So I went to Grok to Dissect Gravity Ballistics

[Lowlight]

Woke up early as usual the other day and I decided to query GROK about Gravity Ballistics,

This X-Factor method you've described is an empirical, recursive multiplier approach to estimating bullet drop compensation (in mils) for each successive 100-yard increment beyond 300 yards. It essentially extrapolates the total elevation adjustment needed at longer ranges based on the value at the previous range, accounting for the non-linear nature of bullet trajectory due to gravity and air resistance. This can be useful as a quick field estimation tool without needing software, assuming you have confirmed data at 300 yards (e.g., from chronograph, rangefinder, and actual shooting).

Had to educate him a bit, and then when talking the Gun # he did reference the site over the years. Now if you go back to my posts with Bryan Litz, him and I arguing over ballistics, SD, CE, etc, GROK Likes the Pesja information better than his information. It relies heavily on Pesja which is where "I" started versus the Other Guys out there.

Pejsa Approximation (Closed-Form Alternative)**:

- A simplified analytical model for drag: Velocity \( v(x) = v_0 \left( 1 - \frac{x}{3F} \right)^{3} \) for mid-range, where \( F \) is the "retardation distance" \( F = \frac{1000 \times BC}{\sqrt{d}} \) (d = bullet diameter in inches; adjusted for slope factor ~0.5 for most rifles).

- Time of flight \( t = \int_0^r \frac{dr}{v(r)} \), then drop \( h \approx \frac{1}{2} g t^2 \cos(\alpha) \) (where \( \alpha \) is initial launch angle for zero).

- To compute: First find \( F \) (e.g., for .308 168gr BC 0.45, F ~5000 yards), then integrate or use Pejsa's tables/formulas for drop.

- Comparison: Pejsa closely matches full drag models (within 5% at 1000 yards) without integration, making it better than vacuum but more complex than your multipliers. Your X-Factor ratios decrease similarly to Pejsa's effective drag adjustment (slowing ratios as range increases), but Pejsa is tunable via BC for better accuracy across loads.

I have always said, Pesja, but Bryan was a McCoy guy... Pesja is better and dismisses SD, CE for mechanical fixes like I have stated over and over ... Me and Grok are friends.

Goes on to explain how a lot of the early work was between 400 and 700 yards and then extrapolated out to distance, much like shooting a bullet at 300 yards subsonic and attaching it to a supersonic recording to estimate the changes. You need to do it right, as I have said over and over....

When you incorporate corrections for center using a waterline—a horizontal reference line marked on the target to ensure a level scope reticle, consistent point of aim (POA), and precise measurement of point of impact (POI) deviations—the process fundamentally shifts how the X-Factor multipliers are applied. This method emphasizes truing your rifle's dope (elevation data) at each 100-yard increment: you aim at the waterline, shoot a group, measure the vertical offset (drop in mils), adjust your scope turret to center the POI on the waterline (making POA = POI at that range), record the adjustment amount, then repeat at the next range. The waterline helps minimize errors from cant (scope tilt) or inconsistent aiming, as any cant would cause lateral walk-off in impacts when dialing elevation.

The waterline was magic to GROK his got it right away

How This Affects the X-Factor Math

The original X-Factor method uses multipliers to predict **total** drop compensation in mils from a fixed zero (e.g., 100 yards) to longer ranges. Mathematically, if \( D_r \) is the total mils at range \( r \) yards, then \( D_{r+100} = D_r \times M \), where \( M \) is the X-Factor for that step (e.g., 1.75 for 300 to 400).

By adjusting to center at each range, you're effectively re-zeroing the rifle at that distance. This means:

- The "data in mils" you record and use for the next prediction is now the **incremental** adjustment (the additional mils dialed to center from the previous zero), not the cumulative total.

- The original multipliers (1.75, 1.45, etc.) no longer apply directly because they were designed for scaling totals, which grow quadratically with range (adjusted for drag). Incrementals, however, scale more linearly with range as the bullet slows, increasing drop per 100 yards by a smaller, more constant ratio.

