How Fast Could Lee Harvey Oswalds Rifle Be Fired An Interesting 1960's Analysis

[Dan O'meara]

Actually, Walter Cronkite was mistaken on a detail. He said the Warren Commission concluded that the first shot was fired at frame 210. And the last shot at frame 313.

While their were some involved in the investigation that thought the first shot occurred at, or shortly after frame 210, some disagreed. While their may have been a small majority (I think) of the investigators who thought the shots were confined between z210 to z313, there was enough doubt to give no definite scenario in the final report. They said there was a shot around z210 and z313 but the other shot could have been before z210 or between z210-z313. This was a wise decision.

In the sixty years since then, with more analysis of the Zapruder film, there is now a general consensus among LNers that the:

* first shot: hardest to pin down, but may have been around z152 (my view). In any case, well before z221.
* second shot: universal consensus that the second shot was at z221-z225.
* third shot: universal consensus that the third shot was at z312-z313.

However, the general consensus among CTers is, well, there is no general consensus among CTers. No CTer has ever come up with a compelling scenario, even among just their fellow CTers.

No CTer has ever come up with a compelling scenario,

I don't ever recall you joining in with the discussion on "The First Shot" thread.
If you did, it was short lived, which would have been due to the mountain of evidence crushing any kind of notion of a first shot as early as z152.

[Andrew Mason]

Well, they didn't say they were looking for a hole or damage. They said they were using a metal detector. I don't think one would find a hole, there would only be some damage to a branch which the tree would party heal and I would think it would not be easy to tell if the old damage was caused by a bullet or something else, like a tree trimmer, which is periodically done for trees growing over a road. In any case, no hole, no damage, was found.

I have heard that small branches can deflect a bullet. Even a minor deflection could cause a bullet to miss the limousine. But this is irrelevant to me because I don't think there was any shot fired while the limousine was behind some branches so there was no deflection.

Why would the bullet miss the entire limousine? I have started a thread on this subject at:

https://www.jfkassassinationforum.com/index.php/topic,3570.0.html

According to my calculations, the angular velocity of a moving target was:

3.2 degrees per second, for the Olympic 1908 Running Deer competition.

4.8 degrees per second, for Oswald’s first shot at z-153, which missed the limousine.
1.9 degrees per second, for Oswald’s second shot at z-222, which wounded both Kennedy and Connally.
0.58 degrees per second, for Oswald’s third shot at z-312, which killed Kennedy.

In 1908, using shooters competing for the Olympic Gold Metal, very good shooters with (I assume) a good deal of practice firing a rifle at a moving target, had trouble firing accurately at a target moving at 3.2 degrees per second, 110 yards from them. Some of them missed the entire target, the size of an adult deer with most of their shots, at a range of 110 yards. I don't find it wildly implausible that Oswald, who never tried to fire a rifle at a moving target before (although he did have excellent training at stationary targets) could miss from 43 yards, at a target with 50 % greater angular velocity than the 1908 Running Deer competition.

As far as missing the street is concerned, the street was never searched for damage, and ballistic experts who have tested this found that the damage to the street would be small, making a small crater that is not too noticeable and maybe not too different from the ordinary damage a busy road receives from traffic were even large potholes can form.

You need to rethink your analogy.  A 10 foot long (giant sized) deer at 110 yards (330 feet) covers an angle from nose to tail of .0303 radians = 1.73 degrees.  That is the target the Olympian shooters were trying to hit. And even if the shot was within the 6' x 10' rectangle covering the deer, there would be a less than 50% chance of actually striking the deer's body.  The limo at z153 was 21 feet long and was 130 feet from the rifle. It covered an angle of 21/130= .16 radians = 9.25 degrees and if the shot was within a 21' x 7' rectangle covering the car, there would have been a 100% chance of it striking the car.   So it would be much less likely for a shooter to miss the entire car, let alone the entire road.

