[Fendlesworth]

What looks odd to me is the images in background appear to be a bit larger than they should be. After watching a few synchronizations with the Nix and Muchmore Films, I haven't been able to spot any blatant discrepencies.

I think one should realize when watching the apparent near-constant speed of the Limo that Zapruders line-of sight was nearly orthogonal to to direction of the Limo when it slowed down. 

Think about this.

This means that at the time the Limo was travelling at it's slowest speed, the perspective of Zapruder would naturally show the Limo passing at the fastest rate. This issue of perspective would greatly mitigate the apparent deceleration of the Limo.

We know that it slowed down, but were frames removed from the Zapruder Film to hide this?

Maybe so; maybe not.

I'll try a little sketch of the math involved:

Take a Limo moving at constant speed with an observer at a fixed point. I'll assume that the Limo's path (Elm St.) is straight for simlicity. We can lay two dimensional cartesian coordinates over the area and take the Elm St. to be the ordinate; the X-axis.

Orthogonal would be the observer on the abcissa; the Y-axis. Assuming a constant speed in the positive x direction, the apparent speed of the observer on the -Y axis would be the change in the angle. This is how humans estimate and speed with thier senses; ans the change of angle per unit time. It depends on the distance away from the moving body as well. 

The speed in an automobile is given ultimately by revolutions per minute; and hence, distance per unit time after the wheel's circumference has been accounted for.

So if we take the Greek letter Theta (θ) to represent the angle, and the dθ/dt to represent the infinitesimal change in angle per unit time, the apparent speed (dθ/dt) is equal to the Limo's speed by this:

tan(θ)=x/y

sec²(θ)dθ=dx/y [taking the derivative]

sec²(θ)dθ/dt=dx/ydt [multiplying both sides by 1/dt. If two things are equal, then they equal eachother still after being multiplied by a constant.}

dθ/dt=dx/ydtsec²(θ) [multiplying both sides by 1/sec²(θ)]

(dθ/dt)=(dx/dt)(1/ysec²(θ)) [rearranging and bracketing]

And we have the apparent speed which is the change in angle (θ) per unit time (dθ/dt) on one side and the Limo's speed via speedometer (dx/dt) on the right. The value of "y" is equal to the closest distance of Zapruder from Elm Street. The inverse of secant is cosine, so it can be rewritten as:

(dθ/dt)=(cos²(θ)/y)(dx/dt)

And where is the rate of change at the maximum? When the angle equals zero; when it is orthogonal. At this angle cos(θ)=1 and at every other angle cos(θ)<1. If the angle is 90° then the rate of change is zero. This would be an object coming straight at you. If it weren't for enlargement you wouldnt be able to tell that it is moving.

Obviously this does not account for enlargement.

You get the idea. Even with a constant speed (dx/dt), the apparent speed by a stationary observer with a line-of-sight orthogonal to the moving path ranges from the actual speed to zero, depending on whether or not the object is coming at you or moving directly across your point of view. We have all seen a train approach, and then pass. The train is travelling at a near-constant speed but it appears to be moving faster the closer it gets and the more orthogonal it gets to our perspective.

Putting this equation into words:

(dθ/dt)=(cos²(θ)/y)(dx/dt)

(apparent speed) = (cos²(θ)/distance) x (limo's speed)

With a constant distance from Elm St. and a constant Limo Speed we basically have a cos²(θ) equation. Here is a graph:



...to give you an idea. The Y-axis of this graph would be the apparent speed and the X-axis would be the angle. This graph is somewhat misleading since there would only be one cycle in the event we are describing, and the angle would never reach 90°. The angle starts off at about 60° or so I think.

So the upper-half of one of the humps would roughly describe the apparent speed, as defined as the change in angle per unit time (dθ/dt).

So what I am getting at is that the apparent increase in speed as the limo approaches Zapruder partially mitigates the real decrease in speed. In other words: the Limo slowed down, but from Zapruder's perspective, it did not appear to slow down as much as it really had.

Just something to consider. You would have to take the math further with frame speeds and such to estimate the true speed of the limo as measure by the angle, distance, and film speed.

You could do this with all three films and plot the velocity vs. time graphs for the Limo and compare them. 

In this way you could determine if the Zapruder film did not match the others in terms of Limo speed.