I did long range testing on my gen 1 .22 royale and .25 s510 last week. I verified muzzle velocity as well as the velocity at set distance targets which were at 50, 60, 70, and 80 yards with the chrony. It turns out chairgun thinks my diablo pellets should be dropping at a substantially higher rates than they actually are. Only when I crank the b.c. up to .09 on the Royale and .046 on my s510 does the trajectory come close to falling in line!

Now I know Matt Dubber just tested the b.c.s of diablos and found them to be 'better than chairgun states' out of smooth twist x barrels but I'm shooting a gen 1. I changed different factors multiple times within the app, to see if I had entered data wrong, but to no avail.

Anyway, I'm going to make a switch with my software. What do y'all recommend, specifically?

The math behind the ballistics in Chairgun is very simple, and yes, the numbers are accurate.

When you find a disagreement between the calculated trajectory (by any decent ballistics program) and your observations, you may want to check the following:

1) Your scope height is really what Chairgun uses internally. Chairgun expects the scope height to be the distance between the optical axis of your scope and the axis of the bore, measured at the muzzle. This is not the same as the distance from the middle of the scope body to the breech, which is what you normally measure.

2) The BC is not defined uniquely, so you must make sure the BC you input is consistent with the way Chairgun uses the BC in its computations. The same projectile has different BCs, depending on the so-called drag function that maps the drag characteristics of the pellet to the BC. The BC is an artificial construct, essentially. Many internet sites don't tell you which drag function their BC is based on, and in some instances they provide wrong numbers for the BC (I have found the BCs in the Straightshooters website, for example, to be wrong.) Providing a BC without saying with drag function it is based on is totally meaningless. Make sure you have the right drag function selected in Chairgun.

3) Make sure the elevation above sea level and temperature are consistent with Chairgun - changes in air density affect the trajectory.

4) Make sure your gun zero is the same as used by Chairgun - at 80 yards, a difference of 5 yards in your zero can translate to almost an inch in drop difference, depending on the pellet.

Remember that the BC is not a property of the rifle, it is property of the projectile. Differences in rifling may change the BC very slightly, but detecting those changes in a statistically meaningful manner is more complicated than it seems.

Anyway, I'm going to make a switch with my software. What do y'all recommend, specifically?

I'd be interested in what you find when you compare your results to this ballistic calculator's predictions.

I have found Chairgun app. to be a great reference tool. However, I found using the default POI distances to be different with different guns than what CG indicated it should be.

My approach to this was simple: (at least to a simple person like myself)

I zeroed the gun using the 1" KZ per CG default.

Entered all the variables in CG and allowing the default BC in the app.

Made note of the different "claimed" POI.

Moved the target to that distance of each successive mildot holdover.

Shot 3 t0 5 shots.

If the POI of the app didn't agree with the POI of the gun, I simply changed the BC in the app.

Interestingly, there was a very very close correlation in doing so from mildot to mildot. And typically, I only take it out to 100y as this is as far as I will take a shot because then it becomes a real "Hail Mary" for someone like me who hunts as the conditions (wind, AOA, hold style, etc, ) becomes an even bigger variable than the BC.

At the end of the day, it really doesn't matter what the true BC is if your gun doesn't reflect that CG says it should be. I guess you could change any of the variables as long as the results are accurate. (i.e. scope height, FPS, temperature, altitude)

Sorry I don't have a mathematical calculation variable to use in the X-Y=Z2 formula.

I was trying to figure the same thing out by using the highly regarded practice of trial and error.

@Steve in NC

What is the drag function used by the calculator you cite?

Here's a link to a (fairly) recent discussion of that very topic.

https://airgunwarriors.com/airgun-talk/how-does-a-hollow-point-pellet-work/#post-3479

I made a simple comparison between CG and my own ballistics system.

0.177 pellet, G1 function in both systems.

Weight = 10.44 grains, BC = 0.027, muzzle vel = 850 ft/sec, zero at 35 y, scope height = 2 in, wind = 5 mph from 9 o'clock

Results at 55 yards

Chairgun - drop: 2.47 in, drift: 2.64 in, velocity: 647 ft/s

My system - drop: 2.47 in, drift: 2.61 in,velocity: 648 ft/s

This type of agreement suggests the internals of Chairgun are just fine.

You are right, Steve. That is why I say "suggests" rather than "confirms"

The probability that two ballistic systems, developed independently and distant in time and space, will be wrong in the exactly the same way is very much smaller than the probability of there both being right. The reason is that there are many ways of being wrong, but only one way of being right. In fact there are infinitely many ways of being wrong. This means the probability of being equally wrong is very very tiny (zero, mathematically speaking 🙂

Btw, there is also the probability they are both wrong, but both produce the correct results by chance. Now this probability is really very small.

2) The BC is not dProviding a BC without saying with drag function it is based on is totally meaningless. Make sure you have the right drag function selected in Chairgun.

Well the drag function was the issue I did not find. Thanks! It now looks alot better with the diablo pellet drag law applied.

Anyway, I'm going to make a switch with my software. What do y'all recommend, specifically?

I'd be interested in what you find when you compare your results to this ballistic calculator's predictions.

Since I set my drag co. on chairgun correctly that system is very, very close to the same.

I don't know about non diablo pellets, but for the diablos I shoot, that system works without minding about drag values.

