The Trajectory Normalizing Factor

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The Trajectory Normalizing Factor
By: Josh Kunz

The long-range shooting community is a niche market of the firearms world, and that niche is full of myths and misunderstandings about a lot of aspects of long-range shooting. One of the most common is the misconception that just because a caliber is larger or a bullet is heavier, it must therefore “cut the wind” better. Here is a simple, effective, and nearly fool-proof method to get a fast answer to, “which has a better wind call?” that doesn’t involve running ballistics through a calculator.

Many folks want a way to figure out what “the best” combination might be for a given task. This need is many times solved by doing detailed ballistics calculations. In today’s world of handheld computers (smartphones) this approach is much less onerous than in years passed but even today it still takes a lot more time to run a set of ballistic simulations than it does to solve a simple math problem on a 4 function calculator.

The Trajectory Normalizing Factor is a seemingly simple approach developed by myself to perform this exact task quickly and effortlessly when discussing caliber options with customers and friends for rifle building needs.

There are 2 basic inputs that are required and we can ignore a lot of the others that we need for the ballistic calculators. We are going to talk about comparing 2 calibers under identical conditions. Always. It’s not useful to compare combination A at sea level and combination B at the top of a mountain on a hot day. We need to simply know which is better under the same conditions because as those conditions change they change for both options.

Some basic rules and assumptions: Atmospherics are assumed identical.

Drop is important but for trajectory comparisons, it is secondary to the wind. Ignore drop concerns and worry about the wind.

The G-standard for the ballistic coefficients must be the same. The units on the muzzle velocity must be the same.

This means if Combo A uses feet/sec then Combo B must use feet/sec as well and if Combo B uses G7 standard, then Combo A must use G7 standard. Likewise, if Combo A only has data for G1 standard, then Combo B must use G1 or take the G7 value and convert it to G1.

Otherwise, the calculation is skewed.

OK, simple enough. What is TNF?

??? = ?? ∗ ??

Truly that simple.

Sample Calculation:
Combo A: Berger Hybrid 6mm 105gr flying at 3,030 fps (0.275 G7) Combo B: Hornady ELD-m 6.5mm 140gr flying at 2,740 fps (0.326 G7)

Which has a better trajectory?

??? =3,030???∗0.275=833.25 ?
??? = 2,740??? ∗ 0.326 = 893.24 ?

Based on the TNF calculated for each the 6.5mm option has a better trajectory. Below is the 1,000yd solution calculated for 0 DA showing the elevation & wind calls.

Screen Shot 2020-01-06 at 11.57.35 AM.png

In this case the larger, heavier bullet going slower did better than the smaller faster bullet. But let’s look add in a 3rd case where that wouldn’t be true. Combo C is using a 100gr 6mm bullet with a very high BC. Lighter, faster, and better trajectory.

??? =3,050???∗0.318=969.9 ?

Screen Shot 2020-01-06 at 12.00.52 PM.png

Let’s take it one step further by asking “If I have Combo A, how fast do I need to shoot Combo B to have an equivalent trajectory?” This is based on the age-old comparison of 2 bullets in the same rifle. Should we use the 180gr or the 162gr bullet because the 180 has more BC but the 162 can be shot a lot faster? Put more directly, if we have Combo A already figured out how fast does Combo B needs to go for it to be equivalent to Combo A?

Let’s take a look at the author’s 7mm SAUM shooting a Hornady 180 ELD-m at 2,870fps and figure out how fast the 162 needs to be shot to equate the wind call for the 180 at 1000yd?

Screen Shot 2020-01-06 at 12.10.01 PM.png

Soon this concept will be built into a calculator will be available for free on www.patriotvalleyarms.com
 

Tremor3Guy

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This has got to be the simplest way I’ve seen to compare projectiles and calibers. Awesome!! I made a excel sheet to compare lots of factors and it takes a minute to fill out, this is was simple to see if a caliber and projectile will meet your needs or not. Thank you!! Love the simplicity in what’s coming around lately!!
 
