Effect of Distance Estimation Errors on Bullet Impact

In the last post, I showed that without a rangefinder, I under-estimated the distance to a 403 yard target by 12%. Some of my colleagues under-estimated the same distance by as much as 49% and the average error was -32%. So, how much can 10%, 20% or 30% errors in the distance estimate affect your shot?

Read Previous Post – Distance Estimation Errors and Why We Need a Rangefinder

Would You Bet on Hitting the Target?

effect of distance estimation errors on bullet impact

Figure 1. Effect of Distance Estimation Errors on Bullet Impact. (Click on graphs to see larger version)

I collected data on myself and other professional wildlife biologists and technicians experienced in estimating distances. Without rangefinders, we under-estimated the distance to the same 403 yard “target” between 208 – 355 yards.

How many of you would bet on hitting the kill zone of an elk at 400 yards with distance estimates ranging between 208 – 355 yards?

You can see in the ballistics graph (Figure 1) that the correct estimate should hit the center of the target at 400 yards (12 inch target or kill zone is shown in Red). If the distance was estimated at 355 yards, the bullet should impact the target 4.9 inches low. Theoretically, that estimation would hit the lower end of a 12 inch kill zone and barely nick a 10 inch kill zone. The lowest estimate of 208 yards (ballistic arc in red) results in a bullet too low to hit a 12 inch kill zone even at 300 yards and is over 18 inches low at 400 yards and completely misses a 12 inch kill zone by 6 inches.

How many of you think you are immune from distance errors of this magnitude because you use the Maximum Point Blank Method (MPBR)? I’m not so sure (I will explore the MPBR Method in the next post), so I wouldn’t bet on anybody and that includes my estimate (closest estimate of 355 yards) and I am not even considering any effect due to wind or variation in the the ammunition, the gun or the shooter.

Effect of Under or Over-estimating Distance

It is interesting that all of my observers and I under-estimated the distance to the target. The Strauss and Carnahan (2012) study that I cited in the last post also showed that most people under-estimate distances. But some people do over-estimate distances, so I examine the effect of both under and over-estimating distance by 10%, 20% and 30%.

The three tables below (Tables, 1,2 & 3) show the difference in elevation of bullet impact with + &- 10%, + &-20% and + &-30% errors in distance estimation.  I used the ballistics for the 7 mm Remington Magnum (my favorite elk rifle) with 160 gr bullet. The 7mm Rem Mag is a very flat shooting bullet making it more forgiving of range estimation errors than many other calibers.

Ballistic  &  Environmental Assumptions for Tables 1 – 3:

  • Bullet – 7mm Remington Magnum with 160 grain bullet (Federal Premium Vital Shok with Barnes Triple Shock X-Bullet)
  • Ballistics – Bullet B.C. = 0.508, muzzle velocity = 2,940 fps
  • Scope Height = 1.5 inches
  • Zero at 200 yards
  • Setting – Elevation 5,600 feet, 60°F
  • I use the free Ballistics Calculator from Point Blank

10% Distance Estimation Error

effect of 10% error of distance estimation on bullet impact

Figure 2. Effect of 10% Distance Error on Bullet Impact.

Figure 2 and Table 1 show ballistic data for a 10% distance estimation errors. For example, you can see in Table 1 that at 250 yards, a 10% error is 25 yards, so a -10% estimate is 225 yards and a +10% estimate is 275 yards. For each case, the rifle is zeroed at 200 yards and the shooter has adjusted the scope or the hold-over for the distance they have estimated.

Table 1. Bullet Impact Due to 10% Distance Estimation Error

Actual Distance (Yards) 250 300 350 400 450 500
-10% (Under-estimate) Distance (Yards)  225  270  315  360  405  450
+10% (Over-estimate) Distance (Yards)  275  330  385  440  495  550
-10% Impact (inches) -1.3 -2.0 -2.9 -4.1 -5.4 -7.0
+10% Impact (inches) +1.4 +2.1 +3.1 +4.3 +5.7 +7.3
Total Vertical Spread (inches)  2.7  4.2  6.0  8.3 11.1 14.4

For a 400 yard shot (Figure 2), the shooter that estimates the distance 10% short, estimates the distance at 360 yards and sets up for that distance. With zero set at 200 yards, hold-over or scope adjustment for 360 yards will be about 13 inches for dead center at 360 yards. But if the real distance is 400 yards, the bullet will impact 4.1 inches low.

The shooter that estimated the distance 10% long would estimate the distance at 440 yards and sets up for that distance with a hold over of 25 inches. But because the distance is really only 400 yards, the bullet will impact 4.3 inches high. The combined range of those errors (+10% & -10%) creates a total vertical spread of 8.3 inches.

The kill zone on an elk is about 14-15 inches from top of the lungs to the bottom of the heart and also about the same spread from left to right (low in the front, high in the back). I think it is best to be more conservative and I practice shooting for a 6 – 8 inch kill zone, but I show 12 inch kill zones in each of the graphs. With a 10% distance estimation error at 400 yards, the shooter would probably be OK if shooting at an elk in light winds, but with an 8.3 inch spread, it would be very questionable for a smaller kill zone like a deer or antelope.

You can see from Table 1, that at 450 yards, the total vertical spread is 11.1 inches and at 500 yards, a 10% error increases the spread to over 14 inches, so even a shot at an elk with a large kill zone is questionable.

With a 10% distance error, you could entirely miss a 12 inch kill zone at 500 yards. You could completely miss a 10 inch kill zone at 450 yards and could even miss a 6 inch kill zone at 300 yards. And remember, anyone that can estimate distances within 10% error is considered to be very good.

