Wind - Near or Far?

One of the questions which comes up occasionally on internet boards and which can cause a bit of consternation is whether greater allowance should be made for wind conditions nearer the shooter or nearer the target. A surprising number of people believe that the wind nearer the target will have a greater effect, after all the bullet is going much more slowly when it gets to the other end.

Let's look the ballistics of a shot fired by a target rifle shooter on a flat, open range with a 10 mile per hour crosswind from 3 o'clock. (S)he is using ammunition with an old-style Sierra 155 HPBT bullet (part number 2155) with an average real-world BC of 0.417 (vid. Brian Litz's superb experimental data) which achieves a muzzle velocity of 2925fps*. Using the JBM Ballistics page, we get the following results:

Range	Muzzle	100x	200x	300x	400x	500x	600x	700x	800x	900x	1000x
Velocity / fps	2925	2711	2505	2306	2117	1937	1764	1596	1443	1307	1193
Wind Drift / Inches	0	0.7	2.9	6.8	12.7	20.7	31.2	44.6	61.4	81.8	106.1
Time Elapsed / s	0	0.107	0.222	0.347	0.482	0.630	0.793	0.972	1.169	1.388	1.629

EDIT: The tables in the figures are now correct! I transposed the times of flight from the 1307fps muzzle velocity calculation onto the data for the 2925fps calculation.

We see that the last 300 yards account for more than 50% of the wind difference. Clearly the wind closer to the target is more important, right?

Not so fast!

I was taught that the wind closer to the shooter has a greater importance, and the various books I've read tend to agree on this point. My experience on most rifle ranges tends to agree; although there are notable exceptions. Let's perform a thought experiment:

Scenario 1 - The same shooter fires a shot on the same flat, open range at a target 1000 yards away. For the first 900 yards, the air is perfectly still. In the final 100 yards, there is a 10mph/16kph wind running at 90 degrees to the line of flight. We know that the wind drift will be zero for the first 900 yards; however we need to calculate what the drift will be in the final 100 yards, which we can do using the ballistic calculator. Using the results from the JBM ballistics page the bullet will be going about 1307fps at 900 yards. Re-entering this value as the muzzle velocity allows us to calculate what the wind will be over the final 100 yards of the range.

Range	Muzzle	100x
Velocity	1307	1193
Wind Drift / Inches	0	1.9

This gives us a total effect of about 1.9 inch or 0.2MOA from the perspective of the shooter 1000 yards away, which is roughly equivalent to the contribution of the final 100 yards to our hypothetical shooter's first shot; therefore the wind in the last 100 yards accounts for only 2% of the total deviation.

It would be interesting to know, by way of contrast, how much wind the first 100 yards would account for. To understand this, let us return to our hypothetical shooter:

Scenario 2 - Our shooter fires another shot at a target 1000 yards away; however this time for the first 100 yards, there is a 10mph/16kph wind running at 90 degrees to the line of flight. In the remaining 900 yards, the air is perfectly still. What will the deflection of the bullet be? We know from our original calculation that the bullet will have drifted about 0.7 inches in the first hundred yards.

This is where is gets interesting. Even though there is no longer any wind, the bullet will continue to move sideways even as it flies downrange because of Newton's 1st Law of Motion**. Thanks once again to Sir Isaac, we can estimate the sideways velocity of the bullet as it transitions from the windy 100 yards into the remaining, still 900 yards; and therefore the total deviation.

If we calculate the acceleration on the bullet over the first 100 yards given the known displacement and time of flight, we can then calculate its sideways velocity at the end of the 100 yards. The bullet will continue to travel sideways at this velocity as it flies down the range, but no faster because there is no more wind.

Following a series of calculations, I make this about 20.6 inches*** however because of errors in assumptions this could be as much as twice the actual contribution. Even so, it is between 5 and 10 times the effect of the wind nearest the target.

Conclusion
Hopefully I've provided a reasonable argument that as a general rule, the wind nearer the muzzle has a greater effect than the wind nearer the target on a flat, open range; however ranges are not always (often?) flat or open in the real world!

Clevedon rifle range is situated just outside Auckland, lies between a series of low hills, and points towards a ridge with several deep ravines leading down to the butts. Particularly at 600 yards, the flags closer to the butts appear to have a greater effect than the ones closest to the firing point. While it is entirely possible that we are mistaken in this; I and other club members think that the funneling effect from the ravines coupled with the shelter of the hills alongside the range leads to this rather odd observation.