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Nik H

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The Trajectory Normalizing Factor
By: Josh Kunz

The long-range shooting community is a niche market of the firearms world, and that niche is full of myths and misunderstandings about a lot of aspects of long-range shooting. One of the most common is the misconception that just because a caliber is larger or a bullet is heavier, it must therefore “cut the wind” better. Here is a simple, effective, and nearly fool-proof method to get a fast answer to, “which has a better wind call?” that doesn’t involve running ballistics through a calculator.

Many folks want a way to figure out what “the best” combination might be for a given task. This need is many times solved by doing detailed ballistics calculations. In today’s world of handheld computers (smartphones) this approach is much less onerous than in years passed but even today it still takes a lot more time to run a set of ballistic simulations than it does to solve a simple math problem on a 4 function calculator.

The Trajectory Normalizing Factor is a seemingly simple approach developed by myself to perform this exact task quickly and effortlessly when discussing caliber options with customers and friends for rifle building needs.

There are 2 basic inputs that are required and we can ignore a lot of the others that we need for the ballistic calculators. We are going to talk about comparing 2 calibers under identical conditions. Always. It’s not useful to compare combination A at sea level and combination B at the top of a mountain on a hot day. We need to simply know which is better under the same conditions because as those conditions change they change for both options.

Some basic rules and assumptions: Atmospherics are assumed identical.

Drop is important but for trajectory comparisons, it is secondary to the wind. Ignore drop concerns and worry about the wind.

The G-standard for the ballistic coefficients must be the same. The units on the muzzle velocity must be the same.

This means if Combo A uses feet/sec then Combo B must use feet/sec as well and if Combo B uses G7 standard, then Combo A must use G7 standard. Likewise, if Combo A only has data for G1 standard, then Combo B must use G1 or take the G7 value and convert it to G1.

Otherwise, the calculation is skewed.

OK, simple enough. What is TNF?

??? = ?? ∗ ??

Truly that simple.

Sample Calculation:
Combo A: Berger Hybrid 6mm 105gr flying at 3,030 fps (0.275 G7) Combo B: Hornady ELD-m 6.5mm 140gr flying at 2,740 fps (0.326 G7)

Which has a better trajectory?

??? =3,030???∗0.275=833.25 ?
??? = 2,740??? ∗ 0.326 = 893.24 ?

Based on the TNF calculated for each the 6.5mm option has a better trajectory. Below is the 1,000yd solution calculated for 0 DA showing the elevation & wind calls.

View attachment 7218637

In this case the larger, heavier bullet going slower did better than the smaller faster bullet. But let’s look add in a 3rd case where that wouldn’t be true. Combo C is using a 100gr 6mm bullet with a very high BC. Lighter, faster, and better trajectory.

??? =3,050???∗0.318=969.9 ?

View attachment 7218638

Let’s take it one step further by asking “If I have Combo A, how fast do I need to shoot Combo B to have an equivalent trajectory?” This is based on the age-old comparison of 2 bullets in the same rifle. Should we use the 180gr or the 162gr bullet because the 180 has more BC but the 162 can be shot a lot faster? Put more directly, if we have Combo A already figured out how fast does Combo B needs to go for it to be equivalent to Combo A?

Let’s take a look at the author’s 7mm SAUM shooting a Hornady 180 ELD-m at 2,870fps and figure out how fast the 162 needs to be shot to equate the wind call for the 180 at 1000yd?

View attachment 7218639

Soon this concept will be built into a calculator will be available for free on www.patriotvalleyarms.com
Great post as usual. I want to run this for 338 LM. I have always believed that the move to heavier (300 grain or more) bullets is a mistake. I would like to run 300 grain against 250 and 285 grain versions
 

W54/XM-388

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Great post as usual. I want to run this for 338 LM. I have always believed that the move to heavier (300 grain or more) bullets is a mistake. I would like to run 300 grain against 250 and 285 grain versions
Warner Flatlines pushed fast will go the distance even better.
 
