Aerodynamic Jump and Ballistic Solutions

[FrankPetersenDK]

Most ballistic solution gadgets and ballistic software solutions, I have reviewed, do not correct for aerodynamic jump. The vertical bullet deflection caused by aerodynamic jump due to wind may be significant at long range. Bryan Litz has developed a very accurate estimation of aerodynamic jump, but, except for Rianov, nobody - to my knowledge - has incorporated aerodynamic jump into their solution. I wonder why!

This issue is of importance to me as I shoot long range in a very flat environment with high winds most of year. I would be grateful to hear from you regarding your solution to solving this problem. Thank you.

 

[Mikecr]

It's called 'magnus effect'
External ballistics - Wikipedia, the free encyclopedia

By the time you did any calculations of it in the field, the conditions would likely change enough to negate results.
I've heard of compensation at pre-chosen values of conditions(many) by turning the scope in it's mount/reseting elevation level. This would work for competitors, given all conditions known/fixed up front.

 

[FrankPetersenDK]

The Magnus effect is even effecting a bullet in no wind conditions, as the rotational movement of the bullet causes airflows to create low pressure under the bullet relative to the top of the bullet (bullet viewed from the back), resulting in a downward force called "Magnus". I am not referring to the Magnus effect.
I am referring to "aerodynamic jump" as described in Bryan Litz's book "Applied Ballistics for Long-range Shooting" – second edition, pages 75-83. A gyroscopic stable bullet will point its nose into the oncoming airflow (wind) and experience precession cycles, which are lop-sided, resulting in a vertical deflection of a constant angular value for the entire trajectory – thereby making aerodynamic jump a deterministic variable, which should be accounted for in the ballistic solution. I have 0.1 mill scope adjustments and at 300 yards, I am one clicks off in low wind conditions.
Bryan's estimated jump (Y) is calculated as follows:

Y = 0.01 x SG – 0.0024 x L +0.032 MOA/MPH​

Where
SG = Gyroscopic Stability Factor (Don Miller; and air density dependent)
L = bullet length in caliber (bullet length in inches/caliber)
Y is up for wind from the right (right twist)
Y is down for wind from the left (right twist)
In order to get vertical wind deflection(up or down), you must multiply Y by wind force in mph, for a deflection in MOA, which is subsequently adjusted for range in order to get vertical deflection in inches (or cm where I come from) at that particular range.
Ballistic solutions, which include spin drift at range already calculate SG and L, as well as air density, so including vertical "jump" adjustments into the solution, should be fairly simple, if horizontal wind deflection is already employed (direction and power of wind is entered into the ballistic solver).
Wind conditions where I live vary a great deal. Calm is 10 mph and windy up to 25 mph. With high winds and long range, the jump adjustments become an important part of the total vertical adjustment - sometimes 3 clicks and 400 yards.
I would be grateful to receive advice, as how to EASILY adjust for vertical jump caused by wind – without carrying a computer and spending precious time making calculations.

 

[Nimrodmar10]

I just usually give it a little Kentucky Windage.

 

[royinidaho]

Frank,

It would have been better for me if you wouldn't have raised this question.

I knew that the into the wind was different than with the wind but didn't know it was readily calculable.

One more thing to worry about.

Is SG a straight forward calculation? If so, one could do a little better than what I've been doing which is combination of guess work and KY windage.

 

[MontanaRifleman]

Frank,

It would have been better for me if you wouldn't have raised this question.

I knew that the into the wind was different than with the wind but didn't know it was readily calculable.

One more thing to worry about.

Is SG a straight forward calculation? If so, one could do a little better than what I've been doing which is combination of guess work and KY windage.

I'm gonna pretend I didn't see this thread

 

[CB11WYO]

I'm gonna pretend I didn't see this thread

+1 ...

Oh boy . . . Definitely don't have any input on this one...

I'm happy this factor can be measured though, might need to check on the sanity of the guy who came up with that equation though . . .

