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# "MATH" illustrated

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How does Clint Hill catch the limo?

At 9.8mph the limo travels 14.4 feet per sec

Hill is off at 313 and reaches the limo at 337 = 24 frames

24 frames / 18.3 fps = 1.3 seconds for Hill to reach limo

Limo travels 18.85 feet at 9.8 mph in 1.3 seconds

Hill is approx 12 feet from limo at 313 which equates to 6 feet from the running board to the front of the Queen Mary plus the 6 feet or so from the QM to the limo...

Total run of 30.85 (18.85 + 12) feet to be covered in 1.3 seconds requires Hill to sprint at over 25mph if limo travels at 9.8mph

If Hill runs the expected average speed of 11.2 mph the limo must be going 2.5 mph for him to reach it in the 1.3 seconds we see.

18.3 fps

9.8 mph

51744 feet per hour

862.4 fpminute

14.4 fpsecond

313 hill off

337 hill on

24 diff

1.3 seconds for 24 frames

18.85 distance at 9.8 mph

12.00 distance from Hill to Limo at 313

30.85 Total distance to cover

25 Hill's speed

15.2 mph differential

80256 feet per hour

1337.6 fpminute

22.3 fpsecond

1.38 seconds needed to overtake limo

If the limo was traveling at 5mph Hill need only run at 16mph to reach the limo... which for a short sprint is possible... it would also result in Hill running at 11mph FASTER than the limo

In the Muchmore collage... from z323 to z333 – about 1/2 second – Hill gets from the front of the QM to the rear of the limo... IN WHAT APPEARS AS A SINGLE STEP –

Step at 318 - left foot

Step at 323 - right foot

By 326 he is accelerating away from SS car and towards limo

Step at 328 - left foot lands on street – by 329 left foot is planted and right foot is moving forward

Between 326 and 329 it appears as if the entire scene in the street has moved west and between 326 and 337 Hill’s left foot has moved considerably down the street – it does not appear as if Muchmore changes her position other than panning left.

Step at 333 SHOULD be right foot on the ground yet left foot still on street but seems to have moved from being in front of Jean Hill to being WEST of Moorman

Step at 337 is right foot ONTO LIMO – notice how far to the west his left foot has moved... from landing in front of Jean to being noticeably west of Moorman

If the limo stopped, then the QM and some of the closer following vehicles would also have had to stop... especially the QM or else it would have hit the limo. After this analysis I feel as if the limo slowed down severely right before 313. The jerkiness of the Nix film thru this sequence is almost absurd and there are definitely frames missing. With many of the other vehicles “stopping” due to the severe slowdown of the limo, the assumption could be easily made that the limo “stopped momentarily” when in reality it was simply inching along.

By watching the stabilized Zfilm it is obvious the limo slows considerably just before 310 as we see the motorcycles ride up beside the limo... given the closeness of the QM and cycle escort, there is no reason to assume the QM or cycles would change speeds significantly during the motorcade... especially BOTH cycles as wee see in the Zfilm just before 313.

So maybe one of our resident experts can explain how this happens and is accomplished on film as well as it jiving with Altgens testimony that from z255 to z313 the limo traveled from a max of 40 feet away to 15 feet away... or moving 25 feet in 58 frames... the limo either has to be going 5mph that entire time or the foreground and background do not match the street scene as we see it in Zapruder.

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thanks Duncan...

I still am having a problem with the extra step...

When Hill takes his first LARGE step with his left leg he lands with it in front of Jean (z326-329)

It takes from 323 to 329 to plant his left leg/foot (6 frames)

By 337 his left foot is once again firmly planted on the ground (6 frames)

Where does the right foot step occur between 329 and 337 and with his left leg planted at 329...

it seems to take about 6 frames per step yet Hill is back on his left leg as he emerges from behind Moorman and is reaching for the limo.

Is that your take or can you squeeze in another right leg step in there somewhere?

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I'll take a look... the MATH threads really got me going as math is one of my passions and it either works or it don't.

Be nice too if Mike Williams could come back over here and address some of my questions in threads that have been long forgotten by now... specific questions about getting to the point where a shot from the 6th floor is even possible... maybe soon

I just posted this over there as well.... looking forward to what Mike has to say.

The frame in which that thread is claiming he left... 283 by some people... is absurd.

If he left that early he's have to all out sprint at over 20 mph for 5-8 seconds... he is not that fast nor does it take that long.

Also, based on the video, Hill loses no ground to the Queen Mary as he steps off... he actually pulls AWAY from the SS follow-up car... which means instant speed in excess of 11 mph -

I am saying the motorcade was traveling much slower than the z film suggests and some of the key frames between 310 and 337 have been removed which would have showed a drastic slow down of the limo, shots fired, Hill racing to the limo, and then what we do see - the limo racing away as Hill holds on for dear life.

