figure out the speed? I know the weight of the bullet as well.

I have not been able to locate any balistics calculators that will allow me to work backwards. Is it possible to accomplish what I'm trying to do, or do I need to spend a $100 or so and purchase a chrony. Seems a shame to do that since it'll only be used on a couple of occasions then put away to gather dust.

So - any math wizzards out here?
 
Knowing the drop and knowing gravity affects an object at 32 feet/sec/sec, can I figure out the speed?
Click to expand...

Nope, you'd need to know several points along the curve of the drop and the distance at which they occur so you could plot the curve of the drop to get the information that would go back into the calculation that you would allow you to derive the velocity of the projectile.

The velocity is the time it takes to travel a specific distance along an axis divided into that distance. If you can't measure the that time then you can't calculate the velocity along that axis. This would only give you an average velocity since ballistically a projectile slows from the point of maximum velocity due to drag and if you don't know the drag on the bullet then you can't derive the max velocity.
 
You could calculate the velocity from the drop IF you cloud ensure that the line of the bore were absolutely dead level. I think that would be the hard part, not the math.
 
The other factor to consider is that the velocity is not constant.
With more data points at longer distance you can use a ballistics calculator to get a good estimate of your initial velocity but you will not get good data from 2 points at relatively close range.
 
It's pretty easy to do although it won't be very accurate. Any ballistic calculator will do it. Easiest thing to do would be zero at 100 yards, then just change the muzzle velocity in the calculator till it shows your actual drop at 200 yards. There's a reason that it's not used. The variation in drop due to velocity will be hidden by the normal dispersion of the shots due to your group size.

For example, if your gun shoots a 1" group at 100 yards, the group size will be about 2" at best at 200 yards. So if a test bullet has 1" more drop than another bullet at 200 yards, is it because the test bullet was slower, or was the test bullet actually moving the same speed or faster? You'll never know because your group size is 2".

The BC (ballistic coefficient), a measure of how much drag your bullet has and how quickly it loses speed, will also be critical. If you don't know the BC for your bullet you're pretty much wasting your time.

If you still want to play with it, easiest way would be to use the calculator like this one:

http://www.shooterscalculator.com/ballistic-trajectory-chart.php?t=f630255c

For example, a .30-06 180gr Matchking at a muzzle velocity of 2750 FPS with a BC of .475 will drop about 3.8" at 200 yards if zeroed at 100 yards.

3a72217f-6370-4d43-bc04-b099eca84aaf_zps87050e7c.jpg

Under the same conditions but with a velocity of 2500 FPS it will drop about 5".

2500_zpsaa0476a8.jpg
 
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I had an old Gun Digest with an article 'Trajectory Chronograph,' including tables, graphs, and nomographs, so it can be done.

These days, easier to back calculate as 45 auto shows.
Doing it from textbook physics would be a challenge.

Fire a lot of shots into your groups so you can reliably locate the center. Nothing matters but the vertical. Don't just eyeball it, measure each individual shot and average.
 
The quick calculation that neglects drag gives you a horizontal velocity of:

v=x*SQRT(g/2*y)

y = distance bullet drops
x = horizontal distance over which drop occurs
g = acceleration due to gravity (in units that match the other variables).

If you want to account for drag, then approximations must be made.
 
To expand on the above equation:

for the vertical direction: 2*y = g*SQUARED(t)
for the horizontal direction: x = v*t

Then, just eliminate t (time) between the above two equations to get the one I posted.

Again, this assumes the horizontal component of velocity remains constant because there is no acceleration in the horizontal direction. In reality, however, the bullet slows due to drag. As I said before, approximations must be made (such as the drag force depends on the square of velocity) and the math gets more complicated.
 
The good news is that a large sample size will work in your favor. You might get to shoot several hundred rounds if you want any kind of statistical significance. The better marksman you are, the fewer rounds necessary to tell your velocity. Likewise if your goal is to determine how well a new powder measure works ir tell speed of different reload recipies then tighter groups and consistent loads are your friend.
 
45_Auto has it right, as far as a practical solution goes.

You can do it from first principles, but it's messy and probably not very accurate.
 
If you know what the BC is, and weight/diameter, then all you have to do is find the same drop from the tables in a loading manual...

DM
 
Seems a shame to do that since it'll only be used on a couple of occasions then put away to gather dust.
Click to expand...

Buy it, use it, then sell it. you wont loose much money.. certainly more valuable then your best guesstimate...
 
OK. My interest has been piqued. This is what happens when you are a math nerd in real life. I agree with the responses above...buy a chrono, use it, sell it.

This would be fun though...

put a horizontal line on a target paper. Line your reticle up with the horizontal line and fire 15 shots. Measure the distance above or below the line and average them, take the standard deviation. Shots below the line are negative numbers, shots above the line are positive number. Repeat for multiple distances and check statistical significance on the average distance between groups. Take enough different distances that you can plot the parabolic shape of the drop and calculate the FPS of the bullet.

Pick a bullet that is pointed to reduce air resistance as much as possible. To check your work, reload the brass with a different powder charge and repeat.

To see the effect of wind resistance, switch to a round-nose or hollow-point or better yet a wad-cutter.

It will probably take about 75-100 rounds to adequately calculate the projectile speed. I don't know what you're shooting, but a chrono may actually be cheaper.
 
AND the quantity of bullets you would need may NOT be available just now.:D That makes a Chrony a better value these days. I am betting that once
you use it one time it will become useful in the future when changing some component (propellant type).;)
 
hso said:
Nope, you'd need to know several points along the curve of the drop and the distance at which they occur so you could plot the curve of the drop to get the information that would go back into the calculation that you would allow you to derive the velocity of the projectile.
Click to expand...

He has three points: 0yd, 100yd and 200yd. Add in ballistic coefficient and sight height (both very important) and 45_auto's technique will work fine. Some ballistic apps will back-solve for velocity given 2+ points on the trajectory.
 
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