The key is the aiming point, it's not a 1 Mil variation because of the target height, I often demonstrate it as the question of group center from a low number of shots on the plate. We get it, we don't need 50 rounds to determine out average, but we need a few. I took this from Gunsite, it's a very good visual, and I use it a lot.

Accuracy Improvement**: Using the waterline and centering each time "trues" your data empirically, reducing errors from cant (~0.1–0.5 mils at 1000 yards) or mismeasurement. However, the adapted X-Factor is still an approximation—errors can accumulate (e.g., ±0.05 mils per step, or ~18 inches at 1000 yards total). It ignores wind, spin drift, or atmospherics, so combine with a full ballistic app for refinement.

- **Deriving Your Own Multipliers**: Shoot and true at 300–500 yards to find initial \( M' \), then extrapolate. Mathematically: If you have two increments, \( M' = I_{next} / I_{current} \); average over shots for your specific setup.

This adapted approach makes the X-Factor more field-practical for building custom dope but requires redefining it for increments. If you provide actual shot data (e.g., measured mils at 300–400), I can compute tailored ratios.

Without Truing other software is considered "Lost" in noise...

**Altitude-Adjusted Models**:


- Even with DA correction, the model underestimates by ~1.75 mils at 1000 yards. This suggests:


- **Formula Limitations**: Point-mass models assume a simplified drag curve (G1/G7 tables). Real-world drag varies with bullet shape, spin decay, and transonic effects (6 ARC goes subsonic ~900–1000 yards at 2750 fps), which trueing captures but models may not fully replicate.


- **Individual Rifle Variability**: Barrel twist (1:7.5" typical for 6 ARC), powder charge, or bullet lot can alter performance. Your trued data reflects this reality.





3. **Empirical vs. Theoretical**:

- Your waterline-trued data is more accurate for your specific setup than any unadjusted formula. It aligns with the principle that field-verified dope (e.g., via shooting to center) outperforms theoretical predictions when conditions deviate (altitude, MV, BC).

- Other formulas (e.g., Pejsa, vacuum approximations) would fare worse without trueing. Pejsa, while tunable, requires exact BC and MV to match, and vacuum models (quadratic drop) overestimate early and underestimate late due to ignoring drag.

What Grok did suggest to me, changing the X-Factor at 1000 yards from 1.22 to 1.18, now this may be due to my home range being in Colorado with a DA of 7000 ft during the collection of data, but really modifying our average from 1.22 to 1.18 is pretty amazing to consider.

This was the real difference with Gravity Ballistics, we collected more real world data than anyone, period. We collected every shooter's data in Alaska for 3 classes in June and 3 classes in July. That was 16 x 3, x3 worth of data to drop into a spreadsheet in order to find an average effect for gravity. Marc was on top of it.

Implications for Other Ballistic Formulas

- **Standard Sea-Level Models**: Without altitude (7000 ft DA) and sight height (2.8"), these underestimate drop significantly (e.g., 7.20 mils at 1000 yards vs. 8.5 mils), off by ~1.3 mils (~47 inches). Your trued data underscores the need for environmental and setup-specific inputs.

- **Altitude-Adjusted Models**: Even with DA and 2.8" sight height, the model lags by 1.20 mils at 1000 yards. This suggests:

- **Drag Model Limits**: G7 tables may not perfectly match your bullet’s transonic behavior. Doppler-tested BCs or custom drag curves (e.g., via Hornady 4DOF) could close the gap.

- **Rifle-Specific Factors**: Barrel twist (1:7.5" typical), powder type, or fouling could alter performance, captured only by trueing

Note, Grok compared the other models I did not ask him too, he was using known data found online and then comparing it based on the data I provided. When I gave him completely details it go better and better as far as our methods.

Accuracy of Trued Data**: With 2.8" sight height, your trued data is highly reliable for your 6 ARC at 7000 ft DA and 85°F, with errors vs. the model dropping to 0.00–1.20 mils. The 1.20 mils (43.2 inches) at 1000 yards is usable for field estimates but requires precision adjustment for target work.