The 500x point on Clevedon rifle range near Auckland. Not flat or open!

Indeed, most ranges have their own quirks which must be learned: it is for this reason that top-level teams frequently send advance parties to recce ranges the year before major championships, the Palma Match in particular. I have no doubt that GB, the US and other teams will be sending shooters and coaches to New Zealand to learn the inimitable character of the mighty, frustrating and rewarding Trentham Rifle range.

* This is roughly equivalent to RUAG or GGG.
** A body will remain in constant motion unless an unbalanced force acts on that body.
*** Actually, it will be a bit less because of wind resistance but this is going to be reasonably close.

Addendum - Scenario 2 Calculations
To calculate the acceleration due to the wind on the bullet, let's use one of Newton's equations of motion...

s = ut + 1/2 at^2

Where:

• s = sideways displacement of 0.7 inches
• u = initial sideways velocity of 0 (the bullet isn't moving sideways when it exits the bore)
• a = acceleration that we want to calculate
• t = time elapsed of 0.107s

s = 1/2 a t^2

2s = at^2

a = 2s / t^2

a = 2 * 0.7 / 0.107^2

a =  122.1 inches per second ^ 2

Using this acceleration and the time of flight for the first 100 yards, we can calculate the sideways velocity of the bullet at the end of the 100 yards.

v = at

Where:

• a = Acceleration of 122.1 inches per second ^ 2
•  t = 0.107 seconds

v = 13.1 inches per second

We can calculate the total wind drift by adding to the 0.7 inches of drift in the first hundred yards the sideways drift over the next 900 resulting from this velocity.

s = 0.7 + 5.8 x (3.158 - 0.241)

s = 20.6 inches

NB - There are two limitations that I can think of to this: Firstly, this discounts wind resistance; and secondly, the acceleration on the bullet will reduce as it approaches the wind velocity. Both of these will tend to over-estimate the effect. By applying a similar calculation to the whole 1000 yard range it is possible to see that the over-estimate is at worst 100%.

What have shooting jackets ever done for us?

A member of the UK Fullbore Facebook Page recently asked a superb question, which I paraphrase below:

Isn't the shooting jacket just a convenient place to attach your sling?

Personally,  I really hope not, otherwise I have wasted a serious amount of cash over the years which could have been better spent on bullets or beer; however the questioner has actually got a bit of a point. What do jackets actually do for us and quite why do we spend so much money on them? First, an experiment...

SCATT Practice in the garage. Hard to see from this angle, but the jacket is completely undone.

If you're a regular reader, it cannot have escaped your attention that I like experimental evidence because it tells us the way the world really works, and not how people believe that it should work. In this case, I wanted to see what effect completely undoing my jacket would have on SCATT as some smallbore shooters are known to do in the prone position. As an experiment to see what effect this has on support and stability*, this was done completely on a whim so I don't pretend that it is statistically valid, but it is at least interesting.

While the group was slightly larger, the vital numbers are essentially no different, even taking account of the odd third shot in the second string, as the screen captures of the SCATT sessions below demonstrate.

Ignore shot 3 in the second string. Probably interference.

 Qualitatively, the hold did not feel as secure without the jacket done up, and certainly when not on final aim it did seem to wave about quite a bit. Additionally, the butt of the rifle was harder to place in the shoulder and I don't feel that it would have behaved quite the same under recoil; however this is essentially conjecture without a trial. In conclusion, despite the results from SCATT being essentially indistinguishable I won't be shooting with my jacket undone any time soon!

So, what have shooting jackets ever done for us?

In addition to being an excellent place to attach your sling and make sure that it stays roughly in the same place relative to your musculo-skeletal system, your jacket fulfils a number of other functions in fullbore rifle shooting: it provides support and allows you to maintain the proper position for longer and more consistently as a result; the rubber on the elbows and in the shoulder prevent you from slipping between shots or while in the aim; the stiffness and thickness of the material helps soak up a little bit of the recoil, which reduces fatigue, and it helps to isolate the rifle from your heartbeat; and finally it gives you some protection from the elements that we have to endure when shooting outdoors.