[Joe Elliott]

You need to rethink your analogy.  A 10 foot long (giant sized) deer at 110 yards (330 feet) covers an angle from nose to tail of .0303 radians = 1.73 degrees.  That is the target the Olympian shooters were trying to hit. And even if the shot was within the 6' x 10' rectangle covering the deer, there would be a less than 50% chance of actually striking the deer's body.  The limo at z153 was 21 feet long and was 130 feet from the rifle. It covered an angle of 21/130= .16 radians = 9.25 degrees and if the shot was within a 21' x 7' rectangle covering the car, there would have been a 100% chance of it striking the car.   So it would be much less likely for a shooter to miss the entire car, let alone the entire road.

On a minor point, Oswald was not looking at right angles to the limousine, which would give a 21 foot wide target, but at an angle, as I recall of 27 degrees. Assuming a 21 foot long limousine with the rear being 3 feet wide (just a guess on my part), that would give a vertical target 'height' of 9.5 + 2.7 or 12.2 feet.

On another minor point, the limousine is not as wide as it is long so certainly a miss to the right by five feet would miss by the entire limousine.

The most major point is the angular speed of the 'Running Deer' target is 3.2 degrees per second. The angular speed of the limousine at z152 is 4.8 degrees per second. I don't think this means the amount an aimed shot would be off would be increased by 50%. The expected or average amount of error in the aim might be doubled or tripled or more. We don't know.

What is known that a target of 3.2 degrees per second was enough to greatly throw off the aim some of the world's best shots (in 1908). Some were able to do fairly well. Others generally missed by a lot. Perhaps all of them would have been very wild with their aims if the target was moving at 4.8 degrees per second. And that seems even more likely for a person like Oswald who never fired at a moving target before with a rifle.

In any case, what you imagine what would happen to the aim at a target moving at 4.8 degrees per second, nor what I imagine what would happen to the aim at a target moving at 4.8 degrees per second, tells us nothing. This could only be decided by real world tests with real world shooters. Ideally with shooters who had similar training as Oswald had at stationary targets but no experience at a moving target.

Assuming some of best shooters (some of the lower scorers in the 1908 Olympics) in the world in 1908 would have a median angular error of 0.3 degrees (miss by 2 feet), while someone with very good training at stationary targets, but no training at moving targets with a rifle would have a median angular error of 0.6 degrees per second, in a Running Deer competition.

If those tests were run with such shooters, perhaps we would discover that the angular error would be:

target moving at 3.2 degrees per second, causes an median error of 0.6 degrees.
target moving at 4.8 degrees per second, causes an median error of 1.0 degrees.

Or maybe we might discover:

target moving at 3.2 degrees per second, causes an median error of 0.6 degrees.
target moving at 4.8 degrees per second, causes an median error of 2.0 degrees.

which would be enough to miss the target by 6 feet at z152, which is enough to miss the limousine entirely if the miss was to the right.

In any case, we cannot say it is wildly unlikely that Oswald would not have had a good chance of missing the entire limousine at z152. We can only do so if the appropriate tests were run and the firing accuracy was surprisingly good (to me) with shooters without moving target experience.

[Joe Elliott]

It has occurred to be that while comparing shots, we should not be comparing apples to oranges but apples to apples. We should not be comparing how many inches a shot was off, but the number of degrees the aim was off. I could use the more mathematical radians but I will stick with degrees.

A shooter in the 1908 Olympics who only scored 3 points, 3 hits out of 10 shots on an adult deer size target, from 110 yards away, might miss the center of the target by a medium of 2 feet (a conservative estimate). This results in an error of 0.33 degrees in the aim.

Oswald for a shot at z152, from 43 yards away, might have missed the center of the target by 5 feet, which could miss the limousine This results in an error of 2.2 degrees.

What is two degrees? Stretch out your arm and point 1 finger. The width (not the length) of your finger covers 2 degrees. It does not seem impossible that a desperately aiming Oswald, trying to get off a shot before the target is covered by the tree, might be off by the width of a finger.

