Shift Speed and Pressure
SHIFT SPEED AND PRESSURETo figure the area of a circle (valve or servo):
Radius (which is 1/2 the diameter) x Radius x 3.14159 = Area
EXAMPLE: A 1" diameter circle has a radius of 0.5"
0.5 x 0.5 x 3.14159 = 0.785
Therefore a 1" diameter circle has an Area of 0.785 sq. inches
Pressure x Area = Force
EXAMPLE: 100 psi line pressure, on a servo with an area of 2 square inches = force
So, 100 psi line pressure x 2 sq in = 200 pounds of force.
Force divided by Area = Pressure
EXAMPLE: 200 lbs divided by 2" = 100 psi
Force divided by Pressure = Area
EXAMPLE: 200 lbs divided by 100 psi = 2 inches
THINGS WE CAN DO WITH THESE FORMULAS:
EXAMPLE: A 700 R4 has 62 psi of line pressure at Idle.
The PR spring weighs 6.5 lbs
The tip (reaction end) of the PR valve has a diameter of 0.365" (0.365 divided by 2 = 0.1825 radius) 0.1825 x 0.1825 x 3.14159 = 0.1046" area
We want 75 psi of line pressure at Idle
First, let's see if those numbers add up, using: Pressure x Area = Force
62 psi x 0.1046 = 6.48, or 6 1/2 lb PR Spring
We want 75 psi:
Pressure x Area = Force (Spring) 75 psi x 0.1046 = 7.85 lb spring
What if we put in an 8 lb Spring? Force divided by Area = Pressure
8 lbs divided by 0.1046 = 76.48 or 76 1/2 line pressure
Now, let's look at RATIO.
Ratio is the relationship in quantity, amount or size, between two or more things.
In our example ratio is: How many psi each pound of spring will add.
Pressure divided by Force = Ratio
EXAMPLE: 62 psi divided by 6.5 lbs = 9.5 ratio Each pound of spring will increase pressure 9.5 psi
Force x Ratio = Pressure
EXAMPLE: 6.5 lbs x 9.5 = 61.75 or 62 psi
(Let's add 1 lb of spring, and see if we get 9.5 more psi.)
Force x Ratio = Pressure
EXAMPLE: 7.5 lbs x 9.5 = 71.25
New pressure Old pressure = Pressure difference
71.25 minus 61.75 = 9.5 psi change (by adding 1 lb of spring)
Once you know the ratio, a lot can be determined. Pressure divided by Ratio = Force
62 psi (actually 61.75) divided by 9.5 = 6.5 lb spring
The ratio never changes. This means that if I know that line pressure is 55 psi at idle, in a 700 R4, the the PR spring must be 5.78 lbs.
Pressure divided by Ratio = Force
So, 55 psi divided by 9.5 = 5.78 lbs.
Now, let's look at a math formula for shift speeds.
Suppose we had shift speeds of 15 mph and 20 mph, for the 1-2 & 2-3 shifts on a transmission. 20 mph may be too early for the 2-3 shift. If we adjust TV modulator, we will move both shifts. We don't want to do that because the 1-2 shift is fine, so let's work with just the 2-3 shift spring.
EXAMPLE: Original spring divided by Original MPH = Ratio
As, 4 lbs divided by 25mph = 0.2
Ratio x Desired MPH = New Spring
0.2 x 25 mph = 5 lb spring
A 5 lb spring will raise the shift on this transmission to 25 mph.
All you need to know is -- Where is it shifting now (at MINIMUM throttle) and what does the spring weigh.
This formula will get you very close, but may be a "tad" off, because we are not accounting for TV pressure helping the spring. This is why you want to check it at minimum throttle, so TV has the least effect.