Ronald, thank you; my apologies for the late reply
Chuck, thanks for asking - I forgot to include that.
Calculating things with CAD is a quick way to do it - like Prop did.
I'm a bit old-fashioned in some instances, so I used good old maths to do it. It's good mental exercise as well.
OK, what follows may be a bit lengthy, but it allows one to calculate the port positions for just about any center-pivoting wobbler engine - or even help design one. If the basic principles of operation of this type of wobbler is understood, it's fairly straight forward.
First a Crap-o-Cad picture. This resembles the important bits of any center-pivoting wobbler engine's layout. - Fig 2 is an enlargement of the blocked section of Fig 1, and is the port layout relative to the pivot pin It might look intimidating at first sight, but it's actually quite simple and is a large part of the important dimensions on which a wobbler engine works:
The definitions of the letters I added to the image:
t: Length of the crank throw from the center of the crankshaft to the center of the crank pin.
D: The length from the center of the crank shaft to the center of the cylinder pivot pin.
C: The center line of the piston rod where the cylinder and piston rod is at maximum angle during operation.
theta: The actual angle when the cylinder is at it's maximum pivot
P: Center of the pivot point of the cylinder
L: The distance the center of the port hole in the cylinder is away from the center of the pivot point.
A: is the arc the center of the cylinder port hole follows along the port face
Pc: the point at which the cylinder port hole is central - this corresponds to top and bottom dead center for the piston.
Pb: is the center of one of the port holes in the block. There's a caveat (in my opinion) to this location that I'll get around to later on.
In Fig. 2, x and y are the values we're interested in for locating the port holes in the block.
x is the distance from the center of the pivot point to the center of the port hole in the block.
y is the offset from the center line to the center of the port hole in the pivot block.
OK, now to get down to things.
In Fig. 1: To locate the coordinates of the port center holes in the block, the maximum angle that the crank would pivot the piston rod is needed. This is also the maximum angle at which the cylinder will pivot (angle theta). This is along line C, and maximum deflection happens where line C intersects with the circle the center of the crank pin makes while the crank rotates. At this point, a rectangular triangle is formed with a 90
o angle between lines "C" and "t" to the center of the crank shaft. Calculating angle theta is simple - it's the sin
-1 (arcsine) of the ratio of the throw length "t" to the distance between the cylinder pivot center and the crankshaft center "D". - (Fig 1).
On to Fig. 2, and the caveat I mentioned. This layout is pretty much optimal for a wobbler engine running on compressed air with symmetrical ports and identical port sizes on the block and cylinder - like Elmer used for all of his wobbler engines. Personally, I have an untested hunch that things may be different for optimal use of live steam in wobblers, but I have to play around with that a bit first...
To calculate the holes for the port holes in the cylinder block, it's once more on to some simple trigonometry. The "x" and "Y" values for the port center hole in the block is easy to calculate using the formulas next to the Fig 2 block. I only showed one coordinate in the image for one port, but the other one is dead easy - just add the same amount of "y" above the center line at the same "x" setting for the top port. For a double-acting wobbler, use the same amount of x to the right of the pivot point "P", with equal offsets for Y above and below the center line.
To use the above, all that's needed to calculate things is the values of D, t and L
Trigonometry does not care about units of measure, so the above can be used to calculate the values needed in both metric and imperial. Just stick to one system; they can't be mixed up during calculations. If you do it in imperial, choose to work in either inches or thou - don't mix them.
You can also choose to work in either degrees or radians for the angles - just stick to one of these and don't mix them. Most people will work in degrees - I'm sometimes inclined to work in radians; that stems mostly from my programming background.
So to put all the above into values for Elmer's #25. I'll do it in imperial, and as the port offsets are relatively small, and we need a bit of accuracy, I'll do it in thou, with angles in degrees.
The drill jig provides most of the dimensions - except for the crank throw which is easily obtained from the crank web layout. From the plans:
D = 1
1/
4 " = 1.250" = 1250 thou
t =
1/
4" = 250 thou
L = 3/8" = 375 thou
Angle theta is = arcsin (t/D)
= arcsin (250/1250)
= 11.537
oto find x: x = L cos theta
= 375 . cos 11.537
= 367.42 thou
Same for y: y = L sin theta
= 375 . sin 11.537
= 75 thou
Depending on how close you want to work, round the values for x and y. I tend to try and work accurate to 0.01mm - or roughly 0.5 thou, so x~= 367.5 = 0.3675" and y~=75 thou = 0.075"
The same, but in metric (mm)
D = 31.75mm
t = 6.35mm
L = 9.53mm
Angle theta is = arcsin (t/D)
= arcsin (6.35 / 31.75)
= 11.537
oto find x: x = L cos theta
= 9.53 . cos 11.537
= 9.34mm
Same for y: y = L sin theta
= 9.53 . sin 11.537
= 1.91mm
Some comments about using the above in the design of a wobbler:
Most wobblers of the center-pivot type follow a design where the ratio of the crank throw to the distance between the crank center and the pivot center is at a ratio of between 1:3 to 1:5. The #25 is on the 1:5 ratio - I think Elmer used the longer ratio to enable him to make a longer piston - thus doing away with a cross-head.
A longer ratio makes for a smaller angle of change on the cylinder, and hence the port holes in the block move closer together, thus restricting the port hole sizes. It does, however add some much-needed space between the cylinder and the crank to add a packing nut and cylinder head if one is making a double-acting wobbler.
A shorter ratio on the other hand allows for bigger port holes - and this is useful for some better performance (air/steam can enter and exhaust more easily), but leaves less room between the crank and cylinder, thus making it more difficult to make a double-acting wobbler, or in the case of a single acting one, preventing the use of a longer cylinder like Elmer used for the #25 and thus necessitating a cross-head of some form.
For an engine with equal-sized ports both on the block and in the cylinder, the maximum port size can easily be worked out from the value gotten for "y" in the calculations above. it must be _just_ smaller than "y" to allow a bit of dead space when the piston is at top or bottom dead center - otherwise blow-by can happen where the port hole actually connects the inlet port to the exhaust port. Depending on how accurate one can work, the port sizes for the #25 can easily be opened up to 1.8mm instead of the 1.6mm (1/16") Elmer specified.
OK, I must be boring everyone to death by now, and MEM can't do with dead members, so I'll get off the soap box.
Chuck, I hope your question is answered - if not, please give a shout
- I got a bit carried away...
Kind regards, Arnold
PS: Marv, if you find some incorrect terms/descriptions, please mention those; when I learned this part of maths, it was all done in Afrikaans, and I haven't had much practice translating my maths terms to English.