Well with out the actual picture this is pretty rough but should give measurements close to an inch or so. This range is from my own experience and I do not have a error propagation proof for it.
Using the Similar Triangle theory from Geometry and the special properties of inverse trig functions over a range of
Theta between 0 and pi(180 degrees) we arrive at
y = x / cos( theta )
where y = length, of component in the picture
x = length, measured directly from picture
Theta = angle calculated, angle of carriage to focal plane of camera
Theta = cos-1(x/3")
where x = length measured from picture of trunnion
3" = known dimension of trunnion (this number is wrong value 3" should be replaced with proper scaled measurement. So really this proof is flawed since you don't know the scale of the photo.) I would guess at it and use it to approximate the values.
Shifting the axis x and y will yield the most accurate means of measurement. I would make all my measurements as the angle between x and y as 90 degrees. The last assumption would be that the angle between the pictures Y axis and the Y axis of the camera focal plane would be 90 degrees also. This results in a 1:1 relationship between height in the picture and the actual mount.
Got it? Pretty simple, no? Glad you grabbed that barrel as a live cannon would not have went over well with the wife had I went over to Jax.