If the POI of the app didn't agree with the POI of the gun, I simply changed the BC in the app.

Well that would be my thinking anyway. BC changes at different velocitys so even within 1 shot the BC changes as it loses speed downrange.

My bottom line is going to be testing several specific ranges by shooting myself and then detemine the BC I'm going to use for calculations in the app. Temperature, elevation ect. do go into account but those things for sure should not be the focus so I'm doing my testing on one day and then let the app calculate for the secondary stuff.

Anyway, I'm going to make a switch with my software. What do y'all recommend, specifically?

I'd be interested in what you find when you compare your results to this ballistic calculator's predictions.

Since I set my drag co. on chairgun correctly that system is very, very close to the same.

I don't know about non diablo pellets, but for the diablos I shoot, that system works without minding about drag values.

Thanks, Ben. The ballistic math in Perry Babin's demo (that I development more than a decade ago) has been used successfully in many trajectory calculators, and in fact was at one time even the basis for ChairGun!

My impression is that ChairGun was complicated with non-diabolo drag functions when it came to be sponsored by a scope manufacturer. While this was a useful extension of an undeniably powerful piece of software for powder-burners with their different projectile shapes and supersonic velocities, it's mostly just a source of unnecessary confusion for airgunners.

Hey thanks for the info Steve. Im now alot smarter than I was before!

Im curious as to how you went abou developing the software. How did you start and what were the basics?

Very flattering, Ben. Thanks!

Well, I started tinkering with simple programs that generated numeric simulations of trajectories, then wondered if I could find an analytical solution for pellet retained velocity and (from that) time of flight.

Beginning with the idea that the deceleration of the pellet in flight is given by...

**dV/dT = -V^2/bc = -VV/bc = -V(dX/dT)/bc**

...dividing both sides by dX/dT...

**dV/dX = -V/bc**

...recognizing the classic property of the EXP function of being proportional to its own derivative and integrating both sides with respect to X...

**V = Vo EXP(-X/bc)**

Most everything necessary to calculate an accurate (subsonic) trajectory, falls out from that. For example(s)...

** Zero Range Calculations****a. Qz = 34500* BC (e^(Z / (11500 * BC )) - 1) / MV****b. X = ((193 * Qz ^2 ) + SH) / Z**

** Target Range Calculations****a. Qt = 34500* BC (e^(R/ (11500 * BC )) - 1) / MV****b. Time_to_target = 24000 * BC (e^(R / (8000 * BC )) - 1) / MV****c. Time_to_zero = 24000 * BC (e^(Z / (8000 * BC )) - 1) / MV****d. POA-POI = (R * X) - (193 * Qt ^2) – SH****e. Holdover = POI-POA****f. Clicks = 95.5 * H / R / MOA****g. Velocity_at_target = MV / e^(R / (8000 * BC))****h. Qa = MV * SQRT(SH) / 45****i. Apogee = 8000 * BC * ln(Qa / 7413.1 / BC + 1)**

**Where...**

**a. BC = Ballistic Coefficient ****b. MV = Muzzle Velocity (fps)****c. MOA = Scope MOA (1 MOA = 1.0472 in @ 100 yards)****d. SH = Sight Height (inches)****e. Z = Zero Distance (yards)****f. R = Target Range (yards)**

Hey thanks for the info Steve. Im now alot smarter than I was before!

Im curious as to how you went abou developing the software. How did you start and what were the basics?

Very flattering, Ben. Thanks!

Well, I started tinkering with simple programs that generated numeric simulations of trajectories, then wondered if I could find an analytical solution for pellet retained velocity and (from that) time of flight.

Beginning with the idea that the deceleration of the pellet in flight is given by...

dV/dT = -V^2/bc = -VV/bc = -V(dX/dT)/bc...dividing both sides by dX/dT...

dV/dX = -V/bc...recognizing the classic property of the EXP function of being proportional to its own derivative and integrating both sides with respect to X...

V = Vo EXP(-X/bc)Most everything necessary to calculate an accurate (subsonic) trajectory, falls out from that. For example(s)...

Zero Range Calculationsa. Qz = 34500* BC (e^(Z / (11500 * BC )) - 1) / MVb. X = ((193 * Qz ^2 ) + SH) / Z

Target Range Calculationsa. Qt = 34500* BC (e^(R/ (11500 * BC )) - 1) / MVb. Time_to_target = 24000 * BC (e^(R / (8000 * BC )) - 1) / MVc. Time_to_zero = 24000 * BC (e^(Z / (8000 * BC )) - 1) / MVd. POA-POI = (R * X) - (193 * Qt ^2) – SHe. Holdover = POI-POAf. Clicks = 95.5 * H / R / MOAg. Velocity_at_target = MV / e^(R / (8000 * BC))h. Qa = MV * SQRT(SH) / 45i. Apogee = 8000 * BC * ln(Qa / 7413.1 / BC + 1)

Where...

a. BC = Ballistic Coefficientb. MV = Muzzle Velocity (fps)c. MOA = Scope MOA (1 MOA = 1.0472 in @ 100 yards)d. SH = Sight Height (inches)e. Z = Zero Distance (yards)f. R = Target Range (yards)

A few years ago I wrote a spreadsheet to generate my dope sheets. It incorporate measured scope subtensions and uses your equations as the basis for the pellet trajectory. They match real world results near perfectly.