If Oswald was half as good as someone who (I assume) had a good deal of practice shooting at moving targets with a rifle, we might expect him to miss by 0.66 degrees in the aim, at a target with an angular velocity of 3.2 degrees per second. If the difficulty goes up steeply, from 3.2 degrees per second to 4.8 degrees per second, if the expected error is not 50 % greater but 3 times greater, than it is not unbelievable for Oswald to be off in his aim by 2 degrees, which is enough to miss the limousine.

Of course, no final conclusion can be reached from this. We would need real world tests, ideally with a shooter (like Oswald) with excellent training at stationary targets, but no experience at moving targets, to see how well they do with targets moving at 3.2 and 4.8 degrees per second. To see if such a shooter should have hit the limousine 15 %, 65 % or 80 % of the times. Right now, we really don't know.

And what if the answer was 15 %? Would that really mean that Oswald could not have attempted a shot at z152 and missed the limousine?

Who knows what we may discover. Maybe we may find that experience at moving targets doesn't matter that much with shooting at moving targets. Maybe we may discover that 'error angles' are strictly proportional to the angular velocity. But I doubt it. But real world tests are needed to find out.

** Extra Note:

To calculate an angle, take:
  d = distance to target
  e = distance a shot missed the center of the target
  a = angle of miss

    a = 2 * atan ( 1/2) * e / d )


Important to take into account the angle the object presents to the shooter. A 21 by 8 foot limousine is not as big as a 21 by 8 foot target, unless the shooter is positioned directly above it. Seen from an angle the target is smaller. Just as a board with a diagram of a deer might by 3 by 5 feet seen at right angles but only 0 by 5 feet seen edgewise.

[Andrew Mason]

It has occurred to be that while comparing shots, we should not be comparing apples to oranges but apples to apples. We should not be comparing how many inches a shot was off, but the number of degrees the aim was off. I could use the more mathematical radians but I will stick with degrees.

A shooter in the 1908 Olympics who only scored 3 points, 3 hits out of 10 shots on an adult deer size target, from 110 yards away, might miss the center of the target by a medium of 2 feet (a conservative estimate). This results in an error of 0.33 degrees in the aim.

Oswald for a shot at z152, from 43 yards away, might have missed the center of the target by 5 feet, which could miss the limousine This results in an error of 2.2 degrees.

What is two degrees? Stretch out your arm and point 1 finger. The width (not the length) of your finger covers 2 degrees. It does not seem impossible that a desperately aiming Oswald, trying to get off a shot before the target is covered by the tree, might be off by the width of a finger.

If Oswald was half as good as someone who (I assume) had a good deal of practice shooting at moving targets with a rifle, we might expect him to miss by 0.66 degrees in the aim, at a target with an angular velocity of 3.2 degrees per second. If the difficulty goes up steeply, from 3.2 degrees per second to 4.8 degrees per second, if the expected error is not 50 % greater but 3 times greater, than it is not unbelievable for Oswald to be off in his aim by 2 degrees, which is enough to miss the limousine.

Of course, no final conclusion can be reached from this. We would need real world tests, ideally with a shooter (like Oswald) with excellent training at stationary targets, but no experience at moving targets, to see how well they do with targets moving at 3.2 and 4.8 degrees per second. To see if such a shooter should have hit the limousine 15 %, 65 % or 80 % of the times. Right now, we really don't know.

And what if the answer was 15 %? Would that really mean that Oswald could not have attempted a shot at z152 and missed the limousine?

Who knows what we may discover. Maybe we may find that experience at moving targets doesn't matter that much with shooting at moving targets. Maybe we may discover that 'error angles' are strictly proportional to the angular velocity. But I doubt it. But real world tests are needed to find out.