It is possible to shoot decent scores without using a full shooting jacket; I remember forgetting my jacket many years ago, improvising with a greatcoat and a belt as slingkeeper and shooting a 35.5 at 300 yards; AP of Australia won the Corporation of the City of London match at 1000 yards with a score of 50.9 (dropping his last shot to a cooking bull, no less) in 2016 using a harness-like arrangement sold by a well-known UK shooting tailor. Despite this, I would suggest that your scores are going to be more consistent using a well-fitting jacket of roughly conventional design.

* Yes, before you all shout at me, I know that a lot of the stability for the sling position in particular comes from the fit across the shoulders and upper arms.

The effect of heart rate on shooting - Part 1

Quite a long time ago now, I noticed that the beating of my heart appeared to slow when I was in the aim. I remarked as such to a medically-qualified friend, who replied that he was not in the least surprised as it is known that it is possible to consciously slow heart rate*. Having recently bought myself a Garmin 225 GPS watch combined with a heart rate monitor as a training aid for running, I decided that it would be interesting to see what results I got when measuring my heart rate during a SCATT session.

The Effect of Heartbeats on Aim
It's logical that heart rate (and possibly strength of heartbeat) will have an effect on aim. The hydrostatic pressure of the surge of blood around the body will disturb the fine aiming required to shoot a rifle accurately, either as it passes through the organs of the body or through the major blood vessels of the upper limb**. Indeed, the disturbance caused by heartbeats can be observed using a SCATT as is shown in the diagram below.

Fig 1.0 - The effect of heartbeats on SCATT traces. The notation indicates the heartbeat number in sequence and the time before the shot broke.

What is perhaps less logical, or at least less well known, is that it is possible to consciously control heart rate to some degree. By extending this, maybe it's possible that some people can subconsciously control their heart rate under circumstances or, to put another way, do I subconsciously decrease my heart rate while shooting?

The Measurement of Heart Rate
I bought my watch primarily for running, as my pace judgement isn't great and this is critically-important when running long distances. Go out 15 seconds per mile too fast in a marathon and the last 10k is likely to be deeply unpleasant, not to mention very slow. The watch that I bought also has an integrated heart monitor, which works by detecting colour changes under the skin of your wrist when bloodflow increases. Once an activity is recorded, the data can be viewed through the Garmin website or through a 3rd party app like Strava. The plan is simple, start the heart rate monitor and then correlate the heart rate output with shots from SCATT.

Fig 1.1 - Strava output for my last 5k parkrun. The red line is heart rate.

Experimental Conditions
I fired a good 10 shot group using my SCATT wearing the heart monitor. I was careful to try and do this as close to normally as I was able using my normal kit and technique. I switched on the heart rate monitor after warming up, but before I got down to shoot.

Fig 1.2 - SCATT results.

Heart rate monitor results
The heart rate trace yielded some great results and demonstrated exactly the effect I wanted to observe; however it also yielded something rather unexpected. Given that my resting heart rate is somewhere around 50bpm*** I was expecting to see my heart rate decrease to around that level or possibly lower while in the aim, and it to increase moderately when back out of the aim to, say 90bpm. The raw graph looks not dissimilar to this expectation.

Fig 1.3 - Heart rate results. Note the average heart rate of 90bpm.

When I superimposed the shots on the graph, as is shown below and then actually looked at the specific heart rate numbers I was rather surprised to see that the average during shots was 60-65bpm and between shots it went as high as 130-135bpm,which is approximately the same as when I run at a 9 minute mile pace on a flat course.

Preliminary conclusions
It is clear from the result that I am subconsciously controlling my heartbeat when doing SCATT sessions; however the range of heart rates was much broader than was expected. In the next article, I'll have a crack at explaining what might account for this variation and whether there's any way of using it to our advantage.

* Vid. http://www.ncbi.nlm.nih.gov/pubmed/22744827
** It is worth noting at this point that at least two aspects of shooting technique are aimed at diminishing the effect of heartbeats on aim: The modified Estonian position is supposed to reduce the effect of bloodflow through your guts on aim, and correct positioning of the sling on the upper arm reduces disturbance from the brachial artery.
** Average for a 40 year-old man is something like 70bpm according to http://www.topendsports.com/testing/heart-rate-resting-chart.htm but I've been running for few years now, which has had a significant effect.

Bugger.

Decided to record my heart rate using my Garmin 225 watch during this evening's SCATT session as part of an experiment but must have accidentally deleted the session. Bugger. Will try again tomorrow.