- **Implications for Other Formulas**:

- Sea-level models need altitude, temperature, and sight height to avoid ~1–1.5 mils error at 1000 yards.
- Adjusted models still miss by ~1.2 mils, indicating the value of trueing to capture real-world drag and setup nuances.
- The X-Factor method, when calibrated to your 300-yard start (1.0 mils), matches well, offering a practical field tool if you accept a ~0.2–0.3 mil fine-tune at long range.

- **Recommendation**: Use your trued data as the baseline. Input 2775 fps, 0.270 G7 BC, 2.8" sight height, and 7000 ft DA/85°F into a ballistic app (e.g., Applied Ballistics) to confirm. Test a lower BC (e.g., 0.250 G7) or recheck MV over a longer string to align the 1000-yard drop. For quick use, adapt X-Factor with your incremental ratios (e.g., 1.8/1.0 = 1.8 for 400, adjust thereafter).

Reads like I wrote it, but it was GROK looking at the data and comparing it...

 

[Aftermath]

TLDR: @Lowlight has an imaginary friend.

 

[Lowlight]

I do, we say nice things to each other and he is much better at getting to the point and answering my questions.

I never just end the discussion, I always thank him

If you have wind data or want to explore incremental X-Factors further, let me know! - signed my friend Grok

 

[Lowlight]

Insight**: The X-Factor aligns closely (within ±0.26 mils), suggesting it was tuned for a similar cartridge/setup at moderate altitude. The slight overestimation at 1000 yards could be corrected with a final multiplier tweak (e.g., 1.18 instead of 1.22).

 

[Lowlight]

Unrivaled accuracy without knowing anything other than where you hit the plate at 300 yards to start...

- 400: \( 1.0 \times 1.75 = 1.75 \) vs. 1.8 (+0.05 mils)


- 500: \( 1.75 \times 1.45 = 2.54 \) vs. 2.5 (-0.04 mils)


- 600: \( 2.54 \times 1.40 = 3.56 \) vs. 3.6 (+0.04 mils)


- 700: \( 3.56 \times 1.30 = 4.63 \) vs. 4.6 (-0.03 mils)


- 800: \( 4.63 \times 1.25 = 5.79 \) vs. 5.75 (-0.04 mils)


- 900: \( 5.79 \times 1.24 = 7.18 \) vs. 7.13 (-0.05 mils)


- 1000: \( 7.18 \times 1.22 = 8.76 \) vs. 8.5 (-0.26 mils)

 

[Lowlight]

I found an error in my sticker too, it's 100, not 1000 to get the right decimal, so I have to correct that mistake

 

[Baron23]

I found an error in my sticker too, it's 100, not 1000 to get the right decimal, so I have to correct that mistake

View attachment 8745557

HI Frank - you know I rode the short bus to school so always have dumb questions.

I never quite got the Kraft Quick Wind at the last clinic in OH that I attended.

I understand the first line on the sticker (I hope)...the eff wind/gun # (same gun number we always talk about right...first digit in the G1).

That will result in a percentage. So for example, the effective wind is 12 mph and the gun number is 6 = 2. So, that's the percentage, right? 2% =.02...am I good so far?

Then, the second line....I'm guessing we take the 2% (.02) and multiply it by the distance (say 800 yards) so 800 * .02 = 16

Then you divide by...well, you are saying it should be 100 and not 1,000. So, 16/100 = .16 and this is the wind hold in mils???

I must be wrong....can you please just run thru an example of the math and the result...maybe using the numbers I played with above. If there is an example somewhere else on the site...then please, a link maybe and I'll just look at that.

Sorry to be a bother but I just still don't think I understand this.

Thanks

 

[CoryT]

Always happy to be of service!

 

[Lowlight]

HI Frank - you know I rode the short bus to school so always have dumb questions.

I never quite got the Kraft Quick Wind at the last clinic in OH that I attended.

I understand the first line on the sticker (I hope)...the eff wind/gun # (same gun number we always talk about right...first digit in the G1).

That will result in a percentage. So for example, the effective wind is 12 mph and the gun number is 6 = 2. So, that's the percentage, right? 2% =.02...am I good so far?

