Math Made Easy

[Chris Davidson]

The following numbers are fairly accurate, within 3 frames I believe in the overall scheme of things.

Frame 161 = Where the WC starts there measurements=161 frames

Frame 322=Halfway point in film

Frame 483=Total frames in MPI version of Z film (Actually 486, but this is not divisible by 4 in whole frames)

Frame 644=End of film.

The relationship of these numbers is 161+161=322+161=483 +161=644

I'll refer to them as four equal zones.

161=1/4 322=2/4 483=3/4 644=4/4

chris

[Chris Davidson]

Films usually have a starting point (frame 1) and end point (last frame).

Math starts with a question and ends with an answer.

I'll start with Zone1 from the previous post since that includes frame 1-(161 WC starting point).

If the WC started their calculations with frame 161, that tells me there must be a frame 1 starting point.

If they didn't have footage of the limo, at the beginning of the Z film, around the Elm St. turn, they could use the Towner film.

How so?

They could have used a landmark within the plaza to align JFK and start their frame counting from that spot. (Landmark would be the physical corner of the TSBD).

Now, to do that, they would have to be in possession of the Towner film back in 1963/64.

What does the Towner film show when JFK is near the TSBD corner? It shows a splice and removal of frames. The position of JFK after the splice is aligned with the corner of the TSBD.

http://i140.photobucket.com/albums/r25/123steamn/TownerSplice-1.gif

So a starting point has been set.

The WC quite easily could have used the Towner frame count at 18.3 FPS to arrive at approx 167 or 168 total frames depending on the missing spliced frame count.

How would the math work on this?

Including the splice frames (approx 8) to where JFK is aligned with the corner of the TSBD is 92 frames. That leaves 76 frames from the corner on down Elm St.

92 frames at 18.3 fps=5.02 sec.

76frames at 18.3 fps=4.15 sec.

Apparently they thought about starting the frame calculations at frame 168 but eventually changed their minds.

http://i140.photobucket.com/albums/r25/123steamn/Frame168.png

Instead, there is an approx 7 to 8 frame splice and their official calculations start with Frame 161.

Frame 168-161 = 7 frames.

http://i140.photobucket.com/albums/r25/123steamn/Frame161-1.png

Also take note of the distance adjustment made for frames 161-166 of .9ft traveled in 5 frames.

chris

[David Josephs]

Films usually have a starting point (frame 1) and end point (last frame).

Math starts with a question and ends with an answer.

I'll start with Zone1 from the previous post since that includes frame 1-(161 WC starting point).

If the WC started their calculations with frame 161, that tells me there must be a frame 1 starting point.

If they didn't have footage of the limo, at the beginning of the Z film, around the Elm St. turn, they could use the Towner film.

How so?

They could have used a landmark within the plaza to align JFK and start their frame counting from that spot. (Landmark would be the physical corner of the TSBD).

Now, to do that, they would have to be in possession of the Towner film back in 1963/64.

What does the Towner film show when JFK is near the TSBD corner? It shows a splice and removal of frames. The position of JFK after the splice is aligned with the corner of the TSBD.

http://i140.photobucket.com/albums/r25/123steamn/TownerSplice-1.gif

So a starting point has been set.

The WC quite easily could have used the Towner frame count at 18.3 FPS to arrive at approx 167 or 168 total frames depending on the missing spliced frame count.

How would the math work on this?

Including the splice frames (approx 8) to where JFK is aligned with the corner of the TSBD is 92 frames. That leaves 76 frames from the corner on down Elm St.

92 frames at 18.3 fps=5.02 sec.

76frames at 18.3 fps=4.15 sec.

Apparently they thought about starting the frame calculations at frame 168 but eventually changed their minds.

http://i140.photobucket.com/albums/r25/123steamn/Frame168.png

Instead, there is an approx 7 to 8 frame splice and their official calculations start with Frame 161.

Frame 168-161 = 7 frames.

http://i140.photobucket.com/albums/r25/123steamn/Frame161-1.png

Also take note of the distance adjustment made for frames 161-166 of .9ft traveled in 5 frames.

chris

There are 3600 seconds in an hour and 5280 feet in a mile

At 1mph the limo would travel 1.47 feet in one second (5280/3600)

At 1mph the limo would travel .4 feet in 5/18.3 of a second (5 frames)

At 2mph the limo would travel .8 feet in 5 frames

At 2.25mph the limo travels the .9 feet in 5 frames

The limo was moving 2.25mph from 161-166...

Moving on... from 166-185 = 19 frames or 1.038 seconds

and equates to 19.2 feet the limo moved

At 1mph the limo moves 1.47 feet....

At 13.5mph the limo moves 19.2 feet in 1.038 seconds

In less than a second the limo accellerated from 2.25mph to 13.5mph?

The distances related to Zframes does not work... Zframes are missing...

