Wind Caused Vertical? The Definitive Answer!
The following is a discussion that I had with Mr. Nennstiel a world renown ballistics expert. The questions were directed to him by me after reading the in-depth information on ballistics that he presents on his web site entitled, "How Do Bullets Fly". It was in regards to the often made claim that a vertical flyers are caused by changing crosswind conditions or head and tail winds. Below is the contents of this discussion.
From: "Jim Nasset" info@stocks-rifle.com
To: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
Sent: Thursday, September 6, 2001 9:22 AM
Subject: Vertical projectile deflection caused by crosswind.
Dear Sir,
I am fascinated by your excellent explanations on bullet flight, however not being and engineer and "mathematically challenged" the most of it is over my head!!
One question that I have not been able to get a definitive answer to is how much vertical deflection and in what direction does a specific cross wind have on a stabilized bullet.
As an example of the problem I am hoping you can enlighten me on, I have included a scenario below.
Bullet diameter 6mm Flat Base Benchrest Bullet Bal/Coff. .271
Velocity 3300 fps
Twist 1-14 Right Hand
Wind Speed 10 mph
Wind Direction 90 Degrees
Target Distance 100 Yards
Over the years there have been numerous discussion in the Benchrest Shooting community as to the vertical deflection of a bullet caused by crosswind. In all of this time no-one has been able to tell me the amount of vertical sighting compensation and in what direction, is required to hit the aim point under cross wind conditions. I have heard some say that a 5 mph cross wind can cause a 0.25" change in vertical in 100 yards.
Is there any table or formula that can be used to determine the vertical component, or is it immaterial at 100 to 200 yard distances.
Also would the effects of a 10 mph headwind during the first shot and no headwind during the second shot have the same effect as an approximately 14 fps change in bullet velocity from the first shot to the second shot.
I know that your time is very valuable but any help would be appreciated in answering these two questions.
Thank You in advance,
Jim Nasset
From: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
To: "Jim Nasset" info@stocks-rifle.com
Sent: Sunday, September 16, 2001 5:00 AM
Subject: Re: Vertical projectile deflection caused by crosswind.
Jim Nasset schrieb:
Thanks for your interest.
Yes there is a simple formula to calculate the deflection due to a crosswind.
z=w*(t-X/v0)
z is the deflection
w is the wind speed
t is the flight time of the bullet to the target
x is the distance
v0 is the muzzle velocity
I prefer ISO units, velocities in m/s; time in seconds, X,z in meters
The only unknown parameter in the above formula is the bullet flight time
(which you may find in manufacturers tables).
For your example (I assumed a bullet mass of 100 grain) I calculated
t = 0.106 seconds for X = 100 m. with v0 = 1000 m/s and w = 5 m/s this ends
with a side deflection of 10.4 mm.
There is no simple formula to calculate the effect of a tail- or headwind. In your example the effect of a
5 m/s headwind is a small downward deflection (less than 0.1 mm) which is far beyond normal scatter.
The effect of a muzzle velocity reduction of 5m/s is a little bit greater but also negligible.
Hope that helps
Greetings
R. Nennstiel
From: "Jim Nasset" info@stocks-rifle.com
To: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
Sent: Sunday, September 16, 2001 7:33 AM
Subject: Vertical projectile deflection caused by crosswind.
Dear Mr. Nennstiel,
I very much appreciate your reply. From your formula below can be determined
the HORIZONTAL or side deflection of a bullet in a given direction and velocity of a crosswind, I however I am unable to determine the VERTICAL or up and down deflection if any, in the impact point of the bullet on the target with a change crosswind velocity, using the formula.
Also if there is any VERTICAL deflection of the bullet caused by a crosswind would it be also negligible such as in the 0.1mm range?
Again I thank you,
Jim Nasset
From: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
To: "Jim Nasset" info@stocks-rifle.com
Sent: Sunday, September 16, 2001 9:50 AM
Subject: Re: Vertical projectile deflection caused by crosswind.
I am not sure if I really understood your question.
A crosswind causes a side deflection (to the left or right)
and no vertical (up and down) deflection. A head or tailwind causes a (very
small) up and down deflection
and no horizontal deflection.
Greetings
Jim Nasset schrieb:
From: "Jim Nasset" info@stocks-rifle.com
To: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
Sent: Sunday, September 16, 2001 11:02 AM
Subject: Re: Vertical projectile deflection caused by crosswind.
Thank you Mr. Nennstiel,
That was precisely the answer that I was looking for. Many times benchrest shooters will blame a crosswind velocity change or slight vector angle change as a reason for an otherwise unexplained change in the vertical impact point on the target of a given shot.
I have maintained, and attempted to demonstrate with examples of targets shot by me in changing crosswind conditions (by holding the same
aimpoint) that the vertical component change in the trajectory was either non-existent or insignificant due to a crosswind.
Again thank you for your help in resolving (I hope) this long hotly debated "theory".
Jim Nasset
From: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
To: "Jim Nasset" info@stocks-rifle.com
Sent: Thursday, September 20, 2001 9:00 AM
Subject: Re: Vertical projectile deflection caused by crosswind.
Dear sir,
Your answer made me rethink the problem and I hope that now I fully understand
your point.
While a bullet is on its way to the target, clearly a crosswind simply causes a
side deviation.