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W54/XM-388

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You might get copper creek to do some loading for you with them, or maybe some other smaller guys would do it.
But you could get into reloading cheap with a single stage press for .338LM
 

Nik H

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You might get copper creek to do some loading for you with them, or maybe some other smaller guys would do it.
But you could get into reloading cheap with a single stage press for .338LM
Cheap means slow and tedious. Reloading is something I am just not interested in doing. Have very little free time between work and family so I would rather spend it shooting than building ammo and driving myself crazy. I don’t shoot benchrest so factory is good enough
 
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Jack Master

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Frank talked with Mr. Kunz on the Everyday Sniper podcast about his Trajectory Normalizing Factor this week.
Find the podcast here - episode-236-josh-kunz-patriot-valley-arms

Here is a post I also made in the Everyday sniper Podcast section with e charts for this normalizing factor. Its easy to start seeing which bullet and velocity will be better in the wind.

Here is the post where Frank put Josh's Trajectory Normalizing Factor on the Hide.
This is also available on the PVA website here Trajectory Normalizing Factor



I know this a simple multiplication process, But I wanted to use the method to compare several calibers and bullet and combinations a once. So, I create the below table to pot the location of the Trajectory normalizing factor. I have found this useful when having conversations with others about calibers and bullet selection.

Step 1 - Find bullet speed on bottom of page.
Step 2 - move up page to your BC value.
Step 3 - see Trajectory Normalizing factor at the right.
Step 4 - Higher on the chart is better WIND performance

View attachment 7265917 View attachment 7265919

I am not sure these velocities are correct but here is an example of how I use this.
View attachment 7265921

Kunz Caliber Factor Model (1) 8x11.jpg
 

Deadly Punk

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Love it.

Since BC is velocity dependent, do you true BC prior to using it your calculation? Does the calculator adjust BC for input velocity?
 

Deadly Punk

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you're WAY overthinking this

use the box BC and your actual velocity as a start. true to your rifle
Works for me. I’ve shared this to a few people and received the question I posed. What can I say? I hang out with some nerds.
 

lash

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Works for me. I’ve shared this to a few people and received the question I posed. What can I say? I hang out with some nerds.
Tell them exactly what @b6graham just said.


you're WAY overthinking this

use the box BC and your actual velocity as a start. true to your rifle
This is a simplified normalizing factor approach and they are looking to complicate it back to an individual 4DOF approach. The real answer is: if this isn’t good enough for you then use your ballistic calculators with custom BC curves and do it the complicated way. Their results will likely be the same but some people just aren’t satisfied with easy and effective.
 

LastShot300

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Tell them exactly what @b6graham just said.
This is a simplified normalizing factor approach and they are looking to complicate it back to an individual 4DOF approach. The real answer is: if this isn’t good enough for you then use your ballistic calculators with custom BC curves and do it the complicated way. Their results will likely be the same but some people just aren’t satisfied with easy and effective.
One question, since I'm having a hard time to grasp the usefulness of this approach over the use of solvers, what would you say its strength really is? Asking because I want to understand the rationale here, perhaps I'm missing some gem hidden by the background noise.
 

lash

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One question, since I'm having a hard time to grasp the usefulness of this approach over the use of solvers, what would you say its strength really is? Asking because I want to understand the rationale here, perhaps I'm missing some gem hidden by the background noise.
To answer your question, I’ll ask that you reread the following intro paragraphs from the article in the OP:


The Trajectory Normalizing Factor
By: Josh Kunz

The long-range shooting community is a niche market of the firearms world, and that niche is full of myths and misunderstandings about a lot of aspects of long-range shooting. One of the most common is the misconception that just because a caliber is larger or a bullet is heavier, it must therefore “cut the wind” better. Here is a simple, effective, and nearly fool-proof method to get a fast answer to, “which has a better wind call?” that doesn’t involve running ballistics through a calculator.

Many folks want a way to figure out what “the best” combination might be for a given task. This need is many times solved by doing detailed ballistics calculations. In today’s world of handheld computers (smartphones) this approach is much less onerous than in years passed but even today it still takes a lot more time to run a set of ballistic simulations than it does to solve a simple math problem on a 4 function calculator.