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While watching the Muchmore video in this thread, I saw something curious in the background. There are 3 men on the steps leading up the grassy knoll. The one in front appears to be wearing a brown shirt. In one of the frames just before Hill reaches the limo, this guy's head disappears. The rest of his body is there, but the head disappears completely and then reappears in the next frame. Any idea on how that could happen?

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While watching the Muchmore video in this thread, I saw something curious in the background. There are 3 men on the steps leading up the grassy knoll. The one in front appears to be wearing a brown shirt. In one of the frames just before Hill reaches the limo, this guy's head disappears. The rest of his body is there, but the head disappears completely and then reappears in the next frame. Any idea on how that could happen?

I see that Richard... about 15 seconds in. I don't have the Muchmore frames so maybe Duncan can take a closer look... my version shows it only slightly and it looks like it could be the sunlight... but a closer look would be nice.

As I am posting on Duncan's forum as well... they felt that Hill starts at 301... which is fine, yet still requires sprinter level speed to catch up in the number of frames we see - OR the limo was going much slower or severely slowed down from 301 thru 315...

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While watching the Muchmore video in this thread, I saw something curious in the background. There are 3 men on the steps leading up the grassy knoll. The one in front appears to be wearing a brown shirt. In one of the frames just before Hill reaches the limo, this guy's head disappears. The rest of his body is there, but the head disappears completely and then reappears in the next frame. Any idea on how that could happen?

Richard

It looks like Marie "jumped" and shook the camera in mainly an upward motion ,it looks compressed slightly but the head is there just lower down the trunk .

Ian

Edited by Ian Kingsbury
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Hi David,

I'm still hanging in there with you.

If you haven't already, I'll try tying some of my previous Math, into what you have presented.

chris

The following in bold, is input from David, in regards to a topic on Duncan's forum:

Math all over again...

If Hill left at 283 he'd have to run at over 30 mph to reach the limo if the limo was traveling at 9.8mph as we are told.

That is impossible.

One must conclude the limo was traveling MUCH SLOWER or must have almost stopped for Hill to have reached it in the number of frames we see.

Even if Hill leaves at 313, as the shot is fired, he still must run better than 25mph to catch it by 337.

The numbers just don't add up.

DJ

18.3 fps

9.8 mph - limo speed

51744 feet per hour

862.4 fpminute

14.4 fpsecond

283 hill off

337 hill on

54 diff in frames

2.95 seconds for diff in frames

42.41 distance at 9.8 mph

12.00 distance from Hill to Limo at 337

54.41 Total distance to cover

14 Hill's speed

4.2 mph differential

22176 feet per hour

369.6 fpminute

6.2 fpsecond

8.83 seconds needed to overtake limo

18.3 fps

9.8 mph - limo speed

51744 feet per hour

862.4 fpminute

14.4 fpsecond

313 hill off

337 hill on

24 diff in frames

1.31 seconds for diff in frames

18.85 distance at 9.8 mph

12.00 distance from Hill to Limo at 337

30.85 Total distance to cover

25 Hill's speed

15.2 mph differential

80256 feet per hour

1337.6 fpminute

22.3 fpsecond

1.38 seconds needed to overtake limo

David,

Take a look at your numbers starting with 283 Hill on, 337 Hill off.

http://educationforum.ipbhost.com/index.php?showtopic=17174&view=findpost&p=216515

Edited by Chris Davidson
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Just bear in mind Hill is actually already moving at whatever speed the follow up car was travelling at.

For arguments sake, let's say the follow up car was roughly matching the speed of the President's Limo. If so, Hill was already travelling at 9 mph + before he even started running.

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Just bear in mind Hill is actually already moving at whatever speed the follow up car was travelling at.

For arguments sake, let's say the follow up car was roughly matching the speed of the President's Limo. If so, Hill was already travelling at 9 mph + before he even started running.

Are you saying that the speed of the QM propels Hill forward? I believe this is faulty thinking relative to the

two vehicles. It is all relative. If Car A is traveling 9mph and Car B is traveling 9mph and Hill is traveling

9mph, then RELATIVELY all are motionless in RELATION to each other, so he would not gain any extra distance

by jumping off the QM. Any gain must come from Hill's actions AFTER leaving the QM, since at the start

all were motionless compared to each other.

If you are on a jetliner traveling 300mph and get up and walk one mph forward, are you walking 301 mph?

Relativity.

Jack

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The jetliner analogy is apples and oranges Jack...

Relative to the ground when you walk forward in the airplane you are going 301 mph, just not relative to others in the plane. Same thing with the QM... relative to the ground Hill is moving at 9 mph and if he can jump of and maintain his motion he has effectively cutout the 0-9 mph acceleration, once he lets go... he either continues at 9mph, slows or accelerates.