At what point does the error in estimating distance make you nervous? For me, any error that approaches a third (33%) the size of the kill zone makes me nervous, so if I were not sure my distance estimate was within 10%, I would not take a shot over 300 yard at an elk (conservative 10 – 12 inch kill zone).  For a smaller 6 inch kill zone, I would not shoot farther than 250 yards if not sure of the distance.

20% Distance Estimation Error

effect of 20% error of distance estimation on bullet impact

Figure 3.  Effect of 20% Distance Error on Bullet Impact.

Figure 3 and Table 2 show 20% errors (plus and minus) in estimating distance. You can see in the table that at 150 yards, a 20% error is 30 yards, so a -20% estimate is 120 yards and a +20% estimate is 180 yards. Again, I assume the shooter adjusts the scope or the hold-over for the estimated distance.

Table 2. Bullet Impact Due to 20% Distance Estimation Error

Actual Distance (Yards) 150 200 250 300 350 400 450 500
-20% (Under-est.) Distance (Yards)  120  160  200  240  280  320  360  400
+20% (Over-est.) Distance (Yards)  180  240  300  360  420  480  540  600
-20% Impact (inches)  -0.6 -1.5 -2.6 -4.0 -5.8 -7.9 -10.6 -13.7
+20% Impact (inches)  +0.8 +1.6 +2.8 +4.3 +6.3 +8.7 +11.6 +15.0
Total Vertical Spread (inches)   1.4   3.1   5.4   8.3  12.0  16.6  22.2  28.7

At 400 yards, 20% short estimates the distance at 320 yards and my 7mm bullet will impact 7.9 inches low. The 20% overestimate will be 480 yards and that bullet will impact 8.7 inches high if the real distance is 400 yards. The combined spread is 16.6 inches. Any shot over over 400 yards creates real problems with bullet impacts over and under 8 inches. I do not show the graph for 400 yards because both the 20% over and underestimations miss the 12 inch kill zone. At 450 yards, the estimation error will cause bullet impact to be off by at least 10.6 inches and at 500 yards bullet impact will be off by at least 13.5 inches.

Even at  350 yards (Figure 3), you could entirely miss a 12 inch kill zone and at 300 yards with a 20% error, you will shoot over or under by at least 4 inches, which completely misses an eight inch kill zone. It is not until the shooting distance is 250 yards or less that a 20% error in estimating distance causes impact errors less than three inches high or low.

If I were not sure my distance estimate was within 20%, I would not take a shot at an elk over 225 yards.

30% Distance Estimation Error

effect of 30% error of distance estimation on bullet impact

Figure 4. Effect of 30% Distance Error on Bullet Impact.

Figure 4 and Table 3 show distance errors of plus and minus 30%. The table show at 150 yards, a 30% error is 45 yards, so a -30% estimate is 105 yards and a +30% estimate is 195 yards. Again, I assume the shooter adjusts the scope or the hold-over for the estimated distance.

Table 3. Bullet Impact Due to 30% Distance Estimation Error

Actual Distance (Yards) 150 200 250 300 350 400 450 500
-30% (Under-est) Distance (Yards)  105  140  175  210  245  280  315  350
+30% (Over-est) Distance (Yards)  195  260  325  390  455  520  585  650
-30% Impact (inches)  -0.9  -2.1  -3.7  -5.8  -5.8 -11.6 -15.4 -20.0
+30% Impact (inches) +1.2  +2.5  +4.3  +6.6  +9.6  +13.3 +17.7 +22.9
Total Vertical Spread (inches)   2.1   4.6   8.0  12.4  15.3  24.9  33.1  42.9

At 400 yards, a distance estimate that is 30% short estimates the distance at 280 yards and the bullet will impact 11.6 inches low. The 30% overestimate will be 520 yards and the bullet will impact 13.3 inches high, for a combined spread of 24.9 inches. Even at 300 yards, the total error spread is over 12 inches and the shot is too risky to take even at a very large kill zone (Figure 4). At 250 yards, the error spread is 8 inches, which is still too risky to take at a smaller kill zone.

If I were not sure my distance estimate was within 30%, I would not take a shot at an elk over 175 yards. But rest assured, I will know the distance within a few yards before I take any shot.

Long Distance Shooting and Ethical Shots

Luckily most shots taken at deer or elk are usually at distances less than 200 yards. The Colorado Division of Wildlife claims the average shot at elk is 170 yards. Just last week, I was ready to shoot my muzzle loader up to 150 yards (distance verified with a range finder and if wind velocity was less than 10 mph), but was able to kill a small buck at 20 yards. There are many examples of extreme long distance shooting today and making long distance shots even seems to be the goal for some. Some folk practice enough to have a realistic chance to make these shots on a regular basis. Most of us do not. I have seen some hunt shows take ridiculous shots and call them ethical. How can the 2nd and 3rd shot at a running animal be ethical when you missed him while he was standing still? How can you call a 400 yard shot in 30 mph winds ethical when we saw the bullet hit 2 feet high and 4 feet behind?

I think it is irresponsible to just zing a bullet out there to see what happens. Just this week, I talked to some young guys that shot (and hopefully missed) at a running spike elk at over 500 yards. You know what could happen and most of it is bad. It is better to control that buck fever and try to become a cold, calculating meat hunter. Yes, we all want to make the shot, but most of all we want a clean kill and to recover the meat and the trophy without having to chase and track a wounded animal all over the country. The last thing we want is to wound an animal so it suffers until it finally dies.

The most important things we can do to make clean kills are:

When I talked to the two young hunters that missed the spike at over 500 yards, I asked them what hold over they used for the 500 yard shot. They didn’t have good answers and one of them didn’t know what hold over was, but I think they knew the shots were not ethical. FYI – If they zeroed their rifles (270 Winchester) at 200 yards (depending on which ammo they used), hold over would be about 35- 40 inches. Good luck with that.

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