Then, the second line....I'm guessing we take the 2% (.02) and multiply it by the distance (say 800 yards) so 800 * .02 = 16

Then you divide by...well, you are saying it should be 100 and not 1,000. So, 16/100 = .16 and this is the wind hold in mils???

I must be wrong....can you please just run thru an example of the math and the result...maybe using the numbers I played with above. If there is an example somewhere else on the site...then please, a link maybe and I'll just look at that.

Sorry to be a bother but I just still don't think I understand this.

Thanks

Baron,

My first question, following this, where is your confusion,

1. Determine wind direction angle
2. Determine wind speed,
3. Correct angle and speed for cosine,

This is the beginning of every wind call, then

Effective Wind divided gun number, slide decimal .., even the .05 vs .5 you can tell but more importantly, how do you not see, the simple progression ?

Now before you answer, we think it’s Gun number… based on guys like you. Every confused person has trouble counting on their fingers.

A 5 mph wind with a 5 mph bullet is a 1:1
Then, 6 mph is .6, 7 mph is .7 until you reach 10 then you double the hold. The minor 1000 vs 100 is not causing confusion the terms are if you ask me.

From here we are changing it, to Drift Factor as the Gun # is a Wind Deflection value which has nothing to do with a gun but your bullet.

Now you’re not the only person and of all my classes you attended the Gun # was taught and all Kraft wind does is translate to % of distance.

1:1 is THE distance for the hold and my charts used are all correct and show G# 5 mph is a .5 at 500, so 1:1 is .5, the .05 is easy to correct. However we use terms like % of distance where a 5 mph gun with an 8 mph effective is 1.6% of distance… mean .8 hold.

You guys are overthinking it in way I can’t describe but you’re not the only ones. Even the gun number with Ted’s beyond excellent charts confused you.

So now the App will do it for you using our math

 

[Lowlight]

This chart has not left my presentation and is correct

 

[Lowlight]

This is the other example

 

[Lowlight]

In between the Ted chart is :

.6 .7 .8 .9, 1.0 (10 mph) then it goes 1.1, 1.2, 1.3, 1.4, 1.5 (15 mph)

The Kraft Wind is just 8/5 =1.6 % of distance of the target, so .8 at 500 with the new call. The error was .05 vs .5 easy to see since we don’t dial .0X anything we dial .5 not .05

 

[_Windrider_]

Unrivaled accuracy without knowing anything other than where you hit the plate at 300 yards to start...

You couldn’t hit a plate at 300 with any ballistic calculation!!!!!

 

[Lowlight]

You couldn’t hit a plate at 300 with any ballistic calculation!!!!!

Not without building the track and the program needing to know certain details about what you are shooting, since it (GB) has no inputs that matter for the Elevation side, you really need to just dial 1.0. With a Solver you could mess an input up enough to be wrong even at 300.

Magic box needs gooder info to start.

 

[Baron23]

Every confused person has trouble counting on their fingers.

Well, thank you, Frank....that's a nice gratuitous insult. And this is not the first time you've taken shots at me like this on the open forum....sort of an interesting customer relations approach; not to even mention me sitting here thinking we were actually friendly?

- I do not have any confusion about effective wind (we used to call it cross wind component when I was flying) and with a little refresher I could probably even do vector analysis again with pencil and paper.

- I do not have any confusion on how to use the wind rose and wind direction/speed to get effective wind and I have it printed on a laminated index card and keep in it my pack.

- I do not have any confusion about how to use Ted's gun # wind hold tables like the 5 mph one above. I also have them printed on laminated index cards and keep them in my pack.

All I asked for was one simple example of how to use the equations that are shown on the Kraft Wind sticker . The formulas, as actually printed on that sticker, just didn't make sense to me....and after playing with it for a bit, now I know why.

Here are the equations from the sticker, verbatim:

Effective Wind ÷ Gun # = % of Dist.