In the case from 161-166 there are as many as 14-15 frames missing if the limo was up to it's 11mph speed

[James R Gordon]

Chris,

If you could bear with me, I am not clear on all you say and this table.

1. I don't follow how you can say the end of the film is 644. How do you come to that figure when you also say the film has 486 frames

2. The table talks about "station A". What is that and where was it. I have no idea where that is and how to reference it.

3. Column 2 has these strange numbers e.g. 3*29.2. What do they mean.

If you could explain it would help me better understand this table.

Thanks

James.

[Chris Davidson]

David,

Thank you for showing the WC "rate x time =distance" formula is bogus.

Hi James,

The 644 frames is an end point for "total frames vs frames per second" when used as a ratio of 3/4.

In other words, a 3/4 ratio would equate to 483/644 which also equates to approx 18.3/24 ratio.

486/644=.754 still very close to 3/4.

Keep in mind, the difference between 644 and 483 is 161.

It's called working both ends of a math problem. What I subtract from the front needs adding back at some point.

I don't want to discuss the distances just yet, pertaining to WC CE884, but I will eventually.

Hang in there.

chris

[Chris Davidson]

In a previous post these are the times and frames I gave for Tina Towner's film.

92frames x 18.3 fps=5.02 seconds. This aligns JFK with the physical corner of the TSBD.

76frames x 18.3 fps=4.15 seconds.

I've always held to the belief that her camera was running at the speed it was manufactured to run at, in this case 18 fps but let's make it 18.3 so it's paralleling Z's camera.

Myers has it syncing with all other films at 22.8 fps a 25% increase over its defined specs.

If Towner is running at approx 18.3 fps then Z should be running at 22.8 fps or above. (More than likely, 24fps).

There is that 18.3/24 fps ratio.

But its Towner to Z, not Z to Towner.

If Z is running at 24 fps for 5.02 seconds, the amount of time it takes to get JFK to the TSBD corner in Towner is:

24 fps x 5.02sec=120frames.

And overall, if the Z film is running at 24 fps for the total frames in Towner, then it becomes:

24fps x 4.15sec=100frames = 120+100

So, a camera running at 24 fps the length of the Towner segment would yield a total of aprox 220 frames.

Frame 1 would start with JFK aligned with the physical corner of the TSBD and end at frame 100 when filming at 24fps.

Frame 100, now there's an easy number to work with.

chris

Edited February 22, 2012 by Chris Davidson

[Chris Davidson]

Chris,

If you could bear with me, I am not clear on all you say and this table.

1. I don't follow how you can say the end of the film is 644. How do you come to that figure when you also say the film has 486 frames

2. The table talks about "station A". What is that and where was it. I have no idea where that is and how to reference it.

3. Column 2 has these strange numbers e.g. 3*29.2. What do they mean.

If you could explain it would help me better understand this table.

Thanks

James.

Hi James,

Now would be an appropriate time to post the partial plat.

A little explanation before I do.

The plat is Drommer and the FBI 2/7/1964 plat combined.

Complete and total credit for the FBI plat goes to TOM PURVIS for graciously providing me with it.

To get these to align as close as possible this is what I have done:

Drommer in its original form has the incorrect width for Houston St. (Thanks to Craig Lamson for pointing that out some time ago)

In order to remedy that, I had to reduce Drommer to 71.5%, now Houston St. is 60ft wide.

The scale is 1inch=10ft.

The FBI plat was reduced down to 35.75% wide x 36% high. I don't like changing the aspect ratio on things, but I believe a 1/4 % difference is within reason due to paper folds, etc etc.

I then rotated the complete plat 26 degrees clockwise.

The fit among the 2 plats is within 1/8 inch or 1.25ft.

The red text and lines are mine along with the thinner blue vertical and horizontal lines.

Using this I will continue on with the shenanigans of the WC.

chris

[James R Gordon]

Hi James,

Now would be an appropriate time to post the partial plat.

chris

Thanks Chris. That is helpful. Would it be possible, at some time, for you to post your complete amended Drommer plat.

That would also be helpful.

Thanks.

James.

[Chris Davidson]

James,

If you have the ability to reduce Drommer down to 71.5%, you would have my amended plat.

If not, I will post it at that size, a little later.

Just a quick recap.

Physical corner of the TSBD is the alignment point for JFK while in the limo (Towner Splice) used by the WC as their starting point for measurements.

Towner film at 18.3 fps runs 76 frames past JFK aligned with the TSBD.

Towner film at 24 fps runs 100 frames past JFK aligned with the TSBD.

Combined Drommer and FBI plat provided with measurements.

chris

[Chris Davidson]

Distance from TSBD physical corner to WC frame 161 approx 86Ft.

Towner film at 18.3 fps runs 76 frames past JFK aligned with the TSBD.

76/18.3fps=4.15 sec.

Myers mufti-film sync study has the limo (18.3 fps) traveling from the end of Towner to Z150 in 32 frames and 1.75 sec.

