MERC - Maximum Effective Range Calculator

Over the past couple of months, I have been creating a Microsoft Excel based tool that calculates your probability of hitting a target. It allows study of the effects of rifle and environmental variables and uncertainties on hit percentage.

Fellow LRH member Scott B. (entoptics) convinced me that it would be worthwhile to release this tool to the shooting community. We jazzed up the user interface, design/layout, instructions, and many other details. The latest version is linked below. Hopefully you find it useful!

Note - you will need Microsoft Excel on a computer in order to run this tool. Versions of Excel for your phone will not work.

MERC Download Link


Introduction to MERC - Maximum Effective Range Calculator
In a perfect world, the bullets would always leave your barrel in the direction you intended with identical velocities, and there would be no uncertainty in your wind or range estimation - you would hit your target's center with every shot. Unfortunately, we have to contend with variation and uncertainty in the real world.

This calculator lets the user specify information about their rifle and the shooting conditions, including the uncertainty in each input. The calculator applies an amount of random variation based on those specified uncertainties, and determines where the bullet would have hit. It then repeats this process for many hundreds of shots, and calculates a hit probability based on the number of hits and misses. It also plots the hit locations for the first 300 of these shots on a graph, to visually show the distribution of their impacts.


What can I use MERC for?
MERC can be used to study many shooting situations. Here are some examples to get you started:

• Comparison of one cartridge/rifle/bullet to another. For a given set of conditions, which has better hit%, etc.
• Identify the longest range you would be comfortable hunting at, given a specific set of conditions and uncertainties.
• Estimating what hit rates to expect for a yardage that's farther than you've shot before.
• Comprehend how errors in your scope zero affect hit probability.
• How much does "x" variable matter. For example, does a 0.5 MOA rifle help my hit% for my shooting scenario? How about StdDev in MV?
• How accurately do you need to estimate range and wind in order to have consistent hits?
• For a desired hit percentage, how much extra range does using a higher BC bullet provide?
• Understanding how wind angle uncertainty can cause groups that aren't centered around your point of aim.

Example screenshot from the calculator:

• Version 2.7.00 had 241 downloads.
• Version 2.7.04 released on 2020/09/08. Minor revision to instructions. Include user defined simulation Titles in the results table headings. Updates to the "Results Output" worksheet.

w00000h0000!

Just a couple things to add.

1) @speedengineer put in a herculean effort in developing the code, interweaving all the calculations, and overall implementation, so throw him a few likes (and perhaps buy him a beer via the instructions page)!

2) You must have an Excel version that supports VBA Macros and, as SE mentioned above, phone versions won't. Don't know about tablets.

3) If you're not familiar with Excel, there are tabs at the bottom, which are each of the sheets needed to use the tool. Click on them to switch between tabs (e.g. Instructions, Simulation A, JBM Paste).

Also, when you first open the workbook, make sure to hit the "Enable Macros" button (on some versions of Excel there may be a little yellow header row that says "Enable Content" instead of a popup dialogue).

For those of you who don't read instructions...(most of us?), a few quick tips to get started.

A) Every cell with a little red triangle in the corner has a "hover over" tip. Hold your mouse over the cell, and instructions/tips will pop up.

B) You must calculate 2 trajectories with your ballistic calculator, which MERC then interpolates between to calculate the effects of your uncertainties. BE CAREFUL IN THIS STEP AND JUST READ THE FN INSTRUCTIONS. Crap in = Crap out!

C) We recommend using a fixed zero angle (angle between scope LOS and bore), and not a fixed zero distance, when calculating your trajectories. JBM ballistics allows this, and is our recommended calculator. We also added a convenient "auto paste" feature for use with JBM. READ THE JBM PASTE instructions for this.

A fixed zero distance will force your bullet through the bullseye at that distance, so when you calculate a trajectory at a different velocity, it will raise/lower the scope to make it pass through whatever distance you have this set at. This isn't how the real world works. If your ammo speed changes from shot to shot (it all does), if you go up 5000 feet in elevation, or if it gets cold outside, your gun won't magically correct your zero for you in the field.

If your preferred calculator doesn't have a zero angle feature, that's fine, just make sure to set your zero pretty close (say 10-20% of the distance you are most interested in studying), to mitigate the errors this causes.

That's all for now. We eagerly await your feedback. This is hopefully an evolving project, so let us know the good/bad/ugly, and maybe we'll fix it...or maybe not...

Fancy! I miss having time to go shooting for fun!

I love how much stuff you can do with Excel! A lot more than just tabulating tables like most people use it for.

Figured I'd go ahead and give some examples of just how powerful this tool is.