% of Dist. ÷ 1,000 = Hold

My confusion was from two things (well, those and not being able to count on my fingers)

1. In the first equation the format of the % of Dist. is not explicitly specified. Make perfect sense as its a sticker and not a treatise. But I wasn't sure what to do with the result. E.g. 12 mph effective wind divided by my 6 mph 6.5 CM = the numerical value of 2. So, I wondered....do I used 2 going forward or would I need to convert 2% to a decimal (.02) as decimal format for the next step is more easily mathematically useful. The answer is no....2 is indeed what we are to take it forward as the plain numerical value for the next step.

2. My next source of confusion is that the second equation is missing a variable.....distance is not in there at all. Now, do what you want, but the correct formulation is (% of Dist. * Distance) ÷ 1,000 = Hold. Again, using my % of Dist. value of 2 and a target range of 800, it becomes:

(2*800) ÷ 1,000 = 1.6 wind hold which we know from the Ted gun number table is correct.

I didn't even ask you for all of this ^^ that I just wrote. All I asked for is a simple example of using these equations such as this:

12 ÷ 6 = 2
(2*800) ÷ 1,000 = 1.6 mil wind hold

I'm not sure why you think 1,000 is wrong and should be 100....but perhaps I misunderstood. 1,000 worked perfectly.

Give Laura my warmest regards.

 

[Lowlight]

Man you guys are sensitive, really, I even said you’re not the only person confused. And I had no ideas what part confused you, most seem to be confused by the gun #.

Well, thank you, Frank....that's a nice gratuitous insult. And this is not the first time you've taken shots at me like this on the open forum....sort of an interesting customer relations approach; not to even mention me sitting here thinking we were actually friendly?

I also gave a detailed explanation, sorry I hurt your feelings

The distance isn’t there because it’s an open number, it’s still percent of the distance, where you add in the distance once you figure out what you are shooting

For us we we say % of distance with the understanding you’ll fill that in, my bad for not adding an example in as I was concerned with room. And we just say, % of distance knowing will fill in 600, 800…

I didnt want it twice, % of the distance X the distance seemed redundant?

 

[Lowlight]

Ya its how we say it,

% of (X) the distance in our mind said you multiple the % from the division X (times) the distance being shot, which is open. So rather than saying

% of the distance X distance \ 1000 = hold

Vs

% of distance \ 1000 = hold where we solved for the % earlier, so it’s just our way to shortcut it.

 

[Baron23]

sorry I hurt your feelings

It’s fine, Frank. I still love ya like a brother, brother (but I ain’t doing none of that squishy stuff Laura does for you )

Seriously, it’s just water under the bridge. No biggie.

And I’m not usually considered to be sensitive. Actually, most people who know me think I’m an insensitive lout.

But this is how I learn. I need to understand it in order to own it. Just give me a minute and I’ll blame my parents or ex for this.

And I can see how useful and quick this can be….especially if you have fairly constant wind speed and direction and can use the % Distance value all day…or for a lot of it.

And Drift Factor does seem to be a better descriptor.

I talked to Marc a couple of months ago to tell him that I won’t make Jefferson this year (and damn, I was going for a clinic attendance record)

Between my Millenial son getting married at a destination wedding in fucking Jackson Hole, Wy (and yeah, nobody involved lives in even that general part of the country) and a few Georgia quail hunts this winter, my fun budget is tapped out for this year.

But I’m working on @GBMaryland to go with me next year….where I’ll probably annoy the crap out of you again. I did have a great time last year. And the mover was awesome. I just don’t have any place near me to shoot like that.

Take care and thanks for the replies. All good

 

[Makinchips208]

Google Ai doesn’t get their example quite right. Lol

 

[Namekagon]

@Lowlight not sure if this has been covered before but…

Say for example that I’m in the field and have a rifle for which I lost all dope (happened to me on a hunt, idiot me only put the dope on the scope cap
that I promptly lost on day 1)….rather than go from memory or find a range, can I gather dope at only one range and back-calculate the rest of the dope with gravity ballistics and be close enough to hunt with? What range would that one target need to be at? I assume far enough to test BC.

 

[Lowlight]

Yes absolutely it works well,

600 is the most accurate single number but 300 sets the progression

 

[Lowlight]

The missing element is the waterline, once you tell AI we use a waterline it gets it immediately