But a good point was raised on Duncan's forum thread regarding this.... relative to each other, as you say Jack, the limo and QM are going virtually the same speed. And since the QM does not ride up the limo's rear, it too must have slowed to less than 9mph from 301 thru 335 or so... some indications are as slow as 7.8mph

now WHY the limo would slow as it travels THRU DP heading towards the freeway, with no one in front of them... is THE real mystery

In any case... If Hill jumps off an is instantly running at the same speed as the limo, he would never catch the limo which was about 12-14 feet from him as he rode on the QM's running board

As my math tried to show, the time it takes for him to catch the limo from 312 thru 337 is just under 1.35 seconds at 18.3fps. now how much faster must Hill be running than the 8mph limo to make up 12-14 feet in 1.35 seconds? He has to run at least 13mph FASTER than the limo or 21mph for that short sprint. If he leaves earlier, say 301, he has 2 whole seconds of frame time - 36 frames - yet still only has to make up the total of 12-14 feet.

My calculations above add back the total distance the limo travels as the amount of ground he has to cover - which he does - yet since he is already moving at the speed of the limo or better, the limo never gets more than 12-14 feet from Hill...

so by adding in the total distance travled - I was wrong. While his running and the left-right-left of his legs seems a bit suspect as one watches it... I do not see how much more than a few random frames could be removed to make it appear the limo did not slow as much as it really did... I dont believe Hill could run as fast or faster than world class sprinters... but the distance is so small he could reach speeds into the high teens, and if the limo slowed more severely - which sounds possible from eye witness testimony - than overtaking it as quick as he did is more than possible.

In my 1st example above we see that Hill is gaining on the limo at the rate of 6.2 feet per second (he runs 14 while the limo stays at 9.8) so the 12 feet is covered easily in 2 seconds. He's running at about 20 feet per second and covers the 40+ feet total distance in the same time... just the limo is only going 14.4 feet per second...

So if Chris could oblige.... what does your MATH ultimately look like within the major films? There are splices in Nix, Zap, Muchmore and Towner... if he was shot 30 feet further west - why/how do these films put him elsewhere..

is it really all about where they start, stop, how much is spliced and where they were spliced?

thanks

DJ

Edited by David Josephs
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The jetliner analogy is apples and oranges Jack...

Relative to the ground when you walk forward in the airplane you are going 301 mph, just not relative to others in the plane. Same thing with the QM... relative to the ground Hill is moving at 9 mph and if he can jump of and maintain his motion he has effectively cutout the 0-9 mph acceleration, once he lets go... he either continues at 9mph, slows or accelerates.

But a good point was raised on Duncan's forum thread regarding this.... relative to each other, as you say Jack, the limo and QM are going virtually the same speed. And since the QM does not ride up the limo's rear, it too must have slowed to less than 9mph from 301 thru 335 or so... some indications are as slow as 7.8mph

now WHY the limo would slow as it travels THRU DP heading towards the freeway, with no one in front of them... is THE real mystery

In any case... If Hill jumps off an is instantly running at the same speed as the limo, he would never catch the limo which was about 12-14 feet from him as he rode on the QM's running board

As my math tried to show, the time it takes for him to catch the limo from 312 thru 337 is just under 1.35 seconds at 18.3fps. now how much faster must Hill be running than the 8mph limo to make up 12-14 feet in 1.35 seconds? He has to run at least 13mph FASTER than the limo or 21mph for that short sprint. If he leaves earlier, say 301, he has 2 whole seconds of frame time - 36 frames - yet still only has to make up the total of 12-14 feet.

My calculations above add back the total distance the limo travels as the amount of ground he has to cover - which he does - yet since he is already moving at the speed of the limo or better, the limo never gets more than 12-14 feet from Hill...

so by adding in the total distance travled - I was wrong. While his running and the left-right-left of his legs seems a bit suspect as one watches it... I do not see how much more than a few random frames could be removed to make it appear the limo did not slow as much as it really did... I dont believe Hill could run as fast or faster than world class sprinters... but the distance is so small he could reach speeds into the high teens, and if the limo slowed more severely - which sounds possible from eye witness testimony - than overtaking it as quick as he did is more than possible.

In my 1st example above we see that Hill is gaining on the limo at the rate of 6.2 feet per second (he runs 14 while the limo stays at 9.8) so the 12 feet is covered easily in 2 seconds. He's running at about 20 feet per second and covers the 40+ feet total distance in the same time... just the limo is only going 14.4 feet per second...

So if Chris could oblige.... what does your MATH ultimately look like within the major films? There are splices in Nix, Zap, Muchmore and Towner... if he was shot 30 feet further west - why/how do these films put him elsewhere..

is it really all about where they start, stop, how much is spliced and where they were spliced?

thanks

DJ

Thanks for agreeing with me (except for the apples-oranges comment). Once Hill leaves the QM, his speed comes from him, not the QM.