For perspective, I've put at least 100 lbs of powder down the tubes of various rifles, and in retrospect, I wish I'd had this puppy a decade ago to help me hone in on my ultimate goal. Hitting what I'm aiming at. I wasted a lot of time, money, and barrel in various experiments that probably could have been far better spent by learning what variables I could control, and what variables I had to learn to deal with.

So...A quick comparison of 30-06 and 7mm Rem Mag. All uncertainties are the same, only the bullet and velocity have changed.

Shooter/Rifle = 0.5 MOA (I've never owned or been such a thing, but one can dream right?)
Muzzle V standard deviation = 10 fps (good quality handloads)
Wind = 10 mph from the right.
Wind uncertainty = 30% (± 3 mph with a 10 mph nominal wind, good mirage and a kestrel?)
Wind direction uncertainty = 45° (shooting in some variable terrain across a canyon for instance)
Range uncertainty = 5 yards (got a pretty good rangefinder reading, but not perfect)

This is what you see after you've run your two simulations. Red is 7mm Mag and blue is 30-06 in all the graphs and table headings.


To zoom in on the information at hand.

1) Note how the groups are not centered around the bullseye (500 yds). This is due to variability in the wind angle and speed. We'll hopefully address this cool insight in another post. The 30-06 with it's slower, lower BC bullet is affected more than the 7mm RM obviously. At 500 yds, it's 8 out of 10 for the '06 vs 9 out of 10 for the 7mm.



2) Will my gun actually get the job done and drop the slavering beast in it's tracks if I make a good hit? We can help answer that with the energy and velocity thresholds you enter. In this scenario, we're asking 1800 fps and 1500 ftlbs of energy on target (you choose values you're comfortable with in the inputs section). The results table will highlight the output in red if it's below this threshold, and there's also a line on the velocity and energy graphs to show this.





Note that the 7mm Rem (red simulation A) is still carrying plenty of speed/energy to 950 yds. The 30-06 (blue simulation B) with its lower B.C., runs out of steam at only 650 yds.

Also note, that despite both rifles having 0.5 MOA precision, the hit percentage drops below "ethuhcul" odds (misspelled to avoid stupid filter) way before the 10" target is half MOA. At 1000 yds (~1 MOA for 10"), it's only 27% even for the superior ballistics of a 7mm Mag. Both rifles run out of accuracy long before they run out of power.

In fact, we hit "coin flip" at 650 yds for the 30-06 and 750 yds for the 7mm.

3) But what about recoil? Of course a more powerful cartridge can go further, but what price am I paying? We've got you covered...

By inputting your rifle's weight (and optionally charge weight for more accurate calculations), MERC will calculate the free recoil, which is displayed on the far right.





Hope that helps clarify some of what you can do with MERC. We're planning to add some more insight and tips in the coming days.

What are the main differences between this and the Applied Ballistics "WEZ".

Dog Rocket said:

What are the main differences between this and the Applied Ballistics "WEZ".

Click to expand...

Price for one...

Don't know what goes into the WEZ calculations, but I'd assume it's something very similar, particularly in the "Monte Carlo" approach to uncertainties. I've not used it, but from what I've read, it has a few things MERC doesn't...

1) Built in ballistic calculator, so no need to pull trajectories from outside source.
2) Ability to add uncertainties to weather variables like pressure/temp/etc.
3) Heading/Location for Coriolis uncertainty
4) Different target shapes.

speedengineer may have some more insight on this.

entoptics said:

Price for one...

Don't know what goes into the WEZ calculations, but I'd assume it's something very similar, particularly in the "Monte Carlo" approach to uncertainties. I've not used it, but from what I've read, it has a few things MERC doesn't...

1) Built in ballistic calculator, so no need to pull trajectories from outside source.
2) Ability to add uncertainties to weather variables like pressure/temp/etc.
3) Heading/Location for Coriolis uncertainty
4) Different target shapes.

speedengineer may have some more insight on this.

Click to expand...

This is my understanding as well. The idea behind the tools is quite similar and they 'should' provide similar results.

AB WEZ appears to have additional features that allow more complex analysis. I haven't used it yet, personally. I'm sure I will at some point.

This is AWESOME

Here is an example of another use for MERC. How much does wind angle uncertainty matter when you are shooting with a headwind or tailwind?

Situation: Shooting a 6.5 PRC with 143 ELDX into a 10mph headwind.
The shooter has to estimate the direction of the wind. There will always be some error in your wind direction call. Plus, wind is rarely steady and the direction is constantly changing. How does this uncertainty in wind angle affect the horizontal spread of your impacts?

