by Tom Gaylord
Writing as B.B. Pelletier

This is another guest blog from reader Dennis Baker. He sent this to me based on the comments several of you made to his last guest blog.

If you’d like to write a guest post for this blog, please email me. Now, over to you, Dennis.

Determining muzzle velocity

By Dennis

This report covers:

  • Introduction
  • Background
  • Trajectory
  • ChairGun Pro trajectory calculation
  • Comparison of observed and calculated trajectories
  • Error assessment
  • Conclusion

Introduction

How does one determine muzzle velocity? Well, mostly with a chronograph. But if you don’t have a chrony, and don’t want to spend the hundred or so bucks to buy one, use it once, and have it sit around the house taking up space and using up air for the rest of its life, there is another, though less convenient, option. Read on …

Background

In my recent review of the BSA GRT Lightning XL SE (.22 caliber), I reported in Part 1 that the ten-for-ten chrony test of the gun on initial purchase had indicated an average muzzle velocity of 767 fps with 11.9-grain pellets. In a comment, I discussed several issues and showed results of several groups shot at 15 yards. I was encouraged to shoot at greater distances and show results in Part 2. Blog reader Yogi noted that the reported velocity was about 100 fps higher than he had seen in other reviews. In response to Yogi’s comment I mentioned how the free application, Hawke ChairGun Pro, could be used to infer the muzzle velocity. Using this application it was possible to infer that the muzzle velocity of my Lightning was indeed about 100 fps below the ten-for-ten measurement: about 665 fps. Note, that my review used a heavier pellet than the one used in the ten-for-ten test. I found the 14.66-grain, H&N Field Target Trophy to be a good pellet for my gun, so this is what I used in the reviews.

Another blog reader, Chris USA, suggested that it might be of value to post a blog article showing how to use trajectory to infer muzzle velocity. So you can blame Chis for this post!
If you wish to read the original review articles here are the links.
Revisiting the BSA GRT Lightning XL SE: Part 1
Revisiting the BSA GRT Lightning XL SE: Part 2

Trajectory

The first step is to determine the actual trajectory of the pellet. This is done by shooting groups at intervals throughout the ranges of interest. In my case, as I am interested in backyard shooting, the ranges of interest were from about 10 yards to about 40 yards. After zeroing at twenty yards, shooting four shot groups (for the most part) at five yard intervals yielded the following trajectory.

trajectory 10 to 40 yards
Trajectory — 10 top 40 yards.

Eyeballing a curve through these groups shows the pellet trajectory through the ranges of interest. The trajectory shows that the POI was about one inch low at ten yards and 40 yards, and about 1/8 inch high at 25 yards.

trajectory 10 to 40 yards with curve
Trajectory, 10 to 40 yards with curve.

ChairGun Pro trajectory calculation

Now, if one can fit a similar trajectory curve using a mathematical calculation (or a computer application), one can determine the muzzle velocity of the pellets. Turns out, there is an application that permits this. It is ChairGun Pro from Hawke. Here is the link to the downloaded page.

The application allows you to play with input parameters in order to attempt to match the trajectory curve. You get a visual response in real time. The critical input parameters are as follows:

• Pellet weight and ballistic coefficient – The application has a database, or you may be able to get these from the manufacturer web page as I did for the H&N FTTs.
• Muzzle velocity – You play with this parameter last as you attempt to match the trajectory. My final result indicated a muzzle velocity of about 665 fps. This compares well with the manufacturers stated velocity of 670 fps. Go figure?
• Zero range – The range at which your rig is zeroed on target.
• Sight height – The distance between the center line of the bore and the center line of the scope. I found this parameter to be very critical.
• Start range/End range – The nearest and farthest ranges to the targets. In this case 10 and 40 yards.

The following image shows the parameters (circled on the image) and the resulting trajectory curve.

ChairGun Pro graph
Screenshot of ChairGun Pro showing critical parameters

Comparison of observed and calculated trajectories

The following table shows a comparison of the POA/POI differences measured in inches from the actual target set (using the curve) and those calculated by ChairGun Pro.

comparison graph
Comparison of observed versus calculated differences in POA and POI at ranges from 10 to 40 yards.

For a visual comparison, here is an overlay of the ChairGun Pro trajectory on the targets image.

overlay of trajectories
Overlay of ChairGun Pro trajectory on targets image.

In this overlay, the scale of the ChairGun Pro image was adjusted to match the scale of the targets image, i.e. the length equal to the 10 to 40 yard scale and the 1 inch vertical scale equal to the 1 inch targets. As can be seen, the images are not an exact match. The observed trajectory (targets image) does not fall off quite as quickly as the ChairGun Pro trajectory (red) at 10 yards and at 40 yards. This will be discussed in the error assessment section that follows.

Error assessment

There are quite a number of possible sources of error in this demonstration. Here are a few.

• All of the distances were paced out, not measured. So each may be off by a foot or so either way. This includes the zero distance.

• The curve fit to the trajectory shot in the field was not calculated but only eyeballed in using a simple graphics application – so not the most precise fit in the world.

• Some error may be introduced in the visual comparison when trying to match the scales of the two trajectory curves.

• The scope height was difficult to measure with precision, and this parameter impacts the velocity used to best fit the target image.

There are uncertainties introduced by each of these possible sources of error. For instance, one can show a flatter trajectory with ChairGun Pro by decreasing the scope height 0.2 inches and increasing the muzzle velocity to 685 fps. This better matches the trajectory that was realized in the field, but it doesn’t match the measured scope height.

All-in-all, I feel pretty confident in saying that the muzzle velocity of this rifle with this pellet is in the neighborhood of 665 to 685 fps. This is pretty close to the 670 fps velocity reported by the manufacturer. That’s my story, and I’m sticking to it!

Conclusion

Clearly it is much easier to determine muzzle velocity by measurement with a chronograph. But if you don’t have one, or if you want the challenge of working it out yourself, or if you just have a lot of spare time on your hands, it is possible to get a good approximation using the approach demonstrated in this article. If you feel I’ve wasted your time here, don’t blame me! As I said in the Background section, blame Chris USA!