 

[BrentM]

Ummmm wow. There is always that one guy................


So do you all have a formula for up and down drafts too? While we are at it how about an angled down/up draft such as shooting along the face of a mountain? Yeah, that one has been fun for me at 1500.

 

[MMERSS]

First, welcome to Long Range Hunting. I am somewhat surprised you did not ask this question on accurateshooter and insisted on a long range hunting forum. None the less you have asked one of the best questions I have seen in quite some time. Your concerns are very notable and well deserved. Bryan's books are fantastic! His end summaries are right on target, no pun intended.

Do I consider vertical deflection caused by the gyration of bullets in a crosswind? In most cases be it hunting or F-Class competition usually not. Here is my explanation of when I would or would not consider the vertical corrections and how I chart the corrections when I do consider them. These are my opinions only based on my shooting habits and others will have their own.

I recently developed a load for a 300 RUM using the Berger Hybrid Target bullet. This is a long range shooting and hunting forum so I will use this combination as an example.

Data required for calculations:
Weight: 230gr
MV: 3171 fps
OAL: 1.640"
Bullet diameter: .308"
Right Twist Barrel
Twist 1 in 10"

Bryan's equation Y=0.01 x Sg-0.0024 x L + 0.032 is dependent on the air density to determine Sg as L is constant (OAL/bullet diameter=1.640/.308=5.32). Asking the question; So what does air density change have to influence Sg as used in this equation? I will use a density altitude of 0 feet and one of 6000 feet for comparison to answer this question.

Using a density altitude of 0 feet and an analyzer using the Miller/Courtney method Sg=1.49.
For a density altitude of 6000 feet Sg=1.79.
Both altitudes should insure stability.

Using Bryan's equation for each air density:
DA 0ft: Y=.01 x 1.49 – 0.0024 x 5.32 + .032 = .034
DA 6000ft: Y= .01 x 1.79 – 0.0024 x 5.32 + .032 = .037

Back to the question; So what does air density change have to influence Sg as used in this equation? Lets assume we are shooting in a 10 MPH cross wind. Vertical correction in a 0ft DA air density equivalent is .34 MOA. Vertical correction in a 6000ft DA air density equivalent is .37MOA. The difference is .03MOA. I'm not aware of any scope capable of making corrections this small. In other words, pick average atmospheric conditions you will be shooting in and calculate your Y. The majority of my scopes have ¼ MOA corrections. The closest conversion is 1 click (.25 MOA) for the .34 MOA correction for a 10 MPH crosswind, 3 clicks for a 20 MPH crosswind (.34 + .34 = .68 i.e. .75 MOA correction is closest), etc.

So what does all this mean to the long range hunter? I limit my maximum range big game hunting shots based off cross wind condition confidence. If I can estimate the crosswind to within 1 MPH my max range with the system above is 1200 yards. 2 MPH 875 yards. 3 MPH 700 yards. How I established these limits is a completely different topic but none the less they serve a purpose here.

I am fortunate if I'm shooting in a 10 MPH full value crosswind to be within 2MPH of actual value when I pull the trigger. This means my max range is 875. In all practicality I will be shooting at an elk sized target at this established maximum effective range. Let's say I do not correct for the vertical correction due to bullet gyration. Approximately how many inches of vertical error am I not accounting for? Just less than three. My muzzle velocity variation and terrain changes will probably produce more error than the vertical correction not accounted for.

However, for your situation where you are more than likely shooting in crosswinds approaching or exceeding 10MPH most of the time and you will be shooting extended distances, simply apply your Y calculation. In my example the average is .35MOA for each 10MPH crosswind. Round to the nearest 1/4MOA and click down for a 90 deg wind and up for a 270 deg wind. You can easily write .35MOA with arrows pointing up/down-wind left/right in the corner of your firing charts indicating a 10MPH crosswind vertical correction. Again this number is an approximation of your average air density and used independent of air density changes due to the little value of the change.

