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Trajectory Normalizing Factor

The Trajectory Normalizing Factor

By: Josh Kunz

(The editing limitations of this web hosting leave us with some messy equations.  If a reader would like a copy of the original PDF of this document please email us and request it. We are happy to provide a copy)

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 ballstics 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 (smart phones) 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?

 TNF=MV*BC

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 the better trajectory?

3030*0.275=833.25

2740*0.326=893.24

 

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

Calculated Table – Combo A 0.275 @3,030fps

Range

Drop

Drop

Windage

Windage

Velocity

Mach

Energy

Time

Lead

Lead

(yd)

(in)

(MOA)

(in)

(MOA)

(ft/s)

(none)

(ft•lbs)

(s)

(in)

(MOA)

1000

-266.5

-25.5

71.8

6.9

1524.3

1.365

910.4

1.396

245.7

23.5

 

Calculated Table – Combo B 0.326 @ 2,740fps

Range

Drop

Drop

Windage

Windage

Velocity

Mach

Energy

Time

Lead

Lead

(yd)

(in)

(MOA)

(in)

(MOA)

(ft/s)

(none)

(ft•lbs)

(s)

(in)

(MOA)

1000

-306.5

-29.3

67.1

6.4

1510.7

1.353

894.3

1.474

259.5

24.8

 

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.

 TNF_c=3050*0.318=969.9

Calculated Table – Combo C 0.318 @ 3,050fps

Range

Drop

Drop

Windage

Windage

Velocity

Mach

Energy

Time

Lead

Lead

(yd)

(in)

(MOA)

(in)

(MOA)

(ft/s)

(none)

(ft•lbs)

(s)

(in)

(MOA)

1000

-240.7

-23.0

58.3

5.6

1712.8

1.534

1149.6

1.313

231.1

22.1

 

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 need to go for it to be equivalent to Combo A?

Let’s take a look with 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?

Combo A: 180 @ 2,870 --> 2870*0.401=1150.9

 

Since we’re setting the TNF factors of A and B equal to each other we can re-arrange and see that

TNF_a = TNF_b and therefore TNF_162 =TNF_180

 

Rearranging:

 MV_162=(MV_180*BC_180)/BC_162 --> 2870*0.401/0.338 =3402fps

So there’s the answer, if the shooter wants to go to a 162 it needs to go SUBSTANTIALLY faster, likely far faster than the rifle can actually push the 162 safely.  So unless there is another reason to use the 162, the 180 is still a better solution in the wind.