Case A (Red): 10mph straight headwind with 5 degrees wind angle uncertainty
Case B (Blue): 10mph straight headwind with 25 degrees wind angle uncertainty

This simple example shows that your estimation of the wind direction can be just as important as your estimation of the wind speed!


Hit dist plot at 600 yards

Wow. that is incredible. Looking forward to using it soon. Great work and THANK YOU

To build on @speedengineer's last post...

How does wind direction affect hit probability? We often assume that a tail wind is ideal, as it has a "zero" value (ignoring resistance and jump affects, which are generally small anyway). This is true if there's no uncertainty in the wind direction. As soon as the wind direction is variable, the tail/head wind can actually cause more dispersion and lower hit probability than a full value wind...

Here's a couple of simulations with a 7mm Mag, with a 0.7 B.C. bullet at 2920 fps, so it's a stellar wind performer.

10 ± 3 mph wind, 30° uncertainty in wind direction, run for "zero value" tail wind (180°) and a "full value" crosswind (90°). Notice that the 90° wind has a 10% better hit percentage!



How can that be?!?!

Well, though the absolute magnitude of the crosswind is greater, it's important to remember that we're adjusting for that with our hold or dials. What MERC simulates is the variation in the wind due to our uncertainty in the wind direction and wind velocity.

So to explain the phenomenon in more detail...

The black arrows are the spread in the wind direction, and the dashed red arrows are the 90° component that actually affects the bullet.

As you can see, the full variation in wind affect is relatively small over large swings in direction for crosswinds.


With a tail wind, relatively small changes in wind angle result in larger variation in the crosswind component, and even will switch the direction of the wind correction!


So, when we look at the hits on our 500 yard target, it should make sense.

With a variable tail wind (or head wind of course), you've made no correction for the windage, so if the wind shifts away from directly behind you, there's now a horizontal dispersion, that can switch depending on which way the wind changes. This shows in the much larger horizontal dispersion in the hit locations.

With a variable crosswind, the maximum and minimum windage change is far less, so the hits won't be spread as widely. One thing to notice though...The hits are not quite centered around the bullseye. They favor the right side a little bit (6 missed to the right, and only one missed to the left). This is another neat phenomenon that we'll address in another post soon...

Wow, and now I know the disadvantage of using a Linix computer.

We don't talk about wind on this forum.

You ain't from around here err ya?

speedengineer said:

Over the past couple of months, I have been creating a Microsoft Excel based tool that calculates your probability of hitting a target. It allows study of the effects of rifle and environmental variables and uncertainties on hit percentage.

Fellow LRH member Scott B. (entoptics) convinced me that it would be worthwhile to release this tool to the shooting community. We jazzed up the user interface, design/layout, instructions, and many other details. Attached is the latest version. Hopefully you find it useful!

Note - you will need Microsoft Excel on a computer in order to run this tool. Versions of Excel for your phone will not work. The MERC Excel file is attached to this post (contained within a .zip file, as that's the only way to attach this type of file here on the forum).


Introduction to MERC - Maximum Effective Range Calculator
In a perfect world, the bullets would always leave your barrel in the direction you intended with identical velocities, and there would be no uncertainty in your wind or range estimation - you would hit your target's center with every shot. Unfortunately, we have to contend with variation and uncertainty in the real world.

This calculator lets the user specify information about their rifle and the shooting conditions, including the uncertainty in each input. The calculator applies an amount of random variation based on those specified uncertainties, and determines where the bullet would have hit. It then repeats this process for many hundreds of shots, and calculates a hit probability based on the number of hits and misses. It also plots the hit locations for the first 300 of these shots on a graph, to visually show the distribution of their impacts.


What can I use MERC for?
MERC can be used to study many shooting situations. Here are some examples to get you started:

• Comparison of one cartridge/rifle/bullet to another. For a given set of conditions, which has better hit%, etc.
• Identify the longest range you would be comfortable hunting at, given a specific set of conditions and uncertainties.
• Estimating what hit rates to expect for a yardage that's farther than you've shot before.
• Comprehend how errors in your scope zero affect hit probability.
• How much does "x" variable matter. For example, does a 0.5 MOA rifle help my hit% for my shooting scenario? How about StdDev in MV?
• How accurately do you need to estimate range and wind in order to have consistent hits?
• For a desired hit percentage, how much extra range does using a higher BC bullet provide?
• Understanding how wind angle uncertainty can cause groups that aren't centered around your point of aim.

Example screenshot from the calculator:
View attachment 210491

Click to expand...

Thanks for your time and effort. Look forward to seeing this operate!