Fuzzy's Notes:

The subject of wind effects on a rimfire bullet in flight is an extremely complex one . . . even more so for an air-rifle pellet with its' generally poorer aerodynamic characteristics !    Virtually never can one expect to shoot at a "target", regardless of its' nature, in which the wind blows from a constant direction, or velocity, thoughout the flight path of the projectile.    Therefore any attempt at analysis of the effects of wind will be, at best, an "educated guess" !

So . . . how does one get around this situation and arrive at a meaningful answer for the vast majority of the shots taken ?

Note that I said "majority of the shots" . . . to be blessed is the shooter who can predict for every shot the random meanderings of the air currents between his rifle muzzle and the intended point of impact !    The very best shooters . . . those who watch for every tiny clue in the air or on the ground . . . who feel the subtle changes of air currents on their ear lobes, or - in my case - their chin whiskers . . . who "see" the mirage down-range flow or boil . . . maybe get it right 90-plus percent of the time.    One has to have a super-sensitive awareness of their surroundings . . . almost a sixth sense as it were . . . some might even call it a premonition.

In essence it boils down to one word . . . OBSERVATION !

From observation of ones' surroundings at the range many clues as to the bullets' in-flight behaviour pattern can be determined.    Let's look at a few.    Has the match director put out wind flags ?   Is the grass downrange tall enough to show flow patterns in the critical surface boundary layer where turbulence is most often discovered ?   Is the sun shining, or is it warm enough to produce a visible mirage ?    Does the mirage show a steady-state flow in a specific direction . . . or is there a pronounced boil to it ?    What does your face . . . and for the ladies with sensitive skin . . . the backs of your hands tell you ?    Finally . . . experience !
Have you shot on this range before ?    Observed prevailing patterns or cyclic variations ?    These are the "secrets" to unlocking the magic of windage correction in your aiming and shooting process.

In the examples below I present several approaches to the solution of windage correction analysis.    Some are based upon exact methodology . . . fine in the text book . . . but also giving us a solid groundwork on which to base our "educated guesses".    Others, depicted in diagramatic form, give non-dimensional indications of the errors likely to occur from generalised wind flow.    Use of these, together with on-site estimation - or even direct measurement for those affluent enough to afford wind speed instrumentation - can be melded to translate into a specific "how many clicks" adjustment of the rear sight or scope.

Now go play in the yard !

 Trajectory Analysis Programmes:

Fortunately for many of us, there are nowadays quite a few such computerised programmes available through the medium of the Internet. Some are "Free", and in some cases can be downloaded to ones' own computer.   Others are available for a nominal fee payable to the author.

My favourite for Rimfire analysis has long been those from an author known to me only as JBM . . . ?

      JBM Trajectory Analysis and Range Cards                  

      Larry Medlers' Silhouette Ballistics:             

      Brad Troyers STP Ballistics Software                          

Miscellaneous Wind-Drift Links:

     Effects of Winds:          

     Deflections and Drift of a Bullet in a Crosswind           

     A Short Course in External Ballistics:           

     Advanced Marksmanship           

     .22 Rimfire Ammunition           

     Shots Ordinary and Extraordinary

    The Wind is Not your Friend          

( taken from notes received from Stacy Kunz, based upon Dr G Kolbe's work - "A Ballistic Handbook" )

The following calculations are based on data and equations provided by Dr. Geoffery Kolbe, in his latest book, A Ballistics Handbook, (2000), pp. 608-615.   Dr. Kolbe informs me (e-mail correspondence, 21 March, 01) that the Time Function data included in Table 6.1: Condensed Ballistics Table for the .22LR Bullet is not carried to enough decimal points to re-produce the Drift vs. Muzzle Velocity (Vo) curves represented by the graph, Figure 6.5, pp. 610 for the ranges, 50m and 100 yards.   Dr. Kolbe also informed me that he will update this (Time Function) data to include 3 decimal places in up-coming editions of the book.

The three equations which describe the external ballistics curve for .22LR are as follows:

dV/dt = 3.26x10-3 V2 3.60x10-6 V3              for V > 1045 eq. 6.3, p. 608

dV/dt = 4.17x10-4 V2 8.82x10-7 V3             for 905 < V < 1045 eq. 6.4, p. 608

dV/dt = 3.82x10-4 V2                     for V < 905         eq. 6.5, p. 608

Meantime, I took the graphical distances for wind drift (50m and 100 yards) from Figure 6.6 and worked the equations backwards [DH = 17.6 Vw (t - R/Vo)], p. 615, to find the time of flight (t) for the various muzzle velocities for the ranges, given    (See: Tables I and II below).

                                     Table I:    50 Metres

                                     Table II:      100 Yards

Fuzzy's Comments:     This, as you can see, is a highly idealised case . . . pure uniform velocity and direction wind blowing from 90 or 270 degrees to flight path.
It is interesting though in that it does show how the turbulence of transonic flight increases the relative amount of wind induced deviation in flight path.    Most match quality ammunition today operates in, or slightly under, this general velocity regime, where the intent is to maximise velocity without actually having the bullet reduce velocity "back down through" that transonic range.    This is one of the primary reasons that Hi-Velocity and Hyper-Velocity rimfire ammunition is so subject to abnormal wind-induced deviations in Point of Impact . . . normal aerodynamic drag will slow it down to a sub-sonic value within the first 20-30 yards of flight !

As a comparison to the above data, I ran a series of check calculations using the Basic JBM programme . . . some very obvious deviations in the results . . . showing how inexact the various techniques actually are.

                                     Table IA:    50 yards

                                      Table IIA:     100 yards

Relative Wind Deflections:

Shown below is a generalised non-dimensional diagram indicating the relative position of a POI with respect to the POA of the shot.    It shows how the bullet flight path is affected laterally by wind . . . and also vertically by the interaction between wind deflection and the rotational spin of the bullet from the barrel rifling.