Zenith Actuating Lever - length and angles!

[rodoredas]

Ok so I’m bored, waiting for my Alternator and Engine Wiring loom to complete an engine rebuild, so that’s my excuse for delving into the mathematics of the angles of the throttle actuating lever on the Zenith 40 TIN carburettors, bear with me or skip this now!

I’ve been rebuilding a set of Zeniths and they are complete, my 3.0 is coming along waiting for Alternator and I started preparing to install the carbies when it dawned on me that the actuating linkage may not fit properly. Based on the fact that the Zeniths came from a 2.2 engine with a stroke of 66mm and were going on a 3.0 with a stoke of 70.4mm I wondered if that translated into a longer actuating lever. I assume it does, the distance between the Inlet ports on the engine must be wider on the 3.0 than on the 2.2, so the lever has to be longer. If the Inlet port position is related to the stroke then I’m assuming the rod must have to be 8.8mm longer. Anyway, while pondering that I then started looking at the angles and length of the arms at each end of the actuating lever, and that lead to some math.

Here's my carbies


The actuating lever is a long connecting rod that runs between the 2 banks of carbies, at each end it has angled arms with ball joints that connect to the throttle linkage. At one end there is, as well as as long arm, a shorter arm that connects to the accelerator lever at the base of the left carburettor.

Here’s a picture, long arms at each end plus a short arm at one end. So I asked myself, why are the arms angled so and what is the relationship between the movement of the short arm to the long arm, and how does that translate into throttle response.


Lets look at some basic maths.The short arm has a radius of 65mm, the long arm 115mm, each rotating around the connecting hub. Logic would say that each movement of the short arm around its axis (the connecting hub) produces a movement of the long arm, connected to the throttle. How much is that? and what affect does it have?

Some simple math concludes that for each 1 degree of movement of the short arm it moves around it’s axis 1.13mm, while the long arm will move 2.00mm on its axis, by that I mean around the circumference of the circles each make. Logical really, the end point of the long arm must move further around the circumfrence than the short arm for each 1 degree of rotation.

Circumference of long arm is 2*pi*r = 722mm / 360 = 2.00 mm.
Circumference of short arm is 2*pi*r = 408mm / 360 = 1.13 mm

refer diagrams below, that's if you got this far!!

Point A moves 2mm around the circumference, when Point B moves 1.13mm for each 1 degree it rotates. This though does reflect the Vertical movement of the ball joint at the end of long arm, Point A, that requires some further math. What is the vertical movement of the ball joint on this arm for each degree?. In the example below we can see that for rotation between what I call 0 Degree and 10 Degree the vertical movement is 19.9mm (sin 10 * 115=19.9), while the vertical movement between 45 and 55 degree is 12.9mm (sin 55 *115 - sin 45 *115, 94.2-81.3=12.9). As we rotate around the pivot point in an anti clockwise direction the value of vertical movement decreases. This degree of vertical movement must be important to the opening of the throttle.

Arc C represents the area where vertical movement of point A is at its greatest, between 1.89 and 2.00mm per degree of rotation, between +20degree and what I call -20degree.

Here we can see the long and short arm rotating in a 40 degree arc. The average vertical movement of points A and B, per degree of movement of point B are, A 1.96mm, B 1.11mm


Point A is connected by fixed rod to point C on the Cam disc. Point C rotates on a 40mm radius, the cam disc, on which is the throttle valve. So how much is the vertical movement of point C, therefore the opening of the throttle, in relation to the vertical movement of Points A and B.

Point A is moving 1.96 (average) per degree, A and C are fixed together, so C must move done vertically 1.96mm as well. C moves 2.8 degree for every 1 degree of rotation of A.
Sin = 1.96 / 40 = 0.049 = 2.8 degrees. If C moves, so does the throttle as the two are connected by the rotating shaft axis of the cam disc.

The throttle moves through approximately 90 degree rotation (and the rest of my calculations assume that, even though this is not actually the case) and is driven by point C, so it too must rotate 90 degree to fully open. To do so Point C moves in a vertical plane of about 32mm (90 / 2.8). Therefore the cam disc moves through an angle of Sin = 32/40 = 0.8 = 54 degrees in order to open the throttle.

The angle AYB must be optimised to provide the best throttle response and the resting angle of Point A must be so that as it moves down it does so at the most efficient rate. What is that angle from the horizontal that the long arm of the connecting rod should be, at rest?

In order for Point A to move vertically 32 mm, in the least number of degree, it’s starting angle must be 8degree from the horizontal and must move to -8degree.
Sin = 115 / 32 = 0.28 = 16degree. So if the arm moves between 8degree+ and 8degree- we have the 32mm of movement of point A and point C and the least angle movement of point A to open the throttle, this translates in the least amount of movement of all other points.


In this position you would obtain the most aggressive opening of the throttle for the least movement of the accelerator, Point B. Maybe that is not what Porsche wanted, and the resting angle of the long arm to horizontal is positioned so it is not so aggressive. I’ve assembled the carbies and rods on a flat bench and measured the resting angle of the long arm with the throttle closed - it is 16degree above the horizontal, therefore rotating from 16degree above horizontal to 0 degree. This angle is easy to calculate by measuring the height of the ball joint on the long arm, it is 159mm (on my table) and subtracting the height of the ball joint on the bracket (bearing lever) that holds the actuating lever in place, it is 126mm, so we get 33mm. 33 / 115 gives us 0.28, the SIN of the angle, 16degree. This give a slightly less aggressive opening of the throttle, if the rotation is from 16degree+ to 0degree and vertical movement of A of 31.6mm - Close enough to the 32mm required to move the throttle from closed to fully open. Well that is going to make a huge difference isn’t it!!!

The angle EDF is the Reverse Lever, pivoting on point D at the base of the left carburettor. Ball joint E rotates on a 30mm radius while ball joint F rotates on a radius of 35mm. That’s interesting because a small movement of point E creates a greater movement (this time in the horizontal) of point F, increasing the ratio of movement on F and B. Point F and B are connected by fixed rod so move in unison and the resting angle (with throttle closed) of the long arm on the connecting rod can be controlled by shortening or lengthening this fixed rod by way of the cupped ball joints.

For less aggressive opening of the throttle, lengthen FB or AC and this will increase the resting angle of point A and reduce the ratio of vertical movement of A and C. Lets do something silly and change these angles (AYB) so that A is vertical and B as it was. If we now rotate A through the same 16degree as we did above, the vertical movement of A is only 5mm. So is the movement of point C, so the cam disc hardly rotates and the throttle barely opens for the same movement on point B and depression of the accelerator pedal. After rotating 16degree from 90degree the height of A is 110mm, the radius is 115mm. Sin 76 * 115 = 110, the height of A. Clearly the angle of the long arm at rest is important, how important and what real affect it has I’m unsure, but the math seems to indicate it is, but not that much!!

Are YOU bored now?

Seriously, what have you other Zenith guys done to the actuating lever when installing on a 3.0l, some photos seem to indicate a longer rod, because the short connecting rods to the cam disc a more vertical than mine shown here?

My carbies have taken some time and will write up my rebuild experience in another post.

cheers