How To Calculate Effect Of Velocity Variability

[CharlieNC]

Simple question but I cannot get a consistent answer using different approaches. How to calculate the effect of velocity variability on target point of impact?

a. With a 100yd zero, simply changing the velocity gives an answer which seems to be low. Since the velocity also affects the holdover required for the 100yd zero, and this is factored into the calculation, the downrange effect is minimized.

b. So to reduce the 100yd effect, using a 1 or 25yd zero says the higher velocity hits LOWER downrange than the lower velocity.

c. Using the same zero, and changing the ammo temperature sensitivity to alter the velocity, the calculated effect seems too large.

Is there a ballistic program which allows a given velocity for zeroing, and a different velocity for shooting? Or is there a more "true" way to do this that I'm missing? Or should I just accept method "a" as being as close as I can get?

 

[Ballisticboy]

Assuming you are just after the vertical dispersion of your shots due to varying muzzle velocities what you need is a simple point mass model where you fix the elevation angle of the gun rather than the zero range. I assume you will be using BC as the source of your trajectory information so it needs to be a model which uses BC rather than drag coefficient. I am not sure where you will find one, a quick look at the JBM site didn't look very promising with most of the software wanting you to set zero range.
If you cannot find a suitable simple model, one way of possibly getting near to the correct value would be from the different times of flight to a given range for the different velocities. You can calculate the drop from the different times of flight and thus the vertical spread. The only problem with this approach is that it will not take into account the effect of the drag force on the acceleration due to gravity. It will hopefully be fairly small for reasonable ranges.
Alternatively, if possible, set your sight height to 0 and the zero range as close to 0 as possible. That should minimise the elevation angle change of the gun in the software and give the spread in impact point to a reasonable degree of accuracy.

 

[chromatica]

Assuming you are just after the vertical dispersion of your shots due to varying muzzle velocities what you need is a simple point mass model where you fix the elevation angle of the gun rather than the zero range. I assume you will be using BC as the source of your trajectory information so it needs to be a model which uses BC rather than drag coefficient. I am not sure where you will find one, a quick look at the JBM site didn't look very promising with most of the software wanting you to set zero range.
If you cannot find a suitable simple model, one way of possibly getting near to the correct value would be from the different times of flight to a given range for the different velocities. You can calculate the drop from the different times of flight and thus the vertical spread. The only problem with this approach is that it will not take into account the effect of the drag force on the acceleration due to gravity. It will hopefully be fairly small for reasonable ranges.
Alternatively, if possible, set your sight height to 0 and the zero range as close to 0 as possible. That should minimise the elevation angle change of the gun in the software and give the spread in impact point to a reasonable degree of accuracy.

 

[chromatica]

If you have access to AB Analytics desktop software, you can do the calculation you are talking about. You can set the standard deviation of muzzle velocity to a desired value and then set the SD of all the other variables to zero. Then sit back and watch a simulation of 1000 trajectories.

If you don't have access to this software:
If you set your zero range to 100 yards, the solutions will be relatively insensitive to small changes in muzzle velocity (even though the zero angle is recomputed from one case to the next). Try inputting muzzle velocities that are + 2 standard deviations and -2 standard deviations. This should give you an idea of the 95% confidence interval.

 

[Ballisticboy]

I have just been looking at the Hawke Chairgun Pro trajectory software and under the toolbox it has a vertical stringing function specifically for the data you are after. I know the software is designed for airguns but it has the G1 and G7 profiles so you should be able to use it successfully for bullets by the use of the appropriate weight, BC and muzzle velocity.