If both camera's are actually running at 18.3 fps, then from the TSBD physical corner to Z150 this is approx 108 frames and 5.9 sec.

To get to frame 161, another 11 frames is needed. Myers has the time between 10 frames (frame150 and 160 as .55sec.) One more frame would be another .05 sec added to .55= approx .6sec

This scenario equates to 119 frames@6.5 sec=18.3fps

A 24fps scenario equates to 24x6.5sec=156 frames. 5 frames short of the magic 161. But right at another splice in the extant film.

Now take a look at WC CE884(provided previously) and the adjustment made between 161 and 166, they have the limo traveling .9ft in 5 frames. Warning!!

Now I have a comparison of 119 frames and 161 frames between the two scenarios.

That is a difference of approx 42 frames.

A little relevant testimony provided. Drive it home Ford!!

Caveat: Distance traveled in 119 frames is approx 78ft. Distance traveled in 161 frames approx 86ft. Still working on that one.

chris

[Chris Davidson]

Caveat: Distance traveled in 119 frames is approx 78ft. Distance traveled in 161 frames approx 86ft. Still working on that one.

Problem solved:

Myers has the limo travel approx 45ft from the TSBD corner to the end of Towner.

Then he has it travel 25ft from the end of Towner to frame 150.

That is a total of 70ft.

If you plot 70ft from the TSBD corner down Elm St on the plat provided, you are 15ft short of frame 161.

His time for frame 150-161 is approx .6sec

This converts to 25ft in 1 second @18.3fps or 17mph.

Or, 32ft in 1 second at 24fps or 22mph.

From the Warren Commission Report Page 86:

http://i140.photobucket.com/albums/r25/123steamn/WCPg86-1.png

I broke this down awhile ago and can now add the bogus "22mph by other witnesses to the mix".

Also, if you read carefully, 186ft immediately preceding the head shot is 50ft before frame 161 when referencing WC CE884.

If you plot that on the plat provided, you'll find it is "POSITION A"

So someone has included "POSITION A" (50ft before the WC starts there calculations) as part of the "rate x time =distance" equation working out to 11.2 mph, while Myers never has the limo going faster than 10.5 mph up to Z175.

chris

P.S.

If you can't figure out where the 15ft error/switch in Myers was made, I'll reveal that in a bit.

A hint is "think in terms of vehicle length".

[Chris Davidson]

At some point, someone has changed from measuring JFK's position in the limo to using the front of the car as their yardstick.

I believe the limo is approx 21ft 2in and more than likely, JFK within the limo is 15ft back from that.

cheers,

chris

Edited February 24, 2012 by Chris Davidson

[Mark Knight]

I think I like where you're headed with this, Chris...As I've heard said before, with the CORRECT survey information, the truth really IS in the Warren Commission report; it's just missing from their conclusions.

[Chris Davidson]

I think I like where you're headed with this, Chris...As I've heard said before, with the CORRECT survey information, the truth really IS in the Warren Commission report; it's just missing from their conclusions.

Hi Mark,

I don't know if you caught this but:

If the yardstick was changed from "JFK in the car" to the "front of the car", then at the 70ft mark, JFK would now actually be 30ft away.

Remember at the 70ft mark the front of the limo is 15ft away, not JFK.

More to come.

chris

[Chris Davidson]

There are two different versions which are evolving.

The first is JFK aligned with the TSBD traveling approx 85ft and ending up at frame161.

This version is using 24fps x 6.5 sec= 156frames + WC distance adjustment from frame161-166.

The second is JFK aligned with the TSBD traveling approx 55ft in 108 frames in 5.9 sec.

This puts it 30ft short of the first scenario.

Since frame 156 is the initial target mark for syncing both versions, I would need to gain 30ft in 48 frames.

This is where Myers helps out again.

In another graphic (provided), he has the limo traveling between 9.8 mph and 10.5 mph from Z150 to Z175.

Since the extant film shows what appears to be a constant speed, I'll use the approx midway point(10.2 mph) between the two speeds, to calculate time and distance traveled.

10.2 mph=15ft per second.

15ft per second x 2 seconds=30ft

2seconds@24fps=48frames

Now adding back to the original starting point of 108 frames at 55ft traveled, the new result is:

108frames +48 frames =156 frames in 7.9 seconds.

55ft + 30ft = 85 ft.

The two different versions are now synced up in distance and in frame count by IMPLEMENTING 2 SECONDS OF FILM AT 24FPS. into the 18.3 fps version.

A 5 frame adjustment(161-166) for 18.3fps@10.2mph=4.09ft.

If the WC based there original calculation on the 2 second segment at 24fps rate running through to frame161, that would be:

5 frames@24fps@10.2mph=3.12ft

A difference of 4.09-3.12=.97ft

The WC in document CE884 has frame 161 at 3+29.2 and frame 166 at 3+30.1.

29.2/30.1=.97ft

BINGO

chris

Edited February 24, 2012 by Chris Davidson