** Extra Note:

To calculate an angle, take:
  d = distance to target
  e = distance a shot missed the center of the target
  a = angle of miss

    a = 2 * atan ( 1/2) * e / d )


Important to take into account the angle the object presents to the shooter. A 21 by 8 foot limousine is not as big as a 21 by 8 foot target, unless the shooter is positioned directly above it. Seen from an angle the target is smaller. Just as a board with a diagram of a deer might by 3 by 5 feet seen at right angles but only 0 by 5 feet seen edgewise.

Let's look at the hardest shot: when JFK passed directly below the SN.

Let's say the car was travelling at 12.5 mph or 18.3 feet per second or exactly one foot per frame as it completed the turn and was parallel to the TSBD directly below the SN.  The aim would not be straight down but would be at a downward angle of about 60 degrees (JFK being 30 feet from the base of the TSBD below the SN which was 60 feet above).  We can work out the angle that the target moves in one frame quite easily. The distance from the rifle to the target would be 67 feet. A foot at a distance of 67 feet is .86 degrees. So the angular speed was 18.3 x .86= 15.7 degrees per second, a much faster angular speed than your deer at 3.2 degrees per second. 

If he had fired as soon as he saw JFK in the sights ie without a lead, he would have missed by the distance JFK moved in the time between pulling the trigger and the bullet going 67 feet ie. 67/2100 =32 milliseconds. In those 32 milliseconds the target moves 32/55 x 1 foot= .58 feet or about 7 inches. How could he have missed the entire car?  And that was the hardest shot. After that, the car is going away from the direction the rifle is pointing instead of perpendicular to the rifle.

More to the point, perhaps, is that Oswald knew how to fire the rifle as he had practised with the bolt action, had a telescopic sight that and had boxes and a strap to support the rifle.  All the FBI shooters who used the rifle had no difficulty coming within a foot of the target on all their tries and no one came close to missing the entire car.

I would suggest that range matters more than angular speed.  At 330 feet, it takes about 330/2000=165 ms for the bullet to get there. A deer running at 44 feet per second (30 mph) will move over 7 feet in that time.  That is enough to miss the entire animal.

[Zeon Mason]

So the shooter had adjust his sight more rapidly to track the  moving limo when it was closer at Z130-160 than when the limo was at Z224 and when it had slowed from 15mph to 8 mph at Z313 due to the angle flattening out ?

Question if there was a  Z160 shot that was fired actually quite high (even above the horizontal line of 72ft high ) because maybe the shooter having to move himself into his shooting position accidentally pulled the trigger… Would that reduce the loudness  of that shot due to an angle of the gun pointed upwards above the 72ft horizontal line?

Would  that be enough reduction  in the “loudness” factor of a 6.5mm shot  from an MC rifle to account for so few people hearing any shot prior to Z186-Z205?

[Joe Elliott]

I assume these questions are directed to me?

So the shooter had adjust his sight more rapidly to track the  moving limo when it was closer at Z130-160 than when the limo was at Z224 and when it had slowed from 15mph to 8 mph at Z313 due to the angle flattening out ?

Yes, the angular velocity of the target dropped rapidly during the three shot sequence. This commonly happens with a target that is moving away and increasing it's distance from the shooter. At some point, due to the sheer distance to the target the shooting would start to become more difficult, despite the angular velocity dropping ever lower. But this point had not been reached for any of the shots. Even the last shot was only 88 yards away.
     at z153, angular velocity 4.8 degrees per second, miss by 5 or more feet
     at z222, angular velocity 1.8 degrees per second, miss by 8 inches
     at z312, angular velocity 0.55 degrees per second, miss by 2 inches
all assuming the target was always the center of the head.

To me it is striking that the accuracy of the three shots corresponds so well to the angular velocity of the shots.

Question if there was a  Z160 shot that was fired actually quite high (even above the horizontal line of 72ft high ) because maybe the shooter having to move himself into his shooting position accidentally pulled the trigger… Would that reduce the loudness  of that shot due to an angle of the gun pointed upwards above the 72ft horizontal line?

