I own a Mark I Tiger, B9471136. I have owned it for 31 years and have over
those years made and unmade many changes, not the least of which were engine
mods. As I read some of the message traffic, I see far too many opinions
stated as fact, or real facts but no reference as to where the information
originated. I'll pick on the latest free for all: rod ratios. Rod ratio or
the rod length to stroke is said to increase torque at (pick your RPM range).
Since I am an old retired aerospace engineer and have both the time and
inclination, I decided to investigate, analytically, what the effects of a
varying rod length for a given crank throw means with respect to torque, rod
axial force and piston side wall force. Each of these parameters is
important: torque because it is what turns the gears to get you down the
road, axial force on the rod because this is partially causes bearing wear,
and side force because it translates into friction and hence heat and wear on
the cylinder walls. As I get time, I will build a model of the cooling system
to see how it operates....
My model is simple. I used a crank and slider mechanism for the analysis. The
model comes from "Kinematic Analysis of Mechanisms", McGraw-Hill, 1969.
Because I wanted to develop axial forces in the rod and side forces on the
piston, I used a parameter called BMEP or brake mean effective pressure
(psig) acting on a piston which had a diameter of 4.00 inches. Since my Tiger
is a Mark I with the 260 cubic inch engine I used the published BMEP value of
124 psi (which occurs at 2200 RPM). This gives an axial piston load of 1558
lbf. I held the crank throw constant, at 1.435 inches, which is half the
stroke of our 260/289 cubic inch engines, and varied the rod length.
Coincidentally, I used our rod length of 5.155 inches as the starting point
and used 5.0, 5.5, 6.0, and 4.5 inches as other lengths.
The math model I developed, based on the crank and slider referenced above,
looks like this:
sin(x)*(1-((r/l)sin(x))^2)^1/2 + cos(x)*sin(x)*(r/l)
M(x) =
F*r*-------------------------------------------------------------------
(1-((r/l)sin(x))^2)^1/2
where:
M(x) = torque (ft-lbs)
F = Piston axial force (lbf)
x = crank rotational angle (radians), evaluated from TDC to
BDC (0-180 degrees)
r = crank throw (inches), stroke/2
l = rod length (inches) pin centerline to bearing journal
center line
As can be seen, it is a reasonable complex trancendental equation. I had
originally planned to take the derivative and set it equal to zero to find
the maximum angle at which torque occurs based on specified rod ratios, but
the complexity got out of hand, at least for me. I would be interested to
hear from anyone whose can accomplish the feat (I used Math Cad 4.0 and it,
for sure, produced the required derivative, but I did not take the time to
evaluate it.). What I did was program the equation, in both Math Cad and
Excel 4.0, to see the results. And interesting results they are!
Results:
1) Longer rods have lower piston/cylinder side loads, hence less
cylinder and piston wear
[note1].
2) Short rods have a higher axial loading, hence potentially more
bearing wear [note 2].
3) Short rods produce higher torque early, less torque later [note 3].
4) Short rods produce a higher peak torque [note 4].
and finally, an astounding (at least to me)
5) No matter what the rod length, the area under the torque curve is
EXACTLY the same for each case! Conservation of energy, perhaps?
note 1. The new 4.6L OHC engine has a very high rod/stroke ratio (2.5+). I
suppose this is one of the ways that Ford manages to have an engine which
will run for a hundred thousand or more miles without significant attention.
note 2. Maybe. Maybe not. Longer rods have higher weight and thusly more
inertial loading as they reciprocate. And for an engine which lives at high
RPM, this might mean the difference between long or short life.
note 3. I can hear it now! There are some of you out there who will throw in
cam timing, valve
lifts etc to make the argument that one rod or the other is better. But, that
would be changing the problem by changing multiple parameters at a time. I
agree that each can be tuned with cam changes, carb or EFI changes to get
more performance for any given particular set of constraints.
note 4. This also surprised me a little. I had expected that the torque would
be less. But I can rationalize the data by short rods having more axial force
which pushes on the crank. But it does happen earlier in the power stroke. As
a matter of fact all rods produced torque peaks before the 90 degree rotation
point and fell off slower.
As an interesting side bar, I computed the rod ratios for all of the engine
types as shown in the Ford Motorsport SVO catalog (1994). The high
performance engines have rod ratios between 1.65 to 1.73. Interesting to note
that the SVO 302 uses the slightly longer rod (5.155 vs 5.092).
For those of you who may want to take me task and to review the model and
data sheets, I will be happy to send you the spread sheet and the three
charts that go along with them. E-mail me directly at either of
mayfield@traveller.com <<<<<<preferred
or
DrMayf@aol.com
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