The Trajectory Normalizing Factor is a seemingly simple approach developed by myself to perform this exact task quickly and effortlessly when discussing caliber options with customers and friends for rifle building needs.
Note the bolded parts. If I’m trying to decide between a number of different options, it’s much quicker to make a simple two factor calculation in a calculator than it is to enter the variables into a ballistic calculator. Plus, I don’t even need to have a ballistic calculator to make this calc.

Of course, there are those that will always choose the technology option. That’s great. It’s just not everyone’s particular obsession.
 

LastShot300

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To answer your question, I’ll ask that you reread the following intro paragraphs from the article in the OP:
Note the bolded parts. If I’m trying to decide between a number of different options, it’s much quicker to make a simple two factor calculation in a calculator than it is to enter the variables into a ballistic calculator. Plus, I don’t even need to have a ballistic calculator to make this calc.

Of course, there are those that will always choose the technology option. That’s great. It’s just not everyone’s particular obsession.
Thanks for your nice explanation. Crystal clear.
 

300wmSlick

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I heard you talking about this on the podcast, thanks for putting it in writing and making it easier for me to refer back to Frank!
 

Dthomas3523

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you're WAY overthinking this

use the box BC and your actual velocity as a start. true to your rifle
I’ve gotten to where I go even more simple.

I dial in 1 mil at 300 yds, get on the plate. Then true it at 300. Somewhere between .8-1.2 depending on rifle/bullet/etc.

Then using Marc’s weaponized math to get in steel and true out various ranges.

Without looking at calculator or software at all. I feel like it keeps me from being biased as to what the bullet is “supposed” to do.

Then I take my paper dope and do whatever I need in the calculator to make it all line up. Never even pay attention to what my chrono says unless it’s to tweak something like BC or sight height more than velocity.
 
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mkollman74

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OK. So, I have a plan to use this method to help me with my training rifle specs... What I am thinking is that I use the formula to closely approximate the characteristics of my 6 creed with a training round that will be cheaper to shoot. Would that be as simple as picking the combo that most closely matches the TNF of my 6 creed combo?
 

b6graham

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i'd say part of the point of a training rifle is to have something that make it harder than the comp rifle

308 = more recoil and more wind (also cheap factory ammo)
223 = more wind and less energy (also cheaper to reload)

to have a training rifle that closely matched the TNF of the 6 creed you're basically shooting a 6creed, or something like a 300PRC or 6.5PRC etc
 

Steel head

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i'd say part of the point of a training rifle is to have something that make it harder than the comp rifle

308 = more recoil and more wind (also cheap factory ammo)
223 = more wind and less energy (also cheaper to reload)

to have a training rifle that closely matched the TNF of the 6 creed you're basically shooting a 6creed, or something like a 300PRC or 6.5PRC etc
This.
 

bohem

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OK. So, I have a plan to use this method to help me with my training rifle specs... What I am thinking is that I use the formula to closely approximate the characteristics of my 6 creed with a training round that will be cheaper to shoot. Would that be as simple as picking the combo that most closely matches the TNF of my 6 creed combo?
You're understanding it correctly however I would point you back to what @b6graham said.

The closest thing you're likely to find to your stated quest is a 6mm BR
 

bohem

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Bohem, I was thinking that a 6BR might fit the bill nicely.
I did the same thing 5 years ago instead of a 223 trainer. Then proceeded to use it as a primary match caliber for a bunch of local matches and do very well.

I cut a lot of 6BR prefits and I have the mag kits very well sorted out for reliable function.
 
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mkollman74

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I did the same thing 5 years ago instead of a 223 trainer. Then proceeded to use it as a primary match caliber for a bunch of local matches and do very well.

I cut a lot of 6BR prefits and I have the mag kits very well sorted out for reliable function.
Are you getting reliable function from AW magazines? I shoot an AT.
 
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BLKWLFK9

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Are you getting reliable function from AW magazines? I shoot an AT.
Im running the PVA kit in my AI dasher and it runs like a champ. You may need to play with the follower spring leafs but you can fiddle fart with it and get it going reliably pretty quick. That concept is true for any dasher kit for all mags. The follower spring is usually the culprit.