Would  that be enough reduction  in the “loudness” factor of a 6.5mm shot  from an MC rifle to account for so few people hearing any shot prior to Z186-Z205?

This is well outside my area of expertise. But I have read that for the first shot at z152, Oswald would have had to be half standing for that shot and so the barrel of the rifle did not extend out beyond the window as the other two shots did and would not have been as loud as the two later shots to people on the street below. I do not know, maybe so.

Besides, I am not certain that few people heard the shot before z186. It is only clear that few people reacted to a shot  before z186. Possibly because they heard it but thought it was a backfire or maybe a firecracker. And the Zapruder film also shows that few people reacted to the shot at z222. Only after the z312 shot do you see people start to react and I think that is more in reaction to what they were seeing than hearing.

[Joe Elliott]

Let's look at the hardest shot: when JFK passed directly below the SN.

Let's say the car was travelling at 12.5 mph or 18.3 feet per second or exactly one foot per frame as it completed the turn and was parallel to the TSBD directly below the SN.  The aim would not be straight down but would be at a downward angle of about 60 degrees (JFK being 30 feet from the base of the TSBD below the SN which was 60 feet above).  We can work out the angle that the target moves in one frame quite easily. The distance from the rifle to the target would be 67 feet. A foot at a distance of 67 feet is .86 degrees. So the angular speed was 18.3 x .86= 15.7 degrees per second, a much faster angular speed than your deer at 3.2 degrees per second. 

If he had fired as soon as he saw JFK in the sights ie without a lead, he would have missed by the distance JFK moved in the time between pulling the trigger and the bullet going 67 feet ie. 67/2100 =32 milliseconds. In those 32 milliseconds the target moves 32/55 x 1 foot= .58 feet or about 7 inches. How could he have missed the entire car?  And that was the hardest shot. After that, the car is going away from the direction the rifle is pointing instead of perpendicular to the rifle.

You are suggesting that the only difficulty Oswald would have with a shot from 67 feet away is with providing the correct lead. So with a good aim at the center of the head, the limousine would only move 7 inches in the time it takes for the bullet to get there so Oswald should only miss by 7 inches.

I would suggest, instead, that with a target moving at 15.7 degrees per second, almost 6 times as fast as the 1908 Olympics Running Deer competition, the main problem would be in aiming. The limousine moving 7 inches before the bullet gets there would be a minor problem. If you can't aim because your blinded by bright lights, your view to the target is blocked, or the angular speed is simply way too high for you to handle, you could easily miss the entire limousine.

More to the point, perhaps, is that Oswald knew how to fire the rifle as he had practised with the bolt action, had a telescopic sight that and had boxes and a strap to support the rifle.  All the FBI shooters who used the rifle had no difficulty coming within a foot of the target on all their tries and no one came close to missing the entire car.

None of the FBI shooters attempted a shot at a target moving at 4.8 degrees per second. And I don't know if any of them had no experience at shooting at a moving target before. I believe the "FBI shooters" test you are referring to was conducted by the Warren Commission and only involved shooting at stationary targets. So these tests tell us nothing of how the angular speed of the target can effect aiming.

I would suggest that range matters more than angular speed.  At 330 feet, it takes about 330/2000=165 ms for the bullet to get there. A deer running at 44 feet per second (30 mph) will move over 7 feet in that time.  That is enough to miss the entire animal.

I would suggest that real world tests are needed. Not you or I guessing what is the most important factor, range, angular speed, or other factors.

And, for what's it is worth, I think the combination of:

* Oswald having no experience at shooting at rifle at a moving target.
* The angular speed being quite large 4.8 degrees per second, much faster than the 1908 Olympic Running Deer competition 3.2 degrees per second.
* Oswald needing a half standing posture to aim at z152, a much less accurate posture than a sitting posture he could have used for shots at z222 and z312.

may cause him to miss (in terms of degrees) by 6 times as much, 2 degrees instead of 0.33 degrees, as some of the Olympic shooters did. But real world tests need to have the final say.