He no longer is carried forward by the movement of the QM. My comment was directed to Mark Haley.

Jack

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The jetliner analogy is apples and oranges Jack...

Relative to the ground when you walk forward in the airplane you are going 301 mph, just not relative to others in the plane. Same thing with the QM... relative to the ground Hill is moving at 9 mph and if he can jump of and maintain his motion he has effectively cutout the 0-9 mph acceleration, once he lets go... he either continues at 9mph, slows or accelerates.

But a good point was raised on Duncan's forum thread regarding this.... relative to each other, as you say Jack, the limo and QM are going virtually the same speed. And since the QM does not ride up the limo's rear, it too must have slowed to less than 9mph from 301 thru 335 or so... some indications are as slow as 7.8mph

now WHY the limo would slow as it travels THRU DP heading towards the freeway, with no one in front of them... is THE real mystery

In any case... If Hill jumps off an is instantly running at the same speed as the limo, he would never catch the limo which was about 12-14 feet from him as he rode on the QM's running board

As my math tried to show, the time it takes for him to catch the limo from 312 thru 337 is just under 1.35 seconds at 18.3fps. now how much faster must Hill be running than the 8mph limo to make up 12-14 feet in 1.35 seconds? He has to run at least 13mph FASTER than the limo or 21mph for that short sprint. If he leaves earlier, say 301, he has 2 whole seconds of frame time - 36 frames - yet still only has to make up the total of 12-14 feet.

My calculations above add back the total distance the limo travels as the amount of ground he has to cover - which he does - yet since he is already moving at the speed of the limo or better, the limo never gets more than 12-14 feet from Hill...

so by adding in the total distance travled - I was wrong. While his running and the left-right-left of his legs seems a bit suspect as one watches it... I do not see how much more than a few random frames could be removed to make it appear the limo did not slow as much as it really did... I dont believe Hill could run as fast or faster than world class sprinters... but the distance is so small he could reach speeds into the high teens, and if the limo slowed more severely - which sounds possible from eye witness testimony - than overtaking it as quick as he did is more than possible.

In my 1st example above we see that Hill is gaining on the limo at the rate of 6.2 feet per second (he runs 14 while the limo stays at 9.8) so the 12 feet is covered easily in 2 seconds. He's running at about 20 feet per second and covers the 40+ feet total distance in the same time... just the limo is only going 14.4 feet per second...

So if Chris could oblige.... what does your MATH ultimately look like within the major films? There are splices in Nix, Zap, Muchmore and Towner... if he was shot 30 feet further west - why/how do these films put him elsewhere..

is it really all about where they start, stop, how much is spliced and where they were spliced?

thanks

DJ

Thanks for agreeing with me (except for the apples-oranges comment). Once Hill leaves the QM, his speed comes from him, not the QM.

He no longer is carried forward by the movement of the QM. My comment was directed to Mark Haley.

Jack

Jack

Hill would decelerate as he landed and would have to accelerate from the first step and continue accelerating until he reached the already moving limo he could not land at 9mph and hit 9mph within the first step Maybe Ed moses could in his prime but I doubt it.The supporting or landing leg has to absorb the deceleration /Compression followed by acceleration with the extension of the leg.

Ian

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You make a good point Ian....

We should assume that Hill needed a few steps whenever he jumped off to reach speed... meanwhile the limo and QM move away from him ever so slightly...

Makes the 12-14 feet more like 14-18 feet... not much difference... but every fraction of a second is a few frames...

As we look at Hill running behind Mary/Jean, I think that would have been the most opportune area to remove frames... which makes sense given the left foot at 337 without the right foot in between 329 and 337.... that step seems to me as partially removed...

that and the limo slowed to less than 5mph, imo, and visibly hesitated making it appear that it stopped to many

Just my opinion at this point yet Hill's ability to reach that limo so quickly suggests it was going much slower than it appears to be in Zapruder.

DJ

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You make a good point Ian....

We should assume that Hill needed a few steps whenever he jumped off to reach speed... meanwhile the limo and QM move away from him ever so slightly...

Makes the 12-14 feet more like 14-18 feet... not much difference... but every fraction of a second is a few frames...

As we look at Hill running behind Mary/Jean, I think that would have been the most opportune area to remove frames... which makes sense given the left foot at 337 without the right foot in between 329 and 337.... that step seems to me as partially removed...

that and the limo slowed to less than 5mph, imo, and visibly hesitated making it appear that it stopped to many

Just my opinion at this point yet Hill's ability to reach that limo so quickly suggests it was going much slower than it appears to be in Zapruder.

DJ

Right.

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I was merely pointing out that Hill wasn't stationary when he began his attempt to catch up with JFK's car.

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