 

[royinidaho]

Squat!!!!!

I think I'll just give up and accept a few misses. . .

 

[FrankPetersenDK]

MMERS.
Thank you for your response. Just what I was looking for. I follow your reasoning all the way.
Even though all calculated deflections (horizontal and vertical) related to wind are scientifically correct, we must – as you point out – remember, that wind by its very nature is non-deterministic. We can only measure direction and wind force at our exact location and not for the entire length of the bullet's flight. Consequently, your comments, regarding confidentiality of our wind reading capabilities, are very appropriate.
I would appreciate it, if you would expand on your method for establishing your maximum effective range (MER). I have read Bryan's article regarding this issue, and understand that he is using simulation software to arrive at his numbers. However, I have tried to emulate his calculations in a excel spreadsheet, and it works, even though I had to spend some time getting it right.
Thanks again for your input.

 

[BrentM]

MMERS- how do you account for angled wind (up and down at an angle) while shooting across a slope? I was taught to go plus and minus for the cross wind at full value such as you reference and have a chart on my iPod that I refer to but I struggle with the a cross wind that is angled. For example I use .25 down for 270 up draft and use .75 of wind value. I use .25 up for a 90 down and .75 of wind value.

This is what I am refering to: with mountain shooting vs flat land, many times the shooter to target wind issues are compounded by gap of ravines/draws/canyons. Personally I find it rather easy to account for wind from any direction when I shoot in the desert. I find mountain shooting, where I hunt, to be significantly more challenging and unpredictable. Shooting from a wind hide location on the backside, across the gap, to the face of another mountain produces at least 3 wind variables.

 

[FrankPetersenDK]

BrentM.
Subject: Angled wind.
Theoretically, you are able to account for angled wind, if and only if, the scientific assumptions for the calculations are present at your location (which they never are). However, I still find it a good exercise to calculate theoretical wind deflection for angled wind, as it helps me understand the dynamics of the subject matter, when I am in the field. Wind doping skills and experience prevail over pure science competencies in this matter, as wind is so very non-deterministic.
In a three dimensional world all winds can be divided into three sub components:
1. Horizontal wind component (left or right)
2. Vertical wind component (up or down)
3. Trajectory directional component (towards the shooter or away from the shooter)
Remember that only the crosswind of horizontal and vertical winds effects the deflection. The illustration below show the calculation of cross wind power and the factor used.
See Attachment.
From the illustration, you can see that a horizontal wind consists of a crosswind power (green -perpendicular to the line of sight) and a trajectory directional component (blue).
An angled wind will consist of a (perpendicular to the line of sight - up or down) vertical crosswind and a horizontal wind. In other words, you have both a horizontal and vertical deflection, when you encounter an angled wind up the hillside. We are only interested in the crosswind components for calculating wind deflection because it is calculated as follows (Bryan Litz):

Wind Deflection = crosswind power x lag time​

In US imperial numbers the formula looks like this: See Attachment.
I hope you can read my native tongue – the abbreviations are almost the same as used above.
You are, of course, able to use excel and calculate the exact deflection by hand for angled wind, but I find it much easier to use Sierra Bullet Infinity Suite software, which include an entre for vertical wind.
In addition, if you are really hooked on wind, you can theoretically calculate total horizontal wind deflection for horizontal winds that prevail in intervals along the line of sight. I do not find it worth the effort. Again, this feature is included in the Sierra Suite.
In conclusion, I am of the opinion, that only experience and common sense will insure a clean kill under difficult mountain hunting conditions. If angled winds are very strong, the only solution may be to get closer to your prey to insure a clean kill.

 

[FrankPetersenDK]

MMERSS.
Aerodynamic Jump.

You wrote that you click DOWN for a 90 degree Wind and UP for a 270 degree Wind. Are you sure? To me 90 degrees = 3 o'clock and 270 degrees = 9 o'clock, and I would click just the other way around. Any comments??