Chrony Beta speed calculations quiz for the math experts...??

[mikeinfwa]

Yesterday I noticed a distinct speed difference display while shooting the same load at 2 different targets.

Both targets were at the 1000 yard berm.

Target 1 was center target: avg speed 2978 fps

Target 2 was left of target 1: avg speed 2896 fps

The chrony sensors are 12 inches apart.

Muzzle was 10 feet from sensor #1

assuming target 1 speeds were 12 inches over the sensors....

What would the distance between the sensors be to account for the slower speeds when shooting at target 2 ?

I'm curious to see if changing the angle across the sensors is the reason for the slower speeds.

Note: all the shots were from the same shooting position. I would vary the shots between target 1 and 2. The shots at target 2 were obviously slower than target 1.

Thanks for the math brain assistance..

Mike

 

[mikeinfwa]

Here's a reply from a co-worker. I posted this on our pilots forum.

Hey Mike,
I sent your ? to my son. He is an engineer with General Atomics. He texted me back, but he mentioned 2 things; he doesn’t know how your sensors work and (2) he doesn’t know what your data looks like. He feels that you may have a systemic error in using the sensors off spec.
He was pretty pumped about getting some Sunday morning math. Here is what he responded with:

I'd say to arrive at an answer, I'd need two things:

-a sketch of the setup he's describing (with distances)
-the velocities of those 20 shots

That info would let you find out the standard deviation of the bullet velocities (and the odds/confidence interval that the speeds being read are correct). The setup would tell you if the sensors are seeing a shot at an angle to them.

If I had to use math to guess though...

V1=2978 fps

V2=2896 fps

V2/V1 = 2896/2978 = 0.97

So the 2nd bullet is traveling at 97% the speed of the first. If the first target is directly in front of the shooter, and the 2nd is a little off to the side of the first, we can use trigonometry to find the angle between the two that would result in that drop:

Cos(a) = .97

a = cos^-1(.97)

a = 13.5 degrees

If we want to then calculate the distance between the two targets, we'd get:

tan(13.5) = x / 1000 yds

x = tan(13.5)*1000 yds

x = (.24)*1000 yds

x = 240 yds

So... for this model to be accurate, the targets would have to be 240 yds apart. This was certainly not the case, which means that the assumptions of this model have to be wrong.

Those assumptions are:
-both bullets have the same true muzzle velocity
-angle between targets is sufficiently large that the small angle theorem doesn't apply (sinx does not = tanx)

Which means:
-the bullets were actually traveling at different speeds
-the distance from gun to target 1 is functionally the same as the distance from gun to target 2

This means one of two things is happening:
1) the bullets have a 3% variance is muzzle speeds
2) something was mechanically different between those two shots

#1 is VERY unlikely since he is recording his bullet speeds. It doesn't make sense to make a post about nominal readings asking for clarification.

So... something was mechanically different. It could have been barrel heating, but I'd expect a trend that follows it (speed change in many shots as barrel warms). However, it would be pretty much impossible to 100% nail down the cause with the data presented.

Thanks!

-Neil


I t appears my sample size was NOT large enough as the distance between targets 1 and 2 are about 5 yards

 

[pell1203]

Interesting exercise in frustration going on here... First rule in using an optical chronograph is to shoot straight down the axis of measurement making sure unit is level and shots are also fired level across the unit. Shooting at any appreciable angle across the sensors, in any direction, pretty much guarantees a garbage in garbage out outcome, which is exactly why your average velocity variation using identical loads is as wide as it is.

Since average velocity varied by 82 fps using identical loads, I'd be interested in finding out what the min and max velocities recorded across both of your measured groups was? The extreme velocity spread across both groups will likely be quite telling as to the quality of the data.

 

[Greg Langelius *]

If these were not consistently high one side, low the other, I'd be thinking we're dealing with error margins. But that's really just me, I just can't cope with a device that simply writes off a 1% error margin.

To iterate; Chrony claims in its user manual that any number calculated may be off by approximately 1% of the displayed value.

I.e., a displayed value of 2500 could actually be as high as 2525, or as low as 2475.

But the distribution of said 'errors' should be random. That doesn't appear to be the case.

That's all I got...

Greg