However an effect is discussed in literature which is called "windage jump" or "aerodynamic jump to a crosswind" which is described as follows: at muzzle exit, a crosswind imposes on the spinning bullet a small moment which causes the nose either to be raised or lowered, depending on wind direction and spin orientation. The effect modifies the angle of departure and thus gives rise to a small up or down deflection. It has been reported that the 10 o'clock / 4 o'clock slant of target groups "observed" by benchrest shooters when firing on windy days is the outcome of this effect.
I would wonder if this effect can be observed with certainty, for shooting distances of
100 - 200 yds.
Greetings
R. Nennstiel
From: "Jim Nasset" info@stocks-rifle.com
To: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
Sent: Thursday, September 20, 2001 9:22 AM
Subject: Vertical projectile deflection caused by crosswind.
Dear Sir,
Thank you for your thoughts, however do you think that a 5 or 10
mph crosswind at the point of the muzzle would have very much effect.
I attached a picture which seem to represent quite a bit of muzzle blast
surrounding the projectile as it leaves the muzzle.
It would be hard for me to understand how such a small movement of air which
would be flowing horizontally past the muzzle at bullet exit would be able
to get through the shock wave and accompanying gasses, to actually raise or
lower the bullet tip inducing a significant yaw.
As the bullet is traveling down the barrel to the muzzle it would be pushing
a column of air in front of it, which would exit the barrel just prior to
the bullet tip and ogive protruding.
If this is the case would not that
very high velocity air which would spread out 180 degrees from the muzzle
negate any slight crosswind, which is then followed by the bullet and the
propellant gasses at extreme velocity behind the bullet also negate the
slight (in comparison) crosswind?
I guess my question is, is there any basis of fact that can be quantified and repeated that would verify (scientifically) the "windage jump" that has been referenced in the literature you speak of. Or do you think that the real cause is, as you stated in your descriptions of how bullets fly, which says: "Innumerable experimental observations have shown that an initial yaw angle at the muzzle of a gun is principally unavoidable and is caused by perturbations like barrel vibrations and muzzle blast disturbances."
Would it follow then that either these perturbations or simple sighting,
mechanical or a slight imperfection in the construction of a specific
bullet, such as voids in the core or slight jacket thickness variations are
more likely the cause?
I really appreciate you taking your time on this matter as I believe if
there were such a "windage jump" occurring, then a formula would be able to
be applied to it just as is done with drag, gravity, and wind deflection.
If it is however really a case of observed random vertical aberrations
during a match that cannot be otherwise explained by the shooters, maybe
this is the reason for the "windage jump" theory, and therefore no ballistic
formula is possible.
Again I thank you as your expertise is greatly appreciated.
Jim
From: "Ruprecht Nennstiel" Ruprecht.Nennstiel@t-online.de
To: "Jim Nasset" Info@stocks-rifle.com
Sent: Thursday, September 26, 2001 8:58 AM
Subject: Re: Vertical projectile deflection caused by crosswind.
Dear sir,
Your questions are aiming at the causes of bullet dispersion.
1. In reality there are many contributions to bullet scatter on a target: (for
now, I do not consider effects of a shooter holding the gun)
muzzle velocity variations, departure angle and azimuth perturbations (mostly
due to barrel vibrations and muzzle blast interactions), variations in the
canting of a gun, drag coefficient variations, variations of wind velocity and
wind direction, bullet static and dynamic unbalances, in-bore yaw and windage
jump should be the most important.
It might be impossible to say in a real shooting environment which effect will
be the major and which is small or negligible.
Normally, departure angle and azimuth perturbations are considered to be most important. Without an in depth analysis it would be "impossible" to associate a certain observed scatter just to the "windage jump".
2. In fact there is a formula to calculate the windage jump. It is a bit too
complicated to be written down in this e mail. It can be found in BRL Report MR
3877, Nov. 1990 written by R.L. McCoy. Recently this author has also published a
book entitled Modern Exterior Ballistics (very mathematical!) and I expect to
find the formula for the windage jump also in this book.
I wish I would find the time to add some chapters to the "How do bullets fly"
web-page that cover the problem of bullet scatter.
3. Example (calculation!): 7.62 Nato bullet M80,
mass=9.5 g;
fired at 870 m/s;
rifling pitch 313 mm;
crosswind speed 5 m/s
All other causes of deflection
neglected, the crosswind causes a side deviation of approx. 45 mm at 200 m range,
the windage jump causes a vertical deflection of approx. 1.6 mm at 200 m range.
Greetings
R. Nennstiel
Metric US Conversion
3. Example (calculation!): 7.62 Nato bullet M80,
bullet dia.
7.62mm
dia.= .308 caliber
mass=9.5 g;
mass= 160 grains
fired at 870 m/s;
velocity= 2854
rifling pitch 313 mm;
twist= 12.3
crosswind speed 5 m/s
wind= 5.6
mph
windage jump 1.6mm vert. def.= 0.063" @ 200 meters = 0.0315 MOA
Conclusion:
I think that we can see from Mr. Nennstiel's answers to this ballistic question, that unless all groups being shot are at or under 0.1 MOA, (one tenth of an inch) then the vertical component in the group caused by changing wind velocity or direction is immaterial, and certainly no where near the 0.25" or even greater vertical deflection that has been claimed as the suspected cause by various competitors.
You can find the full in depth explanation of "How Bullets Fly" on
Mr. Nennstiels web site at: http://www.